diff --git a/css/styles.css b/css/styles.css index b0a4ac6789..a1b46268c3 100644 --- a/css/styles.css +++ b/css/styles.css @@ -168,6 +168,27 @@ a:link, a:visited { pointer-events: none; } +/* Make anchor tags ("a" elements) for activated actions */ +.a-link-button-bought { + text-decoration: none; + background-color: #00AA00; + color: #FFFFFF; + padding: 5px; + margin: 5px; + border: 1px solid #00AA00; + cursor: default; +} + +.a-link-button-bought:hover .tooltiptext, +.a-link-button-bought:hover .tooltiptexthigh, +.a-link-button-bought:hover .tooltiptextleft { + visibility: visible; +} + +.a-link-button-bought:active { + pointer-events: none; +} + /* Notification icon (for create program right now only) */ #create-program-tab { position:relative; diff --git a/dist/engine.bundle.js b/dist/engine.bundle.js index f9978a60b9..4af78711ee 100644 --- a/dist/engine.bundle.js +++ b/dist/engine.bundle.js @@ -95,8 +95,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _Server_js__WEBPACK_IMPORTED_MODULE_12__ = __webpack_require__(/*! ./Server.js */ 10); /* harmony import */ var _SpecialServerIps_js__WEBPACK_IMPORTED_MODULE_13__ = __webpack_require__(/*! ./SpecialServerIps.js */ 17); /* harmony import */ var _SourceFile_js__WEBPACK_IMPORTED_MODULE_14__ = __webpack_require__(/*! ./SourceFile.js */ 44); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_15__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_15__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_16__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_17__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_IPAddress_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! ../utils/IPAddress.js */ 16); @@ -179,9 +178,9 @@ function PlayerObject() { this.faction_rep_mult = 1; //Money - this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(1000); - this.total_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(0); //Total money ever earned in this "simulation" - this.lifetime_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(0); //Total money ever earned + this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](1000); + this.total_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](0); //Total money ever earned in this "simulation" + this.lifetime_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](0); //Total money ever earned //IP Address of Starting (home) computer this.homeComputer = ""; @@ -198,6 +197,7 @@ function PlayerObject() { this.currentServer = ""; //IP address of Server currently being accessed through terminal this.purchasedServers = []; //IP Addresses of purchased servers this.hacknetNodes = []; + this.hacknetNodeWrappers = []; this.totalHacknetNodeProduction = 0; //Factions @@ -345,7 +345,7 @@ PlayerObject.prototype.prestigeAugmentation = function() { this.agility_exp = 0; this.charisma_exp = 0; - this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(1000); + this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](1000); this.city = _Location_js__WEBPACK_IMPORTED_MODULE_10__["Locations"].Sector12; this.location = ""; @@ -426,7 +426,7 @@ PlayerObject.prototype.prestigeSourceFile = function() { this.agility_exp = 0; this.charisma_exp = 0; - this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(1000); + this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](1000); this.city = _Location_js__WEBPACK_IMPORTED_MODULE_10__["Locations"].Sector12; this.location = ""; @@ -486,19 +486,11 @@ PlayerObject.prototype.prestigeSourceFile = function() { this.hasTixApiAccess = false; //BitNode 3: Corporatocracy - if (this.bitNodeN === 3) {this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(150e9);} + if (this.bitNodeN === 3) {this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](150e9);} this.corporation = 0; - //Reset Bladeburner this.bladeburner = 0; - //BitNode 8: Ghost of Wall Street - if (this.bitNodeN === 8) {this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(100000000);} - if (this.bitNodeN === 8 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_11__["hasWallStreetSF"]) { - this.hasWseAccount = true; - this.hasTixApiAccess = true; - } - this.playtimeSinceLastAug = 0; this.scriptProdSinceLastAug = 0; } @@ -2453,21 +2445,21 @@ function loadPlayer(saveString) { Player = JSON.parse(saveString, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_19__["Reviver"]); //Parse Decimal.js objects - Player.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.money); - Player.total_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.total_money); - Player.lifetime_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.lifetime_money); + Player.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.money); + Player.total_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.total_money); + Player.lifetime_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.lifetime_money); if (Player.corporation instanceof _CompanyManagement_js__WEBPACK_IMPORTED_MODULE_4__["Corporation"]) { - Player.corporation.funds = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.corporation.funds); - Player.corporation.revenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.corporation.revenue); - Player.corporation.expenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.corporation.expenses); + Player.corporation.funds = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.corporation.funds); + Player.corporation.revenue = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.corporation.revenue); + Player.corporation.expenses = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.corporation.expenses); for (var i = 0; i < Player.corporation.divisions.length; ++i) { var ind = Player.corporation.divisions[i]; - ind.lastCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.lastCycleRevenue); - ind.lastCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.lastCycleExpenses); - ind.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.thisCycleRevenue); - ind.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.thisCycleExpenses); + ind.lastCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.lastCycleRevenue); + ind.lastCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.lastCycleExpenses); + ind.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.thisCycleRevenue); + ind.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.thisCycleExpenses); } } } @@ -2957,7 +2949,7 @@ function generateRandomString(n) { __webpack_require__.r(__webpack_exports__); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "CONSTANTS", function() { return CONSTANTS; }); let CONSTANTS = { - Version: "0.37.1", + Version: "0.37.2", //Max level for any skill, assuming no multipliers. Determined by max numerical value in javascript for experience //and the skill level formula in Player.js. Note that all this means it that when experience hits MAX_INT, then @@ -3442,16 +3434,13 @@ let CONSTANTS = { "World Stock Exchange account and TIX API Access
", LatestUpdate: - "v0.37.1
" + - "* You now earn money from successfully completing Bladeburner contracts. The amount you earn is based " + - "on the difficulty of the contract.
" + - "* Completing Field Analysis in Bladeburner now grants 0.1 rank
" + - "* The maximum RAM you can get on a purchased server is now 1,048,576GB (2^20)
" + - "* Bug Fix: Fixed Netscript syntax highlighting issues with the new NetscriptJS
" + - "* Bug Fix: Netscript Functions now properly incur RAM costs in NetscriptJS
" + - "* Bug Fix: deleteServer() now fails if its called on the server you are currently connected to
" + - "* Removed in-game Netscript documentation, since it was outdated and difficult to maintain.
" + - "* Bug Fix: Updated the gymWorkout() Singularity function with the new exp/cost values for gyms
" + "v0.37.2
" + + "* After joining the Bladeburners division, there is now a button to go to the Bladeburner content " + + "in the 'City' page
" + + "* You now start with $250m in BitNode-8 (increased from $100m)
" + + "* Bug Fix: You can now no longer directly edit Hacknet Node values through NetscriptJS (hopefully)
" + + "* Bug Fix: Bladeburners is no longer accessible in BN-8
" + + "* Bug Fix: getBitNodeMultipliers() Netscript function now returns a copy rather than the original object
" } @@ -4199,6 +4188,7 @@ function displayLocationContent() { securityJob.style.display = "block"; agentJob.style.display = "block"; if (_Player_js__WEBPACK_IMPORTED_MODULE_8__["Player"].bitNodeN === 6 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_7__["hasBladeburnerSF"] === true) { + if (_Player_js__WEBPACK_IMPORTED_MODULE_8__["Player"].bitNodeN === 8) {break;} if (_Player_js__WEBPACK_IMPORTED_MODULE_8__["Player"].bladeburner instanceof _Bladeburner_js__WEBPACK_IMPORTED_MODULE_0__["Bladeburner"]) { //Note: Can't infiltrate NSA when part of bladeburner nsaBladeburner.innerText = "Enter Bladeburner Headquarters"; @@ -6349,6 +6339,7 @@ let Engine = { //Generic Locations (common to every city): // World Stock Exchange // Corporation (if applicable) + // Bladeburner HQ (if applicable); var genericLocationsList = document.getElementById("generic-locations-list"); genericLocationsList.style.display = "inline"; Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_2__["removeChildrenFromElement"])(genericLocationsList); @@ -6375,6 +6366,18 @@ let Engine = { })); genericLocationsList.appendChild(li); } + + if (_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].bladeburner instanceof _Bladeburner_js__WEBPACK_IMPORTED_MODULE_9__["Bladeburner"]) { + var li = Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_2__["createElement"])("li"); + li.appendChild(Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_2__["createElement"])("a", { + innerText:"Bladeburner Headquarters", class:"a-link-button", + clickListener:()=>{ + Engine.loadBladeburnerContent(); + return false; + } + })); + genericLocationsList.appendChild(li); + } }, displayFactionsInfo: function() { @@ -6437,9 +6440,9 @@ let Engine = { clickListener:()=>{ Object(_Faction_js__WEBPACK_IMPORTED_MODULE_15__["joinFaction"])(_Faction_js__WEBPACK_IMPORTED_MODULE_15__["Factions"][factionName]); for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations.length; ++i) { - if (_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations[i] == factionName) { + if (_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations[i] == factionName || _Faction_js__WEBPACK_IMPORTED_MODULE_15__["Factions"][_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations[i]].isBanned) { _Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations.splice(i, 1); - break; + i--; } } Engine.displayFactionsInfo(); @@ -18856,6 +18859,9 @@ function displayStockMarketContent() { wseAccountButton.innerText = "Buy WSE Account - $" + Object(_utils_StringHelperFunctions_js__WEBPACK_IMPORTED_MODULE_10__["formatNumber"])(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].WSEAccountCost, 2).toString(); if (!_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasWseAccount && _Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].money.gte(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].WSEAccountCost)) { wseAccountButton.setAttribute("class", "a-link-button"); + } else if (_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasWseAccount){ + wseAccountButton.innerText = "WSE Account - Purchased"; + wseAccountButton.setAttribute("class", "a-link-button-bought"); } else { wseAccountButton.setAttribute("class", "a-link-button-inactive"); } @@ -18874,6 +18880,9 @@ function displayStockMarketContent() { Object(_utils_StringHelperFunctions_js__WEBPACK_IMPORTED_MODULE_10__["formatNumber"])(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].TIXAPICost, 2).toString(); if (!_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasTixApiAccess && _Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].money.gte(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].TIXAPICost)) { tixApiAccessButton.setAttribute("class", "a-link-button"); + } else if(_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasTixApiAccess) { + tixApiAccessButton.innerText = "Trade Information eXchange (TIX) API Access - Purchased" + tixApiAccessButton.setAttribute("class", "a-link-button-bought"); } else { tixApiAccessButton.setAttribute("class", "a-link-button-inactive"); } @@ -19625,4807 +19634,4795 @@ function setSettingsLabels() { /***/ }), /* 24 */ -/*!**************************!*\ - !*** ./utils/decimal.js ***! - \**************************/ -/***/ (function(module, exports, __webpack_require__) { +/*!************************************************!*\ + !*** ./node_modules/decimal.js/decimal.es6.js ***! + \************************************************/ +/***/ (function(module, __webpack_exports__, __webpack_require__) { -var __WEBPACK_AMD_DEFINE_RESULT__;/*! decimal.js v7.2.3 https://github.com/MikeMcl/decimal.js/LICENCE */ -;(function (globalScope) { - 'use strict'; +"use strict"; +__webpack_require__.r(__webpack_exports__); +/* + * + * decimal.js v7.2.3 + * An arbitrary-precision Decimal type for JavaScript. + * https://github.com/MikeMcl/decimal.js + * Copyright (c) 2017 Michael Mclaughlin + * MIT Licence + * https://github.com/MikeMcl/decimal.js/LICENCE + * + */ - /* - * decimal.js v7.2.3 - * An arbitrary-precision Decimal type for JavaScript. - * https://github.com/MikeMcl/decimal.js - * Copyright (c) 2017 Michael Mclaughlin - * MIT Licence - */ +// ----------------------------------- EDITABLE DEFAULTS ------------------------------------ // - // ----------------------------------- EDITABLE DEFAULTS ------------------------------------ // - - - // The maximum exponent magnitude. - // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`. - var EXP_LIMIT = 9e15, // 0 to 9e15 - - // The limit on the value of `precision`, and on the value of the first argument to - // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`. - MAX_DIGITS = 1e9, // 0 to 1e9 - - // Base conversion alphabet. - NUMERALS = '0123456789abcdef', - // The natural logarithm of 10 (1025 digits). - LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058', - - // Pi (1025 digits). - PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789', - - - // The initial configuration properties of the Decimal constructor. - Decimal = { - - // These values must be integers within the stated ranges (inclusive). - // Most of these values can be changed at run-time using the `Decimal.config` method. - - // The maximum number of significant digits of the result of a calculation or base conversion. - // E.g. `Decimal.config({ precision: 20 });` - precision: 20, // 1 to MAX_DIGITS - - // The rounding mode used when rounding to `precision`. - // - // ROUND_UP 0 Away from zero. - // ROUND_DOWN 1 Towards zero. - // ROUND_CEIL 2 Towards +Infinity. - // ROUND_FLOOR 3 Towards -Infinity. - // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up. - // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. - // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. - // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. - // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. - // - // E.g. - // `Decimal.rounding = 4;` - // `Decimal.rounding = Decimal.ROUND_HALF_UP;` - rounding: 4, // 0 to 8 - - // The modulo mode used when calculating the modulus: a mod n. - // The quotient (q = a / n) is calculated according to the corresponding rounding mode. - // The remainder (r) is calculated as: r = a - n * q. - // - // UP 0 The remainder is positive if the dividend is negative, else is negative. - // DOWN 1 The remainder has the same sign as the dividend (JavaScript %). - // FLOOR 3 The remainder has the same sign as the divisor (Python %). - // HALF_EVEN 6 The IEEE 754 remainder function. - // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive. - // - // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian - // division (9) are commonly used for the modulus operation. The other rounding modes can also - // be used, but they may not give useful results. - modulo: 1, // 0 to 9 - - // The exponent value at and beneath which `toString` returns exponential notation. - // JavaScript numbers: -7 - toExpNeg: -7, // 0 to -EXP_LIMIT - - // The exponent value at and above which `toString` returns exponential notation. - // JavaScript numbers: 21 - toExpPos: 21, // 0 to EXP_LIMIT - - // The minimum exponent value, beneath which underflow to zero occurs. - // JavaScript numbers: -324 (5e-324) - minE: -EXP_LIMIT, // -1 to -EXP_LIMIT - - // The maximum exponent value, above which overflow to Infinity occurs. - // JavaScript numbers: 308 (1.7976931348623157e+308) - maxE: EXP_LIMIT, // 1 to EXP_LIMIT - - // Whether to use cryptographically-secure random number generation, if available. - crypto: false // true/false - }, + // The maximum exponent magnitude. + // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`. +var EXP_LIMIT = 9e15, // 0 to 9e15 + + // The limit on the value of `precision`, and on the value of the first argument to + // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`. + MAX_DIGITS = 1e9, // 0 to 1e9 + // Base conversion alphabet. + NUMERALS = '0123456789abcdef', - // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- // + // The natural logarithm of 10 (1025 digits). + ln10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058', + // Pi (1025 digits). + pi = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789', - inexact, noConflict, quadrant, - external = true, - decimalError = '[DecimalError] ', - invalidArgument = decimalError + 'Invalid argument: ', - precisionLimitExceeded = decimalError + 'Precision limit exceeded', - cryptoUnavailable = decimalError + 'crypto unavailable', + // The initial configuration properties of the Decimal constructor. + defaults = { - mathfloor = Math.floor, - mathpow = Math.pow, + // These values must be integers within the stated ranges (inclusive). + // Most of these values can be changed at run-time using the `Decimal.config` method. - isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i, - isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i, - isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i, - isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, + // The maximum number of significant digits of the result of a calculation or base conversion. + // E.g. `Decimal.config({ precision: 20 });` + precision: 20, // 1 to MAX_DIGITS - BASE = 1e7, - LOG_BASE = 7, - MAX_SAFE_INTEGER = 9007199254740991, + // The rounding mode used when rounding to `precision`. + // + // ROUND_UP 0 Away from zero. + // ROUND_DOWN 1 Towards zero. + // ROUND_CEIL 2 Towards +Infinity. + // ROUND_FLOOR 3 Towards -Infinity. + // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up. + // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. + // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. + // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. + // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. + // + // E.g. + // `Decimal.rounding = 4;` + // `Decimal.rounding = Decimal.ROUND_HALF_UP;` + rounding: 4, // 0 to 8 + + // The modulo mode used when calculating the modulus: a mod n. + // The quotient (q = a / n) is calculated according to the corresponding rounding mode. + // The remainder (r) is calculated as: r = a - n * q. + // + // UP 0 The remainder is positive if the dividend is negative, else is negative. + // DOWN 1 The remainder has the same sign as the dividend (JavaScript %). + // FLOOR 3 The remainder has the same sign as the divisor (Python %). + // HALF_EVEN 6 The IEEE 754 remainder function. + // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive. + // + // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian + // division (9) are commonly used for the modulus operation. The other rounding modes can also + // be used, but they may not give useful results. + modulo: 1, // 0 to 9 - LN10_PRECISION = LN10.length - 1, - PI_PRECISION = PI.length - 1, + // The exponent value at and beneath which `toString` returns exponential notation. + // JavaScript numbers: -7 + toExpNeg: -7, // 0 to -EXP_LIMIT - // Decimal.prototype object - P = {}; + // The exponent value at and above which `toString` returns exponential notation. + // JavaScript numbers: 21 + toExpPos: 21, // 0 to EXP_LIMIT + // The minimum exponent value, beneath which underflow to zero occurs. + // JavaScript numbers: -324 (5e-324) + minE: -EXP_LIMIT, // -1 to -EXP_LIMIT - // Decimal prototype methods + // The maximum exponent value, above which overflow to Infinity occurs. + // JavaScript numbers: 308 (1.7976931348623157e+308) + maxE: EXP_LIMIT, // 1 to EXP_LIMIT + // Whether to use cryptographically-secure random number generation, if available. + crypto: false // true/false + }, - /* - * absoluteValue abs - * ceil - * comparedTo cmp - * cosine cos - * cubeRoot cbrt - * decimalPlaces dp - * dividedBy div - * dividedToIntegerBy divToInt - * equals eq - * floor - * greaterThan gt - * greaterThanOrEqualTo gte - * hyperbolicCosine cosh - * hyperbolicSine sinh - * hyperbolicTangent tanh - * inverseCosine acos - * inverseHyperbolicCosine acosh - * inverseHyperbolicSine asinh - * inverseHyperbolicTangent atanh - * inverseSine asin - * inverseTangent atan - * isFinite - * isInteger isInt - * isNaN - * isNegative isNeg - * isPositive isPos - * isZero - * lessThan lt - * lessThanOrEqualTo lte - * logarithm log - * [maximum] [max] - * [minimum] [min] - * minus sub - * modulo mod - * naturalExponential exp - * naturalLogarithm ln - * negated neg - * plus add - * precision sd - * round - * sine sin - * squareRoot sqrt - * tangent tan - * times mul - * toBinary - * toDecimalPlaces toDP - * toExponential - * toFixed - * toFraction - * toHexadecimal toHex - * toNearest - * toNumber - * toOctal - * toPower pow - * toPrecision - * toSignificantDigits toSD - * toString - * truncated trunc - * valueOf toJSON - */ +// ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- // - /* - * Return a new Decimal whose value is the absolute value of this Decimal. - * - */ - P.absoluteValue = P.abs = function () { - var x = new this.constructor(this); - if (x.s < 0) x.s = 1; - return finalise(x); - }; + Decimal, LN10, PI, inexact, quadrant, + external = true, - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of positive Infinity. - * - */ - P.ceil = function () { - return finalise(new this.constructor(this), this.e + 1, 2); - }; + decimalError = '[DecimalError] ', + invalidArgument = decimalError + 'Invalid argument: ', + precisionLimitExceeded = decimalError + 'Precision limit exceeded', + cryptoUnavailable = decimalError + 'crypto unavailable', + mathfloor = Math.floor, + mathpow = Math.pow, - /* - * Return - * 1 if the value of this Decimal is greater than the value of `y`, - * -1 if the value of this Decimal is less than the value of `y`, - * 0 if they have the same value, - * NaN if the value of either Decimal is NaN. - * - */ - P.comparedTo = P.cmp = function (y) { - var i, j, xdL, ydL, - x = this, - xd = x.d, - yd = (y = new x.constructor(y)).d, - xs = x.s, - ys = y.s; + isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i, + isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i, + isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i, + isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, - // Either NaN or ±Infinity? - if (!xd || !yd) { - return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1; - } + BASE = 1e7, + LOG_BASE = 7, + MAX_SAFE_INTEGER = 9007199254740991, - // Either zero? - if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0; + LN10_PRECISION = ln10.length - 1, + PI_PRECISION = pi.length - 1, - // Signs differ? - if (xs !== ys) return xs; + // Decimal.prototype object + P = {}; - // Compare exponents. - if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1; - xdL = xd.length; - ydL = yd.length; +// Decimal prototype methods - // Compare digit by digit. - for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) { - if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1; - } - // Compare lengths. - return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1; - }; +/* + * absoluteValue abs + * ceil + * comparedTo cmp + * cosine cos + * cubeRoot cbrt + * decimalPlaces dp + * dividedBy div + * dividedToIntegerBy divToInt + * equals eq + * floor + * greaterThan gt + * greaterThanOrEqualTo gte + * hyperbolicCosine cosh + * hyperbolicSine sinh + * hyperbolicTangent tanh + * inverseCosine acos + * inverseHyperbolicCosine acosh + * inverseHyperbolicSine asinh + * inverseHyperbolicTangent atanh + * inverseSine asin + * inverseTangent atan + * isFinite + * isInteger isInt + * isNaN + * isNegative isNeg + * isPositive isPos + * isZero + * lessThan lt + * lessThanOrEqualTo lte + * logarithm log + * [maximum] [max] + * [minimum] [min] + * minus sub + * modulo mod + * naturalExponential exp + * naturalLogarithm ln + * negated neg + * plus add + * precision sd + * round + * sine sin + * squareRoot sqrt + * tangent tan + * times mul + * toBinary + * toDecimalPlaces toDP + * toExponential + * toFixed + * toFraction + * toHexadecimal toHex + * toNearest + * toNumber + * toOctal + * toPower pow + * toPrecision + * toSignificantDigits toSD + * toString + * truncated trunc + * valueOf toJSON + */ - /* - * Return a new Decimal whose value is the cosine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * cos(0) = 1 - * cos(-0) = 1 - * cos(Infinity) = NaN - * cos(-Infinity) = NaN - * cos(NaN) = NaN - * - */ - P.cosine = P.cos = function () { - var pr, rm, - x = this, - Ctor = x.constructor; +/* + * Return a new Decimal whose value is the absolute value of this Decimal. + * + */ +P.absoluteValue = P.abs = function () { + var x = new this.constructor(this); + if (x.s < 0) x.s = 1; + return finalise(x); +}; - if (!x.d) return new Ctor(NaN); - // cos(0) = cos(-0) = 1 - if (!x.d[0]) return new Ctor(1); +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the + * direction of positive Infinity. + * + */ +P.ceil = function () { + return finalise(new this.constructor(this), this.e + 1, 2); +}; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; - x = cosine(Ctor, toLessThanHalfPi(Ctor, x)); +/* + * Return + * 1 if the value of this Decimal is greater than the value of `y`, + * -1 if the value of this Decimal is less than the value of `y`, + * 0 if they have the same value, + * NaN if the value of either Decimal is NaN. + * + */ +P.comparedTo = P.cmp = function (y) { + var i, j, xdL, ydL, + x = this, + xd = x.d, + yd = (y = new x.constructor(y)).d, + xs = x.s, + ys = y.s; - Ctor.precision = pr; - Ctor.rounding = rm; + // Either NaN or ±Infinity? + if (!xd || !yd) { + return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1; + } - return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true); - }; + // Either zero? + if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0; + // Signs differ? + if (xs !== ys) return xs; - /* - * - * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * cbrt(0) = 0 - * cbrt(-0) = -0 - * cbrt(1) = 1 - * cbrt(-1) = -1 - * cbrt(N) = N - * cbrt(-I) = -I - * cbrt(I) = I - * - * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3)) - * - */ - P.cubeRoot = P.cbrt = function () { - var e, m, n, r, rep, s, sd, t, t3, t3plusx, - x = this, - Ctor = x.constructor; + // Compare exponents. + if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1; - if (!x.isFinite() || x.isZero()) return new Ctor(x); - external = false; + xdL = xd.length; + ydL = yd.length; - // Initial estimate. - s = x.s * Math.pow(x.s * x, 1 / 3); + // Compare digit by digit. + for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) { + if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1; + } - // Math.cbrt underflow/overflow? - // Pass x to Math.pow as integer, then adjust the exponent of the result. - if (!s || Math.abs(s) == 1 / 0) { - n = digitsToString(x.d); - e = x.e; + // Compare lengths. + return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1; +}; - // Adjust n exponent so it is a multiple of 3 away from x exponent. - if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00'); - s = Math.pow(n, 1 / 3); - // Rarely, e may be one less than the result exponent value. - e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2)); +/* + * Return a new Decimal whose value is the cosine of the value in radians of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-1, 1] + * + * cos(0) = 1 + * cos(-0) = 1 + * cos(Infinity) = NaN + * cos(-Infinity) = NaN + * cos(NaN) = NaN + * + */ +P.cosine = P.cos = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - if (s == 1 / 0) { - n = '5e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } + if (!x.d) return new Ctor(NaN); - r = new Ctor(n); - r.s = x.s; - } else { - r = new Ctor(s.toString()); - } + // cos(0) = cos(-0) = 1 + if (!x.d[0]) return new Ctor(1); - sd = (e = Ctor.precision) + 3; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; + Ctor.rounding = 1; - // Halley's method. - // TODO? Compare Newton's method. - for (;;) { - t = r; - t3 = t.times(t).times(t); - t3plusx = t3.plus(x); - r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1); + x = cosine(Ctor, toLessThanHalfPi(Ctor, x)); - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); + Ctor.precision = pr; + Ctor.rounding = rm; - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999 - // , i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { + return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true); +}; - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); - if (t.times(t).times(t).eq(x)) { - r = t; - break; - } - } +/* + * + * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * cbrt(0) = 0 + * cbrt(-0) = -0 + * cbrt(1) = 1 + * cbrt(-1) = -1 + * cbrt(N) = N + * cbrt(-I) = -I + * cbrt(I) = I + * + * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3)) + * + */ +P.cubeRoot = P.cbrt = function () { + var e, m, n, r, rep, s, sd, t, t3, t3plusx, + x = this, + Ctor = x.constructor; - sd += 4; - rep = 1; - } else { + if (!x.isFinite() || x.isZero()) return new Ctor(x); + external = false; - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { + // Initial estimate. + s = x.s * Math.pow(x.s * x, 1 / 3); - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).times(r).eq(x); - } + // Math.cbrt underflow/overflow? + // Pass x to Math.pow as integer, then adjust the exponent of the result. + if (!s || Math.abs(s) == 1 / 0) { + n = digitsToString(x.d); + e = x.e; - break; - } - } + // Adjust n exponent so it is a multiple of 3 away from x exponent. + if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00'); + s = Math.pow(n, 1 / 3); + + // Rarely, e may be one less than the result exponent value. + e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2)); + + if (s == 1 / 0) { + n = '5e' + e; + } else { + n = s.toExponential(); + n = n.slice(0, n.indexOf('e') + 1) + e; } - external = true; + r = new Ctor(n); + r.s = x.s; + } else { + r = new Ctor(s.toString()); + } - return finalise(r, e, Ctor.rounding, m); - }; + sd = (e = Ctor.precision) + 3; + // Halley's method. + // TODO? Compare Newton's method. + for (;;) { + t = r; + t3 = t.times(t).times(t); + t3plusx = t3.plus(x); + r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1); + + // TODO? Replace with for-loop and checkRoundingDigits. + if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { + n = n.slice(sd - 3, sd + 1); + + // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999 + // , i.e. approaching a rounding boundary, continue the iteration. + if (n == '9999' || !rep && n == '4999') { + + // On the first iteration only, check to see if rounding up gives the exact result as the + // nines may infinitely repeat. + if (!rep) { + finalise(t, e + 1, 0); + + if (t.times(t).times(t).eq(x)) { + r = t; + break; + } + } - /* - * Return the number of decimal places of the value of this Decimal. - * - */ - P.decimalPlaces = P.dp = function () { - var w, - d = this.d, - n = NaN; + sd += 4; + rep = 1; + } else { - if (d) { - w = d.length - 1; - n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE; + // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. + // If not, then there are further digits and m will be truthy. + if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - // Subtract the number of trailing zeros of the last word. - w = d[w]; - if (w) for (; w % 10 == 0; w /= 10) n--; - if (n < 0) n = 0; + // Truncate to the first rounding digit. + finalise(r, e + 1, 1); + m = !r.times(r).times(r).eq(x); + } + + break; + } } + } - return n; - }; + external = true; + return finalise(r, e, Ctor.rounding, m); +}; - /* - * n / 0 = I - * n / N = N - * n / I = 0 - * 0 / n = 0 - * 0 / 0 = N - * 0 / N = N - * 0 / I = 0 - * N / n = N - * N / 0 = N - * N / N = N - * N / I = N - * I / n = I - * I / 0 = I - * I / N = N - * I / I = N - * - * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedBy = P.div = function (y) { - return divide(this, new this.constructor(y)); - }; +/* + * Return the number of decimal places of the value of this Decimal. + * + */ +P.decimalPlaces = P.dp = function () { + var w, + d = this.d, + n = NaN; - /* - * Return a new Decimal whose value is the integer part of dividing the value of this Decimal - * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedToIntegerBy = P.divToInt = function (y) { - var x = this, - Ctor = x.constructor; - return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding); - }; + if (d) { + w = d.length - 1; + n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE; + // Subtract the number of trailing zeros of the last word. + w = d[w]; + if (w) for (; w % 10 == 0; w /= 10) n--; + if (n < 0) n = 0; + } - /* - * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false. - * - */ - P.equals = P.eq = function (y) { - return this.cmp(y) === 0; - }; + return n; +}; - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of negative Infinity. - * - */ - P.floor = function () { - return finalise(new this.constructor(this), this.e + 1, 3); - }; +/* + * n / 0 = I + * n / N = N + * n / I = 0 + * 0 / n = 0 + * 0 / 0 = N + * 0 / N = N + * 0 / I = 0 + * N / n = N + * N / 0 = N + * N / N = N + * N / I = N + * I / n = I + * I / 0 = I + * I / N = N + * I / I = N + * + * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + */ +P.dividedBy = P.div = function (y) { + return divide(this, new this.constructor(y)); +}; - /* - * Return true if the value of this Decimal is greater than the value of `y`, otherwise return - * false. - * - */ - P.greaterThan = P.gt = function (y) { - return this.cmp(y) > 0; - }; +/* + * Return a new Decimal whose value is the integer part of dividing the value of this Decimal + * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`. + * + */ +P.dividedToIntegerBy = P.divToInt = function (y) { + var x = this, + Ctor = x.constructor; + return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding); +}; - /* - * Return true if the value of this Decimal is greater than or equal to the value of `y`, - * otherwise return false. - * - */ - P.greaterThanOrEqualTo = P.gte = function (y) { - var k = this.cmp(y); - return k == 1 || k === 0; - }; +/* + * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false. + * + */ +P.equals = P.eq = function (y) { + return this.cmp(y) === 0; +}; - /* - * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [1, Infinity] - * - * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ... - * - * cosh(0) = 1 - * cosh(-0) = 1 - * cosh(Infinity) = Infinity - * cosh(-Infinity) = Infinity - * cosh(NaN) = NaN - * - * x time taken (ms) result - * 1000 9 9.8503555700852349694e+433 - * 10000 25 4.4034091128314607936e+4342 - * 100000 171 1.4033316802130615897e+43429 - * 1000000 3817 1.5166076984010437725e+434294 - * 10000000 abandoned after 2 minute wait - * - * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x)) - * - */ - P.hyperbolicCosine = P.cosh = function () { - var k, n, pr, rm, len, - x = this, - Ctor = x.constructor, - one = new Ctor(1); +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the + * direction of negative Infinity. + * + */ +P.floor = function () { + return finalise(new this.constructor(this), this.e + 1, 3); +}; - if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN); - if (x.isZero()) return one; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; +/* + * Return true if the value of this Decimal is greater than the value of `y`, otherwise return + * false. + * + */ +P.greaterThan = P.gt = function (y) { + return this.cmp(y) > 0; +}; - // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1 - // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4)) - // Estimate the optimum number of times to use the argument reduction. - // TODO? Estimation reused from cosine() and may not be optimal here. - if (len < 32) { - k = Math.ceil(len / 3); - n = Math.pow(4, -k).toString(); - } else { - k = 16; - n = '2.3283064365386962890625e-10'; - } +/* + * Return true if the value of this Decimal is greater than or equal to the value of `y`, + * otherwise return false. + * + */ +P.greaterThanOrEqualTo = P.gte = function (y) { + var k = this.cmp(y); + return k == 1 || k === 0; +}; - x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true); - // Reverse argument reduction - var cosh2_x, - i = k, - d8 = new Ctor(8); - for (; i--;) { - cosh2_x = x.times(x); - x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8)))); - } +/* + * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [1, Infinity] + * + * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ... + * + * cosh(0) = 1 + * cosh(-0) = 1 + * cosh(Infinity) = Infinity + * cosh(-Infinity) = Infinity + * cosh(NaN) = NaN + * + * x time taken (ms) result + * 1000 9 9.8503555700852349694e+433 + * 10000 25 4.4034091128314607936e+4342 + * 100000 171 1.4033316802130615897e+43429 + * 1000000 3817 1.5166076984010437725e+434294 + * 10000000 abandoned after 2 minute wait + * + * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x)) + * + */ +P.hyperbolicCosine = P.cosh = function () { + var k, n, pr, rm, len, + x = this, + Ctor = x.constructor, + one = new Ctor(1); + + if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN); + if (x.isZero()) return one; + + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; + Ctor.rounding = 1; + len = x.d.length; + + // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1 + // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4)) + + // Estimate the optimum number of times to use the argument reduction. + // TODO? Estimation reused from cosine() and may not be optimal here. + if (len < 32) { + k = Math.ceil(len / 3); + n = Math.pow(4, -k).toString(); + } else { + k = 16; + n = '2.3283064365386962890625e-10'; + } - return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true); - }; + x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true); + // Reverse argument reduction + var cosh2_x, + i = k, + d8 = new Ctor(8); + for (; i--;) { + cosh2_x = x.times(x); + x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8)))); + } - /* - * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ... - * - * sinh(0) = 0 - * sinh(-0) = -0 - * sinh(Infinity) = Infinity - * sinh(-Infinity) = -Infinity - * sinh(NaN) = NaN - * - * x time taken (ms) - * 10 2 ms - * 100 5 ms - * 1000 14 ms - * 10000 82 ms - * 100000 886 ms 1.4033316802130615897e+43429 - * 200000 2613 ms - * 300000 5407 ms - * 400000 8824 ms - * 500000 13026 ms 8.7080643612718084129e+217146 - * 1000000 48543 ms - * - * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x)) - * - */ - P.hyperbolicSine = P.sinh = function () { - var k, pr, rm, len, - x = this, - Ctor = x.constructor; + return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true); +}; - if (!x.isFinite() || x.isZero()) return new Ctor(x); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; +/* + * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-Infinity, Infinity] + * + * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ... + * + * sinh(0) = 0 + * sinh(-0) = -0 + * sinh(Infinity) = Infinity + * sinh(-Infinity) = -Infinity + * sinh(NaN) = NaN + * + * x time taken (ms) + * 10 2 ms + * 100 5 ms + * 1000 14 ms + * 10000 82 ms + * 100000 886 ms 1.4033316802130615897e+43429 + * 200000 2613 ms + * 300000 5407 ms + * 400000 8824 ms + * 500000 13026 ms 8.7080643612718084129e+217146 + * 1000000 48543 ms + * + * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x)) + * + */ +P.hyperbolicSine = P.sinh = function () { + var k, pr, rm, len, + x = this, + Ctor = x.constructor; - if (len < 3) { - x = taylorSeries(Ctor, 2, x, x, true); - } else { + if (!x.isFinite() || x.isZero()) return new Ctor(x); - // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x)) - // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3)) - // 3 multiplications and 1 addition + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; + Ctor.rounding = 1; + len = x.d.length; - // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x))) - // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5))) - // 4 multiplications and 2 additions + if (len < 3) { + x = taylorSeries(Ctor, 2, x, x, true); + } else { - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; + // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x)) + // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3)) + // 3 multiplications and 1 addition - x = x.times(Math.pow(5, -k)); + // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x))) + // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5))) + // 4 multiplications and 2 additions - x = taylorSeries(Ctor, 2, x, x, true); + // Estimate the optimum number of times to use the argument reduction. + k = 1.4 * Math.sqrt(len); + k = k > 16 ? 16 : k | 0; - // Reverse argument reduction - var sinh2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sinh2_x = x.times(x); - x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20)))); - } - } + x = x.times(Math.pow(5, -k)); - Ctor.precision = pr; - Ctor.rounding = rm; + x = taylorSeries(Ctor, 2, x, x, true); - return finalise(x, pr, rm, true); - }; + // Reverse argument reduction + var sinh2_x, + d5 = new Ctor(5), + d16 = new Ctor(16), + d20 = new Ctor(20); + for (; k--;) { + sinh2_x = x.times(x); + x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20)))); + } + } + Ctor.precision = pr; + Ctor.rounding = rm; - /* - * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * tanh(x) = sinh(x) / cosh(x) - * - * tanh(0) = 0 - * tanh(-0) = -0 - * tanh(Infinity) = 1 - * tanh(-Infinity) = -1 - * tanh(NaN) = NaN - * - */ - P.hyperbolicTangent = P.tanh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; + return finalise(x, pr, rm, true); +}; - if (!x.isFinite()) return new Ctor(x.s); - if (x.isZero()) return new Ctor(x); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 7; - Ctor.rounding = 1; +/* + * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-1, 1] + * + * tanh(x) = sinh(x) / cosh(x) + * + * tanh(0) = 0 + * tanh(-0) = -0 + * tanh(Infinity) = 1 + * tanh(-Infinity) = -1 + * tanh(NaN) = NaN + * + */ +P.hyperbolicTangent = P.tanh = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm); - }; + if (!x.isFinite()) return new Ctor(x.s); + if (x.isZero()) return new Ctor(x); + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + 7; + Ctor.rounding = 1; - /* - * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of - * this Decimal. - * - * Domain: [-1, 1] - * Range: [0, pi] - * - * acos(x) = pi/2 - asin(x) - * - * acos(0) = pi/2 - * acos(-0) = pi/2 - * acos(1) = 0 - * acos(-1) = pi - * acos(1/2) = pi/3 - * acos(-1/2) = 2*pi/3 - * acos(|x| > 1) = NaN - * acos(NaN) = NaN - * - */ - P.inverseCosine = P.acos = function () { - var halfPi, - x = this, - Ctor = x.constructor, - k = x.abs().cmp(1), - pr = Ctor.precision, - rm = Ctor.rounding; + return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm); +}; - if (k !== -1) { - return k === 0 - // |x| is 1 - ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) - // |x| > 1 or x is NaN - : new Ctor(NaN); - } - if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5); +/* + * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of + * this Decimal. + * + * Domain: [-1, 1] + * Range: [0, pi] + * + * acos(x) = pi/2 - asin(x) + * + * acos(0) = pi/2 + * acos(-0) = pi/2 + * acos(1) = 0 + * acos(-1) = pi + * acos(1/2) = pi/3 + * acos(-1/2) = 2*pi/3 + * acos(|x| > 1) = NaN + * acos(NaN) = NaN + * + */ +P.inverseCosine = P.acos = function () { + var halfPi, + x = this, + Ctor = x.constructor, + k = x.abs().cmp(1), + pr = Ctor.precision, + rm = Ctor.rounding; - // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3 + if (k !== -1) { + return k === 0 + // |x| is 1 + ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) + // |x| > 1 or x is NaN + : new Ctor(NaN); + } - Ctor.precision = pr + 6; - Ctor.rounding = 1; + if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5); - x = x.asin(); - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); + // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3 - Ctor.precision = pr; - Ctor.rounding = rm; + Ctor.precision = pr + 6; + Ctor.rounding = 1; - return halfPi.minus(x); - }; + x = x.asin(); + halfPi = getPi(Ctor, pr + 4, rm).times(0.5); + Ctor.precision = pr; + Ctor.rounding = rm; - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the - * value of this Decimal. - * - * Domain: [1, Infinity] - * Range: [0, Infinity] - * - * acosh(x) = ln(x + sqrt(x^2 - 1)) - * - * acosh(x < 1) = NaN - * acosh(NaN) = NaN - * acosh(Infinity) = Infinity - * acosh(-Infinity) = NaN - * acosh(0) = NaN - * acosh(-0) = NaN - * acosh(1) = 0 - * acosh(-1) = NaN - * - */ - P.inverseHyperbolicCosine = P.acosh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; + return halfPi.minus(x); +}; - if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN); - if (!x.isFinite()) return new Ctor(x); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4; - Ctor.rounding = 1; - external = false; +/* + * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the + * value of this Decimal. + * + * Domain: [1, Infinity] + * Range: [0, Infinity] + * + * acosh(x) = ln(x + sqrt(x^2 - 1)) + * + * acosh(x < 1) = NaN + * acosh(NaN) = NaN + * acosh(Infinity) = Infinity + * acosh(-Infinity) = NaN + * acosh(0) = NaN + * acosh(-0) = NaN + * acosh(1) = 0 + * acosh(-1) = NaN + * + */ +P.inverseHyperbolicCosine = P.acosh = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - x = x.times(x).minus(1).sqrt().plus(x); + if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN); + if (!x.isFinite()) return new Ctor(x); - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4; + Ctor.rounding = 1; + external = false; - return x.ln(); - }; + x = x.times(x).minus(1).sqrt().plus(x); + external = true; + Ctor.precision = pr; + Ctor.rounding = rm; - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * asinh(x) = ln(x + sqrt(x^2 + 1)) - * - * asinh(NaN) = NaN - * asinh(Infinity) = Infinity - * asinh(-Infinity) = -Infinity - * asinh(0) = 0 - * asinh(-0) = -0 - * - */ - P.inverseHyperbolicSine = P.asinh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; + return x.ln(); +}; - if (!x.isFinite() || x.isZero()) return new Ctor(x); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6; - Ctor.rounding = 1; - external = false; +/* + * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value + * of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-Infinity, Infinity] + * + * asinh(x) = ln(x + sqrt(x^2 + 1)) + * + * asinh(NaN) = NaN + * asinh(Infinity) = Infinity + * asinh(-Infinity) = -Infinity + * asinh(0) = 0 + * asinh(-0) = -0 + * + */ +P.inverseHyperbolicSine = P.asinh = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - x = x.times(x).plus(1).sqrt().plus(x); + if (!x.isFinite() || x.isZero()) return new Ctor(x); - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6; + Ctor.rounding = 1; + external = false; - return x.ln(); - }; + x = x.times(x).plus(1).sqrt().plus(x); + external = true; + Ctor.precision = pr; + Ctor.rounding = rm; - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the - * value of this Decimal. - * - * Domain: [-1, 1] - * Range: [-Infinity, Infinity] - * - * atanh(x) = 0.5 * ln((1 + x) / (1 - x)) - * - * atanh(|x| > 1) = NaN - * atanh(NaN) = NaN - * atanh(Infinity) = NaN - * atanh(-Infinity) = NaN - * atanh(0) = 0 - * atanh(-0) = -0 - * atanh(1) = Infinity - * atanh(-1) = -Infinity - * - */ - P.inverseHyperbolicTangent = P.atanh = function () { - var pr, rm, wpr, xsd, - x = this, - Ctor = x.constructor; + return x.ln(); +}; - if (!x.isFinite()) return new Ctor(NaN); - if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN); - pr = Ctor.precision; - rm = Ctor.rounding; - xsd = x.sd(); +/* + * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the + * value of this Decimal. + * + * Domain: [-1, 1] + * Range: [-Infinity, Infinity] + * + * atanh(x) = 0.5 * ln((1 + x) / (1 - x)) + * + * atanh(|x| > 1) = NaN + * atanh(NaN) = NaN + * atanh(Infinity) = NaN + * atanh(-Infinity) = NaN + * atanh(0) = 0 + * atanh(-0) = -0 + * atanh(1) = Infinity + * atanh(-1) = -Infinity + * + */ +P.inverseHyperbolicTangent = P.atanh = function () { + var pr, rm, wpr, xsd, + x = this, + Ctor = x.constructor; - if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true); + if (!x.isFinite()) return new Ctor(NaN); + if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN); - Ctor.precision = wpr = xsd - x.e; + pr = Ctor.precision; + rm = Ctor.rounding; + xsd = x.sd(); - x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1); + if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true); - Ctor.precision = pr + 4; - Ctor.rounding = 1; + Ctor.precision = wpr = xsd - x.e; - x = x.ln(); + x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1); - Ctor.precision = pr; - Ctor.rounding = rm; + Ctor.precision = pr + 4; + Ctor.rounding = 1; - return x.times(0.5); - }; + x = x.ln(); + Ctor.precision = pr; + Ctor.rounding = rm; - /* - * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2))) - * - * asin(0) = 0 - * asin(-0) = -0 - * asin(1/2) = pi/6 - * asin(-1/2) = -pi/6 - * asin(1) = pi/2 - * asin(-1) = -pi/2 - * asin(|x| > 1) = NaN - * asin(NaN) = NaN - * - * TODO? Compare performance of Taylor series. - * - */ - P.inverseSine = P.asin = function () { - var halfPi, k, - pr, rm, - x = this, - Ctor = x.constructor; + return x.times(0.5); +}; - if (x.isZero()) return new Ctor(x); - k = x.abs().cmp(1); - pr = Ctor.precision; - rm = Ctor.rounding; +/* + * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-pi/2, pi/2] + * + * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2))) + * + * asin(0) = 0 + * asin(-0) = -0 + * asin(1/2) = pi/6 + * asin(-1/2) = -pi/6 + * asin(1) = pi/2 + * asin(-1) = -pi/2 + * asin(|x| > 1) = NaN + * asin(NaN) = NaN + * + * TODO? Compare performance of Taylor series. + * + */ +P.inverseSine = P.asin = function () { + var halfPi, k, + pr, rm, + x = this, + Ctor = x.constructor; - if (k !== -1) { + if (x.isZero()) return new Ctor(x); - // |x| is 1 - if (k === 0) { - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); - halfPi.s = x.s; - return halfPi; - } + k = x.abs().cmp(1); + pr = Ctor.precision; + rm = Ctor.rounding; - // |x| > 1 or x is NaN - return new Ctor(NaN); + if (k !== -1) { + + // |x| is 1 + if (k === 0) { + halfPi = getPi(Ctor, pr + 4, rm).times(0.5); + halfPi.s = x.s; + return halfPi; } - // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6 + // |x| > 1 or x is NaN + return new Ctor(NaN); + } - Ctor.precision = pr + 6; - Ctor.rounding = 1; + // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6 - x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan(); + Ctor.precision = pr + 6; + Ctor.rounding = 1; - Ctor.precision = pr; - Ctor.rounding = rm; + x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan(); - return x.times(2); - }; + Ctor.precision = pr; + Ctor.rounding = rm; + return x.times(2); +}; - /* - * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - * - * atan(0) = 0 - * atan(-0) = -0 - * atan(1) = pi/4 - * atan(-1) = -pi/4 - * atan(Infinity) = pi/2 - * atan(-Infinity) = -pi/2 - * atan(NaN) = NaN - * - */ - P.inverseTangent = P.atan = function () { - var i, j, k, n, px, t, r, wpr, x2, - x = this, - Ctor = x.constructor, - pr = Ctor.precision, - rm = Ctor.rounding; - if (!x.isFinite()) { - if (!x.s) return new Ctor(NaN); - if (pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.5); - r.s = x.s; - return r; - } - } else if (x.isZero()) { - return new Ctor(x); - } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.25); +/* + * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value + * of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-pi/2, pi/2] + * + * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... + * + * atan(0) = 0 + * atan(-0) = -0 + * atan(1) = pi/4 + * atan(-1) = -pi/4 + * atan(Infinity) = pi/2 + * atan(-Infinity) = -pi/2 + * atan(NaN) = NaN + * + */ +P.inverseTangent = P.atan = function () { + var i, j, k, n, px, t, r, wpr, x2, + x = this, + Ctor = x.constructor, + pr = Ctor.precision, + rm = Ctor.rounding; + + if (!x.isFinite()) { + if (!x.s) return new Ctor(NaN); + if (pr + 4 <= PI_PRECISION) { + r = getPi(Ctor, pr + 4, rm).times(0.5); r.s = x.s; return r; } + } else if (x.isZero()) { + return new Ctor(x); + } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) { + r = getPi(Ctor, pr + 4, rm).times(0.25); + r.s = x.s; + return r; + } - Ctor.precision = wpr = pr + 10; - Ctor.rounding = 1; + Ctor.precision = wpr = pr + 10; + Ctor.rounding = 1; - // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x); + // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x); - // Argument reduction - // Ensure |x| < 0.42 - // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2))) + // Argument reduction + // Ensure |x| < 0.42 + // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2))) - k = Math.min(28, wpr / LOG_BASE + 2 | 0); + k = Math.min(28, wpr / LOG_BASE + 2 | 0); - for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1)); + for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1)); - external = false; + external = false; - j = Math.ceil(wpr / LOG_BASE); - n = 1; - x2 = x.times(x); - r = new Ctor(x); - px = x; + j = Math.ceil(wpr / LOG_BASE); + n = 1; + x2 = x.times(x); + r = new Ctor(x); + px = x; - // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - for (; i !== -1;) { - px = px.times(x2); - t = r.minus(px.div(n += 2)); + // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... + for (; i !== -1;) { + px = px.times(x2); + t = r.minus(px.div(n += 2)); - px = px.times(x2); - r = t.plus(px.div(n += 2)); + px = px.times(x2); + r = t.plus(px.div(n += 2)); - if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;); - } + if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;); + } - if (k) r = r.times(2 << (k - 1)); + if (k) r = r.times(2 << (k - 1)); - external = true; + external = true; - return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true); - }; + return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true); +}; - /* - * Return true if the value of this Decimal is a finite number, otherwise return false. - * - */ - P.isFinite = function () { - return !!this.d; - }; +/* + * Return true if the value of this Decimal is a finite number, otherwise return false. + * + */ +P.isFinite = function () { + return !!this.d; +}; - /* - * Return true if the value of this Decimal is an integer, otherwise return false. - * - */ - P.isInteger = P.isInt = function () { - return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2; - }; +/* + * Return true if the value of this Decimal is an integer, otherwise return false. + * + */ +P.isInteger = P.isInt = function () { + return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2; +}; - /* - * Return true if the value of this Decimal is NaN, otherwise return false. - * - */ - P.isNaN = function () { - return !this.s; - }; +/* + * Return true if the value of this Decimal is NaN, otherwise return false. + * + */ +P.isNaN = function () { + return !this.s; +}; - /* - * Return true if the value of this Decimal is negative, otherwise return false. - * - */ - P.isNegative = P.isNeg = function () { - return this.s < 0; - }; +/* + * Return true if the value of this Decimal is negative, otherwise return false. + * + */ +P.isNegative = P.isNeg = function () { + return this.s < 0; +}; - /* - * Return true if the value of this Decimal is positive, otherwise return false. - * - */ - P.isPositive = P.isPos = function () { - return this.s > 0; - }; +/* + * Return true if the value of this Decimal is positive, otherwise return false. + * + */ +P.isPositive = P.isPos = function () { + return this.s > 0; +}; - /* - * Return true if the value of this Decimal is 0 or -0, otherwise return false. - * - */ - P.isZero = function () { - return !!this.d && this.d[0] === 0; - }; +/* + * Return true if the value of this Decimal is 0 or -0, otherwise return false. + * + */ +P.isZero = function () { + return !!this.d && this.d[0] === 0; +}; - /* - * Return true if the value of this Decimal is less than `y`, otherwise return false. - * - */ - P.lessThan = P.lt = function (y) { - return this.cmp(y) < 0; - }; +/* + * Return true if the value of this Decimal is less than `y`, otherwise return false. + * + */ +P.lessThan = P.lt = function (y) { + return this.cmp(y) < 0; +}; - /* - * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false. - * - */ - P.lessThanOrEqualTo = P.lte = function (y) { - return this.cmp(y) < 1; - }; +/* + * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false. + * + */ +P.lessThanOrEqualTo = P.lte = function (y) { + return this.cmp(y) < 1; +}; - /* - * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * If no base is specified, return log[10](arg). - * - * log[base](arg) = ln(arg) / ln(base) - * - * The result will always be correctly rounded if the base of the log is 10, and 'almost always' - * otherwise: - * - * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen - * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error - * between the result and the correctly rounded result will be one ulp (unit in the last place). - * - * log[-b](a) = NaN - * log[0](a) = NaN - * log[1](a) = NaN - * log[NaN](a) = NaN - * log[Infinity](a) = NaN - * log[b](0) = -Infinity - * log[b](-0) = -Infinity - * log[b](-a) = NaN - * log[b](1) = 0 - * log[b](Infinity) = Infinity - * log[b](NaN) = NaN - * - * [base] {number|string|Decimal} The base of the logarithm. - * - */ - P.logarithm = P.log = function (base) { - var isBase10, d, denominator, k, inf, num, sd, r, - arg = this, - Ctor = arg.constructor, - pr = Ctor.precision, - rm = Ctor.rounding, - guard = 5; - - // Default base is 10. - if (base == null) { - base = new Ctor(10); - isBase10 = true; - } else { - base = new Ctor(base); - d = base.d; +/* + * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * If no base is specified, return log[10](arg). + * + * log[base](arg) = ln(arg) / ln(base) + * + * The result will always be correctly rounded if the base of the log is 10, and 'almost always' + * otherwise: + * + * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen + * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error + * between the result and the correctly rounded result will be one ulp (unit in the last place). + * + * log[-b](a) = NaN + * log[0](a) = NaN + * log[1](a) = NaN + * log[NaN](a) = NaN + * log[Infinity](a) = NaN + * log[b](0) = -Infinity + * log[b](-0) = -Infinity + * log[b](-a) = NaN + * log[b](1) = 0 + * log[b](Infinity) = Infinity + * log[b](NaN) = NaN + * + * [base] {number|string|Decimal} The base of the logarithm. + * + */ +P.logarithm = P.log = function (base) { + var isBase10, d, denominator, k, inf, num, sd, r, + arg = this, + Ctor = arg.constructor, + pr = Ctor.precision, + rm = Ctor.rounding, + guard = 5; + + // Default base is 10. + if (base == null) { + base = new Ctor(10); + isBase10 = true; + } else { + base = new Ctor(base); + d = base.d; - // Return NaN if base is negative, or non-finite, or is 0 or 1. - if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN); + // Return NaN if base is negative, or non-finite, or is 0 or 1. + if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN); - isBase10 = base.eq(10); - } + isBase10 = base.eq(10); + } - d = arg.d; + d = arg.d; - // Is arg negative, non-finite, 0 or 1? - if (arg.s < 0 || !d || !d[0] || arg.eq(1)) { - return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0); - } + // Is arg negative, non-finite, 0 or 1? + if (arg.s < 0 || !d || !d[0] || arg.eq(1)) { + return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0); + } - // The result will have a non-terminating decimal expansion if base is 10 and arg is not an - // integer power of 10. - if (isBase10) { - if (d.length > 1) { - inf = true; - } else { - for (k = d[0]; k % 10 === 0;) k /= 10; - inf = k !== 1; - } + // The result will have a non-terminating decimal expansion if base is 10 and arg is not an + // integer power of 10. + if (isBase10) { + if (d.length > 1) { + inf = true; + } else { + for (k = d[0]; k % 10 === 0;) k /= 10; + inf = k !== 1; } + } - external = false; - sd = pr + guard; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - - // The result will have 5 rounding digits. - r = divide(num, denominator, sd, 1); + external = false; + sd = pr + guard; + num = naturalLogarithm(arg, sd); + denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000, - // calculate 10 further digits. - // - // If the result is known to have an infinite decimal expansion, repeat this until it is clear - // that the result is above or below the boundary. Otherwise, if after calculating the 10 - // further digits, the last 14 are nines, round up and assume the result is exact. - // Also assume the result is exact if the last 14 are zero. - // - // Example of a result that will be incorrectly rounded: - // log[1048576](4503599627370502) = 2.60000000000000009610279511444746... - // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it - // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so - // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal - // place is still 2.6. - if (checkRoundingDigits(r.d, k = pr, rm)) { + // The result will have 5 rounding digits. + r = divide(num, denominator, sd, 1); - do { - sd += 10; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - r = divide(num, denominator, sd, 1); + // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000, + // calculate 10 further digits. + // + // If the result is known to have an infinite decimal expansion, repeat this until it is clear + // that the result is above or below the boundary. Otherwise, if after calculating the 10 + // further digits, the last 14 are nines, round up and assume the result is exact. + // Also assume the result is exact if the last 14 are zero. + // + // Example of a result that will be incorrectly rounded: + // log[1048576](4503599627370502) = 2.60000000000000009610279511444746... + // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it + // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so + // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal + // place is still 2.6. + if (checkRoundingDigits(r.d, k = pr, rm)) { - if (!inf) { + do { + sd += 10; + num = naturalLogarithm(arg, sd); + denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); + r = divide(num, denominator, sd, 1); - // Check for 14 nines from the 2nd rounding digit, as the first may be 4. - if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } + if (!inf) { - break; + // Check for 14 nines from the 2nd rounding digit, as the first may be 4. + if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) { + r = finalise(r, pr + 1, 0); } - } while (checkRoundingDigits(r.d, k += 10, rm)); - } - external = true; + break; + } + } while (checkRoundingDigits(r.d, k += 10, rm)); + } - return finalise(r, pr, rm); - }; + external = true; + return finalise(r, pr, rm); +}; - /* - * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.max = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'lt'); - }; - */ +/* + * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal. + * + * arguments {number|string|Decimal} + * +P.max = function () { + Array.prototype.push.call(arguments, this); + return maxOrMin(this.constructor, arguments, 'lt'); +}; + */ - /* - * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.min = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'gt'); - }; - */ +/* + * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal. + * + * arguments {number|string|Decimal} + * +P.min = function () { + Array.prototype.push.call(arguments, this); + return maxOrMin(this.constructor, arguments, 'gt'); +}; + */ - /* - * n - 0 = n - * n - N = N - * n - I = -I - * 0 - n = -n - * 0 - 0 = 0 - * 0 - N = N - * 0 - I = -I - * N - n = N - * N - 0 = N - * N - N = N - * N - I = N - * I - n = I - * I - 0 = I - * I - N = N - * I - I = N - * - * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.minus = P.sub = function (y) { - var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd, - x = this, - Ctor = x.constructor; - y = new Ctor(y); +/* + * n - 0 = n + * n - N = N + * n - I = -I + * 0 - n = -n + * 0 - 0 = 0 + * 0 - N = N + * 0 - I = -I + * N - n = N + * N - 0 = N + * N - N = N + * N - I = N + * I - n = I + * I - 0 = I + * I - N = N + * I - I = N + * + * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + */ +P.minus = P.sub = function (y) { + var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd, + x = this, + Ctor = x.constructor; - // If either is not finite... - if (!x.d || !y.d) { + y = new Ctor(y); - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); + // If either is not finite... + if (!x.d || !y.d) { - // Return y negated if x is finite and y is ±Infinity. - else if (x.d) y.s = -y.s; + // Return NaN if either is NaN. + if (!x.s || !y.s) y = new Ctor(NaN); - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with different signs. - // Return NaN if both are ±Infinity with the same sign. - else y = new Ctor(y.d || x.s !== y.s ? x : NaN); + // Return y negated if x is finite and y is ±Infinity. + else if (x.d) y.s = -y.s; - return y; - } + // Return x if y is finite and x is ±Infinity. + // Return x if both are ±Infinity with different signs. + // Return NaN if both are ±Infinity with the same sign. + else y = new Ctor(y.d || x.s !== y.s ? x : NaN); - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.plus(y); - } + return y; + } - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; + // If signs differ... + if (x.s != y.s) { + y.s = -y.s; + return x.plus(y); + } - // If either is zero... - if (!xd[0] || !yd[0]) { + xd = x.d; + yd = y.d; + pr = Ctor.precision; + rm = Ctor.rounding; - // Return y negated if x is zero and y is non-zero. - if (yd[0]) y.s = -y.s; + // If either is zero... + if (!xd[0] || !yd[0]) { - // Return x if y is zero and x is non-zero. - else if (xd[0]) y = new Ctor(x); + // Return y negated if x is zero and y is non-zero. + if (yd[0]) y.s = -y.s; - // Return zero if both are zero. - // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity. - else return new Ctor(rm === 3 ? -0 : 0); + // Return x if y is zero and x is non-zero. + else if (xd[0]) y = new Ctor(x); - return external ? finalise(y, pr, rm) : y; - } + // Return zero if both are zero. + // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity. + else return new Ctor(rm === 3 ? -0 : 0); - // x and y are finite, non-zero numbers with the same sign. + return external ? finalise(y, pr, rm) : y; + } - // Calculate base 1e7 exponents. - e = mathfloor(y.e / LOG_BASE); - xe = mathfloor(x.e / LOG_BASE); + // x and y are finite, non-zero numbers with the same sign. - xd = xd.slice(); - k = xe - e; + // Calculate base 1e7 exponents. + e = mathfloor(y.e / LOG_BASE); + xe = mathfloor(x.e / LOG_BASE); - // If base 1e7 exponents differ... - if (k) { - xLTy = k < 0; + xd = xd.slice(); + k = xe - e; - if (xLTy) { - d = xd; - k = -k; - len = yd.length; - } else { - d = yd; - e = xe; - len = xd.length; - } + // If base 1e7 exponents differ... + if (k) { + xLTy = k < 0; - // Numbers with massively different exponents would result in a very high number of - // zeros needing to be prepended, but this can be avoided while still ensuring correct - // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`. - i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2; + if (xLTy) { + d = xd; + k = -k; + len = yd.length; + } else { + d = yd; + e = xe; + len = xd.length; + } - if (k > i) { - k = i; - d.length = 1; - } + // Numbers with massively different exponents would result in a very high number of + // zeros needing to be prepended, but this can be avoided while still ensuring correct + // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`. + i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2; - // Prepend zeros to equalise exponents. - d.reverse(); - for (i = k; i--;) d.push(0); - d.reverse(); + if (k > i) { + k = i; + d.length = 1; + } - // Base 1e7 exponents equal. - } else { + // Prepend zeros to equalise exponents. + d.reverse(); + for (i = k; i--;) d.push(0); + d.reverse(); - // Check digits to determine which is the bigger number. + // Base 1e7 exponents equal. + } else { - i = xd.length; - len = yd.length; - xLTy = i < len; - if (xLTy) len = i; + // Check digits to determine which is the bigger number. - for (i = 0; i < len; i++) { - if (xd[i] != yd[i]) { - xLTy = xd[i] < yd[i]; - break; - } - } + i = xd.length; + len = yd.length; + xLTy = i < len; + if (xLTy) len = i; - k = 0; + for (i = 0; i < len; i++) { + if (xd[i] != yd[i]) { + xLTy = xd[i] < yd[i]; + break; + } } - if (xLTy) { - d = xd; - xd = yd; - yd = d; - y.s = -y.s; - } + k = 0; + } - len = xd.length; + if (xLTy) { + d = xd; + xd = yd; + yd = d; + y.s = -y.s; + } - // Append zeros to `xd` if shorter. - // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length. - for (i = yd.length - len; i > 0; --i) xd[len++] = 0; + len = xd.length; - // Subtract yd from xd. - for (i = yd.length; i > k;) { + // Append zeros to `xd` if shorter. + // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length. + for (i = yd.length - len; i > 0; --i) xd[len++] = 0; - if (xd[--i] < yd[i]) { - for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1; - --xd[j]; - xd[i] += BASE; - } + // Subtract yd from xd. + for (i = yd.length; i > k;) { - xd[i] -= yd[i]; + if (xd[--i] < yd[i]) { + for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1; + --xd[j]; + xd[i] += BASE; } - // Remove trailing zeros. - for (; xd[--len] === 0;) xd.pop(); - - // Remove leading zeros and adjust exponent accordingly. - for (; xd[0] === 0; xd.shift()) --e; + xd[i] -= yd[i]; + } - // Zero? - if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0); + // Remove trailing zeros. + for (; xd[--len] === 0;) xd.pop(); - y.d = xd; - y.e = getBase10Exponent(xd, e); + // Remove leading zeros and adjust exponent accordingly. + for (; xd[0] === 0; xd.shift()) --e; - return external ? finalise(y, pr, rm) : y; - }; + // Zero? + if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0); + y.d = xd; + y.e = getBase10Exponent(xd, e); - /* - * n % 0 = N - * n % N = N - * n % I = n - * 0 % n = 0 - * -0 % n = -0 - * 0 % 0 = N - * 0 % N = N - * 0 % I = 0 - * N % n = N - * N % 0 = N - * N % N = N - * N % I = N - * I % n = N - * I % 0 = N - * I % N = N - * I % I = N - * - * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * The result depends on the modulo mode. - * - */ - P.modulo = P.mod = function (y) { - var q, - x = this, - Ctor = x.constructor; - - y = new Ctor(y); + return external ? finalise(y, pr, rm) : y; +}; - // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0. - if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN); - // Return x if y is ±Infinity or x is ±0. - if (!y.d || x.d && !x.d[0]) { - return finalise(new Ctor(x), Ctor.precision, Ctor.rounding); - } +/* + * n % 0 = N + * n % N = N + * n % I = n + * 0 % n = 0 + * -0 % n = -0 + * 0 % 0 = N + * 0 % N = N + * 0 % I = 0 + * N % n = N + * N % 0 = N + * N % N = N + * N % I = N + * I % n = N + * I % 0 = N + * I % N = N + * I % I = N + * + * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * The result depends on the modulo mode. + * + */ +P.modulo = P.mod = function (y) { + var q, + x = this, + Ctor = x.constructor; - // Prevent rounding of intermediate calculations. - external = false; + y = new Ctor(y); - if (Ctor.modulo == 9) { + // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0. + if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN); - // Euclidian division: q = sign(y) * floor(x / abs(y)) - // result = x - q * y where 0 <= result < abs(y) - q = divide(x, y.abs(), 0, 3, 1); - q.s *= y.s; - } else { - q = divide(x, y, 0, Ctor.modulo, 1); - } + // Return x if y is ±Infinity or x is ±0. + if (!y.d || x.d && !x.d[0]) { + return finalise(new Ctor(x), Ctor.precision, Ctor.rounding); + } - q = q.times(y); + // Prevent rounding of intermediate calculations. + external = false; - external = true; + if (Ctor.modulo == 9) { - return x.minus(q); - }; + // Euclidian division: q = sign(y) * floor(x / abs(y)) + // result = x - q * y where 0 <= result < abs(y) + q = divide(x, y.abs(), 0, 3, 1); + q.s *= y.s; + } else { + q = divide(x, y, 0, Ctor.modulo, 1); + } + q = q.times(y); - /* - * Return a new Decimal whose value is the natural exponential of the value of this Decimal, - * i.e. the base e raised to the power the value of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.naturalExponential = P.exp = function () { - return naturalExponential(this); - }; + external = true; + return x.minus(q); +}; - /* - * Return a new Decimal whose value is the natural logarithm of the value of this Decimal, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.naturalLogarithm = P.ln = function () { - return naturalLogarithm(this); - }; +/* + * Return a new Decimal whose value is the natural exponential of the value of this Decimal, + * i.e. the base e raised to the power the value of this Decimal, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + */ +P.naturalExponential = P.exp = function () { + return naturalExponential(this); +}; - /* - * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by - * -1. - * - */ - P.negated = P.neg = function () { - var x = new this.constructor(this); - x.s = -x.s; - return finalise(x); - }; +/* + * Return a new Decimal whose value is the natural logarithm of the value of this Decimal, + * rounded to `precision` significant digits using rounding mode `rounding`. + * + */ +P.naturalLogarithm = P.ln = function () { + return naturalLogarithm(this); +}; - /* - * n + 0 = n - * n + N = N - * n + I = I - * 0 + n = n - * 0 + 0 = 0 - * 0 + N = N - * 0 + I = I - * N + n = N - * N + 0 = N - * N + N = N - * N + I = N - * I + n = I - * I + 0 = I - * I + N = N - * I + I = I - * - * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.plus = P.add = function (y) { - var carry, d, e, i, k, len, pr, rm, xd, yd, - x = this, - Ctor = x.constructor; - y = new Ctor(y); +/* + * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by + * -1. + * + */ +P.negated = P.neg = function () { + var x = new this.constructor(this); + x.s = -x.s; + return finalise(x); +}; - // If either is not finite... - if (!x.d || !y.d) { - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); +/* + * n + 0 = n + * n + N = N + * n + I = I + * 0 + n = n + * 0 + 0 = 0 + * 0 + N = N + * 0 + I = I + * N + n = N + * N + 0 = N + * N + N = N + * N + I = N + * I + n = I + * I + 0 = I + * I + N = N + * I + I = I + * + * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + */ +P.plus = P.add = function (y) { + var carry, d, e, i, k, len, pr, rm, xd, yd, + x = this, + Ctor = x.constructor; - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with the same sign. - // Return NaN if both are ±Infinity with different signs. - // Return y if x is finite and y is ±Infinity. - else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN); + y = new Ctor(y); - return y; - } + // If either is not finite... + if (!x.d || !y.d) { - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.minus(y); - } + // Return NaN if either is NaN. + if (!x.s || !y.s) y = new Ctor(NaN); - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; + // Return x if y is finite and x is ±Infinity. + // Return x if both are ±Infinity with the same sign. + // Return NaN if both are ±Infinity with different signs. + // Return y if x is finite and y is ±Infinity. + else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN); - // If either is zero... - if (!xd[0] || !yd[0]) { + return y; + } - // Return x if y is zero. - // Return y if y is non-zero. - if (!yd[0]) y = new Ctor(x); + // If signs differ... + if (x.s != y.s) { + y.s = -y.s; + return x.minus(y); + } - return external ? finalise(y, pr, rm) : y; - } + xd = x.d; + yd = y.d; + pr = Ctor.precision; + rm = Ctor.rounding; - // x and y are finite, non-zero numbers with the same sign. + // If either is zero... + if (!xd[0] || !yd[0]) { - // Calculate base 1e7 exponents. - k = mathfloor(x.e / LOG_BASE); - e = mathfloor(y.e / LOG_BASE); + // Return x if y is zero. + // Return y if y is non-zero. + if (!yd[0]) y = new Ctor(x); - xd = xd.slice(); - i = k - e; + return external ? finalise(y, pr, rm) : y; + } - // If base 1e7 exponents differ... - if (i) { + // x and y are finite, non-zero numbers with the same sign. - if (i < 0) { - d = xd; - i = -i; - len = yd.length; - } else { - d = yd; - e = k; - len = xd.length; - } + // Calculate base 1e7 exponents. + k = mathfloor(x.e / LOG_BASE); + e = mathfloor(y.e / LOG_BASE); - // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1. - k = Math.ceil(pr / LOG_BASE); - len = k > len ? k + 1 : len + 1; + xd = xd.slice(); + i = k - e; - if (i > len) { - i = len; - d.length = 1; - } + // If base 1e7 exponents differ... + if (i) { - // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts. - d.reverse(); - for (; i--;) d.push(0); - d.reverse(); + if (i < 0) { + d = xd; + i = -i; + len = yd.length; + } else { + d = yd; + e = k; + len = xd.length; } - len = xd.length; - i = yd.length; + // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1. + k = Math.ceil(pr / LOG_BASE); + len = k > len ? k + 1 : len + 1; - // If yd is longer than xd, swap xd and yd so xd points to the longer array. - if (len - i < 0) { + if (i > len) { i = len; - d = yd; - yd = xd; - xd = d; + d.length = 1; } - // Only start adding at yd.length - 1 as the further digits of xd can be left as they are. - for (carry = 0; i;) { - carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0; - xd[i] %= BASE; - } + // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts. + d.reverse(); + for (; i--;) d.push(0); + d.reverse(); + } - if (carry) { - xd.unshift(carry); - ++e; - } + len = xd.length; + i = yd.length; - // Remove trailing zeros. - // No need to check for zero, as +x + +y != 0 && -x + -y != 0 - for (len = xd.length; xd[--len] == 0;) xd.pop(); + // If yd is longer than xd, swap xd and yd so xd points to the longer array. + if (len - i < 0) { + i = len; + d = yd; + yd = xd; + xd = d; + } - y.d = xd; - y.e = getBase10Exponent(xd, e); + // Only start adding at yd.length - 1 as the further digits of xd can be left as they are. + for (carry = 0; i;) { + carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0; + xd[i] %= BASE; + } - return external ? finalise(y, pr, rm) : y; - }; + if (carry) { + xd.unshift(carry); + ++e; + } + // Remove trailing zeros. + // No need to check for zero, as +x + +y != 0 && -x + -y != 0 + for (len = xd.length; xd[--len] == 0;) xd.pop(); - /* - * Return the number of significant digits of the value of this Decimal. - * - * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0. - * - */ - P.precision = P.sd = function (z) { - var k, - x = this; + y.d = xd; + y.e = getBase10Exponent(xd, e); - if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z); + return external ? finalise(y, pr, rm) : y; +}; - if (x.d) { - k = getPrecision(x.d); - if (z && x.e + 1 > k) k = x.e + 1; - } else { - k = NaN; - } - return k; - }; +/* + * Return the number of significant digits of the value of this Decimal. + * + * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0. + * + */ +P.precision = P.sd = function (z) { + var k, + x = this; + if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z); - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using - * rounding mode `rounding`. - * - */ - P.round = function () { - var x = this, - Ctor = x.constructor; + if (x.d) { + k = getPrecision(x.d); + if (z && x.e + 1 > k) k = x.e + 1; + } else { + k = NaN; + } - return finalise(new Ctor(x), x.e + 1, Ctor.rounding); - }; + return k; +}; - /* - * Return a new Decimal whose value is the sine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * sin(x) = x - x^3/3! + x^5/5! - ... - * - * sin(0) = 0 - * sin(-0) = -0 - * sin(Infinity) = NaN - * sin(-Infinity) = NaN - * sin(NaN) = NaN - * - */ - P.sine = P.sin = function () { - var pr, rm, - x = this, - Ctor = x.constructor; +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using + * rounding mode `rounding`. + * + */ +P.round = function () { + var x = this, + Ctor = x.constructor; - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); + return finalise(new Ctor(x), x.e + 1, Ctor.rounding); +}; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; - x = sine(Ctor, toLessThanHalfPi(Ctor, x)); +/* + * Return a new Decimal whose value is the sine of the value in radians of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-1, 1] + * + * sin(x) = x - x^3/3! + x^5/5! - ... + * + * sin(0) = 0 + * sin(-0) = -0 + * sin(Infinity) = NaN + * sin(-Infinity) = NaN + * sin(NaN) = NaN + * + */ +P.sine = P.sin = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - Ctor.precision = pr; - Ctor.rounding = rm; + if (!x.isFinite()) return new Ctor(NaN); + if (x.isZero()) return new Ctor(x); - return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true); - }; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; + Ctor.rounding = 1; + x = sine(Ctor, toLessThanHalfPi(Ctor, x)); - /* - * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * sqrt(-n) = N - * sqrt(N) = N - * sqrt(-I) = N - * sqrt(I) = I - * sqrt(0) = 0 - * sqrt(-0) = -0 - * - */ - P.squareRoot = P.sqrt = function () { - var m, n, sd, r, rep, t, - x = this, - d = x.d, - e = x.e, - s = x.s, - Ctor = x.constructor; + Ctor.precision = pr; + Ctor.rounding = rm; - // Negative/NaN/Infinity/zero? - if (s !== 1 || !d || !d[0]) { - return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0); - } + return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true); +}; - external = false; - // Initial estimate. - s = Math.sqrt(+x); +/* + * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * sqrt(-n) = N + * sqrt(N) = N + * sqrt(-I) = N + * sqrt(I) = I + * sqrt(0) = 0 + * sqrt(-0) = -0 + * + */ +P.squareRoot = P.sqrt = function () { + var m, n, sd, r, rep, t, + x = this, + d = x.d, + e = x.e, + s = x.s, + Ctor = x.constructor; + + // Negative/NaN/Infinity/zero? + if (s !== 1 || !d || !d[0]) { + return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0); + } + + external = false; - // Math.sqrt underflow/overflow? - // Pass x to Math.sqrt as integer, then adjust the exponent of the result. - if (s == 0 || s == 1 / 0) { - n = digitsToString(d); + // Initial estimate. + s = Math.sqrt(+x); - if ((n.length + e) % 2 == 0) n += '0'; - s = Math.sqrt(n); - e = mathfloor((e + 1) / 2) - (e < 0 || e % 2); + // Math.sqrt underflow/overflow? + // Pass x to Math.sqrt as integer, then adjust the exponent of the result. + if (s == 0 || s == 1 / 0) { + n = digitsToString(d); - if (s == 1 / 0) { - n = '1e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } + if ((n.length + e) % 2 == 0) n += '0'; + s = Math.sqrt(n); + e = mathfloor((e + 1) / 2) - (e < 0 || e % 2); - r = new Ctor(n); + if (s == 1 / 0) { + n = '1e' + e; } else { - r = new Ctor(s.toString()); + n = s.toExponential(); + n = n.slice(0, n.indexOf('e') + 1) + e; } - sd = (e = Ctor.precision) + 3; + r = new Ctor(n); + } else { + r = new Ctor(s.toString()); + } + + sd = (e = Ctor.precision) + 3; - // Newton-Raphson iteration. - for (;;) { - t = r; - r = t.plus(divide(x, t, sd + 2, 1)).times(0.5); + // Newton-Raphson iteration. + for (;;) { + t = r; + r = t.plus(divide(x, t, sd + 2, 1)).times(0.5); - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); + // TODO? Replace with for-loop and checkRoundingDigits. + if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { + n = n.slice(sd - 3, sd + 1); - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or - // 4999, i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { + // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or + // 4999, i.e. approaching a rounding boundary, continue the iteration. + if (n == '9999' || !rep && n == '4999') { - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); + // On the first iteration only, check to see if rounding up gives the exact result as the + // nines may infinitely repeat. + if (!rep) { + finalise(t, e + 1, 0); - if (t.times(t).eq(x)) { - r = t; - break; - } + if (t.times(t).eq(x)) { + r = t; + break; } + } - sd += 4; - rep = 1; - } else { - - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { + sd += 4; + rep = 1; + } else { - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).eq(x); - } + // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. + // If not, then there are further digits and m will be truthy. + if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - break; + // Truncate to the first rounding digit. + finalise(r, e + 1, 1); + m = !r.times(r).eq(x); } + + break; } } + } - external = true; + external = true; - return finalise(r, e, Ctor.rounding, m); - }; + return finalise(r, e, Ctor.rounding, m); +}; - /* - * Return a new Decimal whose value is the tangent of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * tan(0) = 0 - * tan(-0) = -0 - * tan(Infinity) = NaN - * tan(-Infinity) = NaN - * tan(NaN) = NaN - * - */ - P.tangent = P.tan = function () { - var pr, rm, - x = this, - Ctor = x.constructor; +/* + * Return a new Decimal whose value is the tangent of the value in radians of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-Infinity, Infinity] + * + * tan(0) = 0 + * tan(-0) = -0 + * tan(Infinity) = NaN + * tan(-Infinity) = NaN + * tan(NaN) = NaN + * + */ +P.tangent = P.tan = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); + if (!x.isFinite()) return new Ctor(NaN); + if (x.isZero()) return new Ctor(x); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 10; - Ctor.rounding = 1; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + 10; + Ctor.rounding = 1; - x = x.sin(); - x.s = 1; - x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0); + x = x.sin(); + x.s = 1; + x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0); - Ctor.precision = pr; - Ctor.rounding = rm; + Ctor.precision = pr; + Ctor.rounding = rm; - return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true); - }; + return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true); +}; - /* - * n * 0 = 0 - * n * N = N - * n * I = I - * 0 * n = 0 - * 0 * 0 = 0 - * 0 * N = N - * 0 * I = N - * N * n = N - * N * 0 = N - * N * N = N - * N * I = N - * I * n = I - * I * 0 = N - * I * N = N - * I * I = I - * - * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - */ - P.times = P.mul = function (y) { - var carry, e, i, k, r, rL, t, xdL, ydL, - x = this, - Ctor = x.constructor, - xd = x.d, - yd = (y = new Ctor(y)).d; +/* + * n * 0 = 0 + * n * N = N + * n * I = I + * 0 * n = 0 + * 0 * 0 = 0 + * 0 * N = N + * 0 * I = N + * N * n = N + * N * 0 = N + * N * N = N + * N * I = N + * I * n = I + * I * 0 = N + * I * N = N + * I * I = I + * + * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + */ +P.times = P.mul = function (y) { + var carry, e, i, k, r, rL, t, xdL, ydL, + x = this, + Ctor = x.constructor, + xd = x.d, + yd = (y = new Ctor(y)).d; - y.s *= x.s; + y.s *= x.s; - // If either is NaN, ±Infinity or ±0... - if (!xd || !xd[0] || !yd || !yd[0]) { + // If either is NaN, ±Infinity or ±0... + if (!xd || !xd[0] || !yd || !yd[0]) { - return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd + return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd - // Return NaN if either is NaN. - // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity. - ? NaN + // Return NaN if either is NaN. + // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity. + ? NaN - // Return ±Infinity if either is ±Infinity. - // Return ±0 if either is ±0. - : !xd || !yd ? y.s / 0 : y.s * 0); - } + // Return ±Infinity if either is ±Infinity. + // Return ±0 if either is ±0. + : !xd || !yd ? y.s / 0 : y.s * 0); + } - e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE); - xdL = xd.length; - ydL = yd.length; + e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE); + xdL = xd.length; + ydL = yd.length; - // Ensure xd points to the longer array. - if (xdL < ydL) { - r = xd; - xd = yd; - yd = r; - rL = xdL; - xdL = ydL; - ydL = rL; - } - - // Initialise the result array with zeros. - r = []; - rL = xdL + ydL; - for (i = rL; i--;) r.push(0); + // Ensure xd points to the longer array. + if (xdL < ydL) { + r = xd; + xd = yd; + yd = r; + rL = xdL; + xdL = ydL; + ydL = rL; + } - // Multiply! - for (i = ydL; --i >= 0;) { - carry = 0; - for (k = xdL + i; k > i;) { - t = r[k] + yd[i] * xd[k - i - 1] + carry; - r[k--] = t % BASE | 0; - carry = t / BASE | 0; - } + // Initialise the result array with zeros. + r = []; + rL = xdL + ydL; + for (i = rL; i--;) r.push(0); - r[k] = (r[k] + carry) % BASE | 0; + // Multiply! + for (i = ydL; --i >= 0;) { + carry = 0; + for (k = xdL + i; k > i;) { + t = r[k] + yd[i] * xd[k - i - 1] + carry; + r[k--] = t % BASE | 0; + carry = t / BASE | 0; } - // Remove trailing zeros. - for (; !r[--rL];) r.pop(); - - if (carry) ++e; - else r.shift(); + r[k] = (r[k] + carry) % BASE | 0; + } - y.d = r; - y.e = getBase10Exponent(r, e); + // Remove trailing zeros. + for (; !r[--rL];) r.pop(); - return external ? finalise(y, Ctor.precision, Ctor.rounding) : y; - }; + if (carry) ++e; + else r.shift(); + y.d = r; + y.e = getBase10Exponent(r, e); - /* - * Return a string representing the value of this Decimal in base 2, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toBinary = function (sd, rm) { - return toStringBinary(this, 2, sd, rm); - }; + return external ? finalise(y, Ctor.precision, Ctor.rounding) : y; +}; - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp` - * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted. - * - * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toDecimalPlaces = P.toDP = function (dp, rm) { - var x = this, - Ctor = x.constructor; +/* + * Return a string representing the value of this Decimal in base 2, round to `sd` significant + * digits using rounding mode `rm`. + * + * If the optional `sd` argument is present then return binary exponential notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toBinary = function (sd, rm) { + return toStringBinary(this, 2, sd, rm); +}; - x = new Ctor(x); - if (dp === void 0) return x; - checkInt32(dp, 0, MAX_DIGITS); +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp` + * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted. + * + * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal. + * + * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toDecimalPlaces = P.toDP = function (dp, rm) { + var x = this, + Ctor = x.constructor; - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); + x = new Ctor(x); + if (dp === void 0) return x; - return finalise(x, dp + x.e + 1, rm); - }; + checkInt32(dp, 0, MAX_DIGITS); + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); - /* - * Return a string representing the value of this Decimal in exponential notation rounded to - * `dp` fixed decimal places using rounding mode `rounding`. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toExponential = function (dp, rm) { - var str, - x = this, - Ctor = x.constructor; + return finalise(x, dp + x.e + 1, rm); +}; - if (dp === void 0) { - str = finiteToString(x, true); - } else { - checkInt32(dp, 0, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); +/* + * Return a string representing the value of this Decimal in exponential notation rounded to + * `dp` fixed decimal places using rounding mode `rounding`. + * + * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toExponential = function (dp, rm) { + var str, + x = this, + Ctor = x.constructor; - x = finalise(new Ctor(x), dp + 1, rm); - str = finiteToString(x, true, dp + 1); - } + if (dp === void 0) { + str = finiteToString(x, true); + } else { + checkInt32(dp, 0, MAX_DIGITS); - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + x = finalise(new Ctor(x), dp + 1, rm); + str = finiteToString(x, true, dp + 1); + } - /* - * Return a string representing the value of this Decimal in normal (fixed-point) notation to - * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is - * omitted. - * - * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'. - * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'. - * (-0).toFixed(3) is '0.000'. - * (-0.5).toFixed(0) is '-0'. - * - */ - P.toFixed = function (dp, rm) { - var str, y, - x = this, - Ctor = x.constructor; + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - if (dp === void 0) { - str = finiteToString(x); - } else { - checkInt32(dp, 0, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); +/* + * Return a string representing the value of this Decimal in normal (fixed-point) notation to + * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is + * omitted. + * + * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'. + * + * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'. + * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'. + * (-0).toFixed(3) is '0.000'. + * (-0.5).toFixed(0) is '-0'. + * + */ +P.toFixed = function (dp, rm) { + var str, y, + x = this, + Ctor = x.constructor; - y = finalise(new Ctor(x), dp + x.e + 1, rm); - str = finiteToString(y, false, dp + y.e + 1); - } + if (dp === void 0) { + str = finiteToString(x); + } else { + checkInt32(dp, 0, MAX_DIGITS); - // To determine whether to add the minus sign look at the value before it was rounded, - // i.e. look at `x` rather than `y`. - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + y = finalise(new Ctor(x), dp + x.e + 1, rm); + str = finiteToString(y, false, dp + y.e + 1); + } - /* - * Return an array representing the value of this Decimal as a simple fraction with an integer - * numerator and an integer denominator. - * - * The denominator will be a positive non-zero value less than or equal to the specified maximum - * denominator. If a maximum denominator is not specified, the denominator will be the lowest - * value necessary to represent the number exactly. - * - * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity. - * - */ - P.toFraction = function (maxD) { - var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r, - x = this, - xd = x.d, - Ctor = x.constructor; + // To determine whether to add the minus sign look at the value before it was rounded, + // i.e. look at `x` rather than `y`. + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - if (!xd) return new Ctor(x); - n1 = d0 = new Ctor(1); - d1 = n0 = new Ctor(0); +/* + * Return an array representing the value of this Decimal as a simple fraction with an integer + * numerator and an integer denominator. + * + * The denominator will be a positive non-zero value less than or equal to the specified maximum + * denominator. If a maximum denominator is not specified, the denominator will be the lowest + * value necessary to represent the number exactly. + * + * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity. + * + */ +P.toFraction = function (maxD) { + var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r, + x = this, + xd = x.d, + Ctor = x.constructor; - d = new Ctor(d1); - e = d.e = getPrecision(xd) - x.e - 1; - k = e % LOG_BASE; - d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k); + if (!xd) return new Ctor(x); - if (maxD == null) { + n1 = d0 = new Ctor(1); + d1 = n0 = new Ctor(0); - // d is 10**e, the minimum max-denominator needed. - maxD = e > 0 ? d : n1; - } else { - n = new Ctor(maxD); - if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n); - maxD = n.gt(d) ? (e > 0 ? d : n1) : n; - } + d = new Ctor(d1); + e = d.e = getPrecision(xd) - x.e - 1; + k = e % LOG_BASE; + d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k); - external = false; - n = new Ctor(digitsToString(xd)); - pr = Ctor.precision; - Ctor.precision = e = xd.length * LOG_BASE * 2; - - for (;;) { - q = divide(n, d, 0, 1, 1); - d2 = d0.plus(q.times(d1)); - if (d2.cmp(maxD) == 1) break; - d0 = d1; - d1 = d2; - d2 = n1; - n1 = n0.plus(q.times(d2)); - n0 = d2; - d2 = d; - d = n.minus(q.times(d2)); - n = d2; - } - - d2 = divide(maxD.minus(d0), d1, 0, 1, 1); - n0 = n0.plus(d2.times(n1)); - d0 = d0.plus(d2.times(d1)); - n0.s = n1.s = x.s; - - // Determine which fraction is closer to x, n0/d0 or n1/d1? - r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 - ? [n1, d1] : [n0, d0]; + if (maxD == null) { - Ctor.precision = pr; - external = true; + // d is 10**e, the minimum max-denominator needed. + maxD = e > 0 ? d : n1; + } else { + n = new Ctor(maxD); + if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n); + maxD = n.gt(d) ? (e > 0 ? d : n1) : n; + } + + external = false; + n = new Ctor(digitsToString(xd)); + pr = Ctor.precision; + Ctor.precision = e = xd.length * LOG_BASE * 2; + + for (;;) { + q = divide(n, d, 0, 1, 1); + d2 = d0.plus(q.times(d1)); + if (d2.cmp(maxD) == 1) break; + d0 = d1; + d1 = d2; + d2 = n1; + n1 = n0.plus(q.times(d2)); + n0 = d2; + d2 = d; + d = n.minus(q.times(d2)); + n = d2; + } + + d2 = divide(maxD.minus(d0), d1, 0, 1, 1); + n0 = n0.plus(d2.times(n1)); + d0 = d0.plus(d2.times(d1)); + n0.s = n1.s = x.s; + + // Determine which fraction is closer to x, n0/d0 or n1/d1? + r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 + ? [n1, d1] : [n0, d0]; + + Ctor.precision = pr; + external = true; - return r; - }; + return r; +}; - /* - * Return a string representing the value of this Decimal in base 16, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toHexadecimal = P.toHex = function (sd, rm) { - return toStringBinary(this, 16, sd, rm); - }; +/* + * Return a string representing the value of this Decimal in base 16, round to `sd` significant + * digits using rounding mode `rm`. + * + * If the optional `sd` argument is present then return binary exponential notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toHexadecimal = P.toHex = function (sd, rm) { + return toStringBinary(this, 16, sd, rm); +}; - /* - * Returns a new Decimal whose value is the nearest multiple of the magnitude of `y` to the value - * of this Decimal. - * - * If the value of this Decimal is equidistant from two multiples of `y`, the rounding mode `rm`, - * or `Decimal.rounding` if `rm` is omitted, determines the direction of the nearest multiple. - * - * In the context of this method, rounding mode 4 (ROUND_HALF_UP) is the same as rounding mode 0 - * (ROUND_UP), and so on. - * - * The return value will always have the same sign as this Decimal, unless either this Decimal - * or `y` is NaN, in which case the return value will be also be NaN. - * - * The return value is not affected by the value of `precision`. - * - * y {number|string|Decimal} The magnitude to round to a multiple of. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toNearest() rounding mode not an integer: {rm}' - * 'toNearest() rounding mode out of range: {rm}' - * - */ - P.toNearest = function (y, rm) { - var x = this, - Ctor = x.constructor; +/* + * Returns a new Decimal whose value is the nearest multiple of the magnitude of `y` to the value + * of this Decimal. + * + * If the value of this Decimal is equidistant from two multiples of `y`, the rounding mode `rm`, + * or `Decimal.rounding` if `rm` is omitted, determines the direction of the nearest multiple. + * + * In the context of this method, rounding mode 4 (ROUND_HALF_UP) is the same as rounding mode 0 + * (ROUND_UP), and so on. + * + * The return value will always have the same sign as this Decimal, unless either this Decimal + * or `y` is NaN, in which case the return value will be also be NaN. + * + * The return value is not affected by the value of `precision`. + * + * y {number|string|Decimal} The magnitude to round to a multiple of. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + * 'toNearest() rounding mode not an integer: {rm}' + * 'toNearest() rounding mode out of range: {rm}' + * + */ +P.toNearest = function (y, rm) { + var x = this, + Ctor = x.constructor; - x = new Ctor(x); + x = new Ctor(x); - if (y == null) { + if (y == null) { - // If x is not finite, return x. - if (!x.d) return x; + // If x is not finite, return x. + if (!x.d) return x; - y = new Ctor(1); - rm = Ctor.rounding; - } else { - y = new Ctor(y); - if (rm !== void 0) checkInt32(rm, 0, 8); + y = new Ctor(1); + rm = Ctor.rounding; + } else { + y = new Ctor(y); + if (rm !== void 0) checkInt32(rm, 0, 8); - // If x is not finite, return x if y is not NaN, else NaN. - if (!x.d) return y.s ? x : y; + // If x is not finite, return x if y is not NaN, else NaN. + if (!x.d) return y.s ? x : y; - // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN. - if (!y.d) { - if (y.s) y.s = x.s; - return y; - } + // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN. + if (!y.d) { + if (y.s) y.s = x.s; + return y; } + } - // If y is not zero, calculate the nearest multiple of y to x. - if (y.d[0]) { - external = false; - if (rm < 4) rm = [4, 5, 7, 8][rm]; - x = divide(x, y, 0, rm, 1).times(y); - external = true; - finalise(x); + // If y is not zero, calculate the nearest multiple of y to x. + if (y.d[0]) { + external = false; + if (rm < 4) rm = [4, 5, 7, 8][rm]; + x = divide(x, y, 0, rm, 1).times(y); + external = true; + finalise(x); - // If y is zero, return zero with the sign of x. - } else { - y.s = x.s; - x = y; - } + // If y is zero, return zero with the sign of x. + } else { + y.s = x.s; + x = y; + } - return x; - }; + return x; +}; - /* - * Return the value of this Decimal converted to a number primitive. - * Zero keeps its sign. - * - */ - P.toNumber = function () { - return +this; - }; +/* + * Return the value of this Decimal converted to a number primitive. + * Zero keeps its sign. + * + */ +P.toNumber = function () { + return +this; +}; - /* - * Return a string representing the value of this Decimal in base 8, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toOctal = function (sd, rm) { - return toStringBinary(this, 8, sd, rm); - }; +/* + * Return a string representing the value of this Decimal in base 8, round to `sd` significant + * digits using rounding mode `rm`. + * + * If the optional `sd` argument is present then return binary exponential notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toOctal = function (sd, rm) { + return toStringBinary(this, 8, sd, rm); +}; - /* - * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded - * to `precision` significant digits using rounding mode `rounding`. - * - * ECMAScript compliant. - * - * pow(x, NaN) = NaN - * pow(x, ±0) = 1 - - * pow(NaN, non-zero) = NaN - * pow(abs(x) > 1, +Infinity) = +Infinity - * pow(abs(x) > 1, -Infinity) = +0 - * pow(abs(x) == 1, ±Infinity) = NaN - * pow(abs(x) < 1, +Infinity) = +0 - * pow(abs(x) < 1, -Infinity) = +Infinity - * pow(+Infinity, y > 0) = +Infinity - * pow(+Infinity, y < 0) = +0 - * pow(-Infinity, odd integer > 0) = -Infinity - * pow(-Infinity, even integer > 0) = +Infinity - * pow(-Infinity, odd integer < 0) = -0 - * pow(-Infinity, even integer < 0) = +0 - * pow(+0, y > 0) = +0 - * pow(+0, y < 0) = +Infinity - * pow(-0, odd integer > 0) = -0 - * pow(-0, even integer > 0) = +0 - * pow(-0, odd integer < 0) = -Infinity - * pow(-0, even integer < 0) = +Infinity - * pow(finite x < 0, finite non-integer) = NaN - * - * For non-integer or very large exponents pow(x, y) is calculated using - * - * x^y = exp(y*ln(x)) - * - * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the - * probability of an incorrectly rounded result - * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14 - * i.e. 1 in 250,000,000,000,000 - * - * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place). - * - * y {number|string|Decimal} The power to which to raise this Decimal. - * - */ - P.toPower = P.pow = function (y) { - var e, k, pr, r, rm, s, - x = this, - Ctor = x.constructor, - yn = +(y = new Ctor(y)); +/* + * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded + * to `precision` significant digits using rounding mode `rounding`. + * + * ECMAScript compliant. + * + * pow(x, NaN) = NaN + * pow(x, ±0) = 1 + + * pow(NaN, non-zero) = NaN + * pow(abs(x) > 1, +Infinity) = +Infinity + * pow(abs(x) > 1, -Infinity) = +0 + * pow(abs(x) == 1, ±Infinity) = NaN + * pow(abs(x) < 1, +Infinity) = +0 + * pow(abs(x) < 1, -Infinity) = +Infinity + * pow(+Infinity, y > 0) = +Infinity + * pow(+Infinity, y < 0) = +0 + * pow(-Infinity, odd integer > 0) = -Infinity + * pow(-Infinity, even integer > 0) = +Infinity + * pow(-Infinity, odd integer < 0) = -0 + * pow(-Infinity, even integer < 0) = +0 + * pow(+0, y > 0) = +0 + * pow(+0, y < 0) = +Infinity + * pow(-0, odd integer > 0) = -0 + * pow(-0, even integer > 0) = +0 + * pow(-0, odd integer < 0) = -Infinity + * pow(-0, even integer < 0) = +Infinity + * pow(finite x < 0, finite non-integer) = NaN + * + * For non-integer or very large exponents pow(x, y) is calculated using + * + * x^y = exp(y*ln(x)) + * + * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the + * probability of an incorrectly rounded result + * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14 + * i.e. 1 in 250,000,000,000,000 + * + * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place). + * + * y {number|string|Decimal} The power to which to raise this Decimal. + * + */ +P.toPower = P.pow = function (y) { + var e, k, pr, r, rm, s, + x = this, + Ctor = x.constructor, + yn = +(y = new Ctor(y)); - // Either ±Infinity, NaN or ±0? - if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn)); + // Either ±Infinity, NaN or ±0? + if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn)); - x = new Ctor(x); + x = new Ctor(x); - if (x.eq(1)) return x; + if (x.eq(1)) return x; - pr = Ctor.precision; - rm = Ctor.rounding; + pr = Ctor.precision; + rm = Ctor.rounding; - if (y.eq(1)) return finalise(x, pr, rm); + if (y.eq(1)) return finalise(x, pr, rm); - // y exponent - e = mathfloor(y.e / LOG_BASE); + // y exponent + e = mathfloor(y.e / LOG_BASE); - // If y is a small integer use the 'exponentiation by squaring' algorithm. - if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) { - r = intPow(Ctor, x, k, pr); - return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm); - } + // If y is a small integer use the 'exponentiation by squaring' algorithm. + if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) { + r = intPow(Ctor, x, k, pr); + return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm); + } - s = x.s; + s = x.s; - // if x is negative - if (s < 0) { + // if x is negative + if (s < 0) { - // if y is not an integer - if (e < y.d.length - 1) return new Ctor(NaN); + // if y is not an integer + if (e < y.d.length - 1) return new Ctor(NaN); - // Result is positive if x is negative and the last digit of integer y is even. - if ((y.d[e] & 1) == 0) s = 1; + // Result is positive if x is negative and the last digit of integer y is even. + if ((y.d[e] & 1) == 0) s = 1; - // if x.eq(-1) - if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) { - x.s = s; - return x; - } + // if x.eq(-1) + if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) { + x.s = s; + return x; } + } - // Estimate result exponent. - // x^y = 10^e, where e = y * log10(x) - // log10(x) = log10(x_significand) + x_exponent - // log10(x_significand) = ln(x_significand) / ln(10) - k = mathpow(+x, yn); - e = k == 0 || !isFinite(k) - ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) - : new Ctor(k + '').e; + // Estimate result exponent. + // x^y = 10^e, where e = y * log10(x) + // log10(x) = log10(x_significand) + x_exponent + // log10(x_significand) = ln(x_significand) / ln(10) + k = mathpow(+x, yn); + e = k == 0 || !isFinite(k) + ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) + : new Ctor(k + '').e; - // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1. + // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1. - // Overflow/underflow? - if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0); + // Overflow/underflow? + if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0); - external = false; - Ctor.rounding = x.s = 1; + external = false; + Ctor.rounding = x.s = 1; - // Estimate the extra guard digits needed to ensure five correct rounding digits from - // naturalLogarithm(x). Example of failure without these extra digits (precision: 10): - // new Decimal(2.32456).pow('2087987436534566.46411') - // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815 - k = Math.min(12, (e + '').length); + // Estimate the extra guard digits needed to ensure five correct rounding digits from + // naturalLogarithm(x). Example of failure without these extra digits (precision: 10): + // new Decimal(2.32456).pow('2087987436534566.46411') + // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815 + k = Math.min(12, (e + '').length); - // r = x^y = exp(y*ln(x)) - r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr); + // r = x^y = exp(y*ln(x)) + r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr); - // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40) - if (r.d) { + // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40) + if (r.d) { - // Truncate to the required precision plus five rounding digits. - r = finalise(r, pr + 5, 1); + // Truncate to the required precision plus five rounding digits. + r = finalise(r, pr + 5, 1); - // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate - // the result. - if (checkRoundingDigits(r.d, pr, rm)) { - e = pr + 10; + // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate + // the result. + if (checkRoundingDigits(r.d, pr, rm)) { + e = pr + 10; - // Truncate to the increased precision plus five rounding digits. - r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1); + // Truncate to the increased precision plus five rounding digits. + r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1); - // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9). - if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } + // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9). + if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) { + r = finalise(r, pr + 1, 0); } } + } - r.s = s; - external = true; - Ctor.rounding = rm; - - return finalise(r, pr, rm); - }; + r.s = s; + external = true; + Ctor.rounding = rm; + return finalise(r, pr, rm); +}; - /* - * Return a string representing the value of this Decimal rounded to `sd` significant digits - * using rounding mode `rounding`. - * - * Return exponential notation if `sd` is less than the number of digits necessary to represent - * the integer part of the value in normal notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toPrecision = function (sd, rm) { - var str, - x = this, - Ctor = x.constructor; - if (sd === void 0) { - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - } else { - checkInt32(sd, 1, MAX_DIGITS); +/* + * Return a string representing the value of this Decimal rounded to `sd` significant digits + * using rounding mode `rounding`. + * + * Return exponential notation if `sd` is less than the number of digits necessary to represent + * the integer part of the value in normal notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toPrecision = function (sd, rm) { + var str, + x = this, + Ctor = x.constructor; - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); + if (sd === void 0) { + str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); + } else { + checkInt32(sd, 1, MAX_DIGITS); - x = finalise(new Ctor(x), sd, rm); - str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd); - } + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; + x = finalise(new Ctor(x), sd, rm); + str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd); + } + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd` - * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if - * omitted. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toSD() digits out of range: {sd}' - * 'toSD() digits not an integer: {sd}' - * 'toSD() rounding mode not an integer: {rm}' - * 'toSD() rounding mode out of range: {rm}' - * - */ - P.toSignificantDigits = P.toSD = function (sd, rm) { - var x = this, - Ctor = x.constructor; - if (sd === void 0) { - sd = Ctor.precision; - rm = Ctor.rounding; - } else { - checkInt32(sd, 1, MAX_DIGITS); +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd` + * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if + * omitted. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + * 'toSD() digits out of range: {sd}' + * 'toSD() digits not an integer: {sd}' + * 'toSD() rounding mode not an integer: {rm}' + * 'toSD() rounding mode out of range: {rm}' + * + */ +P.toSignificantDigits = P.toSD = function (sd, rm) { + var x = this, + Ctor = x.constructor; - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - } + if (sd === void 0) { + sd = Ctor.precision; + rm = Ctor.rounding; + } else { + checkInt32(sd, 1, MAX_DIGITS); - return finalise(new Ctor(x), sd, rm); - }; + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + } + return finalise(new Ctor(x), sd, rm); +}; - /* - * Return a string representing the value of this Decimal. - * - * Return exponential notation if this Decimal has a positive exponent equal to or greater than - * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`. - * - */ - P.toString = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; +/* + * Return a string representing the value of this Decimal. + * + * Return exponential notation if this Decimal has a positive exponent equal to or greater than + * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`. + * + */ +P.toString = function () { + var x = this, + Ctor = x.constructor, + str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - /* - * Return a new Decimal whose value is the value of this Decimal truncated to a whole number. - * - */ - P.truncated = P.trunc = function () { - return finalise(new this.constructor(this), this.e + 1, 1); - }; +/* + * Return a new Decimal whose value is the value of this Decimal truncated to a whole number. + * + */ +P.truncated = P.trunc = function () { + return finalise(new this.constructor(this), this.e + 1, 1); +}; - /* - * Return a string representing the value of this Decimal. - * Unlike `toString`, negative zero will include the minus sign. - * - */ - P.valueOf = P.toJSON = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - return x.isNeg() ? '-' + str : str; - }; +/* + * Return a string representing the value of this Decimal. + * Unlike `toString`, negative zero will include the minus sign. + * + */ +P.valueOf = P.toJSON = function () { + var x = this, + Ctor = x.constructor, + str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); + return x.isNeg() ? '-' + str : str; +}; - /* - // Add aliases to match BigDecimal method names. - // P.add = P.plus; - P.subtract = P.minus; - P.multiply = P.times; - P.divide = P.div; - P.remainder = P.mod; - P.compareTo = P.cmp; - P.negate = P.neg; - */ +/* +// Add aliases to match BigDecimal method names. +// P.add = P.plus; +P.subtract = P.minus; +P.multiply = P.times; +P.divide = P.div; +P.remainder = P.mod; +P.compareTo = P.cmp; +P.negate = P.neg; + */ - // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers. +// Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers. - /* - * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower, - * finiteToString, naturalExponential, naturalLogarithm - * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest, - * P.toPrecision, P.toSignificantDigits, toStringBinary, random - * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm - * convertBase toStringBinary, parseOther - * cos P.cos - * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy, - * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction, - * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm, - * taylorSeries, atan2, parseOther - * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh, - * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus, - * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot, - * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed, - * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits, - * P.truncated, divide, getLn10, getPi, naturalExponential, - * naturalLogarithm, ceil, floor, round, trunc - * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf, - * toStringBinary - * getBase10Exponent P.minus, P.plus, P.times, parseOther - * getLn10 P.logarithm, naturalLogarithm - * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2 - * getPrecision P.precision, P.toFraction - * getZeroString digitsToString, finiteToString - * intPow P.toPower, parseOther - * isOdd toLessThanHalfPi - * maxOrMin max, min - * naturalExponential P.naturalExponential, P.toPower - * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm, - * P.toPower, naturalExponential - * nonFiniteToString finiteToString, toStringBinary - * parseDecimal Decimal - * parseOther Decimal - * sin P.sin - * taylorSeries P.cosh, P.sinh, cos, sin - * toLessThanHalfPi P.cos, P.sin - * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal - * truncate intPow - * - * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi, - * naturalLogarithm, config, parseOther, random, Decimal - */ +/* + * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower, + * finiteToString, naturalExponential, naturalLogarithm + * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest, + * P.toPrecision, P.toSignificantDigits, toStringBinary, random + * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm + * convertBase toStringBinary, parseOther + * cos P.cos + * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy, + * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction, + * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm, + * taylorSeries, atan2, parseOther + * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh, + * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus, + * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot, + * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed, + * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits, + * P.truncated, divide, getLn10, getPi, naturalExponential, + * naturalLogarithm, ceil, floor, round, trunc + * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf, + * toStringBinary + * getBase10Exponent P.minus, P.plus, P.times, parseOther + * getLn10 P.logarithm, naturalLogarithm + * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2 + * getPrecision P.precision, P.toFraction + * getZeroString digitsToString, finiteToString + * intPow P.toPower, parseOther + * isOdd toLessThanHalfPi + * maxOrMin max, min + * naturalExponential P.naturalExponential, P.toPower + * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm, + * P.toPower, naturalExponential + * nonFiniteToString finiteToString, toStringBinary + * parseDecimal Decimal + * parseOther Decimal + * sin P.sin + * taylorSeries P.cosh, P.sinh, cos, sin + * toLessThanHalfPi P.cos, P.sin + * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal + * truncate intPow + * + * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi, + * naturalLogarithm, config, parseOther, random, Decimal + */ - function digitsToString(d) { - var i, k, ws, - indexOfLastWord = d.length - 1, - str = '', - w = d[0]; - if (indexOfLastWord > 0) { - str += w; - for (i = 1; i < indexOfLastWord; i++) { - ws = d[i] + ''; - k = LOG_BASE - ws.length; - if (k) str += getZeroString(k); - str += ws; - } +function digitsToString(d) { + var i, k, ws, + indexOfLastWord = d.length - 1, + str = '', + w = d[0]; - w = d[i]; - ws = w + ''; + if (indexOfLastWord > 0) { + str += w; + for (i = 1; i < indexOfLastWord; i++) { + ws = d[i] + ''; k = LOG_BASE - ws.length; if (k) str += getZeroString(k); - } else if (w === 0) { - return '0'; + str += ws; } - // Remove trailing zeros of last w. - for (; w % 10 === 0;) w /= 10; - - return str + w; + w = d[i]; + ws = w + ''; + k = LOG_BASE - ws.length; + if (k) str += getZeroString(k); + } else if (w === 0) { + return '0'; } + // Remove trailing zeros of last w. + for (; w % 10 === 0;) w /= 10; - function checkInt32(i, min, max) { - if (i !== ~~i || i < min || i > max) { - throw Error(invalidArgument + i); - } + return str + w; +} + + +function checkInt32(i, min, max) { + if (i !== ~~i || i < min || i > max) { + throw Error(invalidArgument + i); } +} - /* - * Check 5 rounding digits if `repeating` is null, 4 otherwise. - * `repeating == null` if caller is `log` or `pow`, - * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`. - */ - function checkRoundingDigits(d, i, rm, repeating) { - var di, k, r, rd; +/* + * Check 5 rounding digits if `repeating` is null, 4 otherwise. + * `repeating == null` if caller is `log` or `pow`, + * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`. + */ +function checkRoundingDigits(d, i, rm, repeating) { + var di, k, r, rd; - // Get the length of the first word of the array d. - for (k = d[0]; k >= 10; k /= 10) --i; + // Get the length of the first word of the array d. + for (k = d[0]; k >= 10; k /= 10) --i; - // Is the rounding digit in the first word of d? - if (--i < 0) { - i += LOG_BASE; - di = 0; - } else { - di = Math.ceil((i + 1) / LOG_BASE); - i %= LOG_BASE; - } + // Is the rounding digit in the first word of d? + if (--i < 0) { + i += LOG_BASE; + di = 0; + } else { + di = Math.ceil((i + 1) / LOG_BASE); + i %= LOG_BASE; + } - // i is the index (0 - 6) of the rounding digit. - // E.g. if within the word 3487563 the first rounding digit is 5, - // then i = 4, k = 1000, rd = 3487563 % 1000 = 563 - k = mathpow(10, LOG_BASE - i); - rd = d[di] % k | 0; + // i is the index (0 - 6) of the rounding digit. + // E.g. if within the word 3487563 the first rounding digit is 5, + // then i = 4, k = 1000, rd = 3487563 % 1000 = 563 + k = mathpow(10, LOG_BASE - i); + rd = d[di] % k | 0; - if (repeating == null) { - if (i < 3) { - if (i == 0) rd = rd / 100 | 0; - else if (i == 1) rd = rd / 10 | 0; - r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0; - } else { - r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) && - (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 || - (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0; - } + if (repeating == null) { + if (i < 3) { + if (i == 0) rd = rd / 100 | 0; + else if (i == 1) rd = rd / 10 | 0; + r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0; } else { - if (i < 4) { - if (i == 0) rd = rd / 1000 | 0; - else if (i == 1) rd = rd / 100 | 0; - else if (i == 2) rd = rd / 10 | 0; - r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999; - } else { - r = ((repeating || rm < 4) && rd + 1 == k || - (!repeating && rm > 3) && rd + 1 == k / 2) && - (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1; - } + r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) && + (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 || + (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0; + } + } else { + if (i < 4) { + if (i == 0) rd = rd / 1000 | 0; + else if (i == 1) rd = rd / 100 | 0; + else if (i == 2) rd = rd / 10 | 0; + r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999; + } else { + r = ((repeating || rm < 4) && rd + 1 == k || + (!repeating && rm > 3) && rd + 1 == k / 2) && + (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1; } - - return r; } + return r; +} - // Convert string of `baseIn` to an array of numbers of `baseOut`. - // Eg. convertBase('255', 10, 16) returns [15, 15]. - // Eg. convertBase('ff', 16, 10) returns [2, 5, 5]. - function convertBase(str, baseIn, baseOut) { - var j, - arr = [0], - arrL, - i = 0, - strL = str.length; - for (; i < strL;) { - for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn; - arr[0] += NUMERALS.indexOf(str.charAt(i++)); - for (j = 0; j < arr.length; j++) { - if (arr[j] > baseOut - 1) { - if (arr[j + 1] === void 0) arr[j + 1] = 0; - arr[j + 1] += arr[j] / baseOut | 0; - arr[j] %= baseOut; - } +// Convert string of `baseIn` to an array of numbers of `baseOut`. +// Eg. convertBase('255', 10, 16) returns [15, 15]. +// Eg. convertBase('ff', 16, 10) returns [2, 5, 5]. +function convertBase(str, baseIn, baseOut) { + var j, + arr = [0], + arrL, + i = 0, + strL = str.length; + + for (; i < strL;) { + for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn; + arr[0] += NUMERALS.indexOf(str.charAt(i++)); + for (j = 0; j < arr.length; j++) { + if (arr[j] > baseOut - 1) { + if (arr[j + 1] === void 0) arr[j + 1] = 0; + arr[j + 1] += arr[j] / baseOut | 0; + arr[j] %= baseOut; } } + } + + return arr.reverse(); +} + + +/* + * cos(x) = 1 - x^2/2! + x^4/4! - ... + * |x| < pi/2 + * + */ +function cosine(Ctor, x) { + var k, y, + len = x.d.length; + + // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1 + // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1 - return arr.reverse(); + // Estimate the optimum number of times to use the argument reduction. + if (len < 32) { + k = Math.ceil(len / 3); + y = Math.pow(4, -k).toString(); + } else { + k = 16; + y = '2.3283064365386962890625e-10'; } + Ctor.precision += k; - /* - * cos(x) = 1 - x^2/2! + x^4/4! - ... - * |x| < pi/2 - * - */ - function cosine(Ctor, x) { - var k, y, - len = x.d.length; + x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)); - // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1 - // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1 + // Reverse argument reduction + for (var i = k; i--;) { + var cos2x = x.times(x); + x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1); + } - // Estimate the optimum number of times to use the argument reduction. - if (len < 32) { - k = Math.ceil(len / 3); - y = Math.pow(4, -k).toString(); - } else { - k = 16; - y = '2.3283064365386962890625e-10'; - } + Ctor.precision -= k; - Ctor.precision += k; + return x; +} - x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)); - // Reverse argument reduction - for (var i = k; i--;) { - var cos2x = x.times(x); - x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1); +/* + * Perform division in the specified base. + */ +var divide = (function () { + + // Assumes non-zero x and k, and hence non-zero result. + function multiplyInteger(x, k, base) { + var temp, + carry = 0, + i = x.length; + + for (x = x.slice(); i--;) { + temp = x[i] * k + carry; + x[i] = temp % base | 0; + carry = temp / base | 0; } - Ctor.precision -= k; + if (carry) x.unshift(carry); return x; } + function compare(a, b, aL, bL) { + var i, r; - /* - * Perform division in the specified base. - */ - var divide = (function () { - - // Assumes non-zero x and k, and hence non-zero result. - function multiplyInteger(x, k, base) { - var temp, - carry = 0, - i = x.length; - - for (x = x.slice(); i--;) { - temp = x[i] * k + carry; - x[i] = temp % base | 0; - carry = temp / base | 0; + if (aL != bL) { + r = aL > bL ? 1 : -1; + } else { + for (i = r = 0; i < aL; i++) { + if (a[i] != b[i]) { + r = a[i] > b[i] ? 1 : -1; + break; + } } + } - if (carry) x.unshift(carry); + return r; + } - return x; + function subtract(a, b, aL, base) { + var i = 0; + + // Subtract b from a. + for (; aL--;) { + a[aL] -= i; + i = a[aL] < b[aL] ? 1 : 0; + a[aL] = i * base + a[aL] - b[aL]; } - function compare(a, b, aL, bL) { - var i, r; + // Remove leading zeros. + for (; !a[0] && a.length > 1;) a.shift(); + } - if (aL != bL) { - r = aL > bL ? 1 : -1; - } else { - for (i = r = 0; i < aL; i++) { - if (a[i] != b[i]) { - r = a[i] > b[i] ? 1 : -1; - break; - } - } - } + return function (x, y, pr, rm, dp, base) { + var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, + yL, yz, + Ctor = x.constructor, + sign = x.s == y.s ? 1 : -1, + xd = x.d, + yd = y.d; - return r; - } + // Either NaN, Infinity or 0? + if (!xd || !xd[0] || !yd || !yd[0]) { - function subtract(a, b, aL, base) { - var i = 0; + return new Ctor(// Return NaN if either NaN, or both Infinity or 0. + !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN : - // Subtract b from a. - for (; aL--;) { - a[aL] -= i; - i = a[aL] < b[aL] ? 1 : 0; - a[aL] = i * base + a[aL] - b[aL]; - } + // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0. + xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0); + } - // Remove leading zeros. - for (; !a[0] && a.length > 1;) a.shift(); + if (base) { + logBase = 1; + e = x.e - y.e; + } else { + base = BASE; + logBase = LOG_BASE; + e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase); } - return function (x, y, pr, rm, dp, base) { - var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, - yL, yz, - Ctor = x.constructor, - sign = x.s == y.s ? 1 : -1, - xd = x.d, - yd = y.d; + yL = yd.length; + xL = xd.length; + q = new Ctor(sign); + qd = q.d = []; - // Either NaN, Infinity or 0? - if (!xd || !xd[0] || !yd || !yd[0]) { + // Result exponent may be one less than e. + // The digit array of a Decimal from toStringBinary may have trailing zeros. + for (i = 0; yd[i] == (xd[i] || 0); i++); - return new Ctor(// Return NaN if either NaN, or both Infinity or 0. - !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN : + if (yd[i] > (xd[i] || 0)) e--; - // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0. - xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0); - } + if (pr == null) { + sd = pr = Ctor.precision; + rm = Ctor.rounding; + } else if (dp) { + sd = pr + (x.e - y.e) + 1; + } else { + sd = pr; + } - if (base) { - logBase = 1; - e = x.e - y.e; - } else { - base = BASE; - logBase = LOG_BASE; - e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase); - } + if (sd < 0) { + qd.push(1); + more = true; + } else { + + // Convert precision in number of base 10 digits to base 1e7 digits. + sd = sd / logBase + 2 | 0; + i = 0; - yL = yd.length; - xL = xd.length; - q = new Ctor(sign); - qd = q.d = []; + // divisor < 1e7 + if (yL == 1) { + k = 0; + yd = yd[0]; + sd++; - // Result exponent may be one less than e. - // The digit array of a Decimal from toStringBinary may have trailing zeros. - for (i = 0; yd[i] == (xd[i] || 0); i++); + // k is the carry. + for (; (i < xL || k) && sd--; i++) { + t = k * base + (xd[i] || 0); + qd[i] = t / yd | 0; + k = t % yd | 0; + } - if (yd[i] > (xd[i] || 0)) e--; + more = k || i < xL; - if (pr == null) { - sd = pr = Ctor.precision; - rm = Ctor.rounding; - } else if (dp) { - sd = pr + (x.e - y.e) + 1; + // divisor >= 1e7 } else { - sd = pr; - } - if (sd < 0) { - qd.push(1); - more = true; - } else { + // Normalise xd and yd so highest order digit of yd is >= base/2 + k = base / (yd[0] + 1) | 0; - // Convert precision in number of base 10 digits to base 1e7 digits. - sd = sd / logBase + 2 | 0; - i = 0; + if (k > 1) { + yd = multiplyInteger(yd, k, base); + xd = multiplyInteger(xd, k, base); + yL = yd.length; + xL = xd.length; + } - // divisor < 1e7 - if (yL == 1) { - k = 0; - yd = yd[0]; - sd++; - - // k is the carry. - for (; (i < xL || k) && sd--; i++) { - t = k * base + (xd[i] || 0); - qd[i] = t / yd | 0; - k = t % yd | 0; - } + xi = yL; + rem = xd.slice(0, yL); + remL = rem.length; - more = k || i < xL; + // Add zeros to make remainder as long as divisor. + for (; remL < yL;) rem[remL++] = 0; - // divisor >= 1e7 - } else { + yz = yd.slice(); + yz.unshift(0); + yd0 = yd[0]; - // Normalise xd and yd so highest order digit of yd is >= base/2 - k = base / (yd[0] + 1) | 0; + if (yd[1] >= base / 2) ++yd0; - if (k > 1) { - yd = multiplyInteger(yd, k, base); - xd = multiplyInteger(xd, k, base); - yL = yd.length; - xL = xd.length; - } + do { + k = 0; - xi = yL; - rem = xd.slice(0, yL); - remL = rem.length; + // Compare divisor and remainder. + cmp = compare(yd, rem, yL, remL); - // Add zeros to make remainder as long as divisor. - for (; remL < yL;) rem[remL++] = 0; + // If divisor < remainder. + if (cmp < 0) { - yz = yd.slice(); - yz.unshift(0); - yd0 = yd[0]; + // Calculate trial digit, k. + rem0 = rem[0]; + if (yL != remL) rem0 = rem0 * base + (rem[1] || 0); - if (yd[1] >= base / 2) ++yd0; + // k will be how many times the divisor goes into the current remainder. + k = rem0 / yd0 | 0; - do { - k = 0; + // Algorithm: + // 1. product = divisor * trial digit (k) + // 2. if product > remainder: product -= divisor, k-- + // 3. remainder -= product + // 4. if product was < remainder at 2: + // 5. compare new remainder and divisor + // 6. If remainder > divisor: remainder -= divisor, k++ - // Compare divisor and remainder. - cmp = compare(yd, rem, yL, remL); + if (k > 1) { + if (k >= base) k = base - 1; - // If divisor < remainder. - if (cmp < 0) { + // product = divisor * trial digit. + prod = multiplyInteger(yd, k, base); + prodL = prod.length; + remL = rem.length; - // Calculate trial digit, k. - rem0 = rem[0]; - if (yL != remL) rem0 = rem0 * base + (rem[1] || 0); + // Compare product and remainder. + cmp = compare(prod, rem, prodL, remL); - // k will be how many times the divisor goes into the current remainder. - k = rem0 / yd0 | 0; + // product > remainder. + if (cmp == 1) { + k--; + + // Subtract divisor from product. + subtract(prod, yL < prodL ? yz : yd, prodL, base); + } + } else { - // Algorithm: - // 1. product = divisor * trial digit (k) - // 2. if product > remainder: product -= divisor, k-- - // 3. remainder -= product - // 4. if product was < remainder at 2: - // 5. compare new remainder and divisor - // 6. If remainder > divisor: remainder -= divisor, k++ + // cmp is -1. + // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1 + // to avoid it. If k is 1 there is a need to compare yd and rem again below. + if (k == 0) cmp = k = 1; + prod = yd.slice(); + } - if (k > 1) { - if (k >= base) k = base - 1; + prodL = prod.length; + if (prodL < remL) prod.unshift(0); - // product = divisor * trial digit. - prod = multiplyInteger(yd, k, base); - prodL = prod.length; - remL = rem.length; + // Subtract product from remainder. + subtract(rem, prod, remL, base); - // Compare product and remainder. - cmp = compare(prod, rem, prodL, remL); + // If product was < previous remainder. + if (cmp == -1) { + remL = rem.length; - // product > remainder. - if (cmp == 1) { - k--; + // Compare divisor and new remainder. + cmp = compare(yd, rem, yL, remL); - // Subtract divisor from product. - subtract(prod, yL < prodL ? yz : yd, prodL, base); - } - } else { + // If divisor < new remainder, subtract divisor from remainder. + if (cmp < 1) { + k++; - // cmp is -1. - // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1 - // to avoid it. If k is 1 there is a need to compare yd and rem again below. - if (k == 0) cmp = k = 1; - prod = yd.slice(); + // Subtract divisor from remainder. + subtract(rem, yL < remL ? yz : yd, remL, base); } + } - prodL = prod.length; - if (prodL < remL) prod.unshift(0); - - // Subtract product from remainder. - subtract(rem, prod, remL, base); + remL = rem.length; + } else if (cmp === 0) { + k++; + rem = [0]; + } // if cmp === 1, k will be 0 - // If product was < previous remainder. - if (cmp == -1) { - remL = rem.length; + // Add the next digit, k, to the result array. + qd[i++] = k; - // Compare divisor and new remainder. - cmp = compare(yd, rem, yL, remL); + // Update the remainder. + if (cmp && rem[0]) { + rem[remL++] = xd[xi] || 0; + } else { + rem = [xd[xi]]; + remL = 1; + } - // If divisor < new remainder, subtract divisor from remainder. - if (cmp < 1) { - k++; + } while ((xi++ < xL || rem[0] !== void 0) && sd--); - // Subtract divisor from remainder. - subtract(rem, yL < remL ? yz : yd, remL, base); - } - } + more = rem[0] !== void 0; + } - remL = rem.length; - } else if (cmp === 0) { - k++; - rem = [0]; - } // if cmp === 1, k will be 0 + // Leading zero? + if (!qd[0]) qd.shift(); + } - // Add the next digit, k, to the result array. - qd[i++] = k; + // logBase is 1 when divide is being used for base conversion. + if (logBase == 1) { + q.e = e; + inexact = more; + } else { - // Update the remainder. - if (cmp && rem[0]) { - rem[remL++] = xd[xi] || 0; - } else { - rem = [xd[xi]]; - remL = 1; - } + // To calculate q.e, first get the number of digits of qd[0]. + for (i = 1, k = qd[0]; k >= 10; k /= 10) i++; + q.e = i + e * logBase - 1; - } while ((xi++ < xL || rem[0] !== void 0) && sd--); + finalise(q, dp ? pr + q.e + 1 : pr, rm, more); + } - more = rem[0] !== void 0; - } + return q; + }; +})(); - // Leading zero? - if (!qd[0]) qd.shift(); - } - // logBase is 1 when divide is being used for base conversion. - if (logBase == 1) { - q.e = e; - inexact = more; - } else { +/* + * Round `x` to `sd` significant digits using rounding mode `rm`. + * Check for over/under-flow. + */ + function finalise(x, sd, rm, isTruncated) { + var digits, i, j, k, rd, roundUp, w, xd, xdi, + Ctor = x.constructor; - // To calculate q.e, first get the number of digits of qd[0]. - for (i = 1, k = qd[0]; k >= 10; k /= 10) i++; - q.e = i + e * logBase - 1; + // Don't round if sd is null or undefined. + out: if (sd != null) { + xd = x.d; - finalise(q, dp ? pr + q.e + 1 : pr, rm, more); - } + // Infinity/NaN. + if (!xd) return x; - return q; - }; - })(); + // rd: the rounding digit, i.e. the digit after the digit that may be rounded up. + // w: the word of xd containing rd, a base 1e7 number. + // xdi: the index of w within xd. + // digits: the number of digits of w. + // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if + // they had leading zeros) + // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero). + // Get the length of the first word of the digits array xd. + for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++; + i = sd - digits; - /* - * Round `x` to `sd` significant digits using rounding mode `rm`. - * Check for over/under-flow. - */ - function finalise(x, sd, rm, isTruncated) { - var digits, i, j, k, rd, roundUp, w, xd, xdi, - Ctor = x.constructor; - - // Don't round if sd is null or undefined. - out: if (sd != null) { - xd = x.d; - - // Infinity/NaN. - if (!xd) return x; - - // rd: the rounding digit, i.e. the digit after the digit that may be rounded up. - // w: the word of xd containing rd, a base 1e7 number. - // xdi: the index of w within xd. - // digits: the number of digits of w. - // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if - // they had leading zeros) - // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero). - - // Get the length of the first word of the digits array xd. - for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++; - i = sd - digits; - - // Is the rounding digit in the first word of xd? - if (i < 0) { - i += LOG_BASE; - j = sd; - w = xd[xdi = 0]; + // Is the rounding digit in the first word of xd? + if (i < 0) { + i += LOG_BASE; + j = sd; + w = xd[xdi = 0]; - // Get the rounding digit at index j of w. - rd = w / mathpow(10, digits - j - 1) % 10 | 0; - } else { - xdi = Math.ceil((i + 1) / LOG_BASE); - k = xd.length; - if (xdi >= k) { - if (isTruncated) { - - // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`. - for (; k++ <= xdi;) xd.push(0); - w = rd = 0; - digits = 1; - i %= LOG_BASE; - j = i - LOG_BASE + 1; - } else { - break out; - } + // Get the rounding digit at index j of w. + rd = w / mathpow(10, digits - j - 1) % 10 | 0; + } else { + xdi = Math.ceil((i + 1) / LOG_BASE); + k = xd.length; + if (xdi >= k) { + if (isTruncated) { + + // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`. + for (; k++ <= xdi;) xd.push(0); + w = rd = 0; + digits = 1; + i %= LOG_BASE; + j = i - LOG_BASE + 1; } else { - w = k = xd[xdi]; + break out; + } + } else { + w = k = xd[xdi]; - // Get the number of digits of w. - for (digits = 1; k >= 10; k /= 10) digits++; + // Get the number of digits of w. + for (digits = 1; k >= 10; k /= 10) digits++; - // Get the index of rd within w. - i %= LOG_BASE; + // Get the index of rd within w. + i %= LOG_BASE; - // Get the index of rd within w, adjusted for leading zeros. - // The number of leading zeros of w is given by LOG_BASE - digits. - j = i - LOG_BASE + digits; + // Get the index of rd within w, adjusted for leading zeros. + // The number of leading zeros of w is given by LOG_BASE - digits. + j = i - LOG_BASE + digits; - // Get the rounding digit at index j of w. - rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0; - } + // Get the rounding digit at index j of w. + rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0; } + } - // Are there any non-zero digits after the rounding digit? - isTruncated = isTruncated || sd < 0 || - xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)); - - // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right - // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression - // will give 714. + // Are there any non-zero digits after the rounding digit? + isTruncated = isTruncated || sd < 0 || + xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)); - roundUp = rm < 4 - ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) - : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 && + // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right + // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression + // will give 714. - // Check whether the digit to the left of the rounding digit is odd. - ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 || - rm == (x.s < 0 ? 8 : 7)); + roundUp = rm < 4 + ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) + : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 && - if (sd < 1 || !xd[0]) { - xd.length = 0; - if (roundUp) { + // Check whether the digit to the left of the rounding digit is odd. + ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 || + rm == (x.s < 0 ? 8 : 7)); - // Convert sd to decimal places. - sd -= x.e + 1; + if (sd < 1 || !xd[0]) { + xd.length = 0; + if (roundUp) { - // 1, 0.1, 0.01, 0.001, 0.0001 etc. - xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE); - x.e = -sd || 0; - } else { + // Convert sd to decimal places. + sd -= x.e + 1; - // Zero. - xd[0] = x.e = 0; - } + // 1, 0.1, 0.01, 0.001, 0.0001 etc. + xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE); + x.e = -sd || 0; + } else { - return x; + // Zero. + xd[0] = x.e = 0; } - // Remove excess digits. - if (i == 0) { - xd.length = xdi; - k = 1; - xdi--; - } else { - xd.length = xdi + 1; - k = mathpow(10, LOG_BASE - i); + return x; + } - // E.g. 56700 becomes 56000 if 7 is the rounding digit. - // j > 0 means i > number of leading zeros of w. - xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0; - } + // Remove excess digits. + if (i == 0) { + xd.length = xdi; + k = 1; + xdi--; + } else { + xd.length = xdi + 1; + k = mathpow(10, LOG_BASE - i); - if (roundUp) { - for (;;) { + // E.g. 56700 becomes 56000 if 7 is the rounding digit. + // j > 0 means i > number of leading zeros of w. + xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0; + } - // Is the digit to be rounded up in the first word of xd? - if (xdi == 0) { + if (roundUp) { + for (;;) { - // i will be the length of xd[0] before k is added. - for (i = 1, j = xd[0]; j >= 10; j /= 10) i++; - j = xd[0] += k; - for (k = 1; j >= 10; j /= 10) k++; + // Is the digit to be rounded up in the first word of xd? + if (xdi == 0) { - // if i != k the length has increased. - if (i != k) { - x.e++; - if (xd[0] == BASE) xd[0] = 1; - } + // i will be the length of xd[0] before k is added. + for (i = 1, j = xd[0]; j >= 10; j /= 10) i++; + j = xd[0] += k; + for (k = 1; j >= 10; j /= 10) k++; - break; - } else { - xd[xdi] += k; - if (xd[xdi] != BASE) break; - xd[xdi--] = 0; - k = 1; + // if i != k the length has increased. + if (i != k) { + x.e++; + if (xd[0] == BASE) xd[0] = 1; } + + break; + } else { + xd[xdi] += k; + if (xd[xdi] != BASE) break; + xd[xdi--] = 0; + k = 1; } } - - // Remove trailing zeros. - for (i = xd.length; xd[--i] === 0;) xd.pop(); } - if (external) { + // Remove trailing zeros. + for (i = xd.length; xd[--i] === 0;) xd.pop(); + } - // Overflow? - if (x.e > Ctor.maxE) { + if (external) { - // Infinity. - x.d = null; - x.e = NaN; + // Overflow? + if (x.e > Ctor.maxE) { - // Underflow? - } else if (x.e < Ctor.minE) { + // Infinity. + x.d = null; + x.e = NaN; - // Zero. - x.e = 0; - x.d = [0]; - // Ctor.underflow = true; - } // else Ctor.underflow = false; - } + // Underflow? + } else if (x.e < Ctor.minE) { - return x; + // Zero. + x.e = 0; + x.d = [0]; + // Ctor.underflow = true; + } // else Ctor.underflow = false; } + return x; +} - function finiteToString(x, isExp, sd) { - if (!x.isFinite()) return nonFiniteToString(x); - var k, - e = x.e, - str = digitsToString(x.d), - len = str.length; - if (isExp) { - if (sd && (k = sd - len) > 0) { - str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k); - } else if (len > 1) { - str = str.charAt(0) + '.' + str.slice(1); - } +function finiteToString(x, isExp, sd) { + if (!x.isFinite()) return nonFiniteToString(x); + var k, + e = x.e, + str = digitsToString(x.d), + len = str.length; - str = str + (x.e < 0 ? 'e' : 'e+') + x.e; - } else if (e < 0) { - str = '0.' + getZeroString(-e - 1) + str; - if (sd && (k = sd - len) > 0) str += getZeroString(k); - } else if (e >= len) { - str += getZeroString(e + 1 - len); - if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k); - } else { - if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k); - if (sd && (k = sd - len) > 0) { - if (e + 1 === len) str += '.'; - str += getZeroString(k); - } + if (isExp) { + if (sd && (k = sd - len) > 0) { + str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k); + } else if (len > 1) { + str = str.charAt(0) + '.' + str.slice(1); } - return str; + str = str + (x.e < 0 ? 'e' : 'e+') + x.e; + } else if (e < 0) { + str = '0.' + getZeroString(-e - 1) + str; + if (sd && (k = sd - len) > 0) str += getZeroString(k); + } else if (e >= len) { + str += getZeroString(e + 1 - len); + if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k); + } else { + if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k); + if (sd && (k = sd - len) > 0) { + if (e + 1 === len) str += '.'; + str += getZeroString(k); + } } + return str; +} - // Calculate the base 10 exponent from the base 1e7 exponent. - function getBase10Exponent(digits, e) { - var w = digits[0]; - - // Add the number of digits of the first word of the digits array. - for ( e *= LOG_BASE; w >= 10; w /= 10) e++; - return e; - } +// Calculate the base 10 exponent from the base 1e7 exponent. +function getBase10Exponent(digits, e) { + var w = digits[0]; - function getLn10(Ctor, sd, pr) { - if (sd > LN10_PRECISION) { + // Add the number of digits of the first word of the digits array. + for ( e *= LOG_BASE; w >= 10; w /= 10) e++; + return e; +} - // Reset global state in case the exception is caught. - external = true; - if (pr) Ctor.precision = pr; - throw Error(precisionLimitExceeded); - } - return finalise(new Ctor(LN10), sd, 1, true); - } +function getLn10(Ctor, sd, pr) { + if (sd > LN10_PRECISION) { - function getPi(Ctor, sd, rm) { - if (sd > PI_PRECISION) throw Error(precisionLimitExceeded); - return finalise(new Ctor(PI), sd, rm, true); + // Reset global state in case the exception is caught. + external = true; + if (pr) Ctor.precision = pr; + throw Error(precisionLimitExceeded); } + return finalise(new Ctor(LN10), sd, 1, true); +} - function getPrecision(digits) { - var w = digits.length - 1, - len = w * LOG_BASE + 1; - - w = digits[w]; +function getPi(Ctor, sd, rm) { + if (sd > PI_PRECISION) throw Error(precisionLimitExceeded); + return finalise(new Ctor(PI), sd, rm, true); +} - // If non-zero... - if (w) { - // Subtract the number of trailing zeros of the last word. - for (; w % 10 == 0; w /= 10) len--; +function getPrecision(digits) { + var w = digits.length - 1, + len = w * LOG_BASE + 1; - // Add the number of digits of the first word. - for (w = digits[0]; w >= 10; w /= 10) len++; - } + w = digits[w]; - return len; - } + // If non-zero... + if (w) { + // Subtract the number of trailing zeros of the last word. + for (; w % 10 == 0; w /= 10) len--; - function getZeroString(k) { - var zs = ''; - for (; k--;) zs += '0'; - return zs; + // Add the number of digits of the first word. + for (w = digits[0]; w >= 10; w /= 10) len++; } + return len; +} - /* - * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an - * integer of type number. - * - * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`. - * - */ - function intPow(Ctor, x, n, pr) { - var isTruncated, - r = new Ctor(1), - // Max n of 9007199254740991 takes 53 loop iterations. - // Maximum digits array length; leaves [28, 34] guard digits. - k = Math.ceil(pr / LOG_BASE + 4); +function getZeroString(k) { + var zs = ''; + for (; k--;) zs += '0'; + return zs; +} - external = false; - for (;;) { - if (n % 2) { - r = r.times(x); - if (truncate(r.d, k)) isTruncated = true; - } +/* + * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an + * integer of type number. + * + * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`. + * + */ +function intPow(Ctor, x, n, pr) { + var isTruncated, + r = new Ctor(1), - n = mathfloor(n / 2); - if (n === 0) { + // Max n of 9007199254740991 takes 53 loop iterations. + // Maximum digits array length; leaves [28, 34] guard digits. + k = Math.ceil(pr / LOG_BASE + 4); - // To ensure correct rounding when r.d is truncated, increment the last word if it is zero. - n = r.d.length - 1; - if (isTruncated && r.d[n] === 0) ++r.d[n]; - break; - } + external = false; - x = x.times(x); - truncate(x.d, k); + for (;;) { + if (n % 2) { + r = r.times(x); + if (truncate(r.d, k)) isTruncated = true; } - external = true; - - return r; - } + n = mathfloor(n / 2); + if (n === 0) { + // To ensure correct rounding when r.d is truncated, increment the last word if it is zero. + n = r.d.length - 1; + if (isTruncated && r.d[n] === 0) ++r.d[n]; + break; + } - function isOdd(n) { - return n.d[n.d.length - 1] & 1; + x = x.times(x); + truncate(x.d, k); } + external = true; - /* - * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'. - */ - function maxOrMin(Ctor, args, ltgt) { - var y, - x = new Ctor(args[0]), - i = 0; - - for (; ++i < args.length;) { - y = new Ctor(args[i]); - if (!y.s) { - x = y; - break; - } else if (x[ltgt](y)) { - x = y; - } - } + return r; +} - return x; - } +function isOdd(n) { + return n.d[n.d.length - 1] & 1; +} - /* - * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant - * digits. - * - * Taylor/Maclaurin series. - * - * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ... - * - * Argument reduction: - * Repeat x = x / 32, k += 5, until |x| < 0.1 - * exp(x) = exp(x / 2^k)^(2^k) - * - * Previously, the argument was initially reduced by - * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10) - * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was - * found to be slower than just dividing repeatedly by 32 as above. - * - * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000 - * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000 - * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324) - * - * exp(Infinity) = Infinity - * exp(-Infinity) = 0 - * exp(NaN) = NaN - * exp(±0) = 1 - * - * exp(x) is non-terminating for any finite, non-zero x. - * - * The result will always be correctly rounded. - * - */ - function naturalExponential(x, sd) { - var denominator, guard, j, pow, sum, t, wpr, - rep = 0, - i = 0, - k = 0, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; - // 0/NaN/Infinity? - if (!x.d || !x.d[0] || x.e > 17) { +/* + * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'. + */ +function maxOrMin(Ctor, args, ltgt) { + var y, + x = new Ctor(args[0]), + i = 0; - return new Ctor(x.d - ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0 - : x.s ? x.s < 0 ? 0 : x : 0 / 0); + for (; ++i < args.length;) { + y = new Ctor(args[i]); + if (!y.s) { + x = y; + break; + } else if (x[ltgt](y)) { + x = y; } + } - if (sd == null) { - external = false; - wpr = pr; - } else { - wpr = sd; - } + return x; +} + + +/* + * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant + * digits. + * + * Taylor/Maclaurin series. + * + * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ... + * + * Argument reduction: + * Repeat x = x / 32, k += 5, until |x| < 0.1 + * exp(x) = exp(x / 2^k)^(2^k) + * + * Previously, the argument was initially reduced by + * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10) + * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was + * found to be slower than just dividing repeatedly by 32 as above. + * + * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000 + * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000 + * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324) + * + * exp(Infinity) = Infinity + * exp(-Infinity) = 0 + * exp(NaN) = NaN + * exp(±0) = 1 + * + * exp(x) is non-terminating for any finite, non-zero x. + * + * The result will always be correctly rounded. + * + */ +function naturalExponential(x, sd) { + var denominator, guard, j, pow, sum, t, wpr, + rep = 0, + i = 0, + k = 0, + Ctor = x.constructor, + rm = Ctor.rounding, + pr = Ctor.precision; - t = new Ctor(0.03125); + // 0/NaN/Infinity? + if (!x.d || !x.d[0] || x.e > 17) { - // while abs(x) >= 0.1 - while (x.e > -2) { + return new Ctor(x.d + ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0 + : x.s ? x.s < 0 ? 0 : x : 0 / 0); + } - // x = x / 2^5 - x = x.times(t); - k += 5; - } + if (sd == null) { + external = false; + wpr = pr; + } else { + wpr = sd; + } - // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision - // necessary to ensure the first 4 rounding digits are correct. - guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0; - wpr += guard; - denominator = pow = sum = new Ctor(1); - Ctor.precision = wpr; + t = new Ctor(0.03125); - for (;;) { - pow = finalise(pow.times(x), wpr, 1); - denominator = denominator.times(++i); - t = sum.plus(divide(pow, denominator, wpr, 1)); + // while abs(x) >= 0.1 + while (x.e > -2) { - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - j = k; - while (j--) sum = finalise(sum.times(sum), wpr, 1); + // x = x / 2^5 + x = x.times(t); + k += 5; + } - // Check to see if the first 4 rounding digits are [49]999. - // If so, repeat the summation with a higher precision, otherwise - // e.g. with precision: 18, rounding: 1 - // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123) - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { + // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision + // necessary to ensure the first 4 rounding digits are correct. + guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0; + wpr += guard; + denominator = pow = sum = new Ctor(1); + Ctor.precision = wpr; - if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += 10; - denominator = pow = t = new Ctor(1); - i = 0; - rep++; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } + for (;;) { + pow = finalise(pow.times(x), wpr, 1); + denominator = denominator.times(++i); + t = sum.plus(divide(pow, denominator, wpr, 1)); + + if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { + j = k; + while (j--) sum = finalise(sum.times(sum), wpr, 1); + + // Check to see if the first 4 rounding digits are [49]999. + // If so, repeat the summation with a higher precision, otherwise + // e.g. with precision: 18, rounding: 1 + // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123) + // `wpr - guard` is the index of first rounding digit. + if (sd == null) { + + if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { + Ctor.precision = wpr += 10; + denominator = pow = t = new Ctor(1); + i = 0; + rep++; } else { - Ctor.precision = pr; - return sum; + return finalise(sum, Ctor.precision = pr, rm, external = true); } + } else { + Ctor.precision = pr; + return sum; } - - sum = t; } + + sum = t; } +} - /* - * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant - * digits. - * - * ln(-n) = NaN - * ln(0) = -Infinity - * ln(-0) = -Infinity - * ln(1) = 0 - * ln(Infinity) = Infinity - * ln(-Infinity) = NaN - * ln(NaN) = NaN - * - * ln(n) (n != 1) is non-terminating. - * - */ - function naturalLogarithm(y, sd) { - var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2, - n = 1, - guard = 10, - x = y, - xd = x.d, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; +/* + * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant + * digits. + * + * ln(-n) = NaN + * ln(0) = -Infinity + * ln(-0) = -Infinity + * ln(1) = 0 + * ln(Infinity) = Infinity + * ln(-Infinity) = NaN + * ln(NaN) = NaN + * + * ln(n) (n != 1) is non-terminating. + * + */ +function naturalLogarithm(y, sd) { + var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2, + n = 1, + guard = 10, + x = y, + xd = x.d, + Ctor = x.constructor, + rm = Ctor.rounding, + pr = Ctor.precision; + + // Is x negative or Infinity, NaN, 0 or 1? + if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) { + return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x); + } + + if (sd == null) { + external = false; + wpr = pr; + } else { + wpr = sd; + } + + Ctor.precision = wpr += guard; + c = digitsToString(xd); + c0 = c.charAt(0); - // Is x negative or Infinity, NaN, 0 or 1? - if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) { - return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x); + if (Math.abs(e = x.e) < 1.5e15) { + + // Argument reduction. + // The series converges faster the closer the argument is to 1, so using + // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b + // multiply the argument by itself until the leading digits of the significand are 7, 8, 9, + // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can + // later be divided by this number, then separate out the power of 10 using + // ln(a*10^b) = ln(a) + b*ln(10). + + // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14). + //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) { + // max n is 6 (gives 0.7 - 1.3) + while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) { + x = x.times(y); + c = digitsToString(x.d); + c0 = c.charAt(0); + n++; } - if (sd == null) { - external = false; - wpr = pr; + e = x.e; + + if (c0 > 1) { + x = new Ctor('0.' + c); + e++; } else { - wpr = sd; - } - - Ctor.precision = wpr += guard; - c = digitsToString(xd); - c0 = c.charAt(0); - - if (Math.abs(e = x.e) < 1.5e15) { - - // Argument reduction. - // The series converges faster the closer the argument is to 1, so using - // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b - // multiply the argument by itself until the leading digits of the significand are 7, 8, 9, - // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can - // later be divided by this number, then separate out the power of 10 using - // ln(a*10^b) = ln(a) + b*ln(10). - - // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14). - //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) { - // max n is 6 (gives 0.7 - 1.3) - while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) { - x = x.times(y); - c = digitsToString(x.d); - c0 = c.charAt(0); - n++; - } + x = new Ctor(c0 + '.' + c.slice(1)); + } + } else { - e = x.e; + // The argument reduction method above may result in overflow if the argument y is a massive + // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this + // function using ln(x*10^e) = ln(x) + e*ln(10). + t = getLn10(Ctor, wpr + 2, pr).times(e + ''); + x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t); + Ctor.precision = pr; - if (c0 > 1) { - x = new Ctor('0.' + c); - e++; - } else { - x = new Ctor(c0 + '.' + c.slice(1)); - } - } else { + return sd == null ? finalise(x, pr, rm, external = true) : x; + } - // The argument reduction method above may result in overflow if the argument y is a massive - // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this - // function using ln(x*10^e) = ln(x) + e*ln(10). - t = getLn10(Ctor, wpr + 2, pr).times(e + ''); - x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t); - Ctor.precision = pr; - - return sd == null ? finalise(x, pr, rm, external = true) : x; - } - - // x1 is x reduced to a value near 1. - x1 = x; - - // Taylor series. - // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...) - // where x = (y - 1)/(y + 1) (|x| < 1) - sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = 3; - - for (;;) { - numerator = finalise(numerator.times(x2), wpr, 1); - t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1)); - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - sum = sum.times(2); - - // Reverse the argument reduction. Check that e is not 0 because, besides preventing an - // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0. - if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + '')); - sum = divide(sum, new Ctor(n), wpr, 1); - - // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has - // been repeated previously) and the first 4 rounding digits 9999? - // If so, restart the summation with a higher precision, otherwise - // e.g. with precision: 12, rounding: 1 - // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463. - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += guard; - t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = rep = 1; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } + // x1 is x reduced to a value near 1. + x1 = x; + + // Taylor series. + // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...) + // where x = (y - 1)/(y + 1) (|x| < 1) + sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1); + x2 = finalise(x.times(x), wpr, 1); + denominator = 3; + + for (;;) { + numerator = finalise(numerator.times(x2), wpr, 1); + t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1)); + + if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { + sum = sum.times(2); + + // Reverse the argument reduction. Check that e is not 0 because, besides preventing an + // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0. + if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + '')); + sum = divide(sum, new Ctor(n), wpr, 1); + + // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has + // been repeated previously) and the first 4 rounding digits 9999? + // If so, restart the summation with a higher precision, otherwise + // e.g. with precision: 12, rounding: 1 + // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463. + // `wpr - guard` is the index of first rounding digit. + if (sd == null) { + if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { + Ctor.precision = wpr += guard; + t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1); + x2 = finalise(x.times(x), wpr, 1); + denominator = rep = 1; } else { - Ctor.precision = pr; - return sum; + return finalise(sum, Ctor.precision = pr, rm, external = true); } + } else { + Ctor.precision = pr; + return sum; } - - sum = t; - denominator += 2; } + + sum = t; + denominator += 2; } +} + + +// ±Infinity, NaN. +function nonFiniteToString(x) { + // Unsigned. + return String(x.s * x.s / 0); +} + +/* + * Parse the value of a new Decimal `x` from string `str`. + */ +function parseDecimal(x, str) { + var e, i, len; + + // Decimal point? + if ((e = str.indexOf('.')) > -1) str = str.replace('.', ''); + + // Exponential form? + if ((i = str.search(/e/i)) > 0) { - // ±Infinity, NaN. - function nonFiniteToString(x) { - // Unsigned. - return String(x.s * x.s / 0); + // Determine exponent. + if (e < 0) e = i; + e += +str.slice(i + 1); + str = str.substring(0, i); + } else if (e < 0) { + + // Integer. + e = str.length; } + // Determine leading zeros. + for (i = 0; str.charCodeAt(i) === 48; i++); - /* - * Parse the value of a new Decimal `x` from string `str`. - */ - function parseDecimal(x, str) { - var e, i, len; + // Determine trailing zeros. + for (len = str.length; str.charCodeAt(len - 1) === 48; --len); + str = str.slice(i, len); - // Decimal point? - if ((e = str.indexOf('.')) > -1) str = str.replace('.', ''); + if (str) { + len -= i; + x.e = e = e - i - 1; + x.d = []; - // Exponential form? - if ((i = str.search(/e/i)) > 0) { + // Transform base - // Determine exponent. - if (e < 0) e = i; - e += +str.slice(i + 1); - str = str.substring(0, i); - } else if (e < 0) { + // e is the base 10 exponent. + // i is where to slice str to get the first word of the digits array. + i = (e + 1) % LOG_BASE; + if (e < 0) i += LOG_BASE; - // Integer. - e = str.length; + if (i < len) { + if (i) x.d.push(+str.slice(0, i)); + for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE)); + str = str.slice(i); + i = LOG_BASE - str.length; + } else { + i -= len; } - // Determine leading zeros. - for (i = 0; str.charCodeAt(i) === 48; i++); + for (; i--;) str += '0'; + x.d.push(+str); - // Determine trailing zeros. - for (len = str.length; str.charCodeAt(len - 1) === 48; --len); - str = str.slice(i, len); + if (external) { - if (str) { - len -= i; - x.e = e = e - i - 1; - x.d = []; + // Overflow? + if (x.e > x.constructor.maxE) { - // Transform base + // Infinity. + x.d = null; + x.e = NaN; - // e is the base 10 exponent. - // i is where to slice str to get the first word of the digits array. - i = (e + 1) % LOG_BASE; - if (e < 0) i += LOG_BASE; + // Underflow? + } else if (x.e < x.constructor.minE) { - if (i < len) { - if (i) x.d.push(+str.slice(0, i)); - for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE)); - str = str.slice(i); - i = LOG_BASE - str.length; - } else { - i -= len; - } + // Zero. + x.e = 0; + x.d = [0]; + // x.constructor.underflow = true; + } // else x.constructor.underflow = false; + } + } else { - for (; i--;) str += '0'; - x.d.push(+str); + // Zero. + x.e = 0; + x.d = [0]; + } - if (external) { + return x; +} - // Overflow? - if (x.e > x.constructor.maxE) { - // Infinity. - x.d = null; - x.e = NaN; +/* + * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value. + */ +function parseOther(x, str) { + var base, Ctor, divisor, i, isFloat, len, p, xd, xe; - // Underflow? - } else if (x.e < x.constructor.minE) { + if (str === 'Infinity' || str === 'NaN') { + if (!+str) x.s = NaN; + x.e = NaN; + x.d = null; + return x; + } - // Zero. - x.e = 0; - x.d = [0]; - // x.constructor.underflow = true; - } // else x.constructor.underflow = false; - } - } else { + if (isHex.test(str)) { + base = 16; + str = str.toLowerCase(); + } else if (isBinary.test(str)) { + base = 2; + } else if (isOctal.test(str)) { + base = 8; + } else { + throw Error(invalidArgument + str); + } - // Zero. - x.e = 0; - x.d = [0]; - } + // Is there a binary exponent part? + i = str.search(/p/i); - return x; + if (i > 0) { + p = +str.slice(i + 1); + str = str.substring(2, i); + } else { + str = str.slice(2); } + // Convert `str` as an integer then divide the result by `base` raised to a power such that the + // fraction part will be restored. + i = str.indexOf('.'); + isFloat = i >= 0; + Ctor = x.constructor; - /* - * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value. - */ - function parseOther(x, str) { - var base, Ctor, divisor, i, isFloat, len, p, xd, xe; + if (isFloat) { + str = str.replace('.', ''); + len = str.length; + i = len - i; - if (str === 'Infinity' || str === 'NaN') { - if (!+str) x.s = NaN; - x.e = NaN; - x.d = null; - return x; - } + // log[10](16) = 1.2041... , log[10](88) = 1.9444.... + divisor = intPow(Ctor, new Ctor(base), i, i * 2); + } - if (isHex.test(str)) { - base = 16; - str = str.toLowerCase(); - } else if (isBinary.test(str)) { - base = 2; - } else if (isOctal.test(str)) { - base = 8; - } else { - throw Error(invalidArgument + str); - } + xd = convertBase(str, base, BASE); + xe = xd.length - 1; - // Is there a binary exponent part? - i = str.search(/p/i); + // Remove trailing zeros. + for (i = xe; xd[i] === 0; --i) xd.pop(); + if (i < 0) return new Ctor(x.s * 0); + x.e = getBase10Exponent(xd, xe); + x.d = xd; + external = false; - if (i > 0) { - p = +str.slice(i + 1); - str = str.substring(2, i); - } else { - str = str.slice(2); - } + // At what precision to perform the division to ensure exact conversion? + // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount) + // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412 + // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits. + // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount + // Therefore using 4 * the number of digits of str will always be enough. + if (isFloat) x = divide(x, divisor, len * 4); - // Convert `str` as an integer then divide the result by `base` raised to a power such that the - // fraction part will be restored. - i = str.indexOf('.'); - isFloat = i >= 0; - Ctor = x.constructor; + // Multiply by the binary exponent part if present. + if (p) x = x.times(Math.abs(p) < 54 ? Math.pow(2, p) : Decimal.pow(2, p)); + external = true; - if (isFloat) { - str = str.replace('.', ''); - len = str.length; - i = len - i; + return x; +} - // log[10](16) = 1.2041... , log[10](88) = 1.9444.... - divisor = intPow(Ctor, new Ctor(base), i, i * 2); - } - xd = convertBase(str, base, BASE); - xe = xd.length - 1; +/* + * sin(x) = x - x^3/3! + x^5/5! - ... + * |x| < pi/2 + * + */ +function sine(Ctor, x) { + var k, + len = x.d.length; + + if (len < 3) return taylorSeries(Ctor, 2, x, x); - // Remove trailing zeros. - for (i = xe; xd[i] === 0; --i) xd.pop(); - if (i < 0) return new Ctor(x.s * 0); - x.e = getBase10Exponent(xd, xe); - x.d = xd; - external = false; + // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x) + // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5) + // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20)) - // At what precision to perform the division to ensure exact conversion? - // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount) - // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412 - // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits. - // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount - // Therefore using 4 * the number of digits of str will always be enough. - if (isFloat) x = divide(x, divisor, len * 4); + // Estimate the optimum number of times to use the argument reduction. + k = 1.4 * Math.sqrt(len); + k = k > 16 ? 16 : k | 0; - // Multiply by the binary exponent part if present. - if (p) x = x.times(Math.abs(p) < 54 ? Math.pow(2, p) : Decimal.pow(2, p)); - external = true; + // Max k before Math.pow precision loss is 22 + x = x.times(Math.pow(5, -k)); + x = taylorSeries(Ctor, 2, x, x); - return x; + // Reverse argument reduction + var sin2_x, + d5 = new Ctor(5), + d16 = new Ctor(16), + d20 = new Ctor(20); + for (; k--;) { + sin2_x = x.times(x); + x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20)))); } + return x; +} - /* - * sin(x) = x - x^3/3! + x^5/5! - ... - * |x| < pi/2 - * - */ - function sine(Ctor, x) { - var k, - len = x.d.length; - - if (len < 3) return taylorSeries(Ctor, 2, x, x); - // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x) - // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5) - // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20)) +// Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`. +function taylorSeries(Ctor, n, x, y, isHyperbolic) { + var j, t, u, x2, + i = 1, + pr = Ctor.precision, + k = Math.ceil(pr / LOG_BASE); - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; + external = false; + x2 = x.times(x); + u = new Ctor(y); - // Max k before Math.pow precision loss is 22 - x = x.times(Math.pow(5, -k)); - x = taylorSeries(Ctor, 2, x, x); + for (;;) { + t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1); + u = isHyperbolic ? y.plus(t) : y.minus(t); + y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1); + t = u.plus(y); - // Reverse argument reduction - var sin2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sin2_x = x.times(x); - x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20)))); + if (t.d[k] !== void 0) { + for (j = k; t.d[j] === u.d[j] && j--;); + if (j == -1) break; } - return x; + j = u; + u = y; + y = t; + t = j; + i++; } + external = true; + t.d.length = k + 1; - // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`. - function taylorSeries(Ctor, n, x, y, isHyperbolic) { - var j, t, u, x2, - i = 1, - pr = Ctor.precision, - k = Math.ceil(pr / LOG_BASE); + return t; +} - external = false; - x2 = x.times(x); - u = new Ctor(y); - - for (;;) { - t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1); - u = isHyperbolic ? y.plus(t) : y.minus(t); - y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1); - t = u.plus(y); - - if (t.d[k] !== void 0) { - for (j = k; t.d[j] === u.d[j] && j--;); - if (j == -1) break; - } - j = u; - u = y; - y = t; - t = j; - i++; - } +// Return the absolute value of `x` reduced to less than or equal to half pi. +function toLessThanHalfPi(Ctor, x) { + var t, + isNeg = x.s < 0, + pi = getPi(Ctor, Ctor.precision, 1), + halfPi = pi.times(0.5); - external = true; - t.d.length = k + 1; + x = x.abs(); - return t; + if (x.lte(halfPi)) { + quadrant = isNeg ? 4 : 1; + return x; } + t = x.divToInt(pi); - // Return the absolute value of `x` reduced to less than or equal to half pi. - function toLessThanHalfPi(Ctor, x) { - var t, - isNeg = x.s < 0, - pi = getPi(Ctor, Ctor.precision, 1), - halfPi = pi.times(0.5); - - x = x.abs(); + if (t.isZero()) { + quadrant = isNeg ? 3 : 2; + } else { + x = x.minus(t.times(pi)); + // 0 <= x < pi if (x.lte(halfPi)) { - quadrant = isNeg ? 4 : 1; + quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1); return x; } - t = x.divToInt(pi); + quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2); + } - if (t.isZero()) { - quadrant = isNeg ? 3 : 2; - } else { - x = x.minus(t.times(pi)); + return x.minus(pi).abs(); +} - // 0 <= x < pi - if (x.lte(halfPi)) { - quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1); - return x; - } - quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2); - } +/* + * Return the value of Decimal `x` as a string in base `baseOut`. + * + * If the optional `sd` argument is present include a binary exponent suffix. + */ +function toStringBinary(x, baseOut, sd, rm) { + var base, e, i, k, len, roundUp, str, xd, y, + Ctor = x.constructor, + isExp = sd !== void 0; - return x.minus(pi).abs(); + if (isExp) { + checkInt32(sd, 1, MAX_DIGITS); + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + } else { + sd = Ctor.precision; + rm = Ctor.rounding; } + if (!x.isFinite()) { + str = nonFiniteToString(x); + } else { + str = finiteToString(x); + i = str.indexOf('.'); - /* - * Return the value of Decimal `x` as a string in base `baseOut`. - * - * If the optional `sd` argument is present include a binary exponent suffix. - */ - function toStringBinary(x, baseOut, sd, rm) { - var base, e, i, k, len, roundUp, str, xd, y, - Ctor = x.constructor, - isExp = sd !== void 0; + // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required: + // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10)) + // minBinaryExponent = floor(decimalExponent * log[2](10)) + // log[2](10) = 3.321928094887362347870319429489390175864 if (isExp) { - checkInt32(sd, 1, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); + base = 2; + if (baseOut == 16) { + sd = sd * 4 - 3; + } else if (baseOut == 8) { + sd = sd * 3 - 2; + } } else { - sd = Ctor.precision; - rm = Ctor.rounding; + base = baseOut; } - if (!x.isFinite()) { - str = nonFiniteToString(x); - } else { - str = finiteToString(x); - i = str.indexOf('.'); - - // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required: - // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10)) - // minBinaryExponent = floor(decimalExponent * log[2](10)) - // log[2](10) = 3.321928094887362347870319429489390175864 - - if (isExp) { - base = 2; - if (baseOut == 16) { - sd = sd * 4 - 3; - } else if (baseOut == 8) { - sd = sd * 3 - 2; - } - } else { - base = baseOut; - } - - // Convert the number as an integer then divide the result by its base raised to a power such - // that the fraction part will be restored. + // Convert the number as an integer then divide the result by its base raised to a power such + // that the fraction part will be restored. - // Non-integer. - if (i >= 0) { - str = str.replace('.', ''); - y = new Ctor(1); - y.e = str.length - i; - y.d = convertBase(finiteToString(y), 10, base); - y.e = y.d.length; - } + // Non-integer. + if (i >= 0) { + str = str.replace('.', ''); + y = new Ctor(1); + y.e = str.length - i; + y.d = convertBase(finiteToString(y), 10, base); + y.e = y.d.length; + } - xd = convertBase(str, 10, base); - e = len = xd.length; + xd = convertBase(str, 10, base); + e = len = xd.length; - // Remove trailing zeros. - for (; xd[--len] == 0;) xd.pop(); + // Remove trailing zeros. + for (; xd[--len] == 0;) xd.pop(); - if (!xd[0]) { - str = isExp ? '0p+0' : '0'; + if (!xd[0]) { + str = isExp ? '0p+0' : '0'; + } else { + if (i < 0) { + e--; } else { - if (i < 0) { - e--; - } else { - x = new Ctor(x); - x.d = xd; - x.e = e; - x = divide(x, y, sd, rm, 0, base); - xd = x.d; - e = x.e; - roundUp = inexact; - } + x = new Ctor(x); + x.d = xd; + x.e = e; + x = divide(x, y, sd, rm, 0, base); + xd = x.d; + e = x.e; + roundUp = inexact; + } - // The rounding digit, i.e. the digit after the digit that may be rounded up. - i = xd[sd]; - k = base / 2; - roundUp = roundUp || xd[sd + 1] !== void 0; + // The rounding digit, i.e. the digit after the digit that may be rounded up. + i = xd[sd]; + k = base / 2; + roundUp = roundUp || xd[sd + 1] !== void 0; - roundUp = rm < 4 - ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) - : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 || - rm === (x.s < 0 ? 8 : 7)); + roundUp = rm < 4 + ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) + : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 || + rm === (x.s < 0 ? 8 : 7)); - xd.length = sd; + xd.length = sd; - if (roundUp) { + if (roundUp) { - // Rounding up may mean the previous digit has to be rounded up and so on. - for (; ++xd[--sd] > base - 1;) { - xd[sd] = 0; - if (!sd) { - ++e; - xd.unshift(1); - } + // Rounding up may mean the previous digit has to be rounded up and so on. + for (; ++xd[--sd] > base - 1;) { + xd[sd] = 0; + if (!sd) { + ++e; + xd.unshift(1); } } + } - // Determine trailing zeros. - for (len = xd.length; !xd[len - 1]; --len); - - // E.g. [4, 11, 15] becomes 4bf. - for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]); + // Determine trailing zeros. + for (len = xd.length; !xd[len - 1]; --len); - // Add binary exponent suffix? - if (isExp) { - if (len > 1) { - if (baseOut == 16 || baseOut == 8) { - i = baseOut == 16 ? 4 : 3; - for (--len; len % i; len++) str += '0'; - xd = convertBase(str, base, baseOut); - for (len = xd.length; !xd[len - 1]; --len); + // E.g. [4, 11, 15] becomes 4bf. + for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]); - // xd[0] will always be be 1 - for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]); - } else { - str = str.charAt(0) + '.' + str.slice(1); - } + // Add binary exponent suffix? + if (isExp) { + if (len > 1) { + if (baseOut == 16 || baseOut == 8) { + i = baseOut == 16 ? 4 : 3; + for (--len; len % i; len++) str += '0'; + xd = convertBase(str, base, baseOut); + for (len = xd.length; !xd[len - 1]; --len); + + // xd[0] will always be be 1 + for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]); + } else { + str = str.charAt(0) + '.' + str.slice(1); } - - str = str + (e < 0 ? 'p' : 'p+') + e; - } else if (e < 0) { - for (; ++e;) str = '0' + str; - str = '0.' + str; - } else { - if (++e > len) for (e -= len; e-- ;) str += '0'; - else if (e < len) str = str.slice(0, e) + '.' + str.slice(e); } - } - str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str; + str = str + (e < 0 ? 'p' : 'p+') + e; + } else if (e < 0) { + for (; ++e;) str = '0' + str; + str = '0.' + str; + } else { + if (++e > len) for (e -= len; e-- ;) str += '0'; + else if (e < len) str = str.slice(0, e) + '.' + str.slice(e); + } } - return x.s < 0 ? '-' + str : str; + str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str; } + return x.s < 0 ? '-' + str : str; +} - // Does not strip trailing zeros. - function truncate(arr, len) { - if (arr.length > len) { - arr.length = len; - return true; - } - } +// Does not strip trailing zeros. +function truncate(arr, len) { + if (arr.length > len) { + arr.length = len; + return true; + } +} - // Decimal methods +// Decimal methods - /* - * abs - * acos - * acosh - * add - * asin - * asinh - * atan - * atanh - * atan2 - * cbrt - * ceil - * clone - * config - * cos - * cosh - * div - * exp - * floor - * hypot - * ln - * log - * log2 - * log10 - * max - * min - * mod - * mul - * pow - * random - * round - * set - * sign - * sin - * sinh - * sqrt - * sub - * tan - * tanh - * trunc - */ +/* + * abs + * acos + * acosh + * add + * asin + * asinh + * atan + * atanh + * atan2 + * cbrt + * ceil + * clone + * config + * cos + * cosh + * div + * exp + * floor + * hypot + * ln + * log + * log2 + * log10 + * max + * min + * mod + * mul + * pow + * random + * round + * set + * sign + * sin + * sinh + * sqrt + * sub + * tan + * tanh + * trunc + */ - /* - * Return a new Decimal whose value is the absolute value of `x`. - * - * x {number|string|Decimal} - * - */ - function abs(x) { - return new this(x).abs(); - } +/* + * Return a new Decimal whose value is the absolute value of `x`. + * + * x {number|string|Decimal} + * + */ +function abs(x) { + return new this(x).abs(); +} - /* - * Return a new Decimal whose value is the arccosine in radians of `x`. - * - * x {number|string|Decimal} - * - */ - function acos(x) { - return new this(x).acos(); - } +/* + * Return a new Decimal whose value is the arccosine in radians of `x`. + * + * x {number|string|Decimal} + * + */ +function acos(x) { + return new this(x).acos(); +} - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function acosh(x) { - return new this(x).acosh(); - } +/* + * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function acosh(x) { + return new this(x).acosh(); +} - /* - * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function add(x, y) { - return new this(x).plus(y); - } +/* + * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function add(x, y) { + return new this(x).plus(y); +} - /* - * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function asin(x) { - return new this(x).asin(); - } +/* + * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function asin(x) { + return new this(x).asin(); +} - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function asinh(x) { - return new this(x).asinh(); - } +/* + * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function asinh(x) { + return new this(x).asinh(); +} - /* - * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function atan(x) { - return new this(x).atan(); - } +/* + * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function atan(x) { + return new this(x).atan(); +} - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function atanh(x) { - return new this(x).atanh(); - } +/* + * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function atanh(x) { + return new this(x).atanh(); +} - /* - * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi - * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi, pi] - * - * y {number|string|Decimal} The y-coordinate. - * x {number|string|Decimal} The x-coordinate. - * - * atan2(±0, -0) = ±pi - * atan2(±0, +0) = ±0 - * atan2(±0, -x) = ±pi for x > 0 - * atan2(±0, x) = ±0 for x > 0 - * atan2(-y, ±0) = -pi/2 for y > 0 - * atan2(y, ±0) = pi/2 for y > 0 - * atan2(±y, -Infinity) = ±pi for finite y > 0 - * atan2(±y, +Infinity) = ±0 for finite y > 0 - * atan2(±Infinity, x) = ±pi/2 for finite x - * atan2(±Infinity, -Infinity) = ±3*pi/4 - * atan2(±Infinity, +Infinity) = ±pi/4 - * atan2(NaN, x) = NaN - * atan2(y, NaN) = NaN - * - */ - function atan2(y, x) { - y = new this(y); - x = new this(x); - var r, - pr = this.precision, - rm = this.rounding, - wpr = pr + 4; - - // Either NaN - if (!y.s || !x.s) { - r = new this(NaN); - - // Both ±Infinity - } else if (!y.d && !x.d) { - r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75); - r.s = y.s; - - // x is ±Infinity or y is ±0 - } else if (!x.d || y.isZero()) { - r = x.s < 0 ? getPi(this, pr, rm) : new this(0); - r.s = y.s; - - // y is ±Infinity or x is ±0 - } else if (!y.d || x.isZero()) { - r = getPi(this, wpr, 1).times(0.5); - r.s = y.s; - - // Both non-zero and finite - } else if (x.s < 0) { - this.precision = wpr; - this.rounding = 1; - r = this.atan(divide(y, x, wpr, 1)); - x = getPi(this, wpr, 1); - this.precision = pr; - this.rounding = rm; - r = y.s < 0 ? r.minus(x) : r.plus(x); - } else { - r = this.atan(divide(y, x, wpr, 1)); - } - return r; +/* + * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi + * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`. + * + * Domain: [-Infinity, Infinity] + * Range: [-pi, pi] + * + * y {number|string|Decimal} The y-coordinate. + * x {number|string|Decimal} The x-coordinate. + * + * atan2(±0, -0) = ±pi + * atan2(±0, +0) = ±0 + * atan2(±0, -x) = ±pi for x > 0 + * atan2(±0, x) = ±0 for x > 0 + * atan2(-y, ±0) = -pi/2 for y > 0 + * atan2(y, ±0) = pi/2 for y > 0 + * atan2(±y, -Infinity) = ±pi for finite y > 0 + * atan2(±y, +Infinity) = ±0 for finite y > 0 + * atan2(±Infinity, x) = ±pi/2 for finite x + * atan2(±Infinity, -Infinity) = ±3*pi/4 + * atan2(±Infinity, +Infinity) = ±pi/4 + * atan2(NaN, x) = NaN + * atan2(y, NaN) = NaN + * + */ +function atan2(y, x) { + y = new this(y); + x = new this(x); + var r, + pr = this.precision, + rm = this.rounding, + wpr = pr + 4; + + // Either NaN + if (!y.s || !x.s) { + r = new this(NaN); + + // Both ±Infinity + } else if (!y.d && !x.d) { + r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75); + r.s = y.s; + + // x is ±Infinity or y is ±0 + } else if (!x.d || y.isZero()) { + r = x.s < 0 ? getPi(this, pr, rm) : new this(0); + r.s = y.s; + + // y is ±Infinity or x is ±0 + } else if (!y.d || x.isZero()) { + r = getPi(this, wpr, 1).times(0.5); + r.s = y.s; + + // Both non-zero and finite + } else if (x.s < 0) { + this.precision = wpr; + this.rounding = 1; + r = this.atan(divide(y, x, wpr, 1)); + x = getPi(this, wpr, 1); + this.precision = pr; + this.rounding = rm; + r = y.s < 0 ? r.minus(x) : r.plus(x); + } else { + r = this.atan(divide(y, x, wpr, 1)); } + return r; +} + - /* - * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function cbrt(x) { - return new this(x).cbrt(); - } +/* + * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function cbrt(x) { + return new this(x).cbrt(); +} - /* - * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`. - * - * x {number|string|Decimal} - * - */ - function ceil(x) { - return finalise(x = new this(x), x.e + 1, 2); - } +/* + * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`. + * + * x {number|string|Decimal} + * + */ +function ceil(x) { + return finalise(x = new this(x), x.e + 1, 2); +} - /* - * Configure global settings for a Decimal constructor. - * - * `obj` is an object with one or more of the following properties, - * - * precision {number} - * rounding {number} - * toExpNeg {number} - * toExpPos {number} - * maxE {number} - * minE {number} - * modulo {number} - * crypto {boolean|number} - * - * E.g. Decimal.config({ precision: 20, rounding: 4 }) - * - */ - function config(obj) { - if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected'); - var i, p, v, - ps = [ - 'precision', 1, MAX_DIGITS, - 'rounding', 0, 8, - 'toExpNeg', -EXP_LIMIT, 0, - 'toExpPos', 0, EXP_LIMIT, - 'maxE', 0, EXP_LIMIT, - 'minE', -EXP_LIMIT, 0, - 'modulo', 0, 9 - ]; - - for (i = 0; i < ps.length; i += 3) { - if ((v = obj[p = ps[i]]) !== void 0) { - if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v; - else throw Error(invalidArgument + p + ': ' + v); - } +/* + * Configure global settings for a Decimal constructor. + * + * `obj` is an object with one or more of the following properties, + * + * precision {number} + * rounding {number} + * toExpNeg {number} + * toExpPos {number} + * maxE {number} + * minE {number} + * modulo {number} + * crypto {boolean|number} + * + * E.g. Decimal.config({ precision: 20, rounding: 4 }) + * + */ +function config(obj) { + if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected'); + var i, p, v, + ps = [ + 'precision', 1, MAX_DIGITS, + 'rounding', 0, 8, + 'toExpNeg', -EXP_LIMIT, 0, + 'toExpPos', 0, EXP_LIMIT, + 'maxE', 0, EXP_LIMIT, + 'minE', -EXP_LIMIT, 0, + 'modulo', 0, 9 + ]; + + for (i = 0; i < ps.length; i += 3) { + if ((v = obj[p = ps[i]]) !== void 0) { + if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v; + else throw Error(invalidArgument + p + ': ' + v); } + } - if ((v = obj[p = 'crypto']) !== void 0) { - if (v === true || v === false || v === 0 || v === 1) { - if (v) { - if (typeof crypto != 'undefined' && crypto && - (crypto.getRandomValues || crypto.randomBytes)) { - this[p] = true; - } else { - throw Error(cryptoUnavailable); - } + if ((v = obj[p = 'crypto']) !== void 0) { + if (v === true || v === false || v === 0 || v === 1) { + if (v) { + if (typeof crypto != 'undefined' && crypto && + (crypto.getRandomValues || crypto.randomBytes)) { + this[p] = true; } else { - this[p] = false; + throw Error(cryptoUnavailable); } } else { - throw Error(invalidArgument + p + ': ' + v); + this[p] = false; } + } else { + throw Error(invalidArgument + p + ': ' + v); } - - return this; } + return this; +} - /* - * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cos(x) { - return new this(x).cos(); - } +/* + * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function cos(x) { + return new this(x).cos(); +} - /* - * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cosh(x) { - return new this(x).cosh(); - } +/* + * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function cosh(x) { + return new this(x).cosh(); +} + + +/* + * Create and return a Decimal constructor with the same configuration properties as this Decimal + * constructor. + * + */ +function clone(obj) { + var i, p, ps; /* - * Create and return a Decimal constructor with the same configuration properties as this Decimal - * constructor. + * The Decimal constructor and exported function. + * Return a new Decimal instance. + * + * v {number|string|Decimal} A numeric value. * */ - function clone(obj) { - var i, p, ps; - - /* - * The Decimal constructor and exported function. - * Return a new Decimal instance. - * - * v {number|string|Decimal} A numeric value. - * - */ - function Decimal(v) { - var e, i, t, - x = this; - - // Decimal called without new. - if (!(x instanceof Decimal)) return new Decimal(v); - - // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor - // which points to Object. - x.constructor = Decimal; - - // Duplicate. - if (v instanceof Decimal) { - x.s = v.s; - x.e = v.e; - x.d = (v = v.d) ? v.slice() : v; - return; - } - - t = typeof v; - - if (t === 'number') { - if (v === 0) { - x.s = 1 / v < 0 ? -1 : 1; - x.e = 0; - x.d = [0]; - return; - } + function Decimal(v) { + var e, i, t, + x = this; - if (v < 0) { - v = -v; - x.s = -1; - } else { - x.s = 1; - } + // Decimal called without new. + if (!(x instanceof Decimal)) return new Decimal(v); - // Fast path for small integers. - if (v === ~~v && v < 1e7) { - for (e = 0, i = v; i >= 10; i /= 10) e++; - x.e = e; - x.d = [v]; - return; + // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor + // which points to Object. + x.constructor = Decimal; - // Infinity, NaN. - } else if (v * 0 !== 0) { - if (!v) x.s = NaN; - x.e = NaN; - x.d = null; - return; - } + // Duplicate. + if (v instanceof Decimal) { + x.s = v.s; + x.e = v.e; + x.d = (v = v.d) ? v.slice() : v; + return; + } - return parseDecimal(x, v.toString()); + t = typeof v; - } else if (t !== 'string') { - throw Error(invalidArgument + v); + if (t === 'number') { + if (v === 0) { + x.s = 1 / v < 0 ? -1 : 1; + x.e = 0; + x.d = [0]; + return; } - // Minus sign? - if (v.charCodeAt(0) === 45) { - v = v.slice(1); + if (v < 0) { + v = -v; x.s = -1; } else { x.s = 1; } - return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v); - } - - Decimal.prototype = P; - - Decimal.ROUND_UP = 0; - Decimal.ROUND_DOWN = 1; - Decimal.ROUND_CEIL = 2; - Decimal.ROUND_FLOOR = 3; - Decimal.ROUND_HALF_UP = 4; - Decimal.ROUND_HALF_DOWN = 5; - Decimal.ROUND_HALF_EVEN = 6; - Decimal.ROUND_HALF_CEIL = 7; - Decimal.ROUND_HALF_FLOOR = 8; - Decimal.EUCLID = 9; - - Decimal.config = Decimal.set = config; - Decimal.clone = clone; - - Decimal.abs = abs; - Decimal.acos = acos; - Decimal.acosh = acosh; // ES6 - Decimal.add = add; - Decimal.asin = asin; - Decimal.asinh = asinh; // ES6 - Decimal.atan = atan; - Decimal.atanh = atanh; // ES6 - Decimal.atan2 = atan2; - Decimal.cbrt = cbrt; // ES6 - Decimal.ceil = ceil; - Decimal.cos = cos; - Decimal.cosh = cosh; // ES6 - Decimal.div = div; - Decimal.exp = exp; - Decimal.floor = floor; - Decimal.hypot = hypot; // ES6 - Decimal.ln = ln; - Decimal.log = log; - Decimal.log10 = log10; // ES6 - Decimal.log2 = log2; // ES6 - Decimal.max = max; - Decimal.min = min; - Decimal.mod = mod; - Decimal.mul = mul; - Decimal.pow = pow; - Decimal.random = random; - Decimal.round = round; - Decimal.sign = sign; // ES6 - Decimal.sin = sin; - Decimal.sinh = sinh; // ES6 - Decimal.sqrt = sqrt; - Decimal.sub = sub; - Decimal.tan = tan; - Decimal.tanh = tanh; // ES6 - Decimal.trunc = trunc; // ES6 - - if (obj === void 0) obj = {}; - if (obj) { - ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto']; - for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p]; - } - - Decimal.config(obj); - - return Decimal; - } - - - /* - * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function div(x, y) { - return new this(x).div(y); - } + // Fast path for small integers. + if (v === ~~v && v < 1e7) { + for (e = 0, i = v; i >= 10; i /= 10) e++; + x.e = e; + x.d = [v]; + return; + // Infinity, NaN. + } else if (v * 0 !== 0) { + if (!v) x.s = NaN; + x.e = NaN; + x.d = null; + return; + } - /* - * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The power to which to raise the base of the natural log. - * - */ - function exp(x) { - return new this(x).exp(); - } + return parseDecimal(x, v.toString()); + } else if (t !== 'string') { + throw Error(invalidArgument + v); + } - /* - * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`. - * - * x {number|string|Decimal} - * - */ - function floor(x) { - return finalise(x = new this(x), x.e + 1, 3); + // Minus sign? + if (v.charCodeAt(0) === 45) { + v = v.slice(1); + x.s = -1; + } else { + x.s = 1; + } + + return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v); + } + + Decimal.prototype = P; + + Decimal.ROUND_UP = 0; + Decimal.ROUND_DOWN = 1; + Decimal.ROUND_CEIL = 2; + Decimal.ROUND_FLOOR = 3; + Decimal.ROUND_HALF_UP = 4; + Decimal.ROUND_HALF_DOWN = 5; + Decimal.ROUND_HALF_EVEN = 6; + Decimal.ROUND_HALF_CEIL = 7; + Decimal.ROUND_HALF_FLOOR = 8; + Decimal.EUCLID = 9; + + Decimal.config = Decimal.set = config; + Decimal.clone = clone; + + Decimal.abs = abs; + Decimal.acos = acos; + Decimal.acosh = acosh; // ES6 + Decimal.add = add; + Decimal.asin = asin; + Decimal.asinh = asinh; // ES6 + Decimal.atan = atan; + Decimal.atanh = atanh; // ES6 + Decimal.atan2 = atan2; + Decimal.cbrt = cbrt; // ES6 + Decimal.ceil = ceil; + Decimal.cos = cos; + Decimal.cosh = cosh; // ES6 + Decimal.div = div; + Decimal.exp = exp; + Decimal.floor = floor; + Decimal.hypot = hypot; // ES6 + Decimal.ln = ln; + Decimal.log = log; + Decimal.log10 = log10; // ES6 + Decimal.log2 = log2; // ES6 + Decimal.max = max; + Decimal.min = min; + Decimal.mod = mod; + Decimal.mul = mul; + Decimal.pow = pow; + Decimal.random = random; + Decimal.round = round; + Decimal.sign = sign; // ES6 + Decimal.sin = sin; + Decimal.sinh = sinh; // ES6 + Decimal.sqrt = sqrt; + Decimal.sub = sub; + Decimal.tan = tan; + Decimal.tanh = tanh; // ES6 + Decimal.trunc = trunc; // ES6 + + if (obj === void 0) obj = {}; + if (obj) { + ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto']; + for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p]; } + Decimal.config(obj); - /* - * Return a new Decimal whose value is the square root of the sum of the squares of the arguments, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...) - * - */ - function hypot() { - var i, n, - t = new this(0); + return Decimal; +} - external = false; - for (i = 0; i < arguments.length;) { - n = new this(arguments[i++]); - if (!n.d) { - if (n.s) { - external = true; - return new this(1 / 0); - } - t = n; - } else if (t.d) { - t = t.plus(n.times(n)); - } - } +/* + * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function div(x, y) { + return new this(x).div(y); +} - external = true; - return t.sqrt(); - } +/* + * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} The power to which to raise the base of the natural log. + * + */ +function exp(x) { + return new this(x).exp(); +} - /* - * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function ln(x) { - return new this(x).ln(); - } +/* + * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`. + * + * x {number|string|Decimal} + * + */ +function floor(x) { + return finalise(x = new this(x), x.e + 1, 3); +} - /* - * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base - * is specified, rounded to `precision` significant digits using rounding mode `rounding`. - * - * log[y](x) - * - * x {number|string|Decimal} The argument of the logarithm. - * y {number|string|Decimal} The base of the logarithm. - * - */ - function log(x, y) { - return new this(x).log(y); +/* + * Return a new Decimal whose value is the square root of the sum of the squares of the arguments, + * rounded to `precision` significant digits using rounding mode `rounding`. + * + * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...) + * + */ +function hypot() { + var i, n, + t = new this(0); + + external = false; + + for (i = 0; i < arguments.length;) { + n = new this(arguments[i++]); + if (!n.d) { + if (n.s) { + external = true; + return new this(1 / 0); + } + t = n; + } else if (t.d) { + t = t.plus(n.times(n)); + } } + external = true; - /* - * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log2(x) { - return new this(x).log(2); - } + return t.sqrt(); +} - /* - * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log10(x) { - return new this(x).log(10); - } +/* + * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function ln(x) { + return new this(x).ln(); +} - /* - * Return a new Decimal whose value is the maximum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function max() { - return maxOrMin(this, arguments, 'lt'); - } +/* + * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base + * is specified, rounded to `precision` significant digits using rounding mode `rounding`. + * + * log[y](x) + * + * x {number|string|Decimal} The argument of the logarithm. + * y {number|string|Decimal} The base of the logarithm. + * + */ +function log(x, y) { + return new this(x).log(y); +} - /* - * Return a new Decimal whose value is the minimum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function min() { - return maxOrMin(this, arguments, 'gt'); - } +/* + * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function log2(x) { + return new this(x).log(2); +} - /* - * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mod(x, y) { - return new this(x).mod(y); - } +/* + * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function log10(x) { + return new this(x).log(10); +} - /* - * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mul(x, y) { - return new this(x).mul(y); - } +/* + * Return a new Decimal whose value is the maximum of the arguments. + * + * arguments {number|string|Decimal} + * + */ +function max() { + return maxOrMin(this, arguments, 'lt'); +} - /* - * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The base. - * y {number|string|Decimal} The exponent. - * - */ - function pow(x, y) { - return new this(x).pow(y); - } +/* + * Return a new Decimal whose value is the minimum of the arguments. + * + * arguments {number|string|Decimal} + * + */ +function min() { + return maxOrMin(this, arguments, 'gt'); +} - /* - * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with - * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros - * are produced). - * - * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive. - * - */ - function random(sd) { - var d, e, k, n, - i = 0, - r = new this(1), - rd = []; +/* + * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits + * using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function mod(x, y) { + return new this(x).mod(y); +} - if (sd === void 0) sd = this.precision; - else checkInt32(sd, 1, MAX_DIGITS); - k = Math.ceil(sd / LOG_BASE); +/* + * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function mul(x, y) { + return new this(x).mul(y); +} - if (!this.crypto) { - for (; i < k;) rd[i++] = Math.random() * 1e7 | 0; - // Browsers supporting crypto.getRandomValues. - } else if (crypto.getRandomValues) { - d = crypto.getRandomValues(new Uint32Array(k)); +/* + * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} The base. + * y {number|string|Decimal} The exponent. + * + */ +function pow(x, y) { + return new this(x).pow(y); +} - for (; i < k;) { - n = d[i]; - // 0 <= n < 4294967296 - // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865). - if (n >= 4.29e9) { - d[i] = crypto.getRandomValues(new Uint32Array(1))[0]; - } else { +/* + * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with + * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros + * are produced). + * + * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive. + * + */ +function random(sd) { + var d, e, k, n, + i = 0, + r = new this(1), + rd = []; - // 0 <= n <= 4289999999 - // 0 <= (n % 1e7) <= 9999999 - rd[i++] = n % 1e7; - } - } + if (sd === void 0) sd = this.precision; + else checkInt32(sd, 1, MAX_DIGITS); - // Node.js supporting crypto.randomBytes. - } else if (crypto.randomBytes) { + k = Math.ceil(sd / LOG_BASE); - // buffer - d = crypto.randomBytes(k *= 4); + if (!this.crypto) { + for (; i < k;) rd[i++] = Math.random() * 1e7 | 0; - for (; i < k;) { + // Browsers supporting crypto.getRandomValues. + } else if (crypto.getRandomValues) { + d = crypto.getRandomValues(new Uint32Array(k)); - // 0 <= n < 2147483648 - n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24); + for (; i < k;) { + n = d[i]; - // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286). - if (n >= 2.14e9) { - crypto.randomBytes(4).copy(d, i); - } else { + // 0 <= n < 4294967296 + // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865). + if (n >= 4.29e9) { + d[i] = crypto.getRandomValues(new Uint32Array(1))[0]; + } else { - // 0 <= n <= 2139999999 - // 0 <= (n % 1e7) <= 9999999 - rd.push(n % 1e7); - i += 4; - } + // 0 <= n <= 4289999999 + // 0 <= (n % 1e7) <= 9999999 + rd[i++] = n % 1e7; } - - i = k / 4; - } else { - throw Error(cryptoUnavailable); } - k = rd[--i]; - sd %= LOG_BASE; - - // Convert trailing digits to zeros according to sd. - if (k && sd) { - n = mathpow(10, LOG_BASE - sd); - rd[i] = (k / n | 0) * n; - } + // Node.js supporting crypto.randomBytes. + } else if (crypto.randomBytes) { - // Remove trailing words which are zero. - for (; rd[i] === 0; i--) rd.pop(); + // buffer + d = crypto.randomBytes(k *= 4); - // Zero? - if (i < 0) { - e = 0; - rd = [0]; - } else { - e = -1; + for (; i < k;) { - // Remove leading words which are zero and adjust exponent accordingly. - for (; rd[0] === 0; e -= LOG_BASE) rd.shift(); + // 0 <= n < 2147483648 + n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24); - // Count the digits of the first word of rd to determine leading zeros. - for (k = 1, n = rd[0]; n >= 10; n /= 10) k++; + // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286). + if (n >= 2.14e9) { + crypto.randomBytes(4).copy(d, i); + } else { - // Adjust the exponent for leading zeros of the first word of rd. - if (k < LOG_BASE) e -= LOG_BASE - k; + // 0 <= n <= 2139999999 + // 0 <= (n % 1e7) <= 9999999 + rd.push(n % 1e7); + i += 4; + } } - r.e = e; - r.d = rd; - - return r; + i = k / 4; + } else { + throw Error(cryptoUnavailable); } + k = rd[--i]; + sd %= LOG_BASE; - /* - * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`. - * - * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL). - * - * x {number|string|Decimal} - * - */ - function round(x) { - return finalise(x = new this(x), x.e + 1, this.rounding); + // Convert trailing digits to zeros according to sd. + if (k && sd) { + n = mathpow(10, LOG_BASE - sd); + rd[i] = (k / n | 0) * n; } + // Remove trailing words which are zero. + for (; rd[i] === 0; i--) rd.pop(); - /* - * Return - * 1 if x > 0, - * -1 if x < 0, - * 0 if x is 0, - * -0 if x is -0, - * NaN otherwise - * - */ - function sign(x) { - x = new this(x); - return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN; - } + // Zero? + if (i < 0) { + e = 0; + rd = [0]; + } else { + e = -1; + // Remove leading words which are zero and adjust exponent accordingly. + for (; rd[0] === 0; e -= LOG_BASE) rd.shift(); - /* - * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sin(x) { - return new this(x).sin(); + // Count the digits of the first word of rd to determine leading zeros. + for (k = 1, n = rd[0]; n >= 10; n /= 10) k++; + + // Adjust the exponent for leading zeros of the first word of rd. + if (k < LOG_BASE) e -= LOG_BASE - k; } + r.e = e; + r.d = rd; - /* - * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sinh(x) { - return new this(x).sinh(); - } + return r; +} - /* - * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function sqrt(x) { - return new this(x).sqrt(); - } +/* + * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`. + * + * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL). + * + * x {number|string|Decimal} + * + */ +function round(x) { + return finalise(x = new this(x), x.e + 1, this.rounding); +} - /* - * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function sub(x, y) { - return new this(x).sub(y); - } +/* + * Return + * 1 if x > 0, + * -1 if x < 0, + * 0 if x is 0, + * -0 if x is -0, + * NaN otherwise + * + */ +function sign(x) { + x = new this(x); + return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN; +} - /* - * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tan(x) { - return new this(x).tan(); - } +/* + * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits + * using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function sin(x) { + return new this(x).sin(); +} - /* - * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tanh(x) { - return new this(x).tanh(); - } +/* + * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function sinh(x) { + return new this(x).sinh(); +} - /* - * Return a new Decimal whose value is `x` truncated to an integer. - * - * x {number|string|Decimal} - * - */ - function trunc(x) { - return finalise(x = new this(x), x.e + 1, 1); - } +/* + * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function sqrt(x) { + return new this(x).sqrt(); +} + +/* + * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits + * using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function sub(x, y) { + return new this(x).sub(y); +} - // Create and configure initial Decimal constructor. - Decimal = clone(Decimal); - // Create the internal constants from their string values. - LN10 = new Decimal(LN10); - PI = new Decimal(PI); +/* + * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function tan(x) { + return new this(x).tan(); +} - // Export. +/* + * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function tanh(x) { + return new this(x).tanh(); +} - // AMD. - if (true) { - !(__WEBPACK_AMD_DEFINE_RESULT__ = (function () { - return Decimal; - }).call(exports, __webpack_require__, exports, module), - __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__)); +/* + * Return a new Decimal whose value is `x` truncated to an integer. + * + * x {number|string|Decimal} + * + */ +function trunc(x) { + return finalise(x = new this(x), x.e + 1, 1); +} + + +// Create and configure initial Decimal constructor. +Decimal = clone(defaults); + +// Create the internal constants from their string values. +LN10 = new Decimal(ln10); +PI = new Decimal(pi); - // Node and other environments that support module.exports. - } else {} -})(this); +/* harmony default export */ __webpack_exports__["default"] = (Decimal); /***/ }), @@ -29317,7 +29314,7 @@ function initBladeburner() { Skills[SkillNames.Overclock] = new Skill({ name:SkillNames.Overclock, desc:"Each level of this skill decreases the time it takes " + - "to attempt a contract or operation by 1% (Max Level: 99)", + "to attempt a contract or operation by 1% (Max Level: 95)", baseCost:5, costInc:1, maxLvl:95, actionTime:1 }); @@ -30289,8 +30286,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _NetscriptEvaluator_js__WEBPACK_IMPORTED_MODULE_24__ = __webpack_require__(/*! ./NetscriptEvaluator.js */ 6); /* harmony import */ var _NetscriptEnvironment_js__WEBPACK_IMPORTED_MODULE_25__ = __webpack_require__(/*! ./NetscriptEnvironment.js */ 69); /* harmony import */ var _NetscriptPort_js__WEBPACK_IMPORTED_MODULE_26__ = __webpack_require__(/*! ./NetscriptPort.js */ 46); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_27__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_27___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_27__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_27__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_28__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_29__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_IPAddress_js__WEBPACK_IMPORTED_MODULE_30__ = __webpack_require__(/*! ../utils/IPAddress.js */ 16); @@ -30419,7 +30415,7 @@ function NetscriptFunctions(workerScript) { Math : Math, Date : Date, Number : Number, - hacknetnodes : _Player_js__WEBPACK_IMPORTED_MODULE_15__["Player"].hacknetNodes, + hacknetnodes : _Player_js__WEBPACK_IMPORTED_MODULE_15__["Player"].hacknetNodeWrappers, sprintf : sprintf, vsprintf: vsprintf, scan : function(ip=workerScript.serverIp, hostnames=true){ @@ -31386,7 +31382,8 @@ function NetscriptFunctions(workerScript) { if (!hasAISF) { throw Object(_NetscriptEvaluator_js__WEBPACK_IMPORTED_MODULE_24__["makeRuntimeRejectMsg"])(workerScript, "Cannot run getBitNodeMultipliers(). It requires Source-File 5 to run."); } - return _BitNode_js__WEBPACK_IMPORTED_MODULE_2__["BitNodeMultipliers"]; + let copy = Object.assign({}, _BitNode_js__WEBPACK_IMPORTED_MODULE_2__["BitNodeMultipliers"]); + return copy; }, getServerMoneyAvailable : function(ip){ if (workerScript.checkingRam) { @@ -52297,6 +52294,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "updateHacknetNodesContent", function() { return updateHacknetNodesContent; }); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "processAllHacknetNodeEarnings", function() { return processAllHacknetNodeEarnings; }); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "getHacknetNode", function() { return getHacknetNode; }); +/* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "createPlayerHacknetNodeWrappers", function() { return createPlayerHacknetNodeWrappers; }); /* harmony import */ var _BitNode_js__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(/*! ./BitNode.js */ 15); /* harmony import */ var _Constants_js__WEBPACK_IMPORTED_MODULE_1__ = __webpack_require__(/*! ./Constants.js */ 3); /* harmony import */ var _engine_js__WEBPACK_IMPORTED_MODULE_2__ = __webpack_require__(/*! ./engine.js */ 5); @@ -52362,6 +52360,7 @@ function HacknetNode(name) { this.moneyGainRatePerSecond = 0; } + HacknetNode.prototype.updateMoneyGainRate = function() { //How much extra $/s is gained per level var gainPerLevel = _Constants_js__WEBPACK_IMPORTED_MODULE_1__["CONSTANTS"].HacknetNodeMoneyGainPerLevel; @@ -52486,6 +52485,36 @@ HacknetNode.fromJSON = function(value) { _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_7__["Reviver"].constructors.HacknetNode = HacknetNode; +var HacknetNodeWrapper = function(hacknetNodeObj) { + var _node = hacknetNodeObj; + return { + name : _node.name, + level : _node.level, + ram : _node.ram, + cores : _node.cores, + totalMoneyGenerated : _node.totalMoneyGenerated, + onlineTimeSeconds : _node.onlineTimeSeconds, + moneyGainRatePerSecond : _node.moneyGainRatePerSecond, + upgradeLevel : function(n) { + return _node.upgradeLevel(n); + }, + upgradeRam : function() { + return _node.upgradeRam(); + }, + upgradeCore : function() { + return _node.upgradeCore(); + }, + getLevelUpgradeCost : function(n) { + return _node.getLevelUpgradeCost(n); + }, + getRamUpgradeCost : function() { + return _node.getRamUpgradeCost(); + }, + getCoreUpgradeCost : function() { + return _node.getCoreUpgradeCost(); + } + } +} function purchaseHacknet() { /* INTERACTIVE TUTORIAL */ @@ -52775,8 +52804,31 @@ function updateHacknetNodeDomElement(nodeObj) { } } +function createPlayerHacknetNodeWrappers() { + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers.length = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length; + for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length; ++i) { + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i] = new HacknetNodeWrapper(_Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i]); + } +} + +function updatePlayerHacknetNodeWrappers() { + if (_Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers.length !== _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length) { + return createPlayerHacknetNodeWrappers(); + } + for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers.length; ++i) { + if (!(_Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i] instanceof HacknetNodeWrapper)) {return createPlayerHacknetNodeWrappers();} + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].level = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].level; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].ram = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].ram; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].cores = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].cores; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].totalMoneyGenerated = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].totalMoneyGenerated; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].onlineTimeSeconds = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].onlineTimeSeconds; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].moneyGainRatePerSecond = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].moneyGainRatePerSecond; + } +} + function processAllHacknetNodeEarnings(numCycles) { var total = 0; + updatePlayerHacknetNodeWrappers(); for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length; ++i) { total += processSingleHacknetNodeEarnings(numCycles, _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i]); } @@ -53128,8 +53180,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _Literature_js__WEBPACK_IMPORTED_MODULE_3__ = __webpack_require__(/*! ./Literature.js */ 53); /* harmony import */ var _Location_js__WEBPACK_IMPORTED_MODULE_4__ = __webpack_require__(/*! ./Location.js */ 4); /* harmony import */ var _Player_js__WEBPACK_IMPORTED_MODULE_5__ = __webpack_require__(/*! ./Player.js */ 0); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_6__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_6__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_7__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_8__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_9__ = __webpack_require__(/*! ../utils/JSONReviver.js */ 8); @@ -53763,10 +53814,10 @@ function Industry(params={}) { this.prodMult = 0; //Production multiplier //Financials - this.lastCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.lastCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.lastCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.lastCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); //Upgrades var numUpgrades = Object.keys(IndustryUpgrades).length; @@ -54064,13 +54115,13 @@ Industry.prototype.process = function(marketCycles=1, state, company) { console.log(this.thisCycleRevenue.toString()); console.log(this.thisCycleExpenses.toString()); Object(_utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_7__["dialogBoxCreate"])("Something went wrong when compting Corporation's revenue/expenses. This is a bug. Please report to game developer"); - this.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); } this.lastCycleRevenue = this.thisCycleRevenue.dividedBy(marketCycles * SecsPerMarketCycle); this.lastCycleExpenses = this.thisCycleExpenses.dividedBy(marketCycles * SecsPerMarketCycle); - this.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); //Once you start making revenue, the player should no longer be //considered new, and therefore no longer needs the 'tutorial' UI elements @@ -56181,9 +56232,9 @@ function Corporation(params={}) { this.divisions = []; //Financial stats - this.funds = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(150e9); - this.revenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.expenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.funds = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](150e9); + this.revenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.expenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); this.fundingRound = 0; this.public = false; //Publicly traded this.numShares = TOTALSHARES; @@ -56217,8 +56268,8 @@ Corporation.prototype.process = function() { //At the start of a new cycle, calculate profits from previous cycle if (state === "START") { - this.revenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.expenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.revenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.expenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); this.divisions.forEach((ind)=>{ this.revenue = this.revenue.plus(ind.lastCycleRevenue); this.expenses = this.expenses.plus(ind.lastCycleExpenses); @@ -56229,7 +56280,7 @@ Corporation.prototype.process = function() { Object(_utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_7__["dialogBoxCreate"])("There was an error calculating your Corporations funds and they got reset to 0. " + "This is a bug. Please report to game developer.

" + "(Your funds have been set to $150b for the inconvenience)"); - this.funds = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(150e9); + this.funds = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](150e9); } this.funds = this.funds.plus(cycleProfit); this.updateSharePrice(); @@ -57139,8 +57190,8 @@ Corporation.prototype.updateCorporationOverviewContent = function() { return; } var totalFunds = this.funds, - totalRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0), - totalExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + totalRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0), + totalExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); var profit = this.revenue.minus(this.expenses).toNumber(), profitStr = profit >= 0 ? _utils_numeral_min_js__WEBPACK_IMPORTED_MODULE_10___default()(profit).format("$0.000a") : "-" + _utils_numeral_min_js__WEBPACK_IMPORTED_MODULE_10___default()(-1 * profit).format("$0.000a"); @@ -58810,8 +58861,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_17__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! ../utils/JSONReviver.js */ 8); /* harmony import */ var _utils_StringHelperFunctions_js__WEBPACK_IMPORTED_MODULE_19__ = __webpack_require__(/*! ../utils/StringHelperFunctions.js */ 2); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_20__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_20__ = __webpack_require__(/*! decimal.js */ 24); @@ -59036,6 +59086,8 @@ function loadGame(saveString) { } } + //Re-initialize Hacknet Node Wrappers + Object(_HacknetNode_js__WEBPACK_IMPORTED_MODULE_7__["createPlayerHacknetNodeWrappers"])(); return true; } @@ -59062,9 +59114,9 @@ function loadImportedGame(saveObj, saveString) { tempPlayer = JSON.parse(tempSaveObj.PlayerSave, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__["Reviver"]); //Parse Decimal.js objects - tempPlayer.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default.a(tempPlayer.money); - tempPlayer.total_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default.a(tempPlayer.total_money); - tempPlayer.lifetime_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default.a(tempPlayer.lifetime_money); + tempPlayer.money = new decimal_js__WEBPACK_IMPORTED_MODULE_20__["default"](tempPlayer.money); + tempPlayer.total_money = new decimal_js__WEBPACK_IMPORTED_MODULE_20__["default"](tempPlayer.total_money); + tempPlayer.lifetime_money = new decimal_js__WEBPACK_IMPORTED_MODULE_20__["default"](tempPlayer.lifetime_money); tempAllServers = JSON.parse(tempSaveObj.AllServersSave, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__["Reviver"]); tempCompanies = JSON.parse(tempSaveObj.CompaniesSave, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__["Reviver"]); @@ -59252,6 +59304,9 @@ function loadImportedGame(saveObj, saveString) { } } + //Re-initialize Hacknet Node Wrappers + Object(_HacknetNode_js__WEBPACK_IMPORTED_MODULE_7__["createPlayerHacknetNodeWrappers"])(); + var popupId = "import-game-restart-game-notice"; var txt = Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_17__["createElement"])("p", { innerText:"Imported game! I would suggest saving the game and then reloading the page " + @@ -60687,8 +60742,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _SpecialServerIps_js__WEBPACK_IMPORTED_MODULE_15__ = __webpack_require__(/*! ./SpecialServerIps.js */ 17); /* harmony import */ var _StockMarket_js__WEBPACK_IMPORTED_MODULE_16__ = __webpack_require__(/*! ./StockMarket.js */ 22); /* harmony import */ var _Terminal_js__WEBPACK_IMPORTED_MODULE_17__ = __webpack_require__(/*! ./Terminal.js */ 18); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_18__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_19__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_20__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_YesNoBox_js__WEBPACK_IMPORTED_MODULE_21__ = __webpack_require__(/*! ../utils/YesNoBox.js */ 12); @@ -60715,6 +60769,8 @@ __webpack_require__.r(__webpack_exports__); + +let BitNode8StartingMoney = 250e6; //Prestige by purchasing augmentation function prestigeAugmentation() { @@ -60743,7 +60799,7 @@ function prestigeAugmentation() { } if (Object(_Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["augmentationExists"])(_Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["AugmentationNames"].CashRoot) && _Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["Augmentations"][_Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["AugmentationNames"].CashRoot].owned) { - _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].setMoney(new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default.a(1000000)); + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].setMoney(new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](1000000)); homeComp.programs.push(_CreateProgram_js__WEBPACK_IMPORTED_MODULE_5__["Programs"].BruteSSHProgram); } @@ -60809,7 +60865,7 @@ function prestigeAugmentation() { _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bladeburner = null; //BitNode 8: Ghost of Wall Street - if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8) {_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default.a(100e6);} + if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8) {_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](BitNode8StartingMoney);} if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_11__["hasWallStreetSF"]) { _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasWseAccount = true; _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasTixApiAccess = true; @@ -60937,7 +60993,7 @@ function prestigeSourceFile() { //BitNode 3: Corporatocracy if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 3) { - _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default.a(150e9); + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](150e9); homeComp.messages.push("corporation-management-handbook.lit"); Object(_utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_19__["dialogBoxCreate"])("You received a copy of the Corporation Management Handbook on your home computer. " + "Read it if you need help getting started with Corporations!"); @@ -60987,6 +61043,13 @@ function prestigeSourceFile() { } + //BitNode 8: Ghost of Wall Street + if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8) {_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](BitNode8StartingMoney);} + if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_11__["hasWallStreetSF"]) { + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasWseAccount = true; + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasTixApiAccess = true; + } + //Gain int exp _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].gainIntelligenceExp(5); } @@ -95697,7 +95760,7 @@ var NetscriptHighlightRules = function(options) { "JSON|Math|" + // Other "this|arguments|prototype|window|document" , // Pseudo "keyword": - "const|yield|import|get|set|async|await|foop|" + + "const|yield|import|get|set|async|await|" + "break|case|catch|continue|default|delete|do|else|finally|for|function|" + "if|in|of|instanceof|new|return|switch|throw|try|typeof|let|var|while|with|debugger|" + "__parent__|__count__|escape|unescape|with|__proto__|" + diff --git a/dist/tests.bundle.js b/dist/tests.bundle.js index c9c7a4235f..2fb124d925 100644 --- a/dist/tests.bundle.js +++ b/dist/tests.bundle.js @@ -95,8 +95,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _Server_js__WEBPACK_IMPORTED_MODULE_12__ = __webpack_require__(/*! ./Server.js */ 10); /* harmony import */ var _SpecialServerIps_js__WEBPACK_IMPORTED_MODULE_13__ = __webpack_require__(/*! ./SpecialServerIps.js */ 17); /* harmony import */ var _SourceFile_js__WEBPACK_IMPORTED_MODULE_14__ = __webpack_require__(/*! ./SourceFile.js */ 44); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_15__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_15__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_16__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_17__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_IPAddress_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! ../utils/IPAddress.js */ 16); @@ -179,9 +178,9 @@ function PlayerObject() { this.faction_rep_mult = 1; //Money - this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(1000); - this.total_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(0); //Total money ever earned in this "simulation" - this.lifetime_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(0); //Total money ever earned + this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](1000); + this.total_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](0); //Total money ever earned in this "simulation" + this.lifetime_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](0); //Total money ever earned //IP Address of Starting (home) computer this.homeComputer = ""; @@ -198,6 +197,7 @@ function PlayerObject() { this.currentServer = ""; //IP address of Server currently being accessed through terminal this.purchasedServers = []; //IP Addresses of purchased servers this.hacknetNodes = []; + this.hacknetNodeWrappers = []; this.totalHacknetNodeProduction = 0; //Factions @@ -345,7 +345,7 @@ PlayerObject.prototype.prestigeAugmentation = function() { this.agility_exp = 0; this.charisma_exp = 0; - this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(1000); + this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](1000); this.city = _Location_js__WEBPACK_IMPORTED_MODULE_10__["Locations"].Sector12; this.location = ""; @@ -426,7 +426,7 @@ PlayerObject.prototype.prestigeSourceFile = function() { this.agility_exp = 0; this.charisma_exp = 0; - this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(1000); + this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](1000); this.city = _Location_js__WEBPACK_IMPORTED_MODULE_10__["Locations"].Sector12; this.location = ""; @@ -486,19 +486,11 @@ PlayerObject.prototype.prestigeSourceFile = function() { this.hasTixApiAccess = false; //BitNode 3: Corporatocracy - if (this.bitNodeN === 3) {this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(150e9);} + if (this.bitNodeN === 3) {this.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](150e9);} this.corporation = 0; - //Reset Bladeburner this.bladeburner = 0; - //BitNode 8: Ghost of Wall Street - if (this.bitNodeN === 8) {this.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(100000000);} - if (this.bitNodeN === 8 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_11__["hasWallStreetSF"]) { - this.hasWseAccount = true; - this.hasTixApiAccess = true; - } - this.playtimeSinceLastAug = 0; this.scriptProdSinceLastAug = 0; } @@ -2453,21 +2445,21 @@ function loadPlayer(saveString) { Player = JSON.parse(saveString, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_19__["Reviver"]); //Parse Decimal.js objects - Player.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.money); - Player.total_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.total_money); - Player.lifetime_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.lifetime_money); + Player.money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.money); + Player.total_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.total_money); + Player.lifetime_money = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.lifetime_money); if (Player.corporation instanceof _CompanyManagement_js__WEBPACK_IMPORTED_MODULE_4__["Corporation"]) { - Player.corporation.funds = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.corporation.funds); - Player.corporation.revenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.corporation.revenue); - Player.corporation.expenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(Player.corporation.expenses); + Player.corporation.funds = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.corporation.funds); + Player.corporation.revenue = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.corporation.revenue); + Player.corporation.expenses = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](Player.corporation.expenses); for (var i = 0; i < Player.corporation.divisions.length; ++i) { var ind = Player.corporation.divisions[i]; - ind.lastCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.lastCycleRevenue); - ind.lastCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.lastCycleExpenses); - ind.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.thisCycleRevenue); - ind.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_15___default.a(ind.thisCycleExpenses); + ind.lastCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.lastCycleRevenue); + ind.lastCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.lastCycleExpenses); + ind.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.thisCycleRevenue); + ind.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_15__["default"](ind.thisCycleExpenses); } } } @@ -2957,7 +2949,7 @@ function generateRandomString(n) { __webpack_require__.r(__webpack_exports__); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "CONSTANTS", function() { return CONSTANTS; }); let CONSTANTS = { - Version: "0.37.1", + Version: "0.37.2", //Max level for any skill, assuming no multipliers. Determined by max numerical value in javascript for experience //and the skill level formula in Player.js. Note that all this means it that when experience hits MAX_INT, then @@ -3442,16 +3434,13 @@ let CONSTANTS = { "World Stock Exchange account and TIX API Access
", LatestUpdate: - "v0.37.1
" + - "* You now earn money from successfully completing Bladeburner contracts. The amount you earn is based " + - "on the difficulty of the contract.
" + - "* Completing Field Analysis in Bladeburner now grants 0.1 rank
" + - "* The maximum RAM you can get on a purchased server is now 1,048,576GB (2^20)
" + - "* Bug Fix: Fixed Netscript syntax highlighting issues with the new NetscriptJS
" + - "* Bug Fix: Netscript Functions now properly incur RAM costs in NetscriptJS
" + - "* Bug Fix: deleteServer() now fails if its called on the server you are currently connected to
" + - "* Removed in-game Netscript documentation, since it was outdated and difficult to maintain.
" + - "* Bug Fix: Updated the gymWorkout() Singularity function with the new exp/cost values for gyms
" + "v0.37.2
" + + "* After joining the Bladeburners division, there is now a button to go to the Bladeburner content " + + "in the 'City' page
" + + "* You now start with $250m in BitNode-8 (increased from $100m)
" + + "* Bug Fix: You can now no longer directly edit Hacknet Node values through NetscriptJS (hopefully)
" + + "* Bug Fix: Bladeburners is no longer accessible in BN-8
" + + "* Bug Fix: getBitNodeMultipliers() Netscript function now returns a copy rather than the original object
" } @@ -4199,6 +4188,7 @@ function displayLocationContent() { securityJob.style.display = "block"; agentJob.style.display = "block"; if (_Player_js__WEBPACK_IMPORTED_MODULE_8__["Player"].bitNodeN === 6 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_7__["hasBladeburnerSF"] === true) { + if (_Player_js__WEBPACK_IMPORTED_MODULE_8__["Player"].bitNodeN === 8) {break;} if (_Player_js__WEBPACK_IMPORTED_MODULE_8__["Player"].bladeburner instanceof _Bladeburner_js__WEBPACK_IMPORTED_MODULE_0__["Bladeburner"]) { //Note: Can't infiltrate NSA when part of bladeburner nsaBladeburner.innerText = "Enter Bladeburner Headquarters"; @@ -6349,6 +6339,7 @@ let Engine = { //Generic Locations (common to every city): // World Stock Exchange // Corporation (if applicable) + // Bladeburner HQ (if applicable); var genericLocationsList = document.getElementById("generic-locations-list"); genericLocationsList.style.display = "inline"; Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_2__["removeChildrenFromElement"])(genericLocationsList); @@ -6375,6 +6366,18 @@ let Engine = { })); genericLocationsList.appendChild(li); } + + if (_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].bladeburner instanceof _Bladeburner_js__WEBPACK_IMPORTED_MODULE_9__["Bladeburner"]) { + var li = Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_2__["createElement"])("li"); + li.appendChild(Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_2__["createElement"])("a", { + innerText:"Bladeburner Headquarters", class:"a-link-button", + clickListener:()=>{ + Engine.loadBladeburnerContent(); + return false; + } + })); + genericLocationsList.appendChild(li); + } }, displayFactionsInfo: function() { @@ -6437,9 +6440,9 @@ let Engine = { clickListener:()=>{ Object(_Faction_js__WEBPACK_IMPORTED_MODULE_15__["joinFaction"])(_Faction_js__WEBPACK_IMPORTED_MODULE_15__["Factions"][factionName]); for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations.length; ++i) { - if (_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations[i] == factionName) { + if (_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations[i] == factionName || _Faction_js__WEBPACK_IMPORTED_MODULE_15__["Factions"][_Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations[i]].isBanned) { _Player_js__WEBPACK_IMPORTED_MODULE_26__["Player"].factionInvitations.splice(i, 1); - break; + i--; } } Engine.displayFactionsInfo(); @@ -18856,6 +18859,9 @@ function displayStockMarketContent() { wseAccountButton.innerText = "Buy WSE Account - $" + Object(_utils_StringHelperFunctions_js__WEBPACK_IMPORTED_MODULE_10__["formatNumber"])(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].WSEAccountCost, 2).toString(); if (!_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasWseAccount && _Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].money.gte(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].WSEAccountCost)) { wseAccountButton.setAttribute("class", "a-link-button"); + } else if (_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasWseAccount){ + wseAccountButton.innerText = "WSE Account - Purchased"; + wseAccountButton.setAttribute("class", "a-link-button-bought"); } else { wseAccountButton.setAttribute("class", "a-link-button-inactive"); } @@ -18874,6 +18880,9 @@ function displayStockMarketContent() { Object(_utils_StringHelperFunctions_js__WEBPACK_IMPORTED_MODULE_10__["formatNumber"])(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].TIXAPICost, 2).toString(); if (!_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasTixApiAccess && _Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].money.gte(_Constants_js__WEBPACK_IMPORTED_MODULE_0__["CONSTANTS"].TIXAPICost)) { tixApiAccessButton.setAttribute("class", "a-link-button"); + } else if(_Player_js__WEBPACK_IMPORTED_MODULE_5__["Player"].hasTixApiAccess) { + tixApiAccessButton.innerText = "Trade Information eXchange (TIX) API Access - Purchased" + tixApiAccessButton.setAttribute("class", "a-link-button-bought"); } else { tixApiAccessButton.setAttribute("class", "a-link-button-inactive"); } @@ -19625,4807 +19634,4795 @@ function setSettingsLabels() { /***/ }), /* 24 */ -/*!**************************!*\ - !*** ./utils/decimal.js ***! - \**************************/ -/***/ (function(module, exports, __webpack_require__) { - -var __WEBPACK_AMD_DEFINE_RESULT__;/*! decimal.js v7.2.3 https://github.com/MikeMcl/decimal.js/LICENCE */ -;(function (globalScope) { - 'use strict'; - +/*!************************************************!*\ + !*** ./node_modules/decimal.js/decimal.es6.js ***! + \************************************************/ +/***/ (function(module, __webpack_exports__, __webpack_require__) { - /* - * decimal.js v7.2.3 - * An arbitrary-precision Decimal type for JavaScript. - * https://github.com/MikeMcl/decimal.js - * Copyright (c) 2017 Michael Mclaughlin - * MIT Licence - */ +"use strict"; +__webpack_require__.r(__webpack_exports__); +/* + * + * decimal.js v7.2.3 + * An arbitrary-precision Decimal type for JavaScript. + * https://github.com/MikeMcl/decimal.js + * Copyright (c) 2017 Michael Mclaughlin + * MIT Licence + * https://github.com/MikeMcl/decimal.js/LICENCE + * + */ - // ----------------------------------- EDITABLE DEFAULTS ------------------------------------ // +// ----------------------------------- EDITABLE DEFAULTS ------------------------------------ // - // The maximum exponent magnitude. - // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`. - var EXP_LIMIT = 9e15, // 0 to 9e15 + // The maximum exponent magnitude. + // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`. +var EXP_LIMIT = 9e15, // 0 to 9e15 - // The limit on the value of `precision`, and on the value of the first argument to - // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`. - MAX_DIGITS = 1e9, // 0 to 1e9 + // The limit on the value of `precision`, and on the value of the first argument to + // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`. + MAX_DIGITS = 1e9, // 0 to 1e9 - // Base conversion alphabet. - NUMERALS = '0123456789abcdef', - // The natural logarithm of 10 (1025 digits). - LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058', + // Base conversion alphabet. + NUMERALS = '0123456789abcdef', - // Pi (1025 digits). - PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789', + // The natural logarithm of 10 (1025 digits). + ln10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058', + // Pi (1025 digits). + pi = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789', - // The initial configuration properties of the Decimal constructor. - Decimal = { - // These values must be integers within the stated ranges (inclusive). - // Most of these values can be changed at run-time using the `Decimal.config` method. + // The initial configuration properties of the Decimal constructor. + defaults = { - // The maximum number of significant digits of the result of a calculation or base conversion. - // E.g. `Decimal.config({ precision: 20 });` - precision: 20, // 1 to MAX_DIGITS + // These values must be integers within the stated ranges (inclusive). + // Most of these values can be changed at run-time using the `Decimal.config` method. - // The rounding mode used when rounding to `precision`. - // - // ROUND_UP 0 Away from zero. - // ROUND_DOWN 1 Towards zero. - // ROUND_CEIL 2 Towards +Infinity. - // ROUND_FLOOR 3 Towards -Infinity. - // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up. - // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. - // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. - // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. - // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. - // - // E.g. - // `Decimal.rounding = 4;` - // `Decimal.rounding = Decimal.ROUND_HALF_UP;` - rounding: 4, // 0 to 8 - - // The modulo mode used when calculating the modulus: a mod n. - // The quotient (q = a / n) is calculated according to the corresponding rounding mode. - // The remainder (r) is calculated as: r = a - n * q. - // - // UP 0 The remainder is positive if the dividend is negative, else is negative. - // DOWN 1 The remainder has the same sign as the dividend (JavaScript %). - // FLOOR 3 The remainder has the same sign as the divisor (Python %). - // HALF_EVEN 6 The IEEE 754 remainder function. - // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive. - // - // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian - // division (9) are commonly used for the modulus operation. The other rounding modes can also - // be used, but they may not give useful results. - modulo: 1, // 0 to 9 + // The maximum number of significant digits of the result of a calculation or base conversion. + // E.g. `Decimal.config({ precision: 20 });` + precision: 20, // 1 to MAX_DIGITS - // The exponent value at and beneath which `toString` returns exponential notation. - // JavaScript numbers: -7 - toExpNeg: -7, // 0 to -EXP_LIMIT + // The rounding mode used when rounding to `precision`. + // + // ROUND_UP 0 Away from zero. + // ROUND_DOWN 1 Towards zero. + // ROUND_CEIL 2 Towards +Infinity. + // ROUND_FLOOR 3 Towards -Infinity. + // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up. + // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. + // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. + // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. + // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. + // + // E.g. + // `Decimal.rounding = 4;` + // `Decimal.rounding = Decimal.ROUND_HALF_UP;` + rounding: 4, // 0 to 8 + + // The modulo mode used when calculating the modulus: a mod n. + // The quotient (q = a / n) is calculated according to the corresponding rounding mode. + // The remainder (r) is calculated as: r = a - n * q. + // + // UP 0 The remainder is positive if the dividend is negative, else is negative. + // DOWN 1 The remainder has the same sign as the dividend (JavaScript %). + // FLOOR 3 The remainder has the same sign as the divisor (Python %). + // HALF_EVEN 6 The IEEE 754 remainder function. + // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive. + // + // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian + // division (9) are commonly used for the modulus operation. The other rounding modes can also + // be used, but they may not give useful results. + modulo: 1, // 0 to 9 - // The exponent value at and above which `toString` returns exponential notation. - // JavaScript numbers: 21 - toExpPos: 21, // 0 to EXP_LIMIT + // The exponent value at and beneath which `toString` returns exponential notation. + // JavaScript numbers: -7 + toExpNeg: -7, // 0 to -EXP_LIMIT - // The minimum exponent value, beneath which underflow to zero occurs. - // JavaScript numbers: -324 (5e-324) - minE: -EXP_LIMIT, // -1 to -EXP_LIMIT + // The exponent value at and above which `toString` returns exponential notation. + // JavaScript numbers: 21 + toExpPos: 21, // 0 to EXP_LIMIT - // The maximum exponent value, above which overflow to Infinity occurs. - // JavaScript numbers: 308 (1.7976931348623157e+308) - maxE: EXP_LIMIT, // 1 to EXP_LIMIT + // The minimum exponent value, beneath which underflow to zero occurs. + // JavaScript numbers: -324 (5e-324) + minE: -EXP_LIMIT, // -1 to -EXP_LIMIT - // Whether to use cryptographically-secure random number generation, if available. - crypto: false // true/false - }, + // The maximum exponent value, above which overflow to Infinity occurs. + // JavaScript numbers: 308 (1.7976931348623157e+308) + maxE: EXP_LIMIT, // 1 to EXP_LIMIT + // Whether to use cryptographically-secure random number generation, if available. + crypto: false // true/false + }, - // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- // +// ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- // - inexact, noConflict, quadrant, - external = true, - decimalError = '[DecimalError] ', - invalidArgument = decimalError + 'Invalid argument: ', - precisionLimitExceeded = decimalError + 'Precision limit exceeded', - cryptoUnavailable = decimalError + 'crypto unavailable', + Decimal, LN10, PI, inexact, quadrant, + external = true, - mathfloor = Math.floor, - mathpow = Math.pow, + decimalError = '[DecimalError] ', + invalidArgument = decimalError + 'Invalid argument: ', + precisionLimitExceeded = decimalError + 'Precision limit exceeded', + cryptoUnavailable = decimalError + 'crypto unavailable', - isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i, - isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i, - isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i, - isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, + mathfloor = Math.floor, + mathpow = Math.pow, - BASE = 1e7, - LOG_BASE = 7, - MAX_SAFE_INTEGER = 9007199254740991, + isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i, + isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i, + isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i, + isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, - LN10_PRECISION = LN10.length - 1, - PI_PRECISION = PI.length - 1, + BASE = 1e7, + LOG_BASE = 7, + MAX_SAFE_INTEGER = 9007199254740991, - // Decimal.prototype object - P = {}; + LN10_PRECISION = ln10.length - 1, + PI_PRECISION = pi.length - 1, + // Decimal.prototype object + P = {}; - // Decimal prototype methods +// Decimal prototype methods - /* - * absoluteValue abs - * ceil - * comparedTo cmp - * cosine cos - * cubeRoot cbrt - * decimalPlaces dp - * dividedBy div - * dividedToIntegerBy divToInt - * equals eq - * floor - * greaterThan gt - * greaterThanOrEqualTo gte - * hyperbolicCosine cosh - * hyperbolicSine sinh - * hyperbolicTangent tanh - * inverseCosine acos - * inverseHyperbolicCosine acosh - * inverseHyperbolicSine asinh - * inverseHyperbolicTangent atanh - * inverseSine asin - * inverseTangent atan - * isFinite - * isInteger isInt - * isNaN - * isNegative isNeg - * isPositive isPos - * isZero - * lessThan lt - * lessThanOrEqualTo lte - * logarithm log - * [maximum] [max] - * [minimum] [min] - * minus sub - * modulo mod - * naturalExponential exp - * naturalLogarithm ln - * negated neg - * plus add - * precision sd - * round - * sine sin - * squareRoot sqrt - * tangent tan - * times mul - * toBinary - * toDecimalPlaces toDP - * toExponential - * toFixed - * toFraction - * toHexadecimal toHex - * toNearest - * toNumber - * toOctal - * toPower pow - * toPrecision - * toSignificantDigits toSD - * toString - * truncated trunc - * valueOf toJSON - */ +/* + * absoluteValue abs + * ceil + * comparedTo cmp + * cosine cos + * cubeRoot cbrt + * decimalPlaces dp + * dividedBy div + * dividedToIntegerBy divToInt + * equals eq + * floor + * greaterThan gt + * greaterThanOrEqualTo gte + * hyperbolicCosine cosh + * hyperbolicSine sinh + * hyperbolicTangent tanh + * inverseCosine acos + * inverseHyperbolicCosine acosh + * inverseHyperbolicSine asinh + * inverseHyperbolicTangent atanh + * inverseSine asin + * inverseTangent atan + * isFinite + * isInteger isInt + * isNaN + * isNegative isNeg + * isPositive isPos + * isZero + * lessThan lt + * lessThanOrEqualTo lte + * logarithm log + * [maximum] [max] + * [minimum] [min] + * minus sub + * modulo mod + * naturalExponential exp + * naturalLogarithm ln + * negated neg + * plus add + * precision sd + * round + * sine sin + * squareRoot sqrt + * tangent tan + * times mul + * toBinary + * toDecimalPlaces toDP + * toExponential + * toFixed + * toFraction + * toHexadecimal toHex + * toNearest + * toNumber + * toOctal + * toPower pow + * toPrecision + * toSignificantDigits toSD + * toString + * truncated trunc + * valueOf toJSON + */ - /* - * Return a new Decimal whose value is the absolute value of this Decimal. - * - */ - P.absoluteValue = P.abs = function () { - var x = new this.constructor(this); - if (x.s < 0) x.s = 1; - return finalise(x); - }; +/* + * Return a new Decimal whose value is the absolute value of this Decimal. + * + */ +P.absoluteValue = P.abs = function () { + var x = new this.constructor(this); + if (x.s < 0) x.s = 1; + return finalise(x); +}; - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of positive Infinity. - * - */ - P.ceil = function () { - return finalise(new this.constructor(this), this.e + 1, 2); - }; +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the + * direction of positive Infinity. + * + */ +P.ceil = function () { + return finalise(new this.constructor(this), this.e + 1, 2); +}; - /* - * Return - * 1 if the value of this Decimal is greater than the value of `y`, - * -1 if the value of this Decimal is less than the value of `y`, - * 0 if they have the same value, - * NaN if the value of either Decimal is NaN. - * - */ - P.comparedTo = P.cmp = function (y) { - var i, j, xdL, ydL, - x = this, - xd = x.d, - yd = (y = new x.constructor(y)).d, - xs = x.s, - ys = y.s; - // Either NaN or ±Infinity? - if (!xd || !yd) { - return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1; - } +/* + * Return + * 1 if the value of this Decimal is greater than the value of `y`, + * -1 if the value of this Decimal is less than the value of `y`, + * 0 if they have the same value, + * NaN if the value of either Decimal is NaN. + * + */ +P.comparedTo = P.cmp = function (y) { + var i, j, xdL, ydL, + x = this, + xd = x.d, + yd = (y = new x.constructor(y)).d, + xs = x.s, + ys = y.s; - // Either zero? - if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0; + // Either NaN or ±Infinity? + if (!xd || !yd) { + return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1; + } - // Signs differ? - if (xs !== ys) return xs; + // Either zero? + if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0; - // Compare exponents. - if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1; + // Signs differ? + if (xs !== ys) return xs; - xdL = xd.length; - ydL = yd.length; + // Compare exponents. + if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1; - // Compare digit by digit. - for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) { - if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1; - } + xdL = xd.length; + ydL = yd.length; - // Compare lengths. - return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1; - }; + // Compare digit by digit. + for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) { + if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1; + } + // Compare lengths. + return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1; +}; - /* - * Return a new Decimal whose value is the cosine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * cos(0) = 1 - * cos(-0) = 1 - * cos(Infinity) = NaN - * cos(-Infinity) = NaN - * cos(NaN) = NaN - * - */ - P.cosine = P.cos = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - if (!x.d) return new Ctor(NaN); +/* + * Return a new Decimal whose value is the cosine of the value in radians of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-1, 1] + * + * cos(0) = 1 + * cos(-0) = 1 + * cos(Infinity) = NaN + * cos(-Infinity) = NaN + * cos(NaN) = NaN + * + */ +P.cosine = P.cos = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - // cos(0) = cos(-0) = 1 - if (!x.d[0]) return new Ctor(1); + if (!x.d) return new Ctor(NaN); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; + // cos(0) = cos(-0) = 1 + if (!x.d[0]) return new Ctor(1); - x = cosine(Ctor, toLessThanHalfPi(Ctor, x)); + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; + Ctor.rounding = 1; - Ctor.precision = pr; - Ctor.rounding = rm; + x = cosine(Ctor, toLessThanHalfPi(Ctor, x)); - return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true); - }; + Ctor.precision = pr; + Ctor.rounding = rm; + return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true); +}; - /* - * - * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * cbrt(0) = 0 - * cbrt(-0) = -0 - * cbrt(1) = 1 - * cbrt(-1) = -1 - * cbrt(N) = N - * cbrt(-I) = -I - * cbrt(I) = I - * - * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3)) - * - */ - P.cubeRoot = P.cbrt = function () { - var e, m, n, r, rep, s, sd, t, t3, t3plusx, - x = this, - Ctor = x.constructor; - if (!x.isFinite() || x.isZero()) return new Ctor(x); - external = false; +/* + * + * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * cbrt(0) = 0 + * cbrt(-0) = -0 + * cbrt(1) = 1 + * cbrt(-1) = -1 + * cbrt(N) = N + * cbrt(-I) = -I + * cbrt(I) = I + * + * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3)) + * + */ +P.cubeRoot = P.cbrt = function () { + var e, m, n, r, rep, s, sd, t, t3, t3plusx, + x = this, + Ctor = x.constructor; - // Initial estimate. - s = x.s * Math.pow(x.s * x, 1 / 3); + if (!x.isFinite() || x.isZero()) return new Ctor(x); + external = false; - // Math.cbrt underflow/overflow? - // Pass x to Math.pow as integer, then adjust the exponent of the result. - if (!s || Math.abs(s) == 1 / 0) { - n = digitsToString(x.d); - e = x.e; + // Initial estimate. + s = x.s * Math.pow(x.s * x, 1 / 3); - // Adjust n exponent so it is a multiple of 3 away from x exponent. - if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00'); - s = Math.pow(n, 1 / 3); + // Math.cbrt underflow/overflow? + // Pass x to Math.pow as integer, then adjust the exponent of the result. + if (!s || Math.abs(s) == 1 / 0) { + n = digitsToString(x.d); + e = x.e; - // Rarely, e may be one less than the result exponent value. - e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2)); + // Adjust n exponent so it is a multiple of 3 away from x exponent. + if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00'); + s = Math.pow(n, 1 / 3); - if (s == 1 / 0) { - n = '5e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } + // Rarely, e may be one less than the result exponent value. + e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2)); - r = new Ctor(n); - r.s = x.s; + if (s == 1 / 0) { + n = '5e' + e; } else { - r = new Ctor(s.toString()); + n = s.toExponential(); + n = n.slice(0, n.indexOf('e') + 1) + e; } - sd = (e = Ctor.precision) + 3; - - // Halley's method. - // TODO? Compare Newton's method. - for (;;) { - t = r; - t3 = t.times(t).times(t); - t3plusx = t3.plus(x); - r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1); - - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); - - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999 - // , i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { + r = new Ctor(n); + r.s = x.s; + } else { + r = new Ctor(s.toString()); + } - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); + sd = (e = Ctor.precision) + 3; - if (t.times(t).times(t).eq(x)) { - r = t; - break; - } + // Halley's method. + // TODO? Compare Newton's method. + for (;;) { + t = r; + t3 = t.times(t).times(t); + t3plusx = t3.plus(x); + r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1); + + // TODO? Replace with for-loop and checkRoundingDigits. + if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { + n = n.slice(sd - 3, sd + 1); + + // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999 + // , i.e. approaching a rounding boundary, continue the iteration. + if (n == '9999' || !rep && n == '4999') { + + // On the first iteration only, check to see if rounding up gives the exact result as the + // nines may infinitely repeat. + if (!rep) { + finalise(t, e + 1, 0); + + if (t.times(t).times(t).eq(x)) { + r = t; + break; } + } - sd += 4; - rep = 1; - } else { - - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { + sd += 4; + rep = 1; + } else { - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).times(r).eq(x); - } + // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. + // If not, then there are further digits and m will be truthy. + if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - break; + // Truncate to the first rounding digit. + finalise(r, e + 1, 1); + m = !r.times(r).times(r).eq(x); } + + break; } } + } - external = true; - - return finalise(r, e, Ctor.rounding, m); - }; - - - /* - * Return the number of decimal places of the value of this Decimal. - * - */ - P.decimalPlaces = P.dp = function () { - var w, - d = this.d, - n = NaN; - - if (d) { - w = d.length - 1; - n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE; + external = true; - // Subtract the number of trailing zeros of the last word. - w = d[w]; - if (w) for (; w % 10 == 0; w /= 10) n--; - if (n < 0) n = 0; - } + return finalise(r, e, Ctor.rounding, m); +}; - return n; - }; +/* + * Return the number of decimal places of the value of this Decimal. + * + */ +P.decimalPlaces = P.dp = function () { + var w, + d = this.d, + n = NaN; - /* - * n / 0 = I - * n / N = N - * n / I = 0 - * 0 / n = 0 - * 0 / 0 = N - * 0 / N = N - * 0 / I = 0 - * N / n = N - * N / 0 = N - * N / N = N - * N / I = N - * I / n = I - * I / 0 = I - * I / N = N - * I / I = N - * - * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedBy = P.div = function (y) { - return divide(this, new this.constructor(y)); - }; + if (d) { + w = d.length - 1; + n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE; + // Subtract the number of trailing zeros of the last word. + w = d[w]; + if (w) for (; w % 10 == 0; w /= 10) n--; + if (n < 0) n = 0; + } - /* - * Return a new Decimal whose value is the integer part of dividing the value of this Decimal - * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedToIntegerBy = P.divToInt = function (y) { - var x = this, - Ctor = x.constructor; - return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding); - }; + return n; +}; - /* - * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false. - * - */ - P.equals = P.eq = function (y) { - return this.cmp(y) === 0; - }; +/* + * n / 0 = I + * n / N = N + * n / I = 0 + * 0 / n = 0 + * 0 / 0 = N + * 0 / N = N + * 0 / I = 0 + * N / n = N + * N / 0 = N + * N / N = N + * N / I = N + * I / n = I + * I / 0 = I + * I / N = N + * I / I = N + * + * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + */ +P.dividedBy = P.div = function (y) { + return divide(this, new this.constructor(y)); +}; - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of negative Infinity. - * - */ - P.floor = function () { - return finalise(new this.constructor(this), this.e + 1, 3); - }; +/* + * Return a new Decimal whose value is the integer part of dividing the value of this Decimal + * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`. + * + */ +P.dividedToIntegerBy = P.divToInt = function (y) { + var x = this, + Ctor = x.constructor; + return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding); +}; - /* - * Return true if the value of this Decimal is greater than the value of `y`, otherwise return - * false. - * - */ - P.greaterThan = P.gt = function (y) { - return this.cmp(y) > 0; - }; +/* + * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false. + * + */ +P.equals = P.eq = function (y) { + return this.cmp(y) === 0; +}; - /* - * Return true if the value of this Decimal is greater than or equal to the value of `y`, - * otherwise return false. - * - */ - P.greaterThanOrEqualTo = P.gte = function (y) { - var k = this.cmp(y); - return k == 1 || k === 0; - }; +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the + * direction of negative Infinity. + * + */ +P.floor = function () { + return finalise(new this.constructor(this), this.e + 1, 3); +}; - /* - * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [1, Infinity] - * - * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ... - * - * cosh(0) = 1 - * cosh(-0) = 1 - * cosh(Infinity) = Infinity - * cosh(-Infinity) = Infinity - * cosh(NaN) = NaN - * - * x time taken (ms) result - * 1000 9 9.8503555700852349694e+433 - * 10000 25 4.4034091128314607936e+4342 - * 100000 171 1.4033316802130615897e+43429 - * 1000000 3817 1.5166076984010437725e+434294 - * 10000000 abandoned after 2 minute wait - * - * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x)) - * - */ - P.hyperbolicCosine = P.cosh = function () { - var k, n, pr, rm, len, - x = this, - Ctor = x.constructor, - one = new Ctor(1); +/* + * Return true if the value of this Decimal is greater than the value of `y`, otherwise return + * false. + * + */ +P.greaterThan = P.gt = function (y) { + return this.cmp(y) > 0; +}; - if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN); - if (x.isZero()) return one; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; +/* + * Return true if the value of this Decimal is greater than or equal to the value of `y`, + * otherwise return false. + * + */ +P.greaterThanOrEqualTo = P.gte = function (y) { + var k = this.cmp(y); + return k == 1 || k === 0; +}; - // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1 - // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4)) - // Estimate the optimum number of times to use the argument reduction. - // TODO? Estimation reused from cosine() and may not be optimal here. - if (len < 32) { - k = Math.ceil(len / 3); - n = Math.pow(4, -k).toString(); - } else { - k = 16; - n = '2.3283064365386962890625e-10'; - } +/* + * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [1, Infinity] + * + * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ... + * + * cosh(0) = 1 + * cosh(-0) = 1 + * cosh(Infinity) = Infinity + * cosh(-Infinity) = Infinity + * cosh(NaN) = NaN + * + * x time taken (ms) result + * 1000 9 9.8503555700852349694e+433 + * 10000 25 4.4034091128314607936e+4342 + * 100000 171 1.4033316802130615897e+43429 + * 1000000 3817 1.5166076984010437725e+434294 + * 10000000 abandoned after 2 minute wait + * + * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x)) + * + */ +P.hyperbolicCosine = P.cosh = function () { + var k, n, pr, rm, len, + x = this, + Ctor = x.constructor, + one = new Ctor(1); + + if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN); + if (x.isZero()) return one; + + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; + Ctor.rounding = 1; + len = x.d.length; + + // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1 + // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4)) + + // Estimate the optimum number of times to use the argument reduction. + // TODO? Estimation reused from cosine() and may not be optimal here. + if (len < 32) { + k = Math.ceil(len / 3); + n = Math.pow(4, -k).toString(); + } else { + k = 16; + n = '2.3283064365386962890625e-10'; + } - x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true); + x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true); - // Reverse argument reduction - var cosh2_x, - i = k, - d8 = new Ctor(8); - for (; i--;) { - cosh2_x = x.times(x); - x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8)))); - } + // Reverse argument reduction + var cosh2_x, + i = k, + d8 = new Ctor(8); + for (; i--;) { + cosh2_x = x.times(x); + x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8)))); + } - return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true); - }; + return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true); +}; - /* - * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ... - * - * sinh(0) = 0 - * sinh(-0) = -0 - * sinh(Infinity) = Infinity - * sinh(-Infinity) = -Infinity - * sinh(NaN) = NaN - * - * x time taken (ms) - * 10 2 ms - * 100 5 ms - * 1000 14 ms - * 10000 82 ms - * 100000 886 ms 1.4033316802130615897e+43429 - * 200000 2613 ms - * 300000 5407 ms - * 400000 8824 ms - * 500000 13026 ms 8.7080643612718084129e+217146 - * 1000000 48543 ms - * - * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x)) - * - */ - P.hyperbolicSine = P.sinh = function () { - var k, pr, rm, len, - x = this, - Ctor = x.constructor; +/* + * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-Infinity, Infinity] + * + * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ... + * + * sinh(0) = 0 + * sinh(-0) = -0 + * sinh(Infinity) = Infinity + * sinh(-Infinity) = -Infinity + * sinh(NaN) = NaN + * + * x time taken (ms) + * 10 2 ms + * 100 5 ms + * 1000 14 ms + * 10000 82 ms + * 100000 886 ms 1.4033316802130615897e+43429 + * 200000 2613 ms + * 300000 5407 ms + * 400000 8824 ms + * 500000 13026 ms 8.7080643612718084129e+217146 + * 1000000 48543 ms + * + * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x)) + * + */ +P.hyperbolicSine = P.sinh = function () { + var k, pr, rm, len, + x = this, + Ctor = x.constructor; - if (!x.isFinite() || x.isZero()) return new Ctor(x); + if (!x.isFinite() || x.isZero()) return new Ctor(x); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; + Ctor.rounding = 1; + len = x.d.length; - if (len < 3) { - x = taylorSeries(Ctor, 2, x, x, true); - } else { + if (len < 3) { + x = taylorSeries(Ctor, 2, x, x, true); + } else { - // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x)) - // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3)) - // 3 multiplications and 1 addition + // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x)) + // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3)) + // 3 multiplications and 1 addition - // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x))) - // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5))) - // 4 multiplications and 2 additions + // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x))) + // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5))) + // 4 multiplications and 2 additions - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; + // Estimate the optimum number of times to use the argument reduction. + k = 1.4 * Math.sqrt(len); + k = k > 16 ? 16 : k | 0; - x = x.times(Math.pow(5, -k)); + x = x.times(Math.pow(5, -k)); - x = taylorSeries(Ctor, 2, x, x, true); + x = taylorSeries(Ctor, 2, x, x, true); - // Reverse argument reduction - var sinh2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sinh2_x = x.times(x); - x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20)))); - } + // Reverse argument reduction + var sinh2_x, + d5 = new Ctor(5), + d16 = new Ctor(16), + d20 = new Ctor(20); + for (; k--;) { + sinh2_x = x.times(x); + x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20)))); } + } - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(x, pr, rm, true); - }; + Ctor.precision = pr; + Ctor.rounding = rm; + return finalise(x, pr, rm, true); +}; - /* - * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * tanh(x) = sinh(x) / cosh(x) - * - * tanh(0) = 0 - * tanh(-0) = -0 - * tanh(Infinity) = 1 - * tanh(-Infinity) = -1 - * tanh(NaN) = NaN - * - */ - P.hyperbolicTangent = P.tanh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - if (!x.isFinite()) return new Ctor(x.s); - if (x.isZero()) return new Ctor(x); +/* + * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-1, 1] + * + * tanh(x) = sinh(x) / cosh(x) + * + * tanh(0) = 0 + * tanh(-0) = -0 + * tanh(Infinity) = 1 + * tanh(-Infinity) = -1 + * tanh(NaN) = NaN + * + */ +P.hyperbolicTangent = P.tanh = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 7; - Ctor.rounding = 1; + if (!x.isFinite()) return new Ctor(x.s); + if (x.isZero()) return new Ctor(x); - return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm); - }; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + 7; + Ctor.rounding = 1; + return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm); +}; - /* - * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of - * this Decimal. - * - * Domain: [-1, 1] - * Range: [0, pi] - * - * acos(x) = pi/2 - asin(x) - * - * acos(0) = pi/2 - * acos(-0) = pi/2 - * acos(1) = 0 - * acos(-1) = pi - * acos(1/2) = pi/3 - * acos(-1/2) = 2*pi/3 - * acos(|x| > 1) = NaN - * acos(NaN) = NaN - * - */ - P.inverseCosine = P.acos = function () { - var halfPi, - x = this, - Ctor = x.constructor, - k = x.abs().cmp(1), - pr = Ctor.precision, - rm = Ctor.rounding; - if (k !== -1) { - return k === 0 - // |x| is 1 - ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) - // |x| > 1 or x is NaN - : new Ctor(NaN); - } +/* + * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of + * this Decimal. + * + * Domain: [-1, 1] + * Range: [0, pi] + * + * acos(x) = pi/2 - asin(x) + * + * acos(0) = pi/2 + * acos(-0) = pi/2 + * acos(1) = 0 + * acos(-1) = pi + * acos(1/2) = pi/3 + * acos(-1/2) = 2*pi/3 + * acos(|x| > 1) = NaN + * acos(NaN) = NaN + * + */ +P.inverseCosine = P.acos = function () { + var halfPi, + x = this, + Ctor = x.constructor, + k = x.abs().cmp(1), + pr = Ctor.precision, + rm = Ctor.rounding; - if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5); + if (k !== -1) { + return k === 0 + // |x| is 1 + ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) + // |x| > 1 or x is NaN + : new Ctor(NaN); + } - // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3 + if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5); - Ctor.precision = pr + 6; - Ctor.rounding = 1; + // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3 - x = x.asin(); - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); + Ctor.precision = pr + 6; + Ctor.rounding = 1; - Ctor.precision = pr; - Ctor.rounding = rm; + x = x.asin(); + halfPi = getPi(Ctor, pr + 4, rm).times(0.5); - return halfPi.minus(x); - }; + Ctor.precision = pr; + Ctor.rounding = rm; + return halfPi.minus(x); +}; - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the - * value of this Decimal. - * - * Domain: [1, Infinity] - * Range: [0, Infinity] - * - * acosh(x) = ln(x + sqrt(x^2 - 1)) - * - * acosh(x < 1) = NaN - * acosh(NaN) = NaN - * acosh(Infinity) = Infinity - * acosh(-Infinity) = NaN - * acosh(0) = NaN - * acosh(-0) = NaN - * acosh(1) = 0 - * acosh(-1) = NaN - * - */ - P.inverseHyperbolicCosine = P.acosh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN); - if (!x.isFinite()) return new Ctor(x); +/* + * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the + * value of this Decimal. + * + * Domain: [1, Infinity] + * Range: [0, Infinity] + * + * acosh(x) = ln(x + sqrt(x^2 - 1)) + * + * acosh(x < 1) = NaN + * acosh(NaN) = NaN + * acosh(Infinity) = Infinity + * acosh(-Infinity) = NaN + * acosh(0) = NaN + * acosh(-0) = NaN + * acosh(1) = 0 + * acosh(-1) = NaN + * + */ +P.inverseHyperbolicCosine = P.acosh = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4; - Ctor.rounding = 1; - external = false; + if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN); + if (!x.isFinite()) return new Ctor(x); - x = x.times(x).minus(1).sqrt().plus(x); + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4; + Ctor.rounding = 1; + external = false; - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; + x = x.times(x).minus(1).sqrt().plus(x); - return x.ln(); - }; + external = true; + Ctor.precision = pr; + Ctor.rounding = rm; + return x.ln(); +}; - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * asinh(x) = ln(x + sqrt(x^2 + 1)) - * - * asinh(NaN) = NaN - * asinh(Infinity) = Infinity - * asinh(-Infinity) = -Infinity - * asinh(0) = 0 - * asinh(-0) = -0 - * - */ - P.inverseHyperbolicSine = P.asinh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - if (!x.isFinite() || x.isZero()) return new Ctor(x); +/* + * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value + * of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-Infinity, Infinity] + * + * asinh(x) = ln(x + sqrt(x^2 + 1)) + * + * asinh(NaN) = NaN + * asinh(Infinity) = Infinity + * asinh(-Infinity) = -Infinity + * asinh(0) = 0 + * asinh(-0) = -0 + * + */ +P.inverseHyperbolicSine = P.asinh = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6; - Ctor.rounding = 1; - external = false; + if (!x.isFinite() || x.isZero()) return new Ctor(x); - x = x.times(x).plus(1).sqrt().plus(x); + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6; + Ctor.rounding = 1; + external = false; - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; + x = x.times(x).plus(1).sqrt().plus(x); - return x.ln(); - }; + external = true; + Ctor.precision = pr; + Ctor.rounding = rm; + return x.ln(); +}; - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the - * value of this Decimal. - * - * Domain: [-1, 1] - * Range: [-Infinity, Infinity] - * - * atanh(x) = 0.5 * ln((1 + x) / (1 - x)) - * - * atanh(|x| > 1) = NaN - * atanh(NaN) = NaN - * atanh(Infinity) = NaN - * atanh(-Infinity) = NaN - * atanh(0) = 0 - * atanh(-0) = -0 - * atanh(1) = Infinity - * atanh(-1) = -Infinity - * - */ - P.inverseHyperbolicTangent = P.atanh = function () { - var pr, rm, wpr, xsd, - x = this, - Ctor = x.constructor; - if (!x.isFinite()) return new Ctor(NaN); - if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN); +/* + * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the + * value of this Decimal. + * + * Domain: [-1, 1] + * Range: [-Infinity, Infinity] + * + * atanh(x) = 0.5 * ln((1 + x) / (1 - x)) + * + * atanh(|x| > 1) = NaN + * atanh(NaN) = NaN + * atanh(Infinity) = NaN + * atanh(-Infinity) = NaN + * atanh(0) = 0 + * atanh(-0) = -0 + * atanh(1) = Infinity + * atanh(-1) = -Infinity + * + */ +P.inverseHyperbolicTangent = P.atanh = function () { + var pr, rm, wpr, xsd, + x = this, + Ctor = x.constructor; - pr = Ctor.precision; - rm = Ctor.rounding; - xsd = x.sd(); + if (!x.isFinite()) return new Ctor(NaN); + if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN); - if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true); + pr = Ctor.precision; + rm = Ctor.rounding; + xsd = x.sd(); - Ctor.precision = wpr = xsd - x.e; + if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true); - x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1); + Ctor.precision = wpr = xsd - x.e; - Ctor.precision = pr + 4; - Ctor.rounding = 1; + x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1); - x = x.ln(); + Ctor.precision = pr + 4; + Ctor.rounding = 1; - Ctor.precision = pr; - Ctor.rounding = rm; + x = x.ln(); - return x.times(0.5); - }; + Ctor.precision = pr; + Ctor.rounding = rm; + return x.times(0.5); +}; - /* - * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2))) - * - * asin(0) = 0 - * asin(-0) = -0 - * asin(1/2) = pi/6 - * asin(-1/2) = -pi/6 - * asin(1) = pi/2 - * asin(-1) = -pi/2 - * asin(|x| > 1) = NaN - * asin(NaN) = NaN - * - * TODO? Compare performance of Taylor series. - * - */ - P.inverseSine = P.asin = function () { - var halfPi, k, - pr, rm, - x = this, - Ctor = x.constructor; - if (x.isZero()) return new Ctor(x); +/* + * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this + * Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-pi/2, pi/2] + * + * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2))) + * + * asin(0) = 0 + * asin(-0) = -0 + * asin(1/2) = pi/6 + * asin(-1/2) = -pi/6 + * asin(1) = pi/2 + * asin(-1) = -pi/2 + * asin(|x| > 1) = NaN + * asin(NaN) = NaN + * + * TODO? Compare performance of Taylor series. + * + */ +P.inverseSine = P.asin = function () { + var halfPi, k, + pr, rm, + x = this, + Ctor = x.constructor; - k = x.abs().cmp(1); - pr = Ctor.precision; - rm = Ctor.rounding; + if (x.isZero()) return new Ctor(x); - if (k !== -1) { + k = x.abs().cmp(1); + pr = Ctor.precision; + rm = Ctor.rounding; - // |x| is 1 - if (k === 0) { - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); - halfPi.s = x.s; - return halfPi; - } + if (k !== -1) { - // |x| > 1 or x is NaN - return new Ctor(NaN); + // |x| is 1 + if (k === 0) { + halfPi = getPi(Ctor, pr + 4, rm).times(0.5); + halfPi.s = x.s; + return halfPi; } - // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6 + // |x| > 1 or x is NaN + return new Ctor(NaN); + } - Ctor.precision = pr + 6; - Ctor.rounding = 1; + // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6 - x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan(); + Ctor.precision = pr + 6; + Ctor.rounding = 1; - Ctor.precision = pr; - Ctor.rounding = rm; + x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan(); - return x.times(2); - }; + Ctor.precision = pr; + Ctor.rounding = rm; + return x.times(2); +}; - /* - * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - * - * atan(0) = 0 - * atan(-0) = -0 - * atan(1) = pi/4 - * atan(-1) = -pi/4 - * atan(Infinity) = pi/2 - * atan(-Infinity) = -pi/2 - * atan(NaN) = NaN - * - */ - P.inverseTangent = P.atan = function () { - var i, j, k, n, px, t, r, wpr, x2, - x = this, - Ctor = x.constructor, - pr = Ctor.precision, - rm = Ctor.rounding; - if (!x.isFinite()) { - if (!x.s) return new Ctor(NaN); - if (pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.5); - r.s = x.s; - return r; - } - } else if (x.isZero()) { - return new Ctor(x); - } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.25); +/* + * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value + * of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-pi/2, pi/2] + * + * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... + * + * atan(0) = 0 + * atan(-0) = -0 + * atan(1) = pi/4 + * atan(-1) = -pi/4 + * atan(Infinity) = pi/2 + * atan(-Infinity) = -pi/2 + * atan(NaN) = NaN + * + */ +P.inverseTangent = P.atan = function () { + var i, j, k, n, px, t, r, wpr, x2, + x = this, + Ctor = x.constructor, + pr = Ctor.precision, + rm = Ctor.rounding; + + if (!x.isFinite()) { + if (!x.s) return new Ctor(NaN); + if (pr + 4 <= PI_PRECISION) { + r = getPi(Ctor, pr + 4, rm).times(0.5); r.s = x.s; return r; } + } else if (x.isZero()) { + return new Ctor(x); + } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) { + r = getPi(Ctor, pr + 4, rm).times(0.25); + r.s = x.s; + return r; + } - Ctor.precision = wpr = pr + 10; - Ctor.rounding = 1; + Ctor.precision = wpr = pr + 10; + Ctor.rounding = 1; - // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x); + // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x); - // Argument reduction - // Ensure |x| < 0.42 - // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2))) + // Argument reduction + // Ensure |x| < 0.42 + // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2))) - k = Math.min(28, wpr / LOG_BASE + 2 | 0); + k = Math.min(28, wpr / LOG_BASE + 2 | 0); - for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1)); + for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1)); - external = false; + external = false; - j = Math.ceil(wpr / LOG_BASE); - n = 1; - x2 = x.times(x); - r = new Ctor(x); - px = x; + j = Math.ceil(wpr / LOG_BASE); + n = 1; + x2 = x.times(x); + r = new Ctor(x); + px = x; - // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - for (; i !== -1;) { - px = px.times(x2); - t = r.minus(px.div(n += 2)); + // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... + for (; i !== -1;) { + px = px.times(x2); + t = r.minus(px.div(n += 2)); - px = px.times(x2); - r = t.plus(px.div(n += 2)); + px = px.times(x2); + r = t.plus(px.div(n += 2)); - if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;); - } + if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;); + } - if (k) r = r.times(2 << (k - 1)); + if (k) r = r.times(2 << (k - 1)); - external = true; + external = true; - return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true); - }; + return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true); +}; - /* - * Return true if the value of this Decimal is a finite number, otherwise return false. - * - */ - P.isFinite = function () { - return !!this.d; - }; +/* + * Return true if the value of this Decimal is a finite number, otherwise return false. + * + */ +P.isFinite = function () { + return !!this.d; +}; - /* - * Return true if the value of this Decimal is an integer, otherwise return false. - * - */ - P.isInteger = P.isInt = function () { - return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2; - }; +/* + * Return true if the value of this Decimal is an integer, otherwise return false. + * + */ +P.isInteger = P.isInt = function () { + return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2; +}; - /* - * Return true if the value of this Decimal is NaN, otherwise return false. - * - */ - P.isNaN = function () { - return !this.s; - }; +/* + * Return true if the value of this Decimal is NaN, otherwise return false. + * + */ +P.isNaN = function () { + return !this.s; +}; - /* - * Return true if the value of this Decimal is negative, otherwise return false. - * - */ - P.isNegative = P.isNeg = function () { - return this.s < 0; - }; +/* + * Return true if the value of this Decimal is negative, otherwise return false. + * + */ +P.isNegative = P.isNeg = function () { + return this.s < 0; +}; - /* - * Return true if the value of this Decimal is positive, otherwise return false. - * - */ - P.isPositive = P.isPos = function () { - return this.s > 0; - }; +/* + * Return true if the value of this Decimal is positive, otherwise return false. + * + */ +P.isPositive = P.isPos = function () { + return this.s > 0; +}; - /* - * Return true if the value of this Decimal is 0 or -0, otherwise return false. - * - */ - P.isZero = function () { - return !!this.d && this.d[0] === 0; - }; +/* + * Return true if the value of this Decimal is 0 or -0, otherwise return false. + * + */ +P.isZero = function () { + return !!this.d && this.d[0] === 0; +}; - /* - * Return true if the value of this Decimal is less than `y`, otherwise return false. - * - */ - P.lessThan = P.lt = function (y) { - return this.cmp(y) < 0; - }; +/* + * Return true if the value of this Decimal is less than `y`, otherwise return false. + * + */ +P.lessThan = P.lt = function (y) { + return this.cmp(y) < 0; +}; - /* - * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false. - * - */ - P.lessThanOrEqualTo = P.lte = function (y) { - return this.cmp(y) < 1; - }; +/* + * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false. + * + */ +P.lessThanOrEqualTo = P.lte = function (y) { + return this.cmp(y) < 1; +}; - /* - * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * If no base is specified, return log[10](arg). - * - * log[base](arg) = ln(arg) / ln(base) - * - * The result will always be correctly rounded if the base of the log is 10, and 'almost always' - * otherwise: - * - * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen - * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error - * between the result and the correctly rounded result will be one ulp (unit in the last place). - * - * log[-b](a) = NaN - * log[0](a) = NaN - * log[1](a) = NaN - * log[NaN](a) = NaN - * log[Infinity](a) = NaN - * log[b](0) = -Infinity - * log[b](-0) = -Infinity - * log[b](-a) = NaN - * log[b](1) = 0 - * log[b](Infinity) = Infinity - * log[b](NaN) = NaN - * - * [base] {number|string|Decimal} The base of the logarithm. - * - */ - P.logarithm = P.log = function (base) { - var isBase10, d, denominator, k, inf, num, sd, r, - arg = this, - Ctor = arg.constructor, - pr = Ctor.precision, - rm = Ctor.rounding, - guard = 5; - - // Default base is 10. - if (base == null) { - base = new Ctor(10); - isBase10 = true; - } else { - base = new Ctor(base); - d = base.d; +/* + * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * If no base is specified, return log[10](arg). + * + * log[base](arg) = ln(arg) / ln(base) + * + * The result will always be correctly rounded if the base of the log is 10, and 'almost always' + * otherwise: + * + * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen + * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error + * between the result and the correctly rounded result will be one ulp (unit in the last place). + * + * log[-b](a) = NaN + * log[0](a) = NaN + * log[1](a) = NaN + * log[NaN](a) = NaN + * log[Infinity](a) = NaN + * log[b](0) = -Infinity + * log[b](-0) = -Infinity + * log[b](-a) = NaN + * log[b](1) = 0 + * log[b](Infinity) = Infinity + * log[b](NaN) = NaN + * + * [base] {number|string|Decimal} The base of the logarithm. + * + */ +P.logarithm = P.log = function (base) { + var isBase10, d, denominator, k, inf, num, sd, r, + arg = this, + Ctor = arg.constructor, + pr = Ctor.precision, + rm = Ctor.rounding, + guard = 5; + + // Default base is 10. + if (base == null) { + base = new Ctor(10); + isBase10 = true; + } else { + base = new Ctor(base); + d = base.d; - // Return NaN if base is negative, or non-finite, or is 0 or 1. - if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN); + // Return NaN if base is negative, or non-finite, or is 0 or 1. + if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN); - isBase10 = base.eq(10); - } + isBase10 = base.eq(10); + } - d = arg.d; + d = arg.d; - // Is arg negative, non-finite, 0 or 1? - if (arg.s < 0 || !d || !d[0] || arg.eq(1)) { - return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0); - } + // Is arg negative, non-finite, 0 or 1? + if (arg.s < 0 || !d || !d[0] || arg.eq(1)) { + return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0); + } - // The result will have a non-terminating decimal expansion if base is 10 and arg is not an - // integer power of 10. - if (isBase10) { - if (d.length > 1) { - inf = true; - } else { - for (k = d[0]; k % 10 === 0;) k /= 10; - inf = k !== 1; - } + // The result will have a non-terminating decimal expansion if base is 10 and arg is not an + // integer power of 10. + if (isBase10) { + if (d.length > 1) { + inf = true; + } else { + for (k = d[0]; k % 10 === 0;) k /= 10; + inf = k !== 1; } + } - external = false; - sd = pr + guard; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - - // The result will have 5 rounding digits. - r = divide(num, denominator, sd, 1); + external = false; + sd = pr + guard; + num = naturalLogarithm(arg, sd); + denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000, - // calculate 10 further digits. - // - // If the result is known to have an infinite decimal expansion, repeat this until it is clear - // that the result is above or below the boundary. Otherwise, if after calculating the 10 - // further digits, the last 14 are nines, round up and assume the result is exact. - // Also assume the result is exact if the last 14 are zero. - // - // Example of a result that will be incorrectly rounded: - // log[1048576](4503599627370502) = 2.60000000000000009610279511444746... - // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it - // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so - // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal - // place is still 2.6. - if (checkRoundingDigits(r.d, k = pr, rm)) { + // The result will have 5 rounding digits. + r = divide(num, denominator, sd, 1); - do { - sd += 10; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - r = divide(num, denominator, sd, 1); + // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000, + // calculate 10 further digits. + // + // If the result is known to have an infinite decimal expansion, repeat this until it is clear + // that the result is above or below the boundary. Otherwise, if after calculating the 10 + // further digits, the last 14 are nines, round up and assume the result is exact. + // Also assume the result is exact if the last 14 are zero. + // + // Example of a result that will be incorrectly rounded: + // log[1048576](4503599627370502) = 2.60000000000000009610279511444746... + // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it + // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so + // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal + // place is still 2.6. + if (checkRoundingDigits(r.d, k = pr, rm)) { - if (!inf) { + do { + sd += 10; + num = naturalLogarithm(arg, sd); + denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); + r = divide(num, denominator, sd, 1); - // Check for 14 nines from the 2nd rounding digit, as the first may be 4. - if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } + if (!inf) { - break; + // Check for 14 nines from the 2nd rounding digit, as the first may be 4. + if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) { + r = finalise(r, pr + 1, 0); } - } while (checkRoundingDigits(r.d, k += 10, rm)); - } - external = true; + break; + } + } while (checkRoundingDigits(r.d, k += 10, rm)); + } - return finalise(r, pr, rm); - }; + external = true; + return finalise(r, pr, rm); +}; - /* - * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.max = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'lt'); - }; - */ +/* + * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal. + * + * arguments {number|string|Decimal} + * +P.max = function () { + Array.prototype.push.call(arguments, this); + return maxOrMin(this.constructor, arguments, 'lt'); +}; + */ - /* - * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.min = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'gt'); - }; - */ +/* + * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal. + * + * arguments {number|string|Decimal} + * +P.min = function () { + Array.prototype.push.call(arguments, this); + return maxOrMin(this.constructor, arguments, 'gt'); +}; + */ - /* - * n - 0 = n - * n - N = N - * n - I = -I - * 0 - n = -n - * 0 - 0 = 0 - * 0 - N = N - * 0 - I = -I - * N - n = N - * N - 0 = N - * N - N = N - * N - I = N - * I - n = I - * I - 0 = I - * I - N = N - * I - I = N - * - * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.minus = P.sub = function (y) { - var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd, - x = this, - Ctor = x.constructor; - y = new Ctor(y); +/* + * n - 0 = n + * n - N = N + * n - I = -I + * 0 - n = -n + * 0 - 0 = 0 + * 0 - N = N + * 0 - I = -I + * N - n = N + * N - 0 = N + * N - N = N + * N - I = N + * I - n = I + * I - 0 = I + * I - N = N + * I - I = N + * + * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + */ +P.minus = P.sub = function (y) { + var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd, + x = this, + Ctor = x.constructor; - // If either is not finite... - if (!x.d || !y.d) { + y = new Ctor(y); - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); + // If either is not finite... + if (!x.d || !y.d) { - // Return y negated if x is finite and y is ±Infinity. - else if (x.d) y.s = -y.s; + // Return NaN if either is NaN. + if (!x.s || !y.s) y = new Ctor(NaN); - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with different signs. - // Return NaN if both are ±Infinity with the same sign. - else y = new Ctor(y.d || x.s !== y.s ? x : NaN); + // Return y negated if x is finite and y is ±Infinity. + else if (x.d) y.s = -y.s; - return y; - } + // Return x if y is finite and x is ±Infinity. + // Return x if both are ±Infinity with different signs. + // Return NaN if both are ±Infinity with the same sign. + else y = new Ctor(y.d || x.s !== y.s ? x : NaN); - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.plus(y); - } + return y; + } - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; + // If signs differ... + if (x.s != y.s) { + y.s = -y.s; + return x.plus(y); + } - // If either is zero... - if (!xd[0] || !yd[0]) { + xd = x.d; + yd = y.d; + pr = Ctor.precision; + rm = Ctor.rounding; - // Return y negated if x is zero and y is non-zero. - if (yd[0]) y.s = -y.s; + // If either is zero... + if (!xd[0] || !yd[0]) { - // Return x if y is zero and x is non-zero. - else if (xd[0]) y = new Ctor(x); + // Return y negated if x is zero and y is non-zero. + if (yd[0]) y.s = -y.s; - // Return zero if both are zero. - // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity. - else return new Ctor(rm === 3 ? -0 : 0); + // Return x if y is zero and x is non-zero. + else if (xd[0]) y = new Ctor(x); - return external ? finalise(y, pr, rm) : y; - } + // Return zero if both are zero. + // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity. + else return new Ctor(rm === 3 ? -0 : 0); - // x and y are finite, non-zero numbers with the same sign. + return external ? finalise(y, pr, rm) : y; + } - // Calculate base 1e7 exponents. - e = mathfloor(y.e / LOG_BASE); - xe = mathfloor(x.e / LOG_BASE); + // x and y are finite, non-zero numbers with the same sign. - xd = xd.slice(); - k = xe - e; + // Calculate base 1e7 exponents. + e = mathfloor(y.e / LOG_BASE); + xe = mathfloor(x.e / LOG_BASE); - // If base 1e7 exponents differ... - if (k) { - xLTy = k < 0; + xd = xd.slice(); + k = xe - e; - if (xLTy) { - d = xd; - k = -k; - len = yd.length; - } else { - d = yd; - e = xe; - len = xd.length; - } + // If base 1e7 exponents differ... + if (k) { + xLTy = k < 0; - // Numbers with massively different exponents would result in a very high number of - // zeros needing to be prepended, but this can be avoided while still ensuring correct - // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`. - i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2; + if (xLTy) { + d = xd; + k = -k; + len = yd.length; + } else { + d = yd; + e = xe; + len = xd.length; + } - if (k > i) { - k = i; - d.length = 1; - } + // Numbers with massively different exponents would result in a very high number of + // zeros needing to be prepended, but this can be avoided while still ensuring correct + // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`. + i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2; - // Prepend zeros to equalise exponents. - d.reverse(); - for (i = k; i--;) d.push(0); - d.reverse(); + if (k > i) { + k = i; + d.length = 1; + } - // Base 1e7 exponents equal. - } else { + // Prepend zeros to equalise exponents. + d.reverse(); + for (i = k; i--;) d.push(0); + d.reverse(); - // Check digits to determine which is the bigger number. + // Base 1e7 exponents equal. + } else { - i = xd.length; - len = yd.length; - xLTy = i < len; - if (xLTy) len = i; + // Check digits to determine which is the bigger number. - for (i = 0; i < len; i++) { - if (xd[i] != yd[i]) { - xLTy = xd[i] < yd[i]; - break; - } - } + i = xd.length; + len = yd.length; + xLTy = i < len; + if (xLTy) len = i; - k = 0; + for (i = 0; i < len; i++) { + if (xd[i] != yd[i]) { + xLTy = xd[i] < yd[i]; + break; + } } - if (xLTy) { - d = xd; - xd = yd; - yd = d; - y.s = -y.s; - } + k = 0; + } - len = xd.length; + if (xLTy) { + d = xd; + xd = yd; + yd = d; + y.s = -y.s; + } - // Append zeros to `xd` if shorter. - // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length. - for (i = yd.length - len; i > 0; --i) xd[len++] = 0; + len = xd.length; - // Subtract yd from xd. - for (i = yd.length; i > k;) { + // Append zeros to `xd` if shorter. + // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length. + for (i = yd.length - len; i > 0; --i) xd[len++] = 0; - if (xd[--i] < yd[i]) { - for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1; - --xd[j]; - xd[i] += BASE; - } + // Subtract yd from xd. + for (i = yd.length; i > k;) { - xd[i] -= yd[i]; + if (xd[--i] < yd[i]) { + for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1; + --xd[j]; + xd[i] += BASE; } - // Remove trailing zeros. - for (; xd[--len] === 0;) xd.pop(); - - // Remove leading zeros and adjust exponent accordingly. - for (; xd[0] === 0; xd.shift()) --e; + xd[i] -= yd[i]; + } - // Zero? - if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0); + // Remove trailing zeros. + for (; xd[--len] === 0;) xd.pop(); - y.d = xd; - y.e = getBase10Exponent(xd, e); + // Remove leading zeros and adjust exponent accordingly. + for (; xd[0] === 0; xd.shift()) --e; - return external ? finalise(y, pr, rm) : y; - }; + // Zero? + if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0); + y.d = xd; + y.e = getBase10Exponent(xd, e); - /* - * n % 0 = N - * n % N = N - * n % I = n - * 0 % n = 0 - * -0 % n = -0 - * 0 % 0 = N - * 0 % N = N - * 0 % I = 0 - * N % n = N - * N % 0 = N - * N % N = N - * N % I = N - * I % n = N - * I % 0 = N - * I % N = N - * I % I = N - * - * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * The result depends on the modulo mode. - * - */ - P.modulo = P.mod = function (y) { - var q, - x = this, - Ctor = x.constructor; + return external ? finalise(y, pr, rm) : y; +}; - y = new Ctor(y); - // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0. - if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN); +/* + * n % 0 = N + * n % N = N + * n % I = n + * 0 % n = 0 + * -0 % n = -0 + * 0 % 0 = N + * 0 % N = N + * 0 % I = 0 + * N % n = N + * N % 0 = N + * N % N = N + * N % I = N + * I % n = N + * I % 0 = N + * I % N = N + * I % I = N + * + * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * The result depends on the modulo mode. + * + */ +P.modulo = P.mod = function (y) { + var q, + x = this, + Ctor = x.constructor; - // Return x if y is ±Infinity or x is ±0. - if (!y.d || x.d && !x.d[0]) { - return finalise(new Ctor(x), Ctor.precision, Ctor.rounding); - } + y = new Ctor(y); - // Prevent rounding of intermediate calculations. - external = false; + // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0. + if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN); - if (Ctor.modulo == 9) { + // Return x if y is ±Infinity or x is ±0. + if (!y.d || x.d && !x.d[0]) { + return finalise(new Ctor(x), Ctor.precision, Ctor.rounding); + } - // Euclidian division: q = sign(y) * floor(x / abs(y)) - // result = x - q * y where 0 <= result < abs(y) - q = divide(x, y.abs(), 0, 3, 1); - q.s *= y.s; - } else { - q = divide(x, y, 0, Ctor.modulo, 1); - } + // Prevent rounding of intermediate calculations. + external = false; - q = q.times(y); + if (Ctor.modulo == 9) { - external = true; + // Euclidian division: q = sign(y) * floor(x / abs(y)) + // result = x - q * y where 0 <= result < abs(y) + q = divide(x, y.abs(), 0, 3, 1); + q.s *= y.s; + } else { + q = divide(x, y, 0, Ctor.modulo, 1); + } - return x.minus(q); - }; + q = q.times(y); + external = true; - /* - * Return a new Decimal whose value is the natural exponential of the value of this Decimal, - * i.e. the base e raised to the power the value of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.naturalExponential = P.exp = function () { - return naturalExponential(this); - }; - + return x.minus(q); +}; - /* - * Return a new Decimal whose value is the natural logarithm of the value of this Decimal, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.naturalLogarithm = P.ln = function () { - return naturalLogarithm(this); - }; +/* + * Return a new Decimal whose value is the natural exponential of the value of this Decimal, + * i.e. the base e raised to the power the value of this Decimal, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + */ +P.naturalExponential = P.exp = function () { + return naturalExponential(this); +}; - /* - * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by - * -1. - * - */ - P.negated = P.neg = function () { - var x = new this.constructor(this); - x.s = -x.s; - return finalise(x); - }; +/* + * Return a new Decimal whose value is the natural logarithm of the value of this Decimal, + * rounded to `precision` significant digits using rounding mode `rounding`. + * + */ +P.naturalLogarithm = P.ln = function () { + return naturalLogarithm(this); +}; - /* - * n + 0 = n - * n + N = N - * n + I = I - * 0 + n = n - * 0 + 0 = 0 - * 0 + N = N - * 0 + I = I - * N + n = N - * N + 0 = N - * N + N = N - * N + I = N - * I + n = I - * I + 0 = I - * I + N = N - * I + I = I - * - * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.plus = P.add = function (y) { - var carry, d, e, i, k, len, pr, rm, xd, yd, - x = this, - Ctor = x.constructor; - y = new Ctor(y); +/* + * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by + * -1. + * + */ +P.negated = P.neg = function () { + var x = new this.constructor(this); + x.s = -x.s; + return finalise(x); +}; - // If either is not finite... - if (!x.d || !y.d) { - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); +/* + * n + 0 = n + * n + N = N + * n + I = I + * 0 + n = n + * 0 + 0 = 0 + * 0 + N = N + * 0 + I = I + * N + n = N + * N + 0 = N + * N + N = N + * N + I = N + * I + n = I + * I + 0 = I + * I + N = N + * I + I = I + * + * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + */ +P.plus = P.add = function (y) { + var carry, d, e, i, k, len, pr, rm, xd, yd, + x = this, + Ctor = x.constructor; - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with the same sign. - // Return NaN if both are ±Infinity with different signs. - // Return y if x is finite and y is ±Infinity. - else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN); + y = new Ctor(y); - return y; - } + // If either is not finite... + if (!x.d || !y.d) { - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.minus(y); - } + // Return NaN if either is NaN. + if (!x.s || !y.s) y = new Ctor(NaN); - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; + // Return x if y is finite and x is ±Infinity. + // Return x if both are ±Infinity with the same sign. + // Return NaN if both are ±Infinity with different signs. + // Return y if x is finite and y is ±Infinity. + else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN); - // If either is zero... - if (!xd[0] || !yd[0]) { + return y; + } - // Return x if y is zero. - // Return y if y is non-zero. - if (!yd[0]) y = new Ctor(x); + // If signs differ... + if (x.s != y.s) { + y.s = -y.s; + return x.minus(y); + } - return external ? finalise(y, pr, rm) : y; - } + xd = x.d; + yd = y.d; + pr = Ctor.precision; + rm = Ctor.rounding; - // x and y are finite, non-zero numbers with the same sign. + // If either is zero... + if (!xd[0] || !yd[0]) { - // Calculate base 1e7 exponents. - k = mathfloor(x.e / LOG_BASE); - e = mathfloor(y.e / LOG_BASE); + // Return x if y is zero. + // Return y if y is non-zero. + if (!yd[0]) y = new Ctor(x); - xd = xd.slice(); - i = k - e; + return external ? finalise(y, pr, rm) : y; + } - // If base 1e7 exponents differ... - if (i) { + // x and y are finite, non-zero numbers with the same sign. - if (i < 0) { - d = xd; - i = -i; - len = yd.length; - } else { - d = yd; - e = k; - len = xd.length; - } + // Calculate base 1e7 exponents. + k = mathfloor(x.e / LOG_BASE); + e = mathfloor(y.e / LOG_BASE); - // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1. - k = Math.ceil(pr / LOG_BASE); - len = k > len ? k + 1 : len + 1; + xd = xd.slice(); + i = k - e; - if (i > len) { - i = len; - d.length = 1; - } + // If base 1e7 exponents differ... + if (i) { - // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts. - d.reverse(); - for (; i--;) d.push(0); - d.reverse(); + if (i < 0) { + d = xd; + i = -i; + len = yd.length; + } else { + d = yd; + e = k; + len = xd.length; } - len = xd.length; - i = yd.length; + // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1. + k = Math.ceil(pr / LOG_BASE); + len = k > len ? k + 1 : len + 1; - // If yd is longer than xd, swap xd and yd so xd points to the longer array. - if (len - i < 0) { + if (i > len) { i = len; - d = yd; - yd = xd; - xd = d; + d.length = 1; } - // Only start adding at yd.length - 1 as the further digits of xd can be left as they are. - for (carry = 0; i;) { - carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0; - xd[i] %= BASE; - } + // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts. + d.reverse(); + for (; i--;) d.push(0); + d.reverse(); + } - if (carry) { - xd.unshift(carry); - ++e; - } + len = xd.length; + i = yd.length; - // Remove trailing zeros. - // No need to check for zero, as +x + +y != 0 && -x + -y != 0 - for (len = xd.length; xd[--len] == 0;) xd.pop(); + // If yd is longer than xd, swap xd and yd so xd points to the longer array. + if (len - i < 0) { + i = len; + d = yd; + yd = xd; + xd = d; + } - y.d = xd; - y.e = getBase10Exponent(xd, e); + // Only start adding at yd.length - 1 as the further digits of xd can be left as they are. + for (carry = 0; i;) { + carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0; + xd[i] %= BASE; + } - return external ? finalise(y, pr, rm) : y; - }; + if (carry) { + xd.unshift(carry); + ++e; + } + // Remove trailing zeros. + // No need to check for zero, as +x + +y != 0 && -x + -y != 0 + for (len = xd.length; xd[--len] == 0;) xd.pop(); - /* - * Return the number of significant digits of the value of this Decimal. - * - * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0. - * - */ - P.precision = P.sd = function (z) { - var k, - x = this; + y.d = xd; + y.e = getBase10Exponent(xd, e); - if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z); + return external ? finalise(y, pr, rm) : y; +}; - if (x.d) { - k = getPrecision(x.d); - if (z && x.e + 1 > k) k = x.e + 1; - } else { - k = NaN; - } - return k; - }; +/* + * Return the number of significant digits of the value of this Decimal. + * + * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0. + * + */ +P.precision = P.sd = function (z) { + var k, + x = this; + if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z); - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using - * rounding mode `rounding`. - * - */ - P.round = function () { - var x = this, - Ctor = x.constructor; + if (x.d) { + k = getPrecision(x.d); + if (z && x.e + 1 > k) k = x.e + 1; + } else { + k = NaN; + } - return finalise(new Ctor(x), x.e + 1, Ctor.rounding); - }; + return k; +}; - /* - * Return a new Decimal whose value is the sine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * sin(x) = x - x^3/3! + x^5/5! - ... - * - * sin(0) = 0 - * sin(-0) = -0 - * sin(Infinity) = NaN - * sin(-Infinity) = NaN - * sin(NaN) = NaN - * - */ - P.sine = P.sin = function () { - var pr, rm, - x = this, - Ctor = x.constructor; +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using + * rounding mode `rounding`. + * + */ +P.round = function () { + var x = this, + Ctor = x.constructor; + + return finalise(new Ctor(x), x.e + 1, Ctor.rounding); +}; - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; +/* + * Return a new Decimal whose value is the sine of the value in radians of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-1, 1] + * + * sin(x) = x - x^3/3! + x^5/5! - ... + * + * sin(0) = 0 + * sin(-0) = -0 + * sin(Infinity) = NaN + * sin(-Infinity) = NaN + * sin(NaN) = NaN + * + */ +P.sine = P.sin = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - x = sine(Ctor, toLessThanHalfPi(Ctor, x)); + if (!x.isFinite()) return new Ctor(NaN); + if (x.isZero()) return new Ctor(x); - Ctor.precision = pr; - Ctor.rounding = rm; + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; + Ctor.rounding = 1; - return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true); - }; + x = sine(Ctor, toLessThanHalfPi(Ctor, x)); + Ctor.precision = pr; + Ctor.rounding = rm; - /* - * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * sqrt(-n) = N - * sqrt(N) = N - * sqrt(-I) = N - * sqrt(I) = I - * sqrt(0) = 0 - * sqrt(-0) = -0 - * - */ - P.squareRoot = P.sqrt = function () { - var m, n, sd, r, rep, t, - x = this, - d = x.d, - e = x.e, - s = x.s, - Ctor = x.constructor; + return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true); +}; - // Negative/NaN/Infinity/zero? - if (s !== 1 || !d || !d[0]) { - return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0); - } - external = false; +/* + * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * sqrt(-n) = N + * sqrt(N) = N + * sqrt(-I) = N + * sqrt(I) = I + * sqrt(0) = 0 + * sqrt(-0) = -0 + * + */ +P.squareRoot = P.sqrt = function () { + var m, n, sd, r, rep, t, + x = this, + d = x.d, + e = x.e, + s = x.s, + Ctor = x.constructor; - // Initial estimate. - s = Math.sqrt(+x); + // Negative/NaN/Infinity/zero? + if (s !== 1 || !d || !d[0]) { + return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0); + } - // Math.sqrt underflow/overflow? - // Pass x to Math.sqrt as integer, then adjust the exponent of the result. - if (s == 0 || s == 1 / 0) { - n = digitsToString(d); + external = false; - if ((n.length + e) % 2 == 0) n += '0'; - s = Math.sqrt(n); - e = mathfloor((e + 1) / 2) - (e < 0 || e % 2); + // Initial estimate. + s = Math.sqrt(+x); - if (s == 1 / 0) { - n = '1e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } + // Math.sqrt underflow/overflow? + // Pass x to Math.sqrt as integer, then adjust the exponent of the result. + if (s == 0 || s == 1 / 0) { + n = digitsToString(d); + + if ((n.length + e) % 2 == 0) n += '0'; + s = Math.sqrt(n); + e = mathfloor((e + 1) / 2) - (e < 0 || e % 2); - r = new Ctor(n); + if (s == 1 / 0) { + n = '1e' + e; } else { - r = new Ctor(s.toString()); + n = s.toExponential(); + n = n.slice(0, n.indexOf('e') + 1) + e; } - sd = (e = Ctor.precision) + 3; + r = new Ctor(n); + } else { + r = new Ctor(s.toString()); + } - // Newton-Raphson iteration. - for (;;) { - t = r; - r = t.plus(divide(x, t, sd + 2, 1)).times(0.5); + sd = (e = Ctor.precision) + 3; - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); + // Newton-Raphson iteration. + for (;;) { + t = r; + r = t.plus(divide(x, t, sd + 2, 1)).times(0.5); - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or - // 4999, i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { + // TODO? Replace with for-loop and checkRoundingDigits. + if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { + n = n.slice(sd - 3, sd + 1); - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); + // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or + // 4999, i.e. approaching a rounding boundary, continue the iteration. + if (n == '9999' || !rep && n == '4999') { - if (t.times(t).eq(x)) { - r = t; - break; - } - } + // On the first iteration only, check to see if rounding up gives the exact result as the + // nines may infinitely repeat. + if (!rep) { + finalise(t, e + 1, 0); - sd += 4; - rep = 1; - } else { + if (t.times(t).eq(x)) { + r = t; + break; + } + } - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { + sd += 4; + rep = 1; + } else { - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).eq(x); - } + // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. + // If not, then there are further digits and m will be truthy. + if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - break; + // Truncate to the first rounding digit. + finalise(r, e + 1, 1); + m = !r.times(r).eq(x); } + + break; } } + } - external = true; + external = true; - return finalise(r, e, Ctor.rounding, m); - }; + return finalise(r, e, Ctor.rounding, m); +}; - /* - * Return a new Decimal whose value is the tangent of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * tan(0) = 0 - * tan(-0) = -0 - * tan(Infinity) = NaN - * tan(-Infinity) = NaN - * tan(NaN) = NaN - * - */ - P.tangent = P.tan = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); +/* + * Return a new Decimal whose value is the tangent of the value in radians of this Decimal. + * + * Domain: [-Infinity, Infinity] + * Range: [-Infinity, Infinity] + * + * tan(0) = 0 + * tan(-0) = -0 + * tan(Infinity) = NaN + * tan(-Infinity) = NaN + * tan(NaN) = NaN + * + */ +P.tangent = P.tan = function () { + var pr, rm, + x = this, + Ctor = x.constructor; - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 10; - Ctor.rounding = 1; + if (!x.isFinite()) return new Ctor(NaN); + if (x.isZero()) return new Ctor(x); - x = x.sin(); - x.s = 1; - x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0); + pr = Ctor.precision; + rm = Ctor.rounding; + Ctor.precision = pr + 10; + Ctor.rounding = 1; - Ctor.precision = pr; - Ctor.rounding = rm; + x = x.sin(); + x.s = 1; + x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0); - return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true); - }; + Ctor.precision = pr; + Ctor.rounding = rm; + return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true); +}; - /* - * n * 0 = 0 - * n * N = N - * n * I = I - * 0 * n = 0 - * 0 * 0 = 0 - * 0 * N = N - * 0 * I = N - * N * n = N - * N * 0 = N - * N * N = N - * N * I = N - * I * n = I - * I * 0 = N - * I * N = N - * I * I = I - * - * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - */ - P.times = P.mul = function (y) { - var carry, e, i, k, r, rL, t, xdL, ydL, - x = this, - Ctor = x.constructor, - xd = x.d, - yd = (y = new Ctor(y)).d; - y.s *= x.s; +/* + * n * 0 = 0 + * n * N = N + * n * I = I + * 0 * n = 0 + * 0 * 0 = 0 + * 0 * N = N + * 0 * I = N + * N * n = N + * N * 0 = N + * N * N = N + * N * I = N + * I * n = I + * I * 0 = N + * I * N = N + * I * I = I + * + * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + */ +P.times = P.mul = function (y) { + var carry, e, i, k, r, rL, t, xdL, ydL, + x = this, + Ctor = x.constructor, + xd = x.d, + yd = (y = new Ctor(y)).d; - // If either is NaN, ±Infinity or ±0... - if (!xd || !xd[0] || !yd || !yd[0]) { + y.s *= x.s; - return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd + // If either is NaN, ±Infinity or ±0... + if (!xd || !xd[0] || !yd || !yd[0]) { - // Return NaN if either is NaN. - // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity. - ? NaN + return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd - // Return ±Infinity if either is ±Infinity. - // Return ±0 if either is ±0. - : !xd || !yd ? y.s / 0 : y.s * 0); - } + // Return NaN if either is NaN. + // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity. + ? NaN - e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE); - xdL = xd.length; - ydL = yd.length; + // Return ±Infinity if either is ±Infinity. + // Return ±0 if either is ±0. + : !xd || !yd ? y.s / 0 : y.s * 0); + } - // Ensure xd points to the longer array. - if (xdL < ydL) { - r = xd; - xd = yd; - yd = r; - rL = xdL; - xdL = ydL; - ydL = rL; - } + e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE); + xdL = xd.length; + ydL = yd.length; - // Initialise the result array with zeros. - r = []; - rL = xdL + ydL; - for (i = rL; i--;) r.push(0); + // Ensure xd points to the longer array. + if (xdL < ydL) { + r = xd; + xd = yd; + yd = r; + rL = xdL; + xdL = ydL; + ydL = rL; + } - // Multiply! - for (i = ydL; --i >= 0;) { - carry = 0; - for (k = xdL + i; k > i;) { - t = r[k] + yd[i] * xd[k - i - 1] + carry; - r[k--] = t % BASE | 0; - carry = t / BASE | 0; - } + // Initialise the result array with zeros. + r = []; + rL = xdL + ydL; + for (i = rL; i--;) r.push(0); - r[k] = (r[k] + carry) % BASE | 0; + // Multiply! + for (i = ydL; --i >= 0;) { + carry = 0; + for (k = xdL + i; k > i;) { + t = r[k] + yd[i] * xd[k - i - 1] + carry; + r[k--] = t % BASE | 0; + carry = t / BASE | 0; } - // Remove trailing zeros. - for (; !r[--rL];) r.pop(); - - if (carry) ++e; - else r.shift(); + r[k] = (r[k] + carry) % BASE | 0; + } - y.d = r; - y.e = getBase10Exponent(r, e); + // Remove trailing zeros. + for (; !r[--rL];) r.pop(); - return external ? finalise(y, Ctor.precision, Ctor.rounding) : y; - }; + if (carry) ++e; + else r.shift(); + y.d = r; + y.e = getBase10Exponent(r, e); - /* - * Return a string representing the value of this Decimal in base 2, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toBinary = function (sd, rm) { - return toStringBinary(this, 2, sd, rm); - }; + return external ? finalise(y, Ctor.precision, Ctor.rounding) : y; +}; - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp` - * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted. - * - * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toDecimalPlaces = P.toDP = function (dp, rm) { - var x = this, - Ctor = x.constructor; +/* + * Return a string representing the value of this Decimal in base 2, round to `sd` significant + * digits using rounding mode `rm`. + * + * If the optional `sd` argument is present then return binary exponential notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toBinary = function (sd, rm) { + return toStringBinary(this, 2, sd, rm); +}; - x = new Ctor(x); - if (dp === void 0) return x; - checkInt32(dp, 0, MAX_DIGITS); +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp` + * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted. + * + * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal. + * + * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toDecimalPlaces = P.toDP = function (dp, rm) { + var x = this, + Ctor = x.constructor; - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); + x = new Ctor(x); + if (dp === void 0) return x; - return finalise(x, dp + x.e + 1, rm); - }; + checkInt32(dp, 0, MAX_DIGITS); + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); - /* - * Return a string representing the value of this Decimal in exponential notation rounded to - * `dp` fixed decimal places using rounding mode `rounding`. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toExponential = function (dp, rm) { - var str, - x = this, - Ctor = x.constructor; + return finalise(x, dp + x.e + 1, rm); +}; - if (dp === void 0) { - str = finiteToString(x, true); - } else { - checkInt32(dp, 0, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); +/* + * Return a string representing the value of this Decimal in exponential notation rounded to + * `dp` fixed decimal places using rounding mode `rounding`. + * + * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toExponential = function (dp, rm) { + var str, + x = this, + Ctor = x.constructor; - x = finalise(new Ctor(x), dp + 1, rm); - str = finiteToString(x, true, dp + 1); - } + if (dp === void 0) { + str = finiteToString(x, true); + } else { + checkInt32(dp, 0, MAX_DIGITS); - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + x = finalise(new Ctor(x), dp + 1, rm); + str = finiteToString(x, true, dp + 1); + } - /* - * Return a string representing the value of this Decimal in normal (fixed-point) notation to - * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is - * omitted. - * - * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'. - * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'. - * (-0).toFixed(3) is '0.000'. - * (-0.5).toFixed(0) is '-0'. - * - */ - P.toFixed = function (dp, rm) { - var str, y, - x = this, - Ctor = x.constructor; + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - if (dp === void 0) { - str = finiteToString(x); - } else { - checkInt32(dp, 0, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); +/* + * Return a string representing the value of this Decimal in normal (fixed-point) notation to + * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is + * omitted. + * + * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'. + * + * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'. + * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'. + * (-0).toFixed(3) is '0.000'. + * (-0.5).toFixed(0) is '-0'. + * + */ +P.toFixed = function (dp, rm) { + var str, y, + x = this, + Ctor = x.constructor; - y = finalise(new Ctor(x), dp + x.e + 1, rm); - str = finiteToString(y, false, dp + y.e + 1); - } + if (dp === void 0) { + str = finiteToString(x); + } else { + checkInt32(dp, 0, MAX_DIGITS); - // To determine whether to add the minus sign look at the value before it was rounded, - // i.e. look at `x` rather than `y`. - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + y = finalise(new Ctor(x), dp + x.e + 1, rm); + str = finiteToString(y, false, dp + y.e + 1); + } - /* - * Return an array representing the value of this Decimal as a simple fraction with an integer - * numerator and an integer denominator. - * - * The denominator will be a positive non-zero value less than or equal to the specified maximum - * denominator. If a maximum denominator is not specified, the denominator will be the lowest - * value necessary to represent the number exactly. - * - * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity. - * - */ - P.toFraction = function (maxD) { - var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r, - x = this, - xd = x.d, - Ctor = x.constructor; + // To determine whether to add the minus sign look at the value before it was rounded, + // i.e. look at `x` rather than `y`. + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - if (!xd) return new Ctor(x); - n1 = d0 = new Ctor(1); - d1 = n0 = new Ctor(0); +/* + * Return an array representing the value of this Decimal as a simple fraction with an integer + * numerator and an integer denominator. + * + * The denominator will be a positive non-zero value less than or equal to the specified maximum + * denominator. If a maximum denominator is not specified, the denominator will be the lowest + * value necessary to represent the number exactly. + * + * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity. + * + */ +P.toFraction = function (maxD) { + var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r, + x = this, + xd = x.d, + Ctor = x.constructor; - d = new Ctor(d1); - e = d.e = getPrecision(xd) - x.e - 1; - k = e % LOG_BASE; - d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k); + if (!xd) return new Ctor(x); - if (maxD == null) { + n1 = d0 = new Ctor(1); + d1 = n0 = new Ctor(0); - // d is 10**e, the minimum max-denominator needed. - maxD = e > 0 ? d : n1; - } else { - n = new Ctor(maxD); - if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n); - maxD = n.gt(d) ? (e > 0 ? d : n1) : n; - } + d = new Ctor(d1); + e = d.e = getPrecision(xd) - x.e - 1; + k = e % LOG_BASE; + d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k); - external = false; - n = new Ctor(digitsToString(xd)); - pr = Ctor.precision; - Ctor.precision = e = xd.length * LOG_BASE * 2; - - for (;;) { - q = divide(n, d, 0, 1, 1); - d2 = d0.plus(q.times(d1)); - if (d2.cmp(maxD) == 1) break; - d0 = d1; - d1 = d2; - d2 = n1; - n1 = n0.plus(q.times(d2)); - n0 = d2; - d2 = d; - d = n.minus(q.times(d2)); - n = d2; - } - - d2 = divide(maxD.minus(d0), d1, 0, 1, 1); - n0 = n0.plus(d2.times(n1)); - d0 = d0.plus(d2.times(d1)); - n0.s = n1.s = x.s; - - // Determine which fraction is closer to x, n0/d0 or n1/d1? - r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 - ? [n1, d1] : [n0, d0]; + if (maxD == null) { - Ctor.precision = pr; - external = true; + // d is 10**e, the minimum max-denominator needed. + maxD = e > 0 ? d : n1; + } else { + n = new Ctor(maxD); + if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n); + maxD = n.gt(d) ? (e > 0 ? d : n1) : n; + } + + external = false; + n = new Ctor(digitsToString(xd)); + pr = Ctor.precision; + Ctor.precision = e = xd.length * LOG_BASE * 2; + + for (;;) { + q = divide(n, d, 0, 1, 1); + d2 = d0.plus(q.times(d1)); + if (d2.cmp(maxD) == 1) break; + d0 = d1; + d1 = d2; + d2 = n1; + n1 = n0.plus(q.times(d2)); + n0 = d2; + d2 = d; + d = n.minus(q.times(d2)); + n = d2; + } + + d2 = divide(maxD.minus(d0), d1, 0, 1, 1); + n0 = n0.plus(d2.times(n1)); + d0 = d0.plus(d2.times(d1)); + n0.s = n1.s = x.s; + + // Determine which fraction is closer to x, n0/d0 or n1/d1? + r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 + ? [n1, d1] : [n0, d0]; + + Ctor.precision = pr; + external = true; - return r; - }; + return r; +}; - /* - * Return a string representing the value of this Decimal in base 16, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toHexadecimal = P.toHex = function (sd, rm) { - return toStringBinary(this, 16, sd, rm); - }; +/* + * Return a string representing the value of this Decimal in base 16, round to `sd` significant + * digits using rounding mode `rm`. + * + * If the optional `sd` argument is present then return binary exponential notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toHexadecimal = P.toHex = function (sd, rm) { + return toStringBinary(this, 16, sd, rm); +}; - /* - * Returns a new Decimal whose value is the nearest multiple of the magnitude of `y` to the value - * of this Decimal. - * - * If the value of this Decimal is equidistant from two multiples of `y`, the rounding mode `rm`, - * or `Decimal.rounding` if `rm` is omitted, determines the direction of the nearest multiple. - * - * In the context of this method, rounding mode 4 (ROUND_HALF_UP) is the same as rounding mode 0 - * (ROUND_UP), and so on. - * - * The return value will always have the same sign as this Decimal, unless either this Decimal - * or `y` is NaN, in which case the return value will be also be NaN. - * - * The return value is not affected by the value of `precision`. - * - * y {number|string|Decimal} The magnitude to round to a multiple of. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toNearest() rounding mode not an integer: {rm}' - * 'toNearest() rounding mode out of range: {rm}' - * - */ - P.toNearest = function (y, rm) { - var x = this, - Ctor = x.constructor; +/* + * Returns a new Decimal whose value is the nearest multiple of the magnitude of `y` to the value + * of this Decimal. + * + * If the value of this Decimal is equidistant from two multiples of `y`, the rounding mode `rm`, + * or `Decimal.rounding` if `rm` is omitted, determines the direction of the nearest multiple. + * + * In the context of this method, rounding mode 4 (ROUND_HALF_UP) is the same as rounding mode 0 + * (ROUND_UP), and so on. + * + * The return value will always have the same sign as this Decimal, unless either this Decimal + * or `y` is NaN, in which case the return value will be also be NaN. + * + * The return value is not affected by the value of `precision`. + * + * y {number|string|Decimal} The magnitude to round to a multiple of. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + * 'toNearest() rounding mode not an integer: {rm}' + * 'toNearest() rounding mode out of range: {rm}' + * + */ +P.toNearest = function (y, rm) { + var x = this, + Ctor = x.constructor; - x = new Ctor(x); + x = new Ctor(x); - if (y == null) { + if (y == null) { - // If x is not finite, return x. - if (!x.d) return x; + // If x is not finite, return x. + if (!x.d) return x; - y = new Ctor(1); - rm = Ctor.rounding; - } else { - y = new Ctor(y); - if (rm !== void 0) checkInt32(rm, 0, 8); + y = new Ctor(1); + rm = Ctor.rounding; + } else { + y = new Ctor(y); + if (rm !== void 0) checkInt32(rm, 0, 8); - // If x is not finite, return x if y is not NaN, else NaN. - if (!x.d) return y.s ? x : y; + // If x is not finite, return x if y is not NaN, else NaN. + if (!x.d) return y.s ? x : y; - // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN. - if (!y.d) { - if (y.s) y.s = x.s; - return y; - } + // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN. + if (!y.d) { + if (y.s) y.s = x.s; + return y; } + } - // If y is not zero, calculate the nearest multiple of y to x. - if (y.d[0]) { - external = false; - if (rm < 4) rm = [4, 5, 7, 8][rm]; - x = divide(x, y, 0, rm, 1).times(y); - external = true; - finalise(x); + // If y is not zero, calculate the nearest multiple of y to x. + if (y.d[0]) { + external = false; + if (rm < 4) rm = [4, 5, 7, 8][rm]; + x = divide(x, y, 0, rm, 1).times(y); + external = true; + finalise(x); - // If y is zero, return zero with the sign of x. - } else { - y.s = x.s; - x = y; - } + // If y is zero, return zero with the sign of x. + } else { + y.s = x.s; + x = y; + } - return x; - }; + return x; +}; - /* - * Return the value of this Decimal converted to a number primitive. - * Zero keeps its sign. - * - */ - P.toNumber = function () { - return +this; - }; +/* + * Return the value of this Decimal converted to a number primitive. + * Zero keeps its sign. + * + */ +P.toNumber = function () { + return +this; +}; - /* - * Return a string representing the value of this Decimal in base 8, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toOctal = function (sd, rm) { - return toStringBinary(this, 8, sd, rm); - }; +/* + * Return a string representing the value of this Decimal in base 8, round to `sd` significant + * digits using rounding mode `rm`. + * + * If the optional `sd` argument is present then return binary exponential notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toOctal = function (sd, rm) { + return toStringBinary(this, 8, sd, rm); +}; - /* - * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded - * to `precision` significant digits using rounding mode `rounding`. - * - * ECMAScript compliant. - * - * pow(x, NaN) = NaN - * pow(x, ±0) = 1 - - * pow(NaN, non-zero) = NaN - * pow(abs(x) > 1, +Infinity) = +Infinity - * pow(abs(x) > 1, -Infinity) = +0 - * pow(abs(x) == 1, ±Infinity) = NaN - * pow(abs(x) < 1, +Infinity) = +0 - * pow(abs(x) < 1, -Infinity) = +Infinity - * pow(+Infinity, y > 0) = +Infinity - * pow(+Infinity, y < 0) = +0 - * pow(-Infinity, odd integer > 0) = -Infinity - * pow(-Infinity, even integer > 0) = +Infinity - * pow(-Infinity, odd integer < 0) = -0 - * pow(-Infinity, even integer < 0) = +0 - * pow(+0, y > 0) = +0 - * pow(+0, y < 0) = +Infinity - * pow(-0, odd integer > 0) = -0 - * pow(-0, even integer > 0) = +0 - * pow(-0, odd integer < 0) = -Infinity - * pow(-0, even integer < 0) = +Infinity - * pow(finite x < 0, finite non-integer) = NaN - * - * For non-integer or very large exponents pow(x, y) is calculated using - * - * x^y = exp(y*ln(x)) - * - * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the - * probability of an incorrectly rounded result - * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14 - * i.e. 1 in 250,000,000,000,000 - * - * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place). - * - * y {number|string|Decimal} The power to which to raise this Decimal. - * - */ - P.toPower = P.pow = function (y) { - var e, k, pr, r, rm, s, - x = this, - Ctor = x.constructor, - yn = +(y = new Ctor(y)); +/* + * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded + * to `precision` significant digits using rounding mode `rounding`. + * + * ECMAScript compliant. + * + * pow(x, NaN) = NaN + * pow(x, ±0) = 1 + + * pow(NaN, non-zero) = NaN + * pow(abs(x) > 1, +Infinity) = +Infinity + * pow(abs(x) > 1, -Infinity) = +0 + * pow(abs(x) == 1, ±Infinity) = NaN + * pow(abs(x) < 1, +Infinity) = +0 + * pow(abs(x) < 1, -Infinity) = +Infinity + * pow(+Infinity, y > 0) = +Infinity + * pow(+Infinity, y < 0) = +0 + * pow(-Infinity, odd integer > 0) = -Infinity + * pow(-Infinity, even integer > 0) = +Infinity + * pow(-Infinity, odd integer < 0) = -0 + * pow(-Infinity, even integer < 0) = +0 + * pow(+0, y > 0) = +0 + * pow(+0, y < 0) = +Infinity + * pow(-0, odd integer > 0) = -0 + * pow(-0, even integer > 0) = +0 + * pow(-0, odd integer < 0) = -Infinity + * pow(-0, even integer < 0) = +Infinity + * pow(finite x < 0, finite non-integer) = NaN + * + * For non-integer or very large exponents pow(x, y) is calculated using + * + * x^y = exp(y*ln(x)) + * + * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the + * probability of an incorrectly rounded result + * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14 + * i.e. 1 in 250,000,000,000,000 + * + * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place). + * + * y {number|string|Decimal} The power to which to raise this Decimal. + * + */ +P.toPower = P.pow = function (y) { + var e, k, pr, r, rm, s, + x = this, + Ctor = x.constructor, + yn = +(y = new Ctor(y)); - // Either ±Infinity, NaN or ±0? - if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn)); + // Either ±Infinity, NaN or ±0? + if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn)); - x = new Ctor(x); + x = new Ctor(x); - if (x.eq(1)) return x; + if (x.eq(1)) return x; - pr = Ctor.precision; - rm = Ctor.rounding; + pr = Ctor.precision; + rm = Ctor.rounding; - if (y.eq(1)) return finalise(x, pr, rm); + if (y.eq(1)) return finalise(x, pr, rm); - // y exponent - e = mathfloor(y.e / LOG_BASE); + // y exponent + e = mathfloor(y.e / LOG_BASE); - // If y is a small integer use the 'exponentiation by squaring' algorithm. - if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) { - r = intPow(Ctor, x, k, pr); - return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm); - } + // If y is a small integer use the 'exponentiation by squaring' algorithm. + if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) { + r = intPow(Ctor, x, k, pr); + return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm); + } - s = x.s; + s = x.s; - // if x is negative - if (s < 0) { + // if x is negative + if (s < 0) { - // if y is not an integer - if (e < y.d.length - 1) return new Ctor(NaN); + // if y is not an integer + if (e < y.d.length - 1) return new Ctor(NaN); - // Result is positive if x is negative and the last digit of integer y is even. - if ((y.d[e] & 1) == 0) s = 1; + // Result is positive if x is negative and the last digit of integer y is even. + if ((y.d[e] & 1) == 0) s = 1; - // if x.eq(-1) - if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) { - x.s = s; - return x; - } + // if x.eq(-1) + if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) { + x.s = s; + return x; } + } - // Estimate result exponent. - // x^y = 10^e, where e = y * log10(x) - // log10(x) = log10(x_significand) + x_exponent - // log10(x_significand) = ln(x_significand) / ln(10) - k = mathpow(+x, yn); - e = k == 0 || !isFinite(k) - ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) - : new Ctor(k + '').e; + // Estimate result exponent. + // x^y = 10^e, where e = y * log10(x) + // log10(x) = log10(x_significand) + x_exponent + // log10(x_significand) = ln(x_significand) / ln(10) + k = mathpow(+x, yn); + e = k == 0 || !isFinite(k) + ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) + : new Ctor(k + '').e; - // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1. + // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1. - // Overflow/underflow? - if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0); + // Overflow/underflow? + if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0); - external = false; - Ctor.rounding = x.s = 1; + external = false; + Ctor.rounding = x.s = 1; - // Estimate the extra guard digits needed to ensure five correct rounding digits from - // naturalLogarithm(x). Example of failure without these extra digits (precision: 10): - // new Decimal(2.32456).pow('2087987436534566.46411') - // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815 - k = Math.min(12, (e + '').length); + // Estimate the extra guard digits needed to ensure five correct rounding digits from + // naturalLogarithm(x). Example of failure without these extra digits (precision: 10): + // new Decimal(2.32456).pow('2087987436534566.46411') + // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815 + k = Math.min(12, (e + '').length); - // r = x^y = exp(y*ln(x)) - r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr); + // r = x^y = exp(y*ln(x)) + r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr); - // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40) - if (r.d) { + // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40) + if (r.d) { - // Truncate to the required precision plus five rounding digits. - r = finalise(r, pr + 5, 1); + // Truncate to the required precision plus five rounding digits. + r = finalise(r, pr + 5, 1); - // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate - // the result. - if (checkRoundingDigits(r.d, pr, rm)) { - e = pr + 10; + // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate + // the result. + if (checkRoundingDigits(r.d, pr, rm)) { + e = pr + 10; - // Truncate to the increased precision plus five rounding digits. - r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1); + // Truncate to the increased precision plus five rounding digits. + r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1); - // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9). - if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } + // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9). + if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) { + r = finalise(r, pr + 1, 0); } } + } - r.s = s; - external = true; - Ctor.rounding = rm; - - return finalise(r, pr, rm); - }; + r.s = s; + external = true; + Ctor.rounding = rm; + return finalise(r, pr, rm); +}; - /* - * Return a string representing the value of this Decimal rounded to `sd` significant digits - * using rounding mode `rounding`. - * - * Return exponential notation if `sd` is less than the number of digits necessary to represent - * the integer part of the value in normal notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toPrecision = function (sd, rm) { - var str, - x = this, - Ctor = x.constructor; - if (sd === void 0) { - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - } else { - checkInt32(sd, 1, MAX_DIGITS); +/* + * Return a string representing the value of this Decimal rounded to `sd` significant digits + * using rounding mode `rounding`. + * + * Return exponential notation if `sd` is less than the number of digits necessary to represent + * the integer part of the value in normal notation. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + */ +P.toPrecision = function (sd, rm) { + var str, + x = this, + Ctor = x.constructor; - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); + if (sd === void 0) { + str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); + } else { + checkInt32(sd, 1, MAX_DIGITS); - x = finalise(new Ctor(x), sd, rm); - str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd); - } + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; + x = finalise(new Ctor(x), sd, rm); + str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd); + } + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd` - * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if - * omitted. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toSD() digits out of range: {sd}' - * 'toSD() digits not an integer: {sd}' - * 'toSD() rounding mode not an integer: {rm}' - * 'toSD() rounding mode out of range: {rm}' - * - */ - P.toSignificantDigits = P.toSD = function (sd, rm) { - var x = this, - Ctor = x.constructor; - if (sd === void 0) { - sd = Ctor.precision; - rm = Ctor.rounding; - } else { - checkInt32(sd, 1, MAX_DIGITS); +/* + * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd` + * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if + * omitted. + * + * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. + * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. + * + * 'toSD() digits out of range: {sd}' + * 'toSD() digits not an integer: {sd}' + * 'toSD() rounding mode not an integer: {rm}' + * 'toSD() rounding mode out of range: {rm}' + * + */ +P.toSignificantDigits = P.toSD = function (sd, rm) { + var x = this, + Ctor = x.constructor; - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - } + if (sd === void 0) { + sd = Ctor.precision; + rm = Ctor.rounding; + } else { + checkInt32(sd, 1, MAX_DIGITS); - return finalise(new Ctor(x), sd, rm); - }; + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + } + return finalise(new Ctor(x), sd, rm); +}; - /* - * Return a string representing the value of this Decimal. - * - * Return exponential notation if this Decimal has a positive exponent equal to or greater than - * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`. - * - */ - P.toString = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; +/* + * Return a string representing the value of this Decimal. + * + * Return exponential notation if this Decimal has a positive exponent equal to or greater than + * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`. + * + */ +P.toString = function () { + var x = this, + Ctor = x.constructor, + str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); + return x.isNeg() && !x.isZero() ? '-' + str : str; +}; - /* - * Return a new Decimal whose value is the value of this Decimal truncated to a whole number. - * - */ - P.truncated = P.trunc = function () { - return finalise(new this.constructor(this), this.e + 1, 1); - }; +/* + * Return a new Decimal whose value is the value of this Decimal truncated to a whole number. + * + */ +P.truncated = P.trunc = function () { + return finalise(new this.constructor(this), this.e + 1, 1); +}; - /* - * Return a string representing the value of this Decimal. - * Unlike `toString`, negative zero will include the minus sign. - * - */ - P.valueOf = P.toJSON = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - return x.isNeg() ? '-' + str : str; - }; +/* + * Return a string representing the value of this Decimal. + * Unlike `toString`, negative zero will include the minus sign. + * + */ +P.valueOf = P.toJSON = function () { + var x = this, + Ctor = x.constructor, + str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); + return x.isNeg() ? '-' + str : str; +}; - /* - // Add aliases to match BigDecimal method names. - // P.add = P.plus; - P.subtract = P.minus; - P.multiply = P.times; - P.divide = P.div; - P.remainder = P.mod; - P.compareTo = P.cmp; - P.negate = P.neg; - */ +/* +// Add aliases to match BigDecimal method names. +// P.add = P.plus; +P.subtract = P.minus; +P.multiply = P.times; +P.divide = P.div; +P.remainder = P.mod; +P.compareTo = P.cmp; +P.negate = P.neg; + */ - // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers. +// Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers. - /* - * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower, - * finiteToString, naturalExponential, naturalLogarithm - * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest, - * P.toPrecision, P.toSignificantDigits, toStringBinary, random - * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm - * convertBase toStringBinary, parseOther - * cos P.cos - * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy, - * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction, - * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm, - * taylorSeries, atan2, parseOther - * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh, - * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus, - * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot, - * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed, - * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits, - * P.truncated, divide, getLn10, getPi, naturalExponential, - * naturalLogarithm, ceil, floor, round, trunc - * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf, - * toStringBinary - * getBase10Exponent P.minus, P.plus, P.times, parseOther - * getLn10 P.logarithm, naturalLogarithm - * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2 - * getPrecision P.precision, P.toFraction - * getZeroString digitsToString, finiteToString - * intPow P.toPower, parseOther - * isOdd toLessThanHalfPi - * maxOrMin max, min - * naturalExponential P.naturalExponential, P.toPower - * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm, - * P.toPower, naturalExponential - * nonFiniteToString finiteToString, toStringBinary - * parseDecimal Decimal - * parseOther Decimal - * sin P.sin - * taylorSeries P.cosh, P.sinh, cos, sin - * toLessThanHalfPi P.cos, P.sin - * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal - * truncate intPow - * - * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi, - * naturalLogarithm, config, parseOther, random, Decimal - */ +/* + * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower, + * finiteToString, naturalExponential, naturalLogarithm + * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest, + * P.toPrecision, P.toSignificantDigits, toStringBinary, random + * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm + * convertBase toStringBinary, parseOther + * cos P.cos + * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy, + * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction, + * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm, + * taylorSeries, atan2, parseOther + * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh, + * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus, + * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot, + * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed, + * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits, + * P.truncated, divide, getLn10, getPi, naturalExponential, + * naturalLogarithm, ceil, floor, round, trunc + * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf, + * toStringBinary + * getBase10Exponent P.minus, P.plus, P.times, parseOther + * getLn10 P.logarithm, naturalLogarithm + * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2 + * getPrecision P.precision, P.toFraction + * getZeroString digitsToString, finiteToString + * intPow P.toPower, parseOther + * isOdd toLessThanHalfPi + * maxOrMin max, min + * naturalExponential P.naturalExponential, P.toPower + * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm, + * P.toPower, naturalExponential + * nonFiniteToString finiteToString, toStringBinary + * parseDecimal Decimal + * parseOther Decimal + * sin P.sin + * taylorSeries P.cosh, P.sinh, cos, sin + * toLessThanHalfPi P.cos, P.sin + * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal + * truncate intPow + * + * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi, + * naturalLogarithm, config, parseOther, random, Decimal + */ - function digitsToString(d) { - var i, k, ws, - indexOfLastWord = d.length - 1, - str = '', - w = d[0]; - if (indexOfLastWord > 0) { - str += w; - for (i = 1; i < indexOfLastWord; i++) { - ws = d[i] + ''; - k = LOG_BASE - ws.length; - if (k) str += getZeroString(k); - str += ws; - } +function digitsToString(d) { + var i, k, ws, + indexOfLastWord = d.length - 1, + str = '', + w = d[0]; - w = d[i]; - ws = w + ''; + if (indexOfLastWord > 0) { + str += w; + for (i = 1; i < indexOfLastWord; i++) { + ws = d[i] + ''; k = LOG_BASE - ws.length; if (k) str += getZeroString(k); - } else if (w === 0) { - return '0'; + str += ws; } - // Remove trailing zeros of last w. - for (; w % 10 === 0;) w /= 10; - - return str + w; + w = d[i]; + ws = w + ''; + k = LOG_BASE - ws.length; + if (k) str += getZeroString(k); + } else if (w === 0) { + return '0'; } + // Remove trailing zeros of last w. + for (; w % 10 === 0;) w /= 10; - function checkInt32(i, min, max) { - if (i !== ~~i || i < min || i > max) { - throw Error(invalidArgument + i); - } + return str + w; +} + + +function checkInt32(i, min, max) { + if (i !== ~~i || i < min || i > max) { + throw Error(invalidArgument + i); } +} - /* - * Check 5 rounding digits if `repeating` is null, 4 otherwise. - * `repeating == null` if caller is `log` or `pow`, - * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`. - */ - function checkRoundingDigits(d, i, rm, repeating) { - var di, k, r, rd; +/* + * Check 5 rounding digits if `repeating` is null, 4 otherwise. + * `repeating == null` if caller is `log` or `pow`, + * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`. + */ +function checkRoundingDigits(d, i, rm, repeating) { + var di, k, r, rd; - // Get the length of the first word of the array d. - for (k = d[0]; k >= 10; k /= 10) --i; + // Get the length of the first word of the array d. + for (k = d[0]; k >= 10; k /= 10) --i; - // Is the rounding digit in the first word of d? - if (--i < 0) { - i += LOG_BASE; - di = 0; - } else { - di = Math.ceil((i + 1) / LOG_BASE); - i %= LOG_BASE; - } + // Is the rounding digit in the first word of d? + if (--i < 0) { + i += LOG_BASE; + di = 0; + } else { + di = Math.ceil((i + 1) / LOG_BASE); + i %= LOG_BASE; + } - // i is the index (0 - 6) of the rounding digit. - // E.g. if within the word 3487563 the first rounding digit is 5, - // then i = 4, k = 1000, rd = 3487563 % 1000 = 563 - k = mathpow(10, LOG_BASE - i); - rd = d[di] % k | 0; + // i is the index (0 - 6) of the rounding digit. + // E.g. if within the word 3487563 the first rounding digit is 5, + // then i = 4, k = 1000, rd = 3487563 % 1000 = 563 + k = mathpow(10, LOG_BASE - i); + rd = d[di] % k | 0; - if (repeating == null) { - if (i < 3) { - if (i == 0) rd = rd / 100 | 0; - else if (i == 1) rd = rd / 10 | 0; - r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0; - } else { - r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) && - (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 || - (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0; - } + if (repeating == null) { + if (i < 3) { + if (i == 0) rd = rd / 100 | 0; + else if (i == 1) rd = rd / 10 | 0; + r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0; } else { - if (i < 4) { - if (i == 0) rd = rd / 1000 | 0; - else if (i == 1) rd = rd / 100 | 0; - else if (i == 2) rd = rd / 10 | 0; - r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999; - } else { - r = ((repeating || rm < 4) && rd + 1 == k || - (!repeating && rm > 3) && rd + 1 == k / 2) && - (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1; - } + r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) && + (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 || + (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0; + } + } else { + if (i < 4) { + if (i == 0) rd = rd / 1000 | 0; + else if (i == 1) rd = rd / 100 | 0; + else if (i == 2) rd = rd / 10 | 0; + r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999; + } else { + r = ((repeating || rm < 4) && rd + 1 == k || + (!repeating && rm > 3) && rd + 1 == k / 2) && + (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1; } - - return r; } + return r; +} - // Convert string of `baseIn` to an array of numbers of `baseOut`. - // Eg. convertBase('255', 10, 16) returns [15, 15]. - // Eg. convertBase('ff', 16, 10) returns [2, 5, 5]. - function convertBase(str, baseIn, baseOut) { - var j, - arr = [0], - arrL, - i = 0, - strL = str.length; - for (; i < strL;) { - for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn; - arr[0] += NUMERALS.indexOf(str.charAt(i++)); - for (j = 0; j < arr.length; j++) { - if (arr[j] > baseOut - 1) { - if (arr[j + 1] === void 0) arr[j + 1] = 0; - arr[j + 1] += arr[j] / baseOut | 0; - arr[j] %= baseOut; - } +// Convert string of `baseIn` to an array of numbers of `baseOut`. +// Eg. convertBase('255', 10, 16) returns [15, 15]. +// Eg. convertBase('ff', 16, 10) returns [2, 5, 5]. +function convertBase(str, baseIn, baseOut) { + var j, + arr = [0], + arrL, + i = 0, + strL = str.length; + + for (; i < strL;) { + for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn; + arr[0] += NUMERALS.indexOf(str.charAt(i++)); + for (j = 0; j < arr.length; j++) { + if (arr[j] > baseOut - 1) { + if (arr[j + 1] === void 0) arr[j + 1] = 0; + arr[j + 1] += arr[j] / baseOut | 0; + arr[j] %= baseOut; } } + } + + return arr.reverse(); +} + + +/* + * cos(x) = 1 - x^2/2! + x^4/4! - ... + * |x| < pi/2 + * + */ +function cosine(Ctor, x) { + var k, y, + len = x.d.length; + + // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1 + // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1 - return arr.reverse(); + // Estimate the optimum number of times to use the argument reduction. + if (len < 32) { + k = Math.ceil(len / 3); + y = Math.pow(4, -k).toString(); + } else { + k = 16; + y = '2.3283064365386962890625e-10'; } + Ctor.precision += k; - /* - * cos(x) = 1 - x^2/2! + x^4/4! - ... - * |x| < pi/2 - * - */ - function cosine(Ctor, x) { - var k, y, - len = x.d.length; + x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)); - // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1 - // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1 + // Reverse argument reduction + for (var i = k; i--;) { + var cos2x = x.times(x); + x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1); + } - // Estimate the optimum number of times to use the argument reduction. - if (len < 32) { - k = Math.ceil(len / 3); - y = Math.pow(4, -k).toString(); - } else { - k = 16; - y = '2.3283064365386962890625e-10'; - } + Ctor.precision -= k; - Ctor.precision += k; + return x; +} - x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)); - // Reverse argument reduction - for (var i = k; i--;) { - var cos2x = x.times(x); - x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1); +/* + * Perform division in the specified base. + */ +var divide = (function () { + + // Assumes non-zero x and k, and hence non-zero result. + function multiplyInteger(x, k, base) { + var temp, + carry = 0, + i = x.length; + + for (x = x.slice(); i--;) { + temp = x[i] * k + carry; + x[i] = temp % base | 0; + carry = temp / base | 0; } - Ctor.precision -= k; + if (carry) x.unshift(carry); return x; } + function compare(a, b, aL, bL) { + var i, r; - /* - * Perform division in the specified base. - */ - var divide = (function () { - - // Assumes non-zero x and k, and hence non-zero result. - function multiplyInteger(x, k, base) { - var temp, - carry = 0, - i = x.length; - - for (x = x.slice(); i--;) { - temp = x[i] * k + carry; - x[i] = temp % base | 0; - carry = temp / base | 0; + if (aL != bL) { + r = aL > bL ? 1 : -1; + } else { + for (i = r = 0; i < aL; i++) { + if (a[i] != b[i]) { + r = a[i] > b[i] ? 1 : -1; + break; + } } + } - if (carry) x.unshift(carry); + return r; + } - return x; + function subtract(a, b, aL, base) { + var i = 0; + + // Subtract b from a. + for (; aL--;) { + a[aL] -= i; + i = a[aL] < b[aL] ? 1 : 0; + a[aL] = i * base + a[aL] - b[aL]; } - function compare(a, b, aL, bL) { - var i, r; + // Remove leading zeros. + for (; !a[0] && a.length > 1;) a.shift(); + } - if (aL != bL) { - r = aL > bL ? 1 : -1; - } else { - for (i = r = 0; i < aL; i++) { - if (a[i] != b[i]) { - r = a[i] > b[i] ? 1 : -1; - break; - } - } - } + return function (x, y, pr, rm, dp, base) { + var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, + yL, yz, + Ctor = x.constructor, + sign = x.s == y.s ? 1 : -1, + xd = x.d, + yd = y.d; - return r; - } + // Either NaN, Infinity or 0? + if (!xd || !xd[0] || !yd || !yd[0]) { - function subtract(a, b, aL, base) { - var i = 0; + return new Ctor(// Return NaN if either NaN, or both Infinity or 0. + !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN : - // Subtract b from a. - for (; aL--;) { - a[aL] -= i; - i = a[aL] < b[aL] ? 1 : 0; - a[aL] = i * base + a[aL] - b[aL]; - } + // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0. + xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0); + } - // Remove leading zeros. - for (; !a[0] && a.length > 1;) a.shift(); + if (base) { + logBase = 1; + e = x.e - y.e; + } else { + base = BASE; + logBase = LOG_BASE; + e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase); } - return function (x, y, pr, rm, dp, base) { - var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, - yL, yz, - Ctor = x.constructor, - sign = x.s == y.s ? 1 : -1, - xd = x.d, - yd = y.d; + yL = yd.length; + xL = xd.length; + q = new Ctor(sign); + qd = q.d = []; - // Either NaN, Infinity or 0? - if (!xd || !xd[0] || !yd || !yd[0]) { + // Result exponent may be one less than e. + // The digit array of a Decimal from toStringBinary may have trailing zeros. + for (i = 0; yd[i] == (xd[i] || 0); i++); - return new Ctor(// Return NaN if either NaN, or both Infinity or 0. - !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN : + if (yd[i] > (xd[i] || 0)) e--; - // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0. - xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0); - } + if (pr == null) { + sd = pr = Ctor.precision; + rm = Ctor.rounding; + } else if (dp) { + sd = pr + (x.e - y.e) + 1; + } else { + sd = pr; + } - if (base) { - logBase = 1; - e = x.e - y.e; - } else { - base = BASE; - logBase = LOG_BASE; - e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase); - } + if (sd < 0) { + qd.push(1); + more = true; + } else { - yL = yd.length; - xL = xd.length; - q = new Ctor(sign); - qd = q.d = []; + // Convert precision in number of base 10 digits to base 1e7 digits. + sd = sd / logBase + 2 | 0; + i = 0; - // Result exponent may be one less than e. - // The digit array of a Decimal from toStringBinary may have trailing zeros. - for (i = 0; yd[i] == (xd[i] || 0); i++); + // divisor < 1e7 + if (yL == 1) { + k = 0; + yd = yd[0]; + sd++; - if (yd[i] > (xd[i] || 0)) e--; + // k is the carry. + for (; (i < xL || k) && sd--; i++) { + t = k * base + (xd[i] || 0); + qd[i] = t / yd | 0; + k = t % yd | 0; + } - if (pr == null) { - sd = pr = Ctor.precision; - rm = Ctor.rounding; - } else if (dp) { - sd = pr + (x.e - y.e) + 1; - } else { - sd = pr; - } + more = k || i < xL; - if (sd < 0) { - qd.push(1); - more = true; + // divisor >= 1e7 } else { - // Convert precision in number of base 10 digits to base 1e7 digits. - sd = sd / logBase + 2 | 0; - i = 0; + // Normalise xd and yd so highest order digit of yd is >= base/2 + k = base / (yd[0] + 1) | 0; - // divisor < 1e7 - if (yL == 1) { - k = 0; - yd = yd[0]; - sd++; - - // k is the carry. - for (; (i < xL || k) && sd--; i++) { - t = k * base + (xd[i] || 0); - qd[i] = t / yd | 0; - k = t % yd | 0; - } + if (k > 1) { + yd = multiplyInteger(yd, k, base); + xd = multiplyInteger(xd, k, base); + yL = yd.length; + xL = xd.length; + } - more = k || i < xL; + xi = yL; + rem = xd.slice(0, yL); + remL = rem.length; - // divisor >= 1e7 - } else { + // Add zeros to make remainder as long as divisor. + for (; remL < yL;) rem[remL++] = 0; - // Normalise xd and yd so highest order digit of yd is >= base/2 - k = base / (yd[0] + 1) | 0; + yz = yd.slice(); + yz.unshift(0); + yd0 = yd[0]; - if (k > 1) { - yd = multiplyInteger(yd, k, base); - xd = multiplyInteger(xd, k, base); - yL = yd.length; - xL = xd.length; - } + if (yd[1] >= base / 2) ++yd0; - xi = yL; - rem = xd.slice(0, yL); - remL = rem.length; + do { + k = 0; - // Add zeros to make remainder as long as divisor. - for (; remL < yL;) rem[remL++] = 0; + // Compare divisor and remainder. + cmp = compare(yd, rem, yL, remL); - yz = yd.slice(); - yz.unshift(0); - yd0 = yd[0]; + // If divisor < remainder. + if (cmp < 0) { - if (yd[1] >= base / 2) ++yd0; + // Calculate trial digit, k. + rem0 = rem[0]; + if (yL != remL) rem0 = rem0 * base + (rem[1] || 0); - do { - k = 0; + // k will be how many times the divisor goes into the current remainder. + k = rem0 / yd0 | 0; - // Compare divisor and remainder. - cmp = compare(yd, rem, yL, remL); + // Algorithm: + // 1. product = divisor * trial digit (k) + // 2. if product > remainder: product -= divisor, k-- + // 3. remainder -= product + // 4. if product was < remainder at 2: + // 5. compare new remainder and divisor + // 6. If remainder > divisor: remainder -= divisor, k++ - // If divisor < remainder. - if (cmp < 0) { + if (k > 1) { + if (k >= base) k = base - 1; - // Calculate trial digit, k. - rem0 = rem[0]; - if (yL != remL) rem0 = rem0 * base + (rem[1] || 0); + // product = divisor * trial digit. + prod = multiplyInteger(yd, k, base); + prodL = prod.length; + remL = rem.length; - // k will be how many times the divisor goes into the current remainder. - k = rem0 / yd0 | 0; + // Compare product and remainder. + cmp = compare(prod, rem, prodL, remL); - // Algorithm: - // 1. product = divisor * trial digit (k) - // 2. if product > remainder: product -= divisor, k-- - // 3. remainder -= product - // 4. if product was < remainder at 2: - // 5. compare new remainder and divisor - // 6. If remainder > divisor: remainder -= divisor, k++ + // product > remainder. + if (cmp == 1) { + k--; - if (k > 1) { - if (k >= base) k = base - 1; + // Subtract divisor from product. + subtract(prod, yL < prodL ? yz : yd, prodL, base); + } + } else { - // product = divisor * trial digit. - prod = multiplyInteger(yd, k, base); - prodL = prod.length; - remL = rem.length; + // cmp is -1. + // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1 + // to avoid it. If k is 1 there is a need to compare yd and rem again below. + if (k == 0) cmp = k = 1; + prod = yd.slice(); + } - // Compare product and remainder. - cmp = compare(prod, rem, prodL, remL); + prodL = prod.length; + if (prodL < remL) prod.unshift(0); - // product > remainder. - if (cmp == 1) { - k--; + // Subtract product from remainder. + subtract(rem, prod, remL, base); - // Subtract divisor from product. - subtract(prod, yL < prodL ? yz : yd, prodL, base); - } - } else { + // If product was < previous remainder. + if (cmp == -1) { + remL = rem.length; - // cmp is -1. - // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1 - // to avoid it. If k is 1 there is a need to compare yd and rem again below. - if (k == 0) cmp = k = 1; - prod = yd.slice(); - } + // Compare divisor and new remainder. + cmp = compare(yd, rem, yL, remL); - prodL = prod.length; - if (prodL < remL) prod.unshift(0); + // If divisor < new remainder, subtract divisor from remainder. + if (cmp < 1) { + k++; - // Subtract product from remainder. - subtract(rem, prod, remL, base); + // Subtract divisor from remainder. + subtract(rem, yL < remL ? yz : yd, remL, base); + } + } - // If product was < previous remainder. - if (cmp == -1) { - remL = rem.length; + remL = rem.length; + } else if (cmp === 0) { + k++; + rem = [0]; + } // if cmp === 1, k will be 0 - // Compare divisor and new remainder. - cmp = compare(yd, rem, yL, remL); + // Add the next digit, k, to the result array. + qd[i++] = k; - // If divisor < new remainder, subtract divisor from remainder. - if (cmp < 1) { - k++; + // Update the remainder. + if (cmp && rem[0]) { + rem[remL++] = xd[xi] || 0; + } else { + rem = [xd[xi]]; + remL = 1; + } - // Subtract divisor from remainder. - subtract(rem, yL < remL ? yz : yd, remL, base); - } - } + } while ((xi++ < xL || rem[0] !== void 0) && sd--); - remL = rem.length; - } else if (cmp === 0) { - k++; - rem = [0]; - } // if cmp === 1, k will be 0 + more = rem[0] !== void 0; + } - // Add the next digit, k, to the result array. - qd[i++] = k; + // Leading zero? + if (!qd[0]) qd.shift(); + } - // Update the remainder. - if (cmp && rem[0]) { - rem[remL++] = xd[xi] || 0; - } else { - rem = [xd[xi]]; - remL = 1; - } + // logBase is 1 when divide is being used for base conversion. + if (logBase == 1) { + q.e = e; + inexact = more; + } else { - } while ((xi++ < xL || rem[0] !== void 0) && sd--); + // To calculate q.e, first get the number of digits of qd[0]. + for (i = 1, k = qd[0]; k >= 10; k /= 10) i++; + q.e = i + e * logBase - 1; - more = rem[0] !== void 0; - } + finalise(q, dp ? pr + q.e + 1 : pr, rm, more); + } - // Leading zero? - if (!qd[0]) qd.shift(); - } + return q; + }; +})(); - // logBase is 1 when divide is being used for base conversion. - if (logBase == 1) { - q.e = e; - inexact = more; - } else { - // To calculate q.e, first get the number of digits of qd[0]. - for (i = 1, k = qd[0]; k >= 10; k /= 10) i++; - q.e = i + e * logBase - 1; +/* + * Round `x` to `sd` significant digits using rounding mode `rm`. + * Check for over/under-flow. + */ + function finalise(x, sd, rm, isTruncated) { + var digits, i, j, k, rd, roundUp, w, xd, xdi, + Ctor = x.constructor; - finalise(q, dp ? pr + q.e + 1 : pr, rm, more); - } + // Don't round if sd is null or undefined. + out: if (sd != null) { + xd = x.d; - return q; - }; - })(); + // Infinity/NaN. + if (!xd) return x; + // rd: the rounding digit, i.e. the digit after the digit that may be rounded up. + // w: the word of xd containing rd, a base 1e7 number. + // xdi: the index of w within xd. + // digits: the number of digits of w. + // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if + // they had leading zeros) + // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero). - /* - * Round `x` to `sd` significant digits using rounding mode `rm`. - * Check for over/under-flow. - */ - function finalise(x, sd, rm, isTruncated) { - var digits, i, j, k, rd, roundUp, w, xd, xdi, - Ctor = x.constructor; - - // Don't round if sd is null or undefined. - out: if (sd != null) { - xd = x.d; - - // Infinity/NaN. - if (!xd) return x; - - // rd: the rounding digit, i.e. the digit after the digit that may be rounded up. - // w: the word of xd containing rd, a base 1e7 number. - // xdi: the index of w within xd. - // digits: the number of digits of w. - // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if - // they had leading zeros) - // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero). - - // Get the length of the first word of the digits array xd. - for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++; - i = sd - digits; - - // Is the rounding digit in the first word of xd? - if (i < 0) { - i += LOG_BASE; - j = sd; - w = xd[xdi = 0]; + // Get the length of the first word of the digits array xd. + for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++; + i = sd - digits; - // Get the rounding digit at index j of w. - rd = w / mathpow(10, digits - j - 1) % 10 | 0; - } else { - xdi = Math.ceil((i + 1) / LOG_BASE); - k = xd.length; - if (xdi >= k) { - if (isTruncated) { - - // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`. - for (; k++ <= xdi;) xd.push(0); - w = rd = 0; - digits = 1; - i %= LOG_BASE; - j = i - LOG_BASE + 1; - } else { - break out; - } + // Is the rounding digit in the first word of xd? + if (i < 0) { + i += LOG_BASE; + j = sd; + w = xd[xdi = 0]; + + // Get the rounding digit at index j of w. + rd = w / mathpow(10, digits - j - 1) % 10 | 0; + } else { + xdi = Math.ceil((i + 1) / LOG_BASE); + k = xd.length; + if (xdi >= k) { + if (isTruncated) { + + // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`. + for (; k++ <= xdi;) xd.push(0); + w = rd = 0; + digits = 1; + i %= LOG_BASE; + j = i - LOG_BASE + 1; } else { - w = k = xd[xdi]; + break out; + } + } else { + w = k = xd[xdi]; - // Get the number of digits of w. - for (digits = 1; k >= 10; k /= 10) digits++; + // Get the number of digits of w. + for (digits = 1; k >= 10; k /= 10) digits++; - // Get the index of rd within w. - i %= LOG_BASE; + // Get the index of rd within w. + i %= LOG_BASE; - // Get the index of rd within w, adjusted for leading zeros. - // The number of leading zeros of w is given by LOG_BASE - digits. - j = i - LOG_BASE + digits; + // Get the index of rd within w, adjusted for leading zeros. + // The number of leading zeros of w is given by LOG_BASE - digits. + j = i - LOG_BASE + digits; - // Get the rounding digit at index j of w. - rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0; - } + // Get the rounding digit at index j of w. + rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0; } + } - // Are there any non-zero digits after the rounding digit? - isTruncated = isTruncated || sd < 0 || - xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)); - - // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right - // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression - // will give 714. + // Are there any non-zero digits after the rounding digit? + isTruncated = isTruncated || sd < 0 || + xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)); - roundUp = rm < 4 - ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) - : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 && + // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right + // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression + // will give 714. - // Check whether the digit to the left of the rounding digit is odd. - ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 || - rm == (x.s < 0 ? 8 : 7)); + roundUp = rm < 4 + ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) + : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 && - if (sd < 1 || !xd[0]) { - xd.length = 0; - if (roundUp) { + // Check whether the digit to the left of the rounding digit is odd. + ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 || + rm == (x.s < 0 ? 8 : 7)); - // Convert sd to decimal places. - sd -= x.e + 1; + if (sd < 1 || !xd[0]) { + xd.length = 0; + if (roundUp) { - // 1, 0.1, 0.01, 0.001, 0.0001 etc. - xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE); - x.e = -sd || 0; - } else { + // Convert sd to decimal places. + sd -= x.e + 1; - // Zero. - xd[0] = x.e = 0; - } + // 1, 0.1, 0.01, 0.001, 0.0001 etc. + xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE); + x.e = -sd || 0; + } else { - return x; + // Zero. + xd[0] = x.e = 0; } - // Remove excess digits. - if (i == 0) { - xd.length = xdi; - k = 1; - xdi--; - } else { - xd.length = xdi + 1; - k = mathpow(10, LOG_BASE - i); + return x; + } - // E.g. 56700 becomes 56000 if 7 is the rounding digit. - // j > 0 means i > number of leading zeros of w. - xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0; - } + // Remove excess digits. + if (i == 0) { + xd.length = xdi; + k = 1; + xdi--; + } else { + xd.length = xdi + 1; + k = mathpow(10, LOG_BASE - i); - if (roundUp) { - for (;;) { + // E.g. 56700 becomes 56000 if 7 is the rounding digit. + // j > 0 means i > number of leading zeros of w. + xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0; + } - // Is the digit to be rounded up in the first word of xd? - if (xdi == 0) { + if (roundUp) { + for (;;) { - // i will be the length of xd[0] before k is added. - for (i = 1, j = xd[0]; j >= 10; j /= 10) i++; - j = xd[0] += k; - for (k = 1; j >= 10; j /= 10) k++; + // Is the digit to be rounded up in the first word of xd? + if (xdi == 0) { - // if i != k the length has increased. - if (i != k) { - x.e++; - if (xd[0] == BASE) xd[0] = 1; - } + // i will be the length of xd[0] before k is added. + for (i = 1, j = xd[0]; j >= 10; j /= 10) i++; + j = xd[0] += k; + for (k = 1; j >= 10; j /= 10) k++; - break; - } else { - xd[xdi] += k; - if (xd[xdi] != BASE) break; - xd[xdi--] = 0; - k = 1; + // if i != k the length has increased. + if (i != k) { + x.e++; + if (xd[0] == BASE) xd[0] = 1; } + + break; + } else { + xd[xdi] += k; + if (xd[xdi] != BASE) break; + xd[xdi--] = 0; + k = 1; } } - - // Remove trailing zeros. - for (i = xd.length; xd[--i] === 0;) xd.pop(); } - if (external) { + // Remove trailing zeros. + for (i = xd.length; xd[--i] === 0;) xd.pop(); + } - // Overflow? - if (x.e > Ctor.maxE) { + if (external) { - // Infinity. - x.d = null; - x.e = NaN; + // Overflow? + if (x.e > Ctor.maxE) { - // Underflow? - } else if (x.e < Ctor.minE) { + // Infinity. + x.d = null; + x.e = NaN; - // Zero. - x.e = 0; - x.d = [0]; - // Ctor.underflow = true; - } // else Ctor.underflow = false; - } + // Underflow? + } else if (x.e < Ctor.minE) { - return x; + // Zero. + x.e = 0; + x.d = [0]; + // Ctor.underflow = true; + } // else Ctor.underflow = false; } + return x; +} - function finiteToString(x, isExp, sd) { - if (!x.isFinite()) return nonFiniteToString(x); - var k, - e = x.e, - str = digitsToString(x.d), - len = str.length; - if (isExp) { - if (sd && (k = sd - len) > 0) { - str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k); - } else if (len > 1) { - str = str.charAt(0) + '.' + str.slice(1); - } +function finiteToString(x, isExp, sd) { + if (!x.isFinite()) return nonFiniteToString(x); + var k, + e = x.e, + str = digitsToString(x.d), + len = str.length; - str = str + (x.e < 0 ? 'e' : 'e+') + x.e; - } else if (e < 0) { - str = '0.' + getZeroString(-e - 1) + str; - if (sd && (k = sd - len) > 0) str += getZeroString(k); - } else if (e >= len) { - str += getZeroString(e + 1 - len); - if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k); - } else { - if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k); - if (sd && (k = sd - len) > 0) { - if (e + 1 === len) str += '.'; - str += getZeroString(k); - } + if (isExp) { + if (sd && (k = sd - len) > 0) { + str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k); + } else if (len > 1) { + str = str.charAt(0) + '.' + str.slice(1); } - return str; + str = str + (x.e < 0 ? 'e' : 'e+') + x.e; + } else if (e < 0) { + str = '0.' + getZeroString(-e - 1) + str; + if (sd && (k = sd - len) > 0) str += getZeroString(k); + } else if (e >= len) { + str += getZeroString(e + 1 - len); + if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k); + } else { + if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k); + if (sd && (k = sd - len) > 0) { + if (e + 1 === len) str += '.'; + str += getZeroString(k); + } } + return str; +} - // Calculate the base 10 exponent from the base 1e7 exponent. - function getBase10Exponent(digits, e) { - var w = digits[0]; - - // Add the number of digits of the first word of the digits array. - for ( e *= LOG_BASE; w >= 10; w /= 10) e++; - return e; - } +// Calculate the base 10 exponent from the base 1e7 exponent. +function getBase10Exponent(digits, e) { + var w = digits[0]; - function getLn10(Ctor, sd, pr) { - if (sd > LN10_PRECISION) { + // Add the number of digits of the first word of the digits array. + for ( e *= LOG_BASE; w >= 10; w /= 10) e++; + return e; +} - // Reset global state in case the exception is caught. - external = true; - if (pr) Ctor.precision = pr; - throw Error(precisionLimitExceeded); - } - return finalise(new Ctor(LN10), sd, 1, true); - } +function getLn10(Ctor, sd, pr) { + if (sd > LN10_PRECISION) { - function getPi(Ctor, sd, rm) { - if (sd > PI_PRECISION) throw Error(precisionLimitExceeded); - return finalise(new Ctor(PI), sd, rm, true); + // Reset global state in case the exception is caught. + external = true; + if (pr) Ctor.precision = pr; + throw Error(precisionLimitExceeded); } + return finalise(new Ctor(LN10), sd, 1, true); +} - function getPrecision(digits) { - var w = digits.length - 1, - len = w * LOG_BASE + 1; - - w = digits[w]; +function getPi(Ctor, sd, rm) { + if (sd > PI_PRECISION) throw Error(precisionLimitExceeded); + return finalise(new Ctor(PI), sd, rm, true); +} - // If non-zero... - if (w) { - // Subtract the number of trailing zeros of the last word. - for (; w % 10 == 0; w /= 10) len--; +function getPrecision(digits) { + var w = digits.length - 1, + len = w * LOG_BASE + 1; - // Add the number of digits of the first word. - for (w = digits[0]; w >= 10; w /= 10) len++; - } + w = digits[w]; - return len; - } + // If non-zero... + if (w) { + // Subtract the number of trailing zeros of the last word. + for (; w % 10 == 0; w /= 10) len--; - function getZeroString(k) { - var zs = ''; - for (; k--;) zs += '0'; - return zs; + // Add the number of digits of the first word. + for (w = digits[0]; w >= 10; w /= 10) len++; } + return len; +} - /* - * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an - * integer of type number. - * - * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`. - * - */ - function intPow(Ctor, x, n, pr) { - var isTruncated, - r = new Ctor(1), - // Max n of 9007199254740991 takes 53 loop iterations. - // Maximum digits array length; leaves [28, 34] guard digits. - k = Math.ceil(pr / LOG_BASE + 4); +function getZeroString(k) { + var zs = ''; + for (; k--;) zs += '0'; + return zs; +} - external = false; - for (;;) { - if (n % 2) { - r = r.times(x); - if (truncate(r.d, k)) isTruncated = true; - } +/* + * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an + * integer of type number. + * + * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`. + * + */ +function intPow(Ctor, x, n, pr) { + var isTruncated, + r = new Ctor(1), - n = mathfloor(n / 2); - if (n === 0) { + // Max n of 9007199254740991 takes 53 loop iterations. + // Maximum digits array length; leaves [28, 34] guard digits. + k = Math.ceil(pr / LOG_BASE + 4); - // To ensure correct rounding when r.d is truncated, increment the last word if it is zero. - n = r.d.length - 1; - if (isTruncated && r.d[n] === 0) ++r.d[n]; - break; - } + external = false; - x = x.times(x); - truncate(x.d, k); + for (;;) { + if (n % 2) { + r = r.times(x); + if (truncate(r.d, k)) isTruncated = true; } - external = true; - - return r; - } + n = mathfloor(n / 2); + if (n === 0) { + // To ensure correct rounding when r.d is truncated, increment the last word if it is zero. + n = r.d.length - 1; + if (isTruncated && r.d[n] === 0) ++r.d[n]; + break; + } - function isOdd(n) { - return n.d[n.d.length - 1] & 1; + x = x.times(x); + truncate(x.d, k); } + external = true; - /* - * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'. - */ - function maxOrMin(Ctor, args, ltgt) { - var y, - x = new Ctor(args[0]), - i = 0; - - for (; ++i < args.length;) { - y = new Ctor(args[i]); - if (!y.s) { - x = y; - break; - } else if (x[ltgt](y)) { - x = y; - } - } + return r; +} - return x; - } +function isOdd(n) { + return n.d[n.d.length - 1] & 1; +} - /* - * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant - * digits. - * - * Taylor/Maclaurin series. - * - * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ... - * - * Argument reduction: - * Repeat x = x / 32, k += 5, until |x| < 0.1 - * exp(x) = exp(x / 2^k)^(2^k) - * - * Previously, the argument was initially reduced by - * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10) - * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was - * found to be slower than just dividing repeatedly by 32 as above. - * - * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000 - * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000 - * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324) - * - * exp(Infinity) = Infinity - * exp(-Infinity) = 0 - * exp(NaN) = NaN - * exp(±0) = 1 - * - * exp(x) is non-terminating for any finite, non-zero x. - * - * The result will always be correctly rounded. - * - */ - function naturalExponential(x, sd) { - var denominator, guard, j, pow, sum, t, wpr, - rep = 0, - i = 0, - k = 0, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; - // 0/NaN/Infinity? - if (!x.d || !x.d[0] || x.e > 17) { +/* + * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'. + */ +function maxOrMin(Ctor, args, ltgt) { + var y, + x = new Ctor(args[0]), + i = 0; - return new Ctor(x.d - ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0 - : x.s ? x.s < 0 ? 0 : x : 0 / 0); + for (; ++i < args.length;) { + y = new Ctor(args[i]); + if (!y.s) { + x = y; + break; + } else if (x[ltgt](y)) { + x = y; } + } - if (sd == null) { - external = false; - wpr = pr; - } else { - wpr = sd; - } + return x; +} + + +/* + * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant + * digits. + * + * Taylor/Maclaurin series. + * + * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ... + * + * Argument reduction: + * Repeat x = x / 32, k += 5, until |x| < 0.1 + * exp(x) = exp(x / 2^k)^(2^k) + * + * Previously, the argument was initially reduced by + * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10) + * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was + * found to be slower than just dividing repeatedly by 32 as above. + * + * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000 + * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000 + * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324) + * + * exp(Infinity) = Infinity + * exp(-Infinity) = 0 + * exp(NaN) = NaN + * exp(±0) = 1 + * + * exp(x) is non-terminating for any finite, non-zero x. + * + * The result will always be correctly rounded. + * + */ +function naturalExponential(x, sd) { + var denominator, guard, j, pow, sum, t, wpr, + rep = 0, + i = 0, + k = 0, + Ctor = x.constructor, + rm = Ctor.rounding, + pr = Ctor.precision; - t = new Ctor(0.03125); + // 0/NaN/Infinity? + if (!x.d || !x.d[0] || x.e > 17) { - // while abs(x) >= 0.1 - while (x.e > -2) { + return new Ctor(x.d + ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0 + : x.s ? x.s < 0 ? 0 : x : 0 / 0); + } - // x = x / 2^5 - x = x.times(t); - k += 5; - } + if (sd == null) { + external = false; + wpr = pr; + } else { + wpr = sd; + } - // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision - // necessary to ensure the first 4 rounding digits are correct. - guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0; - wpr += guard; - denominator = pow = sum = new Ctor(1); - Ctor.precision = wpr; + t = new Ctor(0.03125); - for (;;) { - pow = finalise(pow.times(x), wpr, 1); - denominator = denominator.times(++i); - t = sum.plus(divide(pow, denominator, wpr, 1)); + // while abs(x) >= 0.1 + while (x.e > -2) { - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - j = k; - while (j--) sum = finalise(sum.times(sum), wpr, 1); + // x = x / 2^5 + x = x.times(t); + k += 5; + } - // Check to see if the first 4 rounding digits are [49]999. - // If so, repeat the summation with a higher precision, otherwise - // e.g. with precision: 18, rounding: 1 - // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123) - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { + // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision + // necessary to ensure the first 4 rounding digits are correct. + guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0; + wpr += guard; + denominator = pow = sum = new Ctor(1); + Ctor.precision = wpr; - if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += 10; - denominator = pow = t = new Ctor(1); - i = 0; - rep++; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } + for (;;) { + pow = finalise(pow.times(x), wpr, 1); + denominator = denominator.times(++i); + t = sum.plus(divide(pow, denominator, wpr, 1)); + + if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { + j = k; + while (j--) sum = finalise(sum.times(sum), wpr, 1); + + // Check to see if the first 4 rounding digits are [49]999. + // If so, repeat the summation with a higher precision, otherwise + // e.g. with precision: 18, rounding: 1 + // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123) + // `wpr - guard` is the index of first rounding digit. + if (sd == null) { + + if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { + Ctor.precision = wpr += 10; + denominator = pow = t = new Ctor(1); + i = 0; + rep++; } else { - Ctor.precision = pr; - return sum; + return finalise(sum, Ctor.precision = pr, rm, external = true); } + } else { + Ctor.precision = pr; + return sum; } - - sum = t; } + + sum = t; } +} - /* - * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant - * digits. - * - * ln(-n) = NaN - * ln(0) = -Infinity - * ln(-0) = -Infinity - * ln(1) = 0 - * ln(Infinity) = Infinity - * ln(-Infinity) = NaN - * ln(NaN) = NaN - * - * ln(n) (n != 1) is non-terminating. - * - */ - function naturalLogarithm(y, sd) { - var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2, - n = 1, - guard = 10, - x = y, - xd = x.d, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; +/* + * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant + * digits. + * + * ln(-n) = NaN + * ln(0) = -Infinity + * ln(-0) = -Infinity + * ln(1) = 0 + * ln(Infinity) = Infinity + * ln(-Infinity) = NaN + * ln(NaN) = NaN + * + * ln(n) (n != 1) is non-terminating. + * + */ +function naturalLogarithm(y, sd) { + var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2, + n = 1, + guard = 10, + x = y, + xd = x.d, + Ctor = x.constructor, + rm = Ctor.rounding, + pr = Ctor.precision; + + // Is x negative or Infinity, NaN, 0 or 1? + if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) { + return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x); + } + + if (sd == null) { + external = false; + wpr = pr; + } else { + wpr = sd; + } + + Ctor.precision = wpr += guard; + c = digitsToString(xd); + c0 = c.charAt(0); - // Is x negative or Infinity, NaN, 0 or 1? - if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) { - return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x); + if (Math.abs(e = x.e) < 1.5e15) { + + // Argument reduction. + // The series converges faster the closer the argument is to 1, so using + // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b + // multiply the argument by itself until the leading digits of the significand are 7, 8, 9, + // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can + // later be divided by this number, then separate out the power of 10 using + // ln(a*10^b) = ln(a) + b*ln(10). + + // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14). + //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) { + // max n is 6 (gives 0.7 - 1.3) + while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) { + x = x.times(y); + c = digitsToString(x.d); + c0 = c.charAt(0); + n++; } - if (sd == null) { - external = false; - wpr = pr; + e = x.e; + + if (c0 > 1) { + x = new Ctor('0.' + c); + e++; } else { - wpr = sd; - } - - Ctor.precision = wpr += guard; - c = digitsToString(xd); - c0 = c.charAt(0); - - if (Math.abs(e = x.e) < 1.5e15) { - - // Argument reduction. - // The series converges faster the closer the argument is to 1, so using - // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b - // multiply the argument by itself until the leading digits of the significand are 7, 8, 9, - // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can - // later be divided by this number, then separate out the power of 10 using - // ln(a*10^b) = ln(a) + b*ln(10). - - // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14). - //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) { - // max n is 6 (gives 0.7 - 1.3) - while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) { - x = x.times(y); - c = digitsToString(x.d); - c0 = c.charAt(0); - n++; - } + x = new Ctor(c0 + '.' + c.slice(1)); + } + } else { - e = x.e; + // The argument reduction method above may result in overflow if the argument y is a massive + // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this + // function using ln(x*10^e) = ln(x) + e*ln(10). + t = getLn10(Ctor, wpr + 2, pr).times(e + ''); + x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t); + Ctor.precision = pr; - if (c0 > 1) { - x = new Ctor('0.' + c); - e++; - } else { - x = new Ctor(c0 + '.' + c.slice(1)); - } - } else { + return sd == null ? finalise(x, pr, rm, external = true) : x; + } - // The argument reduction method above may result in overflow if the argument y is a massive - // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this - // function using ln(x*10^e) = ln(x) + e*ln(10). - t = getLn10(Ctor, wpr + 2, pr).times(e + ''); - x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t); - Ctor.precision = pr; - - return sd == null ? finalise(x, pr, rm, external = true) : x; - } - - // x1 is x reduced to a value near 1. - x1 = x; - - // Taylor series. - // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...) - // where x = (y - 1)/(y + 1) (|x| < 1) - sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = 3; - - for (;;) { - numerator = finalise(numerator.times(x2), wpr, 1); - t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1)); - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - sum = sum.times(2); - - // Reverse the argument reduction. Check that e is not 0 because, besides preventing an - // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0. - if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + '')); - sum = divide(sum, new Ctor(n), wpr, 1); - - // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has - // been repeated previously) and the first 4 rounding digits 9999? - // If so, restart the summation with a higher precision, otherwise - // e.g. with precision: 12, rounding: 1 - // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463. - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += guard; - t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = rep = 1; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } + // x1 is x reduced to a value near 1. + x1 = x; + + // Taylor series. + // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...) + // where x = (y - 1)/(y + 1) (|x| < 1) + sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1); + x2 = finalise(x.times(x), wpr, 1); + denominator = 3; + + for (;;) { + numerator = finalise(numerator.times(x2), wpr, 1); + t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1)); + + if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { + sum = sum.times(2); + + // Reverse the argument reduction. Check that e is not 0 because, besides preventing an + // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0. + if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + '')); + sum = divide(sum, new Ctor(n), wpr, 1); + + // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has + // been repeated previously) and the first 4 rounding digits 9999? + // If so, restart the summation with a higher precision, otherwise + // e.g. with precision: 12, rounding: 1 + // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463. + // `wpr - guard` is the index of first rounding digit. + if (sd == null) { + if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { + Ctor.precision = wpr += guard; + t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1); + x2 = finalise(x.times(x), wpr, 1); + denominator = rep = 1; } else { - Ctor.precision = pr; - return sum; + return finalise(sum, Ctor.precision = pr, rm, external = true); } + } else { + Ctor.precision = pr; + return sum; } - - sum = t; - denominator += 2; } + + sum = t; + denominator += 2; } +} + + +// ±Infinity, NaN. +function nonFiniteToString(x) { + // Unsigned. + return String(x.s * x.s / 0); +} - // ±Infinity, NaN. - function nonFiniteToString(x) { - // Unsigned. - return String(x.s * x.s / 0); +/* + * Parse the value of a new Decimal `x` from string `str`. + */ +function parseDecimal(x, str) { + var e, i, len; + + // Decimal point? + if ((e = str.indexOf('.')) > -1) str = str.replace('.', ''); + + // Exponential form? + if ((i = str.search(/e/i)) > 0) { + + // Determine exponent. + if (e < 0) e = i; + e += +str.slice(i + 1); + str = str.substring(0, i); + } else if (e < 0) { + + // Integer. + e = str.length; } + // Determine leading zeros. + for (i = 0; str.charCodeAt(i) === 48; i++); - /* - * Parse the value of a new Decimal `x` from string `str`. - */ - function parseDecimal(x, str) { - var e, i, len; + // Determine trailing zeros. + for (len = str.length; str.charCodeAt(len - 1) === 48; --len); + str = str.slice(i, len); - // Decimal point? - if ((e = str.indexOf('.')) > -1) str = str.replace('.', ''); + if (str) { + len -= i; + x.e = e = e - i - 1; + x.d = []; - // Exponential form? - if ((i = str.search(/e/i)) > 0) { + // Transform base - // Determine exponent. - if (e < 0) e = i; - e += +str.slice(i + 1); - str = str.substring(0, i); - } else if (e < 0) { + // e is the base 10 exponent. + // i is where to slice str to get the first word of the digits array. + i = (e + 1) % LOG_BASE; + if (e < 0) i += LOG_BASE; - // Integer. - e = str.length; + if (i < len) { + if (i) x.d.push(+str.slice(0, i)); + for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE)); + str = str.slice(i); + i = LOG_BASE - str.length; + } else { + i -= len; } - // Determine leading zeros. - for (i = 0; str.charCodeAt(i) === 48; i++); + for (; i--;) str += '0'; + x.d.push(+str); - // Determine trailing zeros. - for (len = str.length; str.charCodeAt(len - 1) === 48; --len); - str = str.slice(i, len); + if (external) { - if (str) { - len -= i; - x.e = e = e - i - 1; - x.d = []; + // Overflow? + if (x.e > x.constructor.maxE) { - // Transform base + // Infinity. + x.d = null; + x.e = NaN; - // e is the base 10 exponent. - // i is where to slice str to get the first word of the digits array. - i = (e + 1) % LOG_BASE; - if (e < 0) i += LOG_BASE; + // Underflow? + } else if (x.e < x.constructor.minE) { - if (i < len) { - if (i) x.d.push(+str.slice(0, i)); - for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE)); - str = str.slice(i); - i = LOG_BASE - str.length; - } else { - i -= len; - } + // Zero. + x.e = 0; + x.d = [0]; + // x.constructor.underflow = true; + } // else x.constructor.underflow = false; + } + } else { - for (; i--;) str += '0'; - x.d.push(+str); + // Zero. + x.e = 0; + x.d = [0]; + } - if (external) { + return x; +} - // Overflow? - if (x.e > x.constructor.maxE) { - // Infinity. - x.d = null; - x.e = NaN; +/* + * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value. + */ +function parseOther(x, str) { + var base, Ctor, divisor, i, isFloat, len, p, xd, xe; - // Underflow? - } else if (x.e < x.constructor.minE) { + if (str === 'Infinity' || str === 'NaN') { + if (!+str) x.s = NaN; + x.e = NaN; + x.d = null; + return x; + } - // Zero. - x.e = 0; - x.d = [0]; - // x.constructor.underflow = true; - } // else x.constructor.underflow = false; - } - } else { + if (isHex.test(str)) { + base = 16; + str = str.toLowerCase(); + } else if (isBinary.test(str)) { + base = 2; + } else if (isOctal.test(str)) { + base = 8; + } else { + throw Error(invalidArgument + str); + } - // Zero. - x.e = 0; - x.d = [0]; - } + // Is there a binary exponent part? + i = str.search(/p/i); - return x; + if (i > 0) { + p = +str.slice(i + 1); + str = str.substring(2, i); + } else { + str = str.slice(2); } + // Convert `str` as an integer then divide the result by `base` raised to a power such that the + // fraction part will be restored. + i = str.indexOf('.'); + isFloat = i >= 0; + Ctor = x.constructor; - /* - * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value. - */ - function parseOther(x, str) { - var base, Ctor, divisor, i, isFloat, len, p, xd, xe; + if (isFloat) { + str = str.replace('.', ''); + len = str.length; + i = len - i; - if (str === 'Infinity' || str === 'NaN') { - if (!+str) x.s = NaN; - x.e = NaN; - x.d = null; - return x; - } + // log[10](16) = 1.2041... , log[10](88) = 1.9444.... + divisor = intPow(Ctor, new Ctor(base), i, i * 2); + } - if (isHex.test(str)) { - base = 16; - str = str.toLowerCase(); - } else if (isBinary.test(str)) { - base = 2; - } else if (isOctal.test(str)) { - base = 8; - } else { - throw Error(invalidArgument + str); - } + xd = convertBase(str, base, BASE); + xe = xd.length - 1; - // Is there a binary exponent part? - i = str.search(/p/i); + // Remove trailing zeros. + for (i = xe; xd[i] === 0; --i) xd.pop(); + if (i < 0) return new Ctor(x.s * 0); + x.e = getBase10Exponent(xd, xe); + x.d = xd; + external = false; - if (i > 0) { - p = +str.slice(i + 1); - str = str.substring(2, i); - } else { - str = str.slice(2); - } + // At what precision to perform the division to ensure exact conversion? + // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount) + // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412 + // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits. + // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount + // Therefore using 4 * the number of digits of str will always be enough. + if (isFloat) x = divide(x, divisor, len * 4); - // Convert `str` as an integer then divide the result by `base` raised to a power such that the - // fraction part will be restored. - i = str.indexOf('.'); - isFloat = i >= 0; - Ctor = x.constructor; + // Multiply by the binary exponent part if present. + if (p) x = x.times(Math.abs(p) < 54 ? Math.pow(2, p) : Decimal.pow(2, p)); + external = true; - if (isFloat) { - str = str.replace('.', ''); - len = str.length; - i = len - i; + return x; +} - // log[10](16) = 1.2041... , log[10](88) = 1.9444.... - divisor = intPow(Ctor, new Ctor(base), i, i * 2); - } - xd = convertBase(str, base, BASE); - xe = xd.length - 1; +/* + * sin(x) = x - x^3/3! + x^5/5! - ... + * |x| < pi/2 + * + */ +function sine(Ctor, x) { + var k, + len = x.d.length; - // Remove trailing zeros. - for (i = xe; xd[i] === 0; --i) xd.pop(); - if (i < 0) return new Ctor(x.s * 0); - x.e = getBase10Exponent(xd, xe); - x.d = xd; - external = false; + if (len < 3) return taylorSeries(Ctor, 2, x, x); - // At what precision to perform the division to ensure exact conversion? - // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount) - // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412 - // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits. - // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount - // Therefore using 4 * the number of digits of str will always be enough. - if (isFloat) x = divide(x, divisor, len * 4); + // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x) + // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5) + // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20)) - // Multiply by the binary exponent part if present. - if (p) x = x.times(Math.abs(p) < 54 ? Math.pow(2, p) : Decimal.pow(2, p)); - external = true; + // Estimate the optimum number of times to use the argument reduction. + k = 1.4 * Math.sqrt(len); + k = k > 16 ? 16 : k | 0; - return x; - } + // Max k before Math.pow precision loss is 22 + x = x.times(Math.pow(5, -k)); + x = taylorSeries(Ctor, 2, x, x); + // Reverse argument reduction + var sin2_x, + d5 = new Ctor(5), + d16 = new Ctor(16), + d20 = new Ctor(20); + for (; k--;) { + sin2_x = x.times(x); + x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20)))); + } - /* - * sin(x) = x - x^3/3! + x^5/5! - ... - * |x| < pi/2 - * - */ - function sine(Ctor, x) { - var k, - len = x.d.length; + return x; +} - if (len < 3) return taylorSeries(Ctor, 2, x, x); - // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x) - // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5) - // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20)) +// Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`. +function taylorSeries(Ctor, n, x, y, isHyperbolic) { + var j, t, u, x2, + i = 1, + pr = Ctor.precision, + k = Math.ceil(pr / LOG_BASE); - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; + external = false; + x2 = x.times(x); + u = new Ctor(y); - // Max k before Math.pow precision loss is 22 - x = x.times(Math.pow(5, -k)); - x = taylorSeries(Ctor, 2, x, x); + for (;;) { + t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1); + u = isHyperbolic ? y.plus(t) : y.minus(t); + y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1); + t = u.plus(y); - // Reverse argument reduction - var sin2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sin2_x = x.times(x); - x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20)))); + if (t.d[k] !== void 0) { + for (j = k; t.d[j] === u.d[j] && j--;); + if (j == -1) break; } - return x; + j = u; + u = y; + y = t; + t = j; + i++; } + external = true; + t.d.length = k + 1; - // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`. - function taylorSeries(Ctor, n, x, y, isHyperbolic) { - var j, t, u, x2, - i = 1, - pr = Ctor.precision, - k = Math.ceil(pr / LOG_BASE); + return t; +} - external = false; - x2 = x.times(x); - u = new Ctor(y); - - for (;;) { - t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1); - u = isHyperbolic ? y.plus(t) : y.minus(t); - y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1); - t = u.plus(y); - - if (t.d[k] !== void 0) { - for (j = k; t.d[j] === u.d[j] && j--;); - if (j == -1) break; - } - j = u; - u = y; - y = t; - t = j; - i++; - } +// Return the absolute value of `x` reduced to less than or equal to half pi. +function toLessThanHalfPi(Ctor, x) { + var t, + isNeg = x.s < 0, + pi = getPi(Ctor, Ctor.precision, 1), + halfPi = pi.times(0.5); - external = true; - t.d.length = k + 1; + x = x.abs(); - return t; + if (x.lte(halfPi)) { + quadrant = isNeg ? 4 : 1; + return x; } + t = x.divToInt(pi); - // Return the absolute value of `x` reduced to less than or equal to half pi. - function toLessThanHalfPi(Ctor, x) { - var t, - isNeg = x.s < 0, - pi = getPi(Ctor, Ctor.precision, 1), - halfPi = pi.times(0.5); - - x = x.abs(); + if (t.isZero()) { + quadrant = isNeg ? 3 : 2; + } else { + x = x.minus(t.times(pi)); + // 0 <= x < pi if (x.lte(halfPi)) { - quadrant = isNeg ? 4 : 1; + quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1); return x; } - t = x.divToInt(pi); + quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2); + } - if (t.isZero()) { - quadrant = isNeg ? 3 : 2; - } else { - x = x.minus(t.times(pi)); + return x.minus(pi).abs(); +} - // 0 <= x < pi - if (x.lte(halfPi)) { - quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1); - return x; - } - quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2); - } +/* + * Return the value of Decimal `x` as a string in base `baseOut`. + * + * If the optional `sd` argument is present include a binary exponent suffix. + */ +function toStringBinary(x, baseOut, sd, rm) { + var base, e, i, k, len, roundUp, str, xd, y, + Ctor = x.constructor, + isExp = sd !== void 0; - return x.minus(pi).abs(); + if (isExp) { + checkInt32(sd, 1, MAX_DIGITS); + if (rm === void 0) rm = Ctor.rounding; + else checkInt32(rm, 0, 8); + } else { + sd = Ctor.precision; + rm = Ctor.rounding; } + if (!x.isFinite()) { + str = nonFiniteToString(x); + } else { + str = finiteToString(x); + i = str.indexOf('.'); - /* - * Return the value of Decimal `x` as a string in base `baseOut`. - * - * If the optional `sd` argument is present include a binary exponent suffix. - */ - function toStringBinary(x, baseOut, sd, rm) { - var base, e, i, k, len, roundUp, str, xd, y, - Ctor = x.constructor, - isExp = sd !== void 0; + // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required: + // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10)) + // minBinaryExponent = floor(decimalExponent * log[2](10)) + // log[2](10) = 3.321928094887362347870319429489390175864 if (isExp) { - checkInt32(sd, 1, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); + base = 2; + if (baseOut == 16) { + sd = sd * 4 - 3; + } else if (baseOut == 8) { + sd = sd * 3 - 2; + } } else { - sd = Ctor.precision; - rm = Ctor.rounding; + base = baseOut; } - if (!x.isFinite()) { - str = nonFiniteToString(x); - } else { - str = finiteToString(x); - i = str.indexOf('.'); - - // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required: - // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10)) - // minBinaryExponent = floor(decimalExponent * log[2](10)) - // log[2](10) = 3.321928094887362347870319429489390175864 + // Convert the number as an integer then divide the result by its base raised to a power such + // that the fraction part will be restored. - if (isExp) { - base = 2; - if (baseOut == 16) { - sd = sd * 4 - 3; - } else if (baseOut == 8) { - sd = sd * 3 - 2; - } - } else { - base = baseOut; - } - - // Convert the number as an integer then divide the result by its base raised to a power such - // that the fraction part will be restored. - - // Non-integer. - if (i >= 0) { - str = str.replace('.', ''); - y = new Ctor(1); - y.e = str.length - i; - y.d = convertBase(finiteToString(y), 10, base); - y.e = y.d.length; - } + // Non-integer. + if (i >= 0) { + str = str.replace('.', ''); + y = new Ctor(1); + y.e = str.length - i; + y.d = convertBase(finiteToString(y), 10, base); + y.e = y.d.length; + } - xd = convertBase(str, 10, base); - e = len = xd.length; + xd = convertBase(str, 10, base); + e = len = xd.length; - // Remove trailing zeros. - for (; xd[--len] == 0;) xd.pop(); + // Remove trailing zeros. + for (; xd[--len] == 0;) xd.pop(); - if (!xd[0]) { - str = isExp ? '0p+0' : '0'; + if (!xd[0]) { + str = isExp ? '0p+0' : '0'; + } else { + if (i < 0) { + e--; } else { - if (i < 0) { - e--; - } else { - x = new Ctor(x); - x.d = xd; - x.e = e; - x = divide(x, y, sd, rm, 0, base); - xd = x.d; - e = x.e; - roundUp = inexact; - } + x = new Ctor(x); + x.d = xd; + x.e = e; + x = divide(x, y, sd, rm, 0, base); + xd = x.d; + e = x.e; + roundUp = inexact; + } - // The rounding digit, i.e. the digit after the digit that may be rounded up. - i = xd[sd]; - k = base / 2; - roundUp = roundUp || xd[sd + 1] !== void 0; + // The rounding digit, i.e. the digit after the digit that may be rounded up. + i = xd[sd]; + k = base / 2; + roundUp = roundUp || xd[sd + 1] !== void 0; - roundUp = rm < 4 - ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) - : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 || - rm === (x.s < 0 ? 8 : 7)); + roundUp = rm < 4 + ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) + : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 || + rm === (x.s < 0 ? 8 : 7)); - xd.length = sd; + xd.length = sd; - if (roundUp) { + if (roundUp) { - // Rounding up may mean the previous digit has to be rounded up and so on. - for (; ++xd[--sd] > base - 1;) { - xd[sd] = 0; - if (!sd) { - ++e; - xd.unshift(1); - } + // Rounding up may mean the previous digit has to be rounded up and so on. + for (; ++xd[--sd] > base - 1;) { + xd[sd] = 0; + if (!sd) { + ++e; + xd.unshift(1); } } + } - // Determine trailing zeros. - for (len = xd.length; !xd[len - 1]; --len); - - // E.g. [4, 11, 15] becomes 4bf. - for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]); + // Determine trailing zeros. + for (len = xd.length; !xd[len - 1]; --len); - // Add binary exponent suffix? - if (isExp) { - if (len > 1) { - if (baseOut == 16 || baseOut == 8) { - i = baseOut == 16 ? 4 : 3; - for (--len; len % i; len++) str += '0'; - xd = convertBase(str, base, baseOut); - for (len = xd.length; !xd[len - 1]; --len); + // E.g. [4, 11, 15] becomes 4bf. + for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]); - // xd[0] will always be be 1 - for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]); - } else { - str = str.charAt(0) + '.' + str.slice(1); - } + // Add binary exponent suffix? + if (isExp) { + if (len > 1) { + if (baseOut == 16 || baseOut == 8) { + i = baseOut == 16 ? 4 : 3; + for (--len; len % i; len++) str += '0'; + xd = convertBase(str, base, baseOut); + for (len = xd.length; !xd[len - 1]; --len); + + // xd[0] will always be be 1 + for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]); + } else { + str = str.charAt(0) + '.' + str.slice(1); } - - str = str + (e < 0 ? 'p' : 'p+') + e; - } else if (e < 0) { - for (; ++e;) str = '0' + str; - str = '0.' + str; - } else { - if (++e > len) for (e -= len; e-- ;) str += '0'; - else if (e < len) str = str.slice(0, e) + '.' + str.slice(e); } - } - str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str; + str = str + (e < 0 ? 'p' : 'p+') + e; + } else if (e < 0) { + for (; ++e;) str = '0' + str; + str = '0.' + str; + } else { + if (++e > len) for (e -= len; e-- ;) str += '0'; + else if (e < len) str = str.slice(0, e) + '.' + str.slice(e); + } } - return x.s < 0 ? '-' + str : str; + str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str; } + return x.s < 0 ? '-' + str : str; +} + - // Does not strip trailing zeros. - function truncate(arr, len) { - if (arr.length > len) { - arr.length = len; - return true; - } +// Does not strip trailing zeros. +function truncate(arr, len) { + if (arr.length > len) { + arr.length = len; + return true; } +} - // Decimal methods - +// Decimal methods - /* - * abs - * acos - * acosh - * add - * asin - * asinh - * atan - * atanh - * atan2 - * cbrt - * ceil - * clone - * config - * cos - * cosh - * div - * exp - * floor - * hypot - * ln - * log - * log2 - * log10 - * max - * min - * mod - * mul - * pow - * random - * round - * set - * sign - * sin - * sinh - * sqrt - * sub - * tan - * tanh - * trunc - */ +/* + * abs + * acos + * acosh + * add + * asin + * asinh + * atan + * atanh + * atan2 + * cbrt + * ceil + * clone + * config + * cos + * cosh + * div + * exp + * floor + * hypot + * ln + * log + * log2 + * log10 + * max + * min + * mod + * mul + * pow + * random + * round + * set + * sign + * sin + * sinh + * sqrt + * sub + * tan + * tanh + * trunc + */ - /* - * Return a new Decimal whose value is the absolute value of `x`. - * - * x {number|string|Decimal} - * - */ - function abs(x) { - return new this(x).abs(); - } +/* + * Return a new Decimal whose value is the absolute value of `x`. + * + * x {number|string|Decimal} + * + */ +function abs(x) { + return new this(x).abs(); +} - /* - * Return a new Decimal whose value is the arccosine in radians of `x`. - * - * x {number|string|Decimal} - * - */ - function acos(x) { - return new this(x).acos(); - } +/* + * Return a new Decimal whose value is the arccosine in radians of `x`. + * + * x {number|string|Decimal} + * + */ +function acos(x) { + return new this(x).acos(); +} - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function acosh(x) { - return new this(x).acosh(); - } +/* + * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function acosh(x) { + return new this(x).acosh(); +} - /* - * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function add(x, y) { - return new this(x).plus(y); - } +/* + * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function add(x, y) { + return new this(x).plus(y); +} - /* - * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function asin(x) { - return new this(x).asin(); - } +/* + * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function asin(x) { + return new this(x).asin(); +} - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function asinh(x) { - return new this(x).asinh(); - } +/* + * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function asinh(x) { + return new this(x).asinh(); +} - /* - * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function atan(x) { - return new this(x).atan(); - } +/* + * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function atan(x) { + return new this(x).atan(); +} - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function atanh(x) { - return new this(x).atanh(); - } +/* + * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to + * `precision` significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function atanh(x) { + return new this(x).atanh(); +} - /* - * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi - * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi, pi] - * - * y {number|string|Decimal} The y-coordinate. - * x {number|string|Decimal} The x-coordinate. - * - * atan2(±0, -0) = ±pi - * atan2(±0, +0) = ±0 - * atan2(±0, -x) = ±pi for x > 0 - * atan2(±0, x) = ±0 for x > 0 - * atan2(-y, ±0) = -pi/2 for y > 0 - * atan2(y, ±0) = pi/2 for y > 0 - * atan2(±y, -Infinity) = ±pi for finite y > 0 - * atan2(±y, +Infinity) = ±0 for finite y > 0 - * atan2(±Infinity, x) = ±pi/2 for finite x - * atan2(±Infinity, -Infinity) = ±3*pi/4 - * atan2(±Infinity, +Infinity) = ±pi/4 - * atan2(NaN, x) = NaN - * atan2(y, NaN) = NaN - * - */ - function atan2(y, x) { - y = new this(y); - x = new this(x); - var r, - pr = this.precision, - rm = this.rounding, - wpr = pr + 4; - - // Either NaN - if (!y.s || !x.s) { - r = new this(NaN); - - // Both ±Infinity - } else if (!y.d && !x.d) { - r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75); - r.s = y.s; - - // x is ±Infinity or y is ±0 - } else if (!x.d || y.isZero()) { - r = x.s < 0 ? getPi(this, pr, rm) : new this(0); - r.s = y.s; - - // y is ±Infinity or x is ±0 - } else if (!y.d || x.isZero()) { - r = getPi(this, wpr, 1).times(0.5); - r.s = y.s; - - // Both non-zero and finite - } else if (x.s < 0) { - this.precision = wpr; - this.rounding = 1; - r = this.atan(divide(y, x, wpr, 1)); - x = getPi(this, wpr, 1); - this.precision = pr; - this.rounding = rm; - r = y.s < 0 ? r.minus(x) : r.plus(x); - } else { - r = this.atan(divide(y, x, wpr, 1)); - } - return r; +/* + * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi + * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`. + * + * Domain: [-Infinity, Infinity] + * Range: [-pi, pi] + * + * y {number|string|Decimal} The y-coordinate. + * x {number|string|Decimal} The x-coordinate. + * + * atan2(±0, -0) = ±pi + * atan2(±0, +0) = ±0 + * atan2(±0, -x) = ±pi for x > 0 + * atan2(±0, x) = ±0 for x > 0 + * atan2(-y, ±0) = -pi/2 for y > 0 + * atan2(y, ±0) = pi/2 for y > 0 + * atan2(±y, -Infinity) = ±pi for finite y > 0 + * atan2(±y, +Infinity) = ±0 for finite y > 0 + * atan2(±Infinity, x) = ±pi/2 for finite x + * atan2(±Infinity, -Infinity) = ±3*pi/4 + * atan2(±Infinity, +Infinity) = ±pi/4 + * atan2(NaN, x) = NaN + * atan2(y, NaN) = NaN + * + */ +function atan2(y, x) { + y = new this(y); + x = new this(x); + var r, + pr = this.precision, + rm = this.rounding, + wpr = pr + 4; + + // Either NaN + if (!y.s || !x.s) { + r = new this(NaN); + + // Both ±Infinity + } else if (!y.d && !x.d) { + r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75); + r.s = y.s; + + // x is ±Infinity or y is ±0 + } else if (!x.d || y.isZero()) { + r = x.s < 0 ? getPi(this, pr, rm) : new this(0); + r.s = y.s; + + // y is ±Infinity or x is ±0 + } else if (!y.d || x.isZero()) { + r = getPi(this, wpr, 1).times(0.5); + r.s = y.s; + + // Both non-zero and finite + } else if (x.s < 0) { + this.precision = wpr; + this.rounding = 1; + r = this.atan(divide(y, x, wpr, 1)); + x = getPi(this, wpr, 1); + this.precision = pr; + this.rounding = rm; + r = y.s < 0 ? r.minus(x) : r.plus(x); + } else { + r = this.atan(divide(y, x, wpr, 1)); } + return r; +} + - /* - * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function cbrt(x) { - return new this(x).cbrt(); - } +/* + * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function cbrt(x) { + return new this(x).cbrt(); +} - /* - * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`. - * - * x {number|string|Decimal} - * - */ - function ceil(x) { - return finalise(x = new this(x), x.e + 1, 2); - } +/* + * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`. + * + * x {number|string|Decimal} + * + */ +function ceil(x) { + return finalise(x = new this(x), x.e + 1, 2); +} - /* - * Configure global settings for a Decimal constructor. - * - * `obj` is an object with one or more of the following properties, - * - * precision {number} - * rounding {number} - * toExpNeg {number} - * toExpPos {number} - * maxE {number} - * minE {number} - * modulo {number} - * crypto {boolean|number} - * - * E.g. Decimal.config({ precision: 20, rounding: 4 }) - * - */ - function config(obj) { - if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected'); - var i, p, v, - ps = [ - 'precision', 1, MAX_DIGITS, - 'rounding', 0, 8, - 'toExpNeg', -EXP_LIMIT, 0, - 'toExpPos', 0, EXP_LIMIT, - 'maxE', 0, EXP_LIMIT, - 'minE', -EXP_LIMIT, 0, - 'modulo', 0, 9 - ]; - - for (i = 0; i < ps.length; i += 3) { - if ((v = obj[p = ps[i]]) !== void 0) { - if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v; - else throw Error(invalidArgument + p + ': ' + v); - } +/* + * Configure global settings for a Decimal constructor. + * + * `obj` is an object with one or more of the following properties, + * + * precision {number} + * rounding {number} + * toExpNeg {number} + * toExpPos {number} + * maxE {number} + * minE {number} + * modulo {number} + * crypto {boolean|number} + * + * E.g. Decimal.config({ precision: 20, rounding: 4 }) + * + */ +function config(obj) { + if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected'); + var i, p, v, + ps = [ + 'precision', 1, MAX_DIGITS, + 'rounding', 0, 8, + 'toExpNeg', -EXP_LIMIT, 0, + 'toExpPos', 0, EXP_LIMIT, + 'maxE', 0, EXP_LIMIT, + 'minE', -EXP_LIMIT, 0, + 'modulo', 0, 9 + ]; + + for (i = 0; i < ps.length; i += 3) { + if ((v = obj[p = ps[i]]) !== void 0) { + if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v; + else throw Error(invalidArgument + p + ': ' + v); } + } - if ((v = obj[p = 'crypto']) !== void 0) { - if (v === true || v === false || v === 0 || v === 1) { - if (v) { - if (typeof crypto != 'undefined' && crypto && - (crypto.getRandomValues || crypto.randomBytes)) { - this[p] = true; - } else { - throw Error(cryptoUnavailable); - } + if ((v = obj[p = 'crypto']) !== void 0) { + if (v === true || v === false || v === 0 || v === 1) { + if (v) { + if (typeof crypto != 'undefined' && crypto && + (crypto.getRandomValues || crypto.randomBytes)) { + this[p] = true; } else { - this[p] = false; + throw Error(cryptoUnavailable); } } else { - throw Error(invalidArgument + p + ': ' + v); + this[p] = false; } + } else { + throw Error(invalidArgument + p + ': ' + v); } - - return this; } + return this; +} - /* - * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cos(x) { - return new this(x).cos(); - } +/* + * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function cos(x) { + return new this(x).cos(); +} - /* - * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cosh(x) { - return new this(x).cosh(); - } +/* + * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function cosh(x) { + return new this(x).cosh(); +} + + +/* + * Create and return a Decimal constructor with the same configuration properties as this Decimal + * constructor. + * + */ +function clone(obj) { + var i, p, ps; /* - * Create and return a Decimal constructor with the same configuration properties as this Decimal - * constructor. + * The Decimal constructor and exported function. + * Return a new Decimal instance. + * + * v {number|string|Decimal} A numeric value. * */ - function clone(obj) { - var i, p, ps; - - /* - * The Decimal constructor and exported function. - * Return a new Decimal instance. - * - * v {number|string|Decimal} A numeric value. - * - */ - function Decimal(v) { - var e, i, t, - x = this; - - // Decimal called without new. - if (!(x instanceof Decimal)) return new Decimal(v); - - // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor - // which points to Object. - x.constructor = Decimal; - - // Duplicate. - if (v instanceof Decimal) { - x.s = v.s; - x.e = v.e; - x.d = (v = v.d) ? v.slice() : v; - return; - } - - t = typeof v; - - if (t === 'number') { - if (v === 0) { - x.s = 1 / v < 0 ? -1 : 1; - x.e = 0; - x.d = [0]; - return; - } + function Decimal(v) { + var e, i, t, + x = this; - if (v < 0) { - v = -v; - x.s = -1; - } else { - x.s = 1; - } + // Decimal called without new. + if (!(x instanceof Decimal)) return new Decimal(v); - // Fast path for small integers. - if (v === ~~v && v < 1e7) { - for (e = 0, i = v; i >= 10; i /= 10) e++; - x.e = e; - x.d = [v]; - return; + // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor + // which points to Object. + x.constructor = Decimal; - // Infinity, NaN. - } else if (v * 0 !== 0) { - if (!v) x.s = NaN; - x.e = NaN; - x.d = null; - return; - } + // Duplicate. + if (v instanceof Decimal) { + x.s = v.s; + x.e = v.e; + x.d = (v = v.d) ? v.slice() : v; + return; + } - return parseDecimal(x, v.toString()); + t = typeof v; - } else if (t !== 'string') { - throw Error(invalidArgument + v); + if (t === 'number') { + if (v === 0) { + x.s = 1 / v < 0 ? -1 : 1; + x.e = 0; + x.d = [0]; + return; } - // Minus sign? - if (v.charCodeAt(0) === 45) { - v = v.slice(1); + if (v < 0) { + v = -v; x.s = -1; } else { x.s = 1; } - return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v); - } - - Decimal.prototype = P; - - Decimal.ROUND_UP = 0; - Decimal.ROUND_DOWN = 1; - Decimal.ROUND_CEIL = 2; - Decimal.ROUND_FLOOR = 3; - Decimal.ROUND_HALF_UP = 4; - Decimal.ROUND_HALF_DOWN = 5; - Decimal.ROUND_HALF_EVEN = 6; - Decimal.ROUND_HALF_CEIL = 7; - Decimal.ROUND_HALF_FLOOR = 8; - Decimal.EUCLID = 9; - - Decimal.config = Decimal.set = config; - Decimal.clone = clone; - - Decimal.abs = abs; - Decimal.acos = acos; - Decimal.acosh = acosh; // ES6 - Decimal.add = add; - Decimal.asin = asin; - Decimal.asinh = asinh; // ES6 - Decimal.atan = atan; - Decimal.atanh = atanh; // ES6 - Decimal.atan2 = atan2; - Decimal.cbrt = cbrt; // ES6 - Decimal.ceil = ceil; - Decimal.cos = cos; - Decimal.cosh = cosh; // ES6 - Decimal.div = div; - Decimal.exp = exp; - Decimal.floor = floor; - Decimal.hypot = hypot; // ES6 - Decimal.ln = ln; - Decimal.log = log; - Decimal.log10 = log10; // ES6 - Decimal.log2 = log2; // ES6 - Decimal.max = max; - Decimal.min = min; - Decimal.mod = mod; - Decimal.mul = mul; - Decimal.pow = pow; - Decimal.random = random; - Decimal.round = round; - Decimal.sign = sign; // ES6 - Decimal.sin = sin; - Decimal.sinh = sinh; // ES6 - Decimal.sqrt = sqrt; - Decimal.sub = sub; - Decimal.tan = tan; - Decimal.tanh = tanh; // ES6 - Decimal.trunc = trunc; // ES6 - - if (obj === void 0) obj = {}; - if (obj) { - ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto']; - for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p]; - } - - Decimal.config(obj); - - return Decimal; - } - - - /* - * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function div(x, y) { - return new this(x).div(y); - } + // Fast path for small integers. + if (v === ~~v && v < 1e7) { + for (e = 0, i = v; i >= 10; i /= 10) e++; + x.e = e; + x.d = [v]; + return; + // Infinity, NaN. + } else if (v * 0 !== 0) { + if (!v) x.s = NaN; + x.e = NaN; + x.d = null; + return; + } - /* - * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The power to which to raise the base of the natural log. - * - */ - function exp(x) { - return new this(x).exp(); - } + return parseDecimal(x, v.toString()); + } else if (t !== 'string') { + throw Error(invalidArgument + v); + } - /* - * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`. - * - * x {number|string|Decimal} - * - */ - function floor(x) { - return finalise(x = new this(x), x.e + 1, 3); + // Minus sign? + if (v.charCodeAt(0) === 45) { + v = v.slice(1); + x.s = -1; + } else { + x.s = 1; + } + + return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v); + } + + Decimal.prototype = P; + + Decimal.ROUND_UP = 0; + Decimal.ROUND_DOWN = 1; + Decimal.ROUND_CEIL = 2; + Decimal.ROUND_FLOOR = 3; + Decimal.ROUND_HALF_UP = 4; + Decimal.ROUND_HALF_DOWN = 5; + Decimal.ROUND_HALF_EVEN = 6; + Decimal.ROUND_HALF_CEIL = 7; + Decimal.ROUND_HALF_FLOOR = 8; + Decimal.EUCLID = 9; + + Decimal.config = Decimal.set = config; + Decimal.clone = clone; + + Decimal.abs = abs; + Decimal.acos = acos; + Decimal.acosh = acosh; // ES6 + Decimal.add = add; + Decimal.asin = asin; + Decimal.asinh = asinh; // ES6 + Decimal.atan = atan; + Decimal.atanh = atanh; // ES6 + Decimal.atan2 = atan2; + Decimal.cbrt = cbrt; // ES6 + Decimal.ceil = ceil; + Decimal.cos = cos; + Decimal.cosh = cosh; // ES6 + Decimal.div = div; + Decimal.exp = exp; + Decimal.floor = floor; + Decimal.hypot = hypot; // ES6 + Decimal.ln = ln; + Decimal.log = log; + Decimal.log10 = log10; // ES6 + Decimal.log2 = log2; // ES6 + Decimal.max = max; + Decimal.min = min; + Decimal.mod = mod; + Decimal.mul = mul; + Decimal.pow = pow; + Decimal.random = random; + Decimal.round = round; + Decimal.sign = sign; // ES6 + Decimal.sin = sin; + Decimal.sinh = sinh; // ES6 + Decimal.sqrt = sqrt; + Decimal.sub = sub; + Decimal.tan = tan; + Decimal.tanh = tanh; // ES6 + Decimal.trunc = trunc; // ES6 + + if (obj === void 0) obj = {}; + if (obj) { + ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto']; + for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p]; } + Decimal.config(obj); - /* - * Return a new Decimal whose value is the square root of the sum of the squares of the arguments, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...) - * - */ - function hypot() { - var i, n, - t = new this(0); + return Decimal; +} - external = false; - for (i = 0; i < arguments.length;) { - n = new this(arguments[i++]); - if (!n.d) { - if (n.s) { - external = true; - return new this(1 / 0); - } - t = n; - } else if (t.d) { - t = t.plus(n.times(n)); - } - } +/* + * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function div(x, y) { + return new this(x).div(y); +} - external = true; - return t.sqrt(); - } +/* + * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} The power to which to raise the base of the natural log. + * + */ +function exp(x) { + return new this(x).exp(); +} - /* - * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function ln(x) { - return new this(x).ln(); - } +/* + * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`. + * + * x {number|string|Decimal} + * + */ +function floor(x) { + return finalise(x = new this(x), x.e + 1, 3); +} - /* - * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base - * is specified, rounded to `precision` significant digits using rounding mode `rounding`. - * - * log[y](x) - * - * x {number|string|Decimal} The argument of the logarithm. - * y {number|string|Decimal} The base of the logarithm. - * - */ - function log(x, y) { - return new this(x).log(y); +/* + * Return a new Decimal whose value is the square root of the sum of the squares of the arguments, + * rounded to `precision` significant digits using rounding mode `rounding`. + * + * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...) + * + */ +function hypot() { + var i, n, + t = new this(0); + + external = false; + + for (i = 0; i < arguments.length;) { + n = new this(arguments[i++]); + if (!n.d) { + if (n.s) { + external = true; + return new this(1 / 0); + } + t = n; + } else if (t.d) { + t = t.plus(n.times(n)); + } } + external = true; - /* - * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log2(x) { - return new this(x).log(2); - } + return t.sqrt(); +} - /* - * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log10(x) { - return new this(x).log(10); - } +/* + * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function ln(x) { + return new this(x).ln(); +} - /* - * Return a new Decimal whose value is the maximum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function max() { - return maxOrMin(this, arguments, 'lt'); - } +/* + * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base + * is specified, rounded to `precision` significant digits using rounding mode `rounding`. + * + * log[y](x) + * + * x {number|string|Decimal} The argument of the logarithm. + * y {number|string|Decimal} The base of the logarithm. + * + */ +function log(x, y) { + return new this(x).log(y); +} - /* - * Return a new Decimal whose value is the minimum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function min() { - return maxOrMin(this, arguments, 'gt'); - } +/* + * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function log2(x) { + return new this(x).log(2); +} - /* - * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mod(x, y) { - return new this(x).mod(y); - } +/* + * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function log10(x) { + return new this(x).log(10); +} - /* - * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mul(x, y) { - return new this(x).mul(y); - } +/* + * Return a new Decimal whose value is the maximum of the arguments. + * + * arguments {number|string|Decimal} + * + */ +function max() { + return maxOrMin(this, arguments, 'lt'); +} - /* - * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The base. - * y {number|string|Decimal} The exponent. - * - */ - function pow(x, y) { - return new this(x).pow(y); - } +/* + * Return a new Decimal whose value is the minimum of the arguments. + * + * arguments {number|string|Decimal} + * + */ +function min() { + return maxOrMin(this, arguments, 'gt'); +} - /* - * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with - * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros - * are produced). - * - * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive. - * - */ - function random(sd) { - var d, e, k, n, - i = 0, - r = new this(1), - rd = []; +/* + * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits + * using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function mod(x, y) { + return new this(x).mod(y); +} - if (sd === void 0) sd = this.precision; - else checkInt32(sd, 1, MAX_DIGITS); - k = Math.ceil(sd / LOG_BASE); +/* + * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function mul(x, y) { + return new this(x).mul(y); +} - if (!this.crypto) { - for (; i < k;) rd[i++] = Math.random() * 1e7 | 0; - // Browsers supporting crypto.getRandomValues. - } else if (crypto.getRandomValues) { - d = crypto.getRandomValues(new Uint32Array(k)); +/* + * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} The base. + * y {number|string|Decimal} The exponent. + * + */ +function pow(x, y) { + return new this(x).pow(y); +} - for (; i < k;) { - n = d[i]; - // 0 <= n < 4294967296 - // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865). - if (n >= 4.29e9) { - d[i] = crypto.getRandomValues(new Uint32Array(1))[0]; - } else { +/* + * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with + * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros + * are produced). + * + * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive. + * + */ +function random(sd) { + var d, e, k, n, + i = 0, + r = new this(1), + rd = []; - // 0 <= n <= 4289999999 - // 0 <= (n % 1e7) <= 9999999 - rd[i++] = n % 1e7; - } - } + if (sd === void 0) sd = this.precision; + else checkInt32(sd, 1, MAX_DIGITS); - // Node.js supporting crypto.randomBytes. - } else if (crypto.randomBytes) { + k = Math.ceil(sd / LOG_BASE); - // buffer - d = crypto.randomBytes(k *= 4); + if (!this.crypto) { + for (; i < k;) rd[i++] = Math.random() * 1e7 | 0; - for (; i < k;) { + // Browsers supporting crypto.getRandomValues. + } else if (crypto.getRandomValues) { + d = crypto.getRandomValues(new Uint32Array(k)); - // 0 <= n < 2147483648 - n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24); + for (; i < k;) { + n = d[i]; - // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286). - if (n >= 2.14e9) { - crypto.randomBytes(4).copy(d, i); - } else { + // 0 <= n < 4294967296 + // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865). + if (n >= 4.29e9) { + d[i] = crypto.getRandomValues(new Uint32Array(1))[0]; + } else { - // 0 <= n <= 2139999999 - // 0 <= (n % 1e7) <= 9999999 - rd.push(n % 1e7); - i += 4; - } + // 0 <= n <= 4289999999 + // 0 <= (n % 1e7) <= 9999999 + rd[i++] = n % 1e7; } - - i = k / 4; - } else { - throw Error(cryptoUnavailable); } - k = rd[--i]; - sd %= LOG_BASE; - - // Convert trailing digits to zeros according to sd. - if (k && sd) { - n = mathpow(10, LOG_BASE - sd); - rd[i] = (k / n | 0) * n; - } + // Node.js supporting crypto.randomBytes. + } else if (crypto.randomBytes) { - // Remove trailing words which are zero. - for (; rd[i] === 0; i--) rd.pop(); + // buffer + d = crypto.randomBytes(k *= 4); - // Zero? - if (i < 0) { - e = 0; - rd = [0]; - } else { - e = -1; + for (; i < k;) { - // Remove leading words which are zero and adjust exponent accordingly. - for (; rd[0] === 0; e -= LOG_BASE) rd.shift(); + // 0 <= n < 2147483648 + n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24); - // Count the digits of the first word of rd to determine leading zeros. - for (k = 1, n = rd[0]; n >= 10; n /= 10) k++; + // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286). + if (n >= 2.14e9) { + crypto.randomBytes(4).copy(d, i); + } else { - // Adjust the exponent for leading zeros of the first word of rd. - if (k < LOG_BASE) e -= LOG_BASE - k; + // 0 <= n <= 2139999999 + // 0 <= (n % 1e7) <= 9999999 + rd.push(n % 1e7); + i += 4; + } } - r.e = e; - r.d = rd; - - return r; + i = k / 4; + } else { + throw Error(cryptoUnavailable); } + k = rd[--i]; + sd %= LOG_BASE; - /* - * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`. - * - * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL). - * - * x {number|string|Decimal} - * - */ - function round(x) { - return finalise(x = new this(x), x.e + 1, this.rounding); + // Convert trailing digits to zeros according to sd. + if (k && sd) { + n = mathpow(10, LOG_BASE - sd); + rd[i] = (k / n | 0) * n; } + // Remove trailing words which are zero. + for (; rd[i] === 0; i--) rd.pop(); - /* - * Return - * 1 if x > 0, - * -1 if x < 0, - * 0 if x is 0, - * -0 if x is -0, - * NaN otherwise - * - */ - function sign(x) { - x = new this(x); - return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN; - } + // Zero? + if (i < 0) { + e = 0; + rd = [0]; + } else { + e = -1; + // Remove leading words which are zero and adjust exponent accordingly. + for (; rd[0] === 0; e -= LOG_BASE) rd.shift(); - /* - * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sin(x) { - return new this(x).sin(); + // Count the digits of the first word of rd to determine leading zeros. + for (k = 1, n = rd[0]; n >= 10; n /= 10) k++; + + // Adjust the exponent for leading zeros of the first word of rd. + if (k < LOG_BASE) e -= LOG_BASE - k; } + r.e = e; + r.d = rd; - /* - * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sinh(x) { - return new this(x).sinh(); - } + return r; +} - /* - * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function sqrt(x) { - return new this(x).sqrt(); - } +/* + * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`. + * + * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL). + * + * x {number|string|Decimal} + * + */ +function round(x) { + return finalise(x = new this(x), x.e + 1, this.rounding); +} - /* - * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function sub(x, y) { - return new this(x).sub(y); - } +/* + * Return + * 1 if x > 0, + * -1 if x < 0, + * 0 if x is 0, + * -0 if x is -0, + * NaN otherwise + * + */ +function sign(x) { + x = new this(x); + return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN; +} - /* - * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tan(x) { - return new this(x).tan(); - } +/* + * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits + * using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function sin(x) { + return new this(x).sin(); +} - /* - * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tanh(x) { - return new this(x).tanh(); - } +/* + * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function sinh(x) { + return new this(x).sinh(); +} - /* - * Return a new Decimal whose value is `x` truncated to an integer. - * - * x {number|string|Decimal} - * - */ - function trunc(x) { - return finalise(x = new this(x), x.e + 1, 1); - } +/* + * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} + * + */ +function sqrt(x) { + return new this(x).sqrt(); +} + +/* + * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits + * using rounding mode `rounding`. + * + * x {number|string|Decimal} + * y {number|string|Decimal} + * + */ +function sub(x, y) { + return new this(x).sub(y); +} - // Create and configure initial Decimal constructor. - Decimal = clone(Decimal); - // Create the internal constants from their string values. - LN10 = new Decimal(LN10); - PI = new Decimal(PI); +/* + * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant + * digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function tan(x) { + return new this(x).tan(); +} - // Export. +/* + * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision` + * significant digits using rounding mode `rounding`. + * + * x {number|string|Decimal} A value in radians. + * + */ +function tanh(x) { + return new this(x).tanh(); +} - // AMD. - if (true) { - !(__WEBPACK_AMD_DEFINE_RESULT__ = (function () { - return Decimal; - }).call(exports, __webpack_require__, exports, module), - __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__)); +/* + * Return a new Decimal whose value is `x` truncated to an integer. + * + * x {number|string|Decimal} + * + */ +function trunc(x) { + return finalise(x = new this(x), x.e + 1, 1); +} + + +// Create and configure initial Decimal constructor. +Decimal = clone(defaults); + +// Create the internal constants from their string values. +LN10 = new Decimal(ln10); +PI = new Decimal(pi); - // Node and other environments that support module.exports. - } else {} -})(this); +/* harmony default export */ __webpack_exports__["default"] = (Decimal); /***/ }), @@ -29317,7 +29314,7 @@ function initBladeburner() { Skills[SkillNames.Overclock] = new Skill({ name:SkillNames.Overclock, desc:"Each level of this skill decreases the time it takes " + - "to attempt a contract or operation by 1% (Max Level: 99)", + "to attempt a contract or operation by 1% (Max Level: 95)", baseCost:5, costInc:1, maxLvl:95, actionTime:1 }); @@ -30289,8 +30286,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _NetscriptEvaluator_js__WEBPACK_IMPORTED_MODULE_24__ = __webpack_require__(/*! ./NetscriptEvaluator.js */ 6); /* harmony import */ var _NetscriptEnvironment_js__WEBPACK_IMPORTED_MODULE_25__ = __webpack_require__(/*! ./NetscriptEnvironment.js */ 69); /* harmony import */ var _NetscriptPort_js__WEBPACK_IMPORTED_MODULE_26__ = __webpack_require__(/*! ./NetscriptPort.js */ 46); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_27__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_27___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_27__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_27__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_28__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_29__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_IPAddress_js__WEBPACK_IMPORTED_MODULE_30__ = __webpack_require__(/*! ../utils/IPAddress.js */ 16); @@ -30419,7 +30415,7 @@ function NetscriptFunctions(workerScript) { Math : Math, Date : Date, Number : Number, - hacknetnodes : _Player_js__WEBPACK_IMPORTED_MODULE_15__["Player"].hacknetNodes, + hacknetnodes : _Player_js__WEBPACK_IMPORTED_MODULE_15__["Player"].hacknetNodeWrappers, sprintf : sprintf, vsprintf: vsprintf, scan : function(ip=workerScript.serverIp, hostnames=true){ @@ -31386,7 +31382,8 @@ function NetscriptFunctions(workerScript) { if (!hasAISF) { throw Object(_NetscriptEvaluator_js__WEBPACK_IMPORTED_MODULE_24__["makeRuntimeRejectMsg"])(workerScript, "Cannot run getBitNodeMultipliers(). It requires Source-File 5 to run."); } - return _BitNode_js__WEBPACK_IMPORTED_MODULE_2__["BitNodeMultipliers"]; + let copy = Object.assign({}, _BitNode_js__WEBPACK_IMPORTED_MODULE_2__["BitNodeMultipliers"]); + return copy; }, getServerMoneyAvailable : function(ip){ if (workerScript.checkingRam) { @@ -52297,6 +52294,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "updateHacknetNodesContent", function() { return updateHacknetNodesContent; }); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "processAllHacknetNodeEarnings", function() { return processAllHacknetNodeEarnings; }); /* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "getHacknetNode", function() { return getHacknetNode; }); +/* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, "createPlayerHacknetNodeWrappers", function() { return createPlayerHacknetNodeWrappers; }); /* harmony import */ var _BitNode_js__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(/*! ./BitNode.js */ 15); /* harmony import */ var _Constants_js__WEBPACK_IMPORTED_MODULE_1__ = __webpack_require__(/*! ./Constants.js */ 3); /* harmony import */ var _engine_js__WEBPACK_IMPORTED_MODULE_2__ = __webpack_require__(/*! ./engine.js */ 5); @@ -52362,6 +52360,7 @@ function HacknetNode(name) { this.moneyGainRatePerSecond = 0; } + HacknetNode.prototype.updateMoneyGainRate = function() { //How much extra $/s is gained per level var gainPerLevel = _Constants_js__WEBPACK_IMPORTED_MODULE_1__["CONSTANTS"].HacknetNodeMoneyGainPerLevel; @@ -52486,6 +52485,36 @@ HacknetNode.fromJSON = function(value) { _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_7__["Reviver"].constructors.HacknetNode = HacknetNode; +var HacknetNodeWrapper = function(hacknetNodeObj) { + var _node = hacknetNodeObj; + return { + name : _node.name, + level : _node.level, + ram : _node.ram, + cores : _node.cores, + totalMoneyGenerated : _node.totalMoneyGenerated, + onlineTimeSeconds : _node.onlineTimeSeconds, + moneyGainRatePerSecond : _node.moneyGainRatePerSecond, + upgradeLevel : function(n) { + return _node.upgradeLevel(n); + }, + upgradeRam : function() { + return _node.upgradeRam(); + }, + upgradeCore : function() { + return _node.upgradeCore(); + }, + getLevelUpgradeCost : function(n) { + return _node.getLevelUpgradeCost(n); + }, + getRamUpgradeCost : function() { + return _node.getRamUpgradeCost(); + }, + getCoreUpgradeCost : function() { + return _node.getCoreUpgradeCost(); + } + } +} function purchaseHacknet() { /* INTERACTIVE TUTORIAL */ @@ -52775,8 +52804,31 @@ function updateHacknetNodeDomElement(nodeObj) { } } +function createPlayerHacknetNodeWrappers() { + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers.length = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length; + for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length; ++i) { + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i] = new HacknetNodeWrapper(_Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i]); + } +} + +function updatePlayerHacknetNodeWrappers() { + if (_Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers.length !== _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length) { + return createPlayerHacknetNodeWrappers(); + } + for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers.length; ++i) { + if (!(_Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i] instanceof HacknetNodeWrapper)) {return createPlayerHacknetNodeWrappers();} + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].level = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].level; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].ram = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].ram; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].cores = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].cores; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].totalMoneyGenerated = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].totalMoneyGenerated; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].onlineTimeSeconds = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].onlineTimeSeconds; + _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodeWrappers[i].moneyGainRatePerSecond = _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i].moneyGainRatePerSecond; + } +} + function processAllHacknetNodeEarnings(numCycles) { var total = 0; + updatePlayerHacknetNodeWrappers(); for (var i = 0; i < _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes.length; ++i) { total += processSingleHacknetNodeEarnings(numCycles, _Player_js__WEBPACK_IMPORTED_MODULE_4__["Player"].hacknetNodes[i]); } @@ -53128,8 +53180,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _Literature_js__WEBPACK_IMPORTED_MODULE_3__ = __webpack_require__(/*! ./Literature.js */ 53); /* harmony import */ var _Location_js__WEBPACK_IMPORTED_MODULE_4__ = __webpack_require__(/*! ./Location.js */ 4); /* harmony import */ var _Player_js__WEBPACK_IMPORTED_MODULE_5__ = __webpack_require__(/*! ./Player.js */ 0); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_6__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_6__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_7__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_8__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_9__ = __webpack_require__(/*! ../utils/JSONReviver.js */ 8); @@ -53763,10 +53814,10 @@ function Industry(params={}) { this.prodMult = 0; //Production multiplier //Financials - this.lastCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.lastCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.lastCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.lastCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); //Upgrades var numUpgrades = Object.keys(IndustryUpgrades).length; @@ -54064,13 +54115,13 @@ Industry.prototype.process = function(marketCycles=1, state, company) { console.log(this.thisCycleRevenue.toString()); console.log(this.thisCycleExpenses.toString()); Object(_utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_7__["dialogBoxCreate"])("Something went wrong when compting Corporation's revenue/expenses. This is a bug. Please report to game developer"); - this.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); } this.lastCycleRevenue = this.thisCycleRevenue.dividedBy(marketCycles * SecsPerMarketCycle); this.lastCycleExpenses = this.thisCycleExpenses.dividedBy(marketCycles * SecsPerMarketCycle); - this.thisCycleRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.thisCycleExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.thisCycleRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.thisCycleExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); //Once you start making revenue, the player should no longer be //considered new, and therefore no longer needs the 'tutorial' UI elements @@ -56181,9 +56232,9 @@ function Corporation(params={}) { this.divisions = []; //Financial stats - this.funds = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(150e9); - this.revenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.expenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.funds = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](150e9); + this.revenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.expenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); this.fundingRound = 0; this.public = false; //Publicly traded this.numShares = TOTALSHARES; @@ -56217,8 +56268,8 @@ Corporation.prototype.process = function() { //At the start of a new cycle, calculate profits from previous cycle if (state === "START") { - this.revenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); - this.expenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + this.revenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); + this.expenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); this.divisions.forEach((ind)=>{ this.revenue = this.revenue.plus(ind.lastCycleRevenue); this.expenses = this.expenses.plus(ind.lastCycleExpenses); @@ -56229,7 +56280,7 @@ Corporation.prototype.process = function() { Object(_utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_7__["dialogBoxCreate"])("There was an error calculating your Corporations funds and they got reset to 0. " + "This is a bug. Please report to game developer.

" + "(Your funds have been set to $150b for the inconvenience)"); - this.funds = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(150e9); + this.funds = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](150e9); } this.funds = this.funds.plus(cycleProfit); this.updateSharePrice(); @@ -57139,8 +57190,8 @@ Corporation.prototype.updateCorporationOverviewContent = function() { return; } var totalFunds = this.funds, - totalRevenue = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0), - totalExpenses = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_6___default.a(0); + totalRevenue = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0), + totalExpenses = new decimal_js__WEBPACK_IMPORTED_MODULE_6__["default"](0); var profit = this.revenue.minus(this.expenses).toNumber(), profitStr = profit >= 0 ? _utils_numeral_min_js__WEBPACK_IMPORTED_MODULE_10___default()(profit).format("$0.000a") : "-" + _utils_numeral_min_js__WEBPACK_IMPORTED_MODULE_10___default()(-1 * profit).format("$0.000a"); @@ -58810,8 +58861,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_17__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! ../utils/JSONReviver.js */ 8); /* harmony import */ var _utils_StringHelperFunctions_js__WEBPACK_IMPORTED_MODULE_19__ = __webpack_require__(/*! ../utils/StringHelperFunctions.js */ 2); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_20__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_20__ = __webpack_require__(/*! decimal.js */ 24); @@ -59036,6 +59086,8 @@ function loadGame(saveString) { } } + //Re-initialize Hacknet Node Wrappers + Object(_HacknetNode_js__WEBPACK_IMPORTED_MODULE_7__["createPlayerHacknetNodeWrappers"])(); return true; } @@ -59062,9 +59114,9 @@ function loadImportedGame(saveObj, saveString) { tempPlayer = JSON.parse(tempSaveObj.PlayerSave, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__["Reviver"]); //Parse Decimal.js objects - tempPlayer.money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default.a(tempPlayer.money); - tempPlayer.total_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default.a(tempPlayer.total_money); - tempPlayer.lifetime_money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_20___default.a(tempPlayer.lifetime_money); + tempPlayer.money = new decimal_js__WEBPACK_IMPORTED_MODULE_20__["default"](tempPlayer.money); + tempPlayer.total_money = new decimal_js__WEBPACK_IMPORTED_MODULE_20__["default"](tempPlayer.total_money); + tempPlayer.lifetime_money = new decimal_js__WEBPACK_IMPORTED_MODULE_20__["default"](tempPlayer.lifetime_money); tempAllServers = JSON.parse(tempSaveObj.AllServersSave, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__["Reviver"]); tempCompanies = JSON.parse(tempSaveObj.CompaniesSave, _utils_JSONReviver_js__WEBPACK_IMPORTED_MODULE_18__["Reviver"]); @@ -59252,6 +59304,9 @@ function loadImportedGame(saveObj, saveString) { } } + //Re-initialize Hacknet Node Wrappers + Object(_HacknetNode_js__WEBPACK_IMPORTED_MODULE_7__["createPlayerHacknetNodeWrappers"])(); + var popupId = "import-game-restart-game-notice"; var txt = Object(_utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_17__["createElement"])("p", { innerText:"Imported game! I would suggest saving the game and then reloading the page " + @@ -60687,8 +60742,7 @@ __webpack_require__.r(__webpack_exports__); /* harmony import */ var _SpecialServerIps_js__WEBPACK_IMPORTED_MODULE_15__ = __webpack_require__(/*! ./SpecialServerIps.js */ 17); /* harmony import */ var _StockMarket_js__WEBPACK_IMPORTED_MODULE_16__ = __webpack_require__(/*! ./StockMarket.js */ 22); /* harmony import */ var _Terminal_js__WEBPACK_IMPORTED_MODULE_17__ = __webpack_require__(/*! ./Terminal.js */ 18); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! ../utils/decimal.js */ 24); -/* harmony import */ var _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default = /*#__PURE__*/__webpack_require__.n(_utils_decimal_js__WEBPACK_IMPORTED_MODULE_18__); +/* harmony import */ var decimal_js__WEBPACK_IMPORTED_MODULE_18__ = __webpack_require__(/*! decimal.js */ 24); /* harmony import */ var _utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_19__ = __webpack_require__(/*! ../utils/DialogBox.js */ 7); /* harmony import */ var _utils_HelperFunctions_js__WEBPACK_IMPORTED_MODULE_20__ = __webpack_require__(/*! ../utils/HelperFunctions.js */ 1); /* harmony import */ var _utils_YesNoBox_js__WEBPACK_IMPORTED_MODULE_21__ = __webpack_require__(/*! ../utils/YesNoBox.js */ 12); @@ -60715,6 +60769,8 @@ __webpack_require__.r(__webpack_exports__); + +let BitNode8StartingMoney = 250e6; //Prestige by purchasing augmentation function prestigeAugmentation() { @@ -60743,7 +60799,7 @@ function prestigeAugmentation() { } if (Object(_Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["augmentationExists"])(_Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["AugmentationNames"].CashRoot) && _Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["Augmentations"][_Augmentations_js__WEBPACK_IMPORTED_MODULE_1__["AugmentationNames"].CashRoot].owned) { - _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].setMoney(new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default.a(1000000)); + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].setMoney(new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](1000000)); homeComp.programs.push(_CreateProgram_js__WEBPACK_IMPORTED_MODULE_5__["Programs"].BruteSSHProgram); } @@ -60809,7 +60865,7 @@ function prestigeAugmentation() { _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bladeburner = null; //BitNode 8: Ghost of Wall Street - if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8) {_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default.a(100e6);} + if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8) {_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](BitNode8StartingMoney);} if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_11__["hasWallStreetSF"]) { _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasWseAccount = true; _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasTixApiAccess = true; @@ -60937,7 +60993,7 @@ function prestigeSourceFile() { //BitNode 3: Corporatocracy if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 3) { - _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new _utils_decimal_js__WEBPACK_IMPORTED_MODULE_18___default.a(150e9); + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](150e9); homeComp.messages.push("corporation-management-handbook.lit"); Object(_utils_DialogBox_js__WEBPACK_IMPORTED_MODULE_19__["dialogBoxCreate"])("You received a copy of the Corporation Management Handbook on your home computer. " + "Read it if you need help getting started with Corporations!"); @@ -60987,6 +61043,13 @@ function prestigeSourceFile() { } + //BitNode 8: Ghost of Wall Street + if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8) {_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].money = new decimal_js__WEBPACK_IMPORTED_MODULE_18__["default"](BitNode8StartingMoney);} + if (_Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].bitNodeN === 8 || _NetscriptFunctions_js__WEBPACK_IMPORTED_MODULE_11__["hasWallStreetSF"]) { + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasWseAccount = true; + _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].hasTixApiAccess = true; + } + //Gain int exp _Player_js__WEBPACK_IMPORTED_MODULE_13__["Player"].gainIntelligenceExp(5); } @@ -97015,7 +97078,7 @@ var NetscriptHighlightRules = function(options) { "JSON|Math|" + // Other "this|arguments|prototype|window|document" , // Pseudo "keyword": - "const|yield|import|get|set|async|await|foop|" + + "const|yield|import|get|set|async|await|" + "break|case|catch|continue|default|delete|do|else|finally|for|function|" + "if|in|of|instanceof|new|return|switch|throw|try|typeof|let|var|while|with|debugger|" + "__parent__|__count__|escape|unescape|with|__proto__|" + diff --git a/doc/build/doctrees/changelog.doctree b/doc/build/doctrees/changelog.doctree index 68d425d855..1c53164d2e 100644 Binary files a/doc/build/doctrees/changelog.doctree and b/doc/build/doctrees/changelog.doctree differ diff --git a/doc/build/doctrees/environment.pickle b/doc/build/doctrees/environment.pickle index 3425ba2b13..0ae7a90c33 100644 Binary files a/doc/build/doctrees/environment.pickle and b/doc/build/doctrees/environment.pickle differ diff --git a/doc/build/html/_sources/changelog.rst.txt b/doc/build/html/_sources/changelog.rst.txt index 4dcd7947f1..03d84f44ae 100644 --- a/doc/build/html/_sources/changelog.rst.txt +++ b/doc/build/html/_sources/changelog.rst.txt @@ -3,8 +3,18 @@ Changelog ========= -v0.37.1 -------- +v0.37.2 - 6/2/2018 +------------------ + +* After joining the Bladeburners division, there is now a button to go to the Bladeburner content + in the 'City' page +* You now start with $250m in BitNode-8 (increased from $100m) +* Bug Fix: You can now no longer directly edit Hacknet Node values through NetscriptJS (hopefully) +* Bug Fix: Bladeburners is no longer accessible in BN-8 +* Bug Fix: getBitNodeMultipliers() Netscript function now returns a copy rather than the original object + +v0.37.1 - 5/22/2018 +------------------- * You now earn money from successfully completing Bladeburner contracts. The amount you earn is based on the difficulty of the contract. * Completing Field Analysis in Bladeburner now grants 0.1 rank diff --git a/doc/build/html/changelog.html b/doc/build/html/changelog.html index b4181b9c58..d0d6b296ea 100644 --- a/doc/build/html/changelog.html +++ b/doc/build/html/changelog.html @@ -50,8 +50,19 @@

Changelog

-
-

v0.37.1

+
+

v0.37.2 - 6/2/2018

+
    +
  • After joining the Bladeburners division, there is now a button to go to the Bladeburner content +in the 'City' page
    • +
  • You now start with $250m in BitNode-8 (increased from $100m)
    • +
  • Bug Fix: You can now no longer directly edit Hacknet Node values through NetscriptJS (hopefully)
    • +
  • Bug Fix: Bladeburners is no longer accessible in BN-8
    • +
  • Bug Fix: getBitNodeMultipliers() Netscript function now returns a copy rather than the original object
    • +
+
+
+

v0.37.1 - 5/22/2018

  • You now earn money from successfully completing Bladeburner contracts. The amount you earn is based on the difficulty of the contract.
    • @@ -971,7 +982,8 @@

    Table Of Contents

  • Terminal
  • Keyboard Shortcuts
  • Changelog
      -
    • v0.37.1
      • +
    • v0.37.2 - 6/2/2018
      • +
    • v0.37.1 - 5/22/2018
    • v0.37.0 - 5/20/2018
    • v0.36.1 - 5/11/2018
    • v0.36.0 - 5/2/2018
      • diff --git a/doc/build/html/index.html b/doc/build/html/index.html index 13a64c95f0..8e384e7958 100644 --- a/doc/build/html/index.html +++ b/doc/build/html/index.html @@ -268,7 +268,8 @@

      What is Bitburner? Changelog
        -
      • v0.37.1
        • +
      • v0.37.2 - 6/2/2018
        • +
      • v0.37.1 - 5/22/2018
      • v0.37.0 - 5/20/2018
      • v0.36.1 - 5/11/2018
      • v0.36.0 - 5/2/2018
        • diff --git a/doc/build/html/searchindex.js b/doc/build/html/searchindex.js index f0ef76224e..0439368a68 100644 --- a/doc/build/html/searchindex.js +++ b/doc/build/html/searchindex.js @@ -1 +1 @@ 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\ No newline at end of file diff --git a/doc/source/changelog.rst b/doc/source/changelog.rst index 4dcd7947f1..03d84f44ae 100644 --- a/doc/source/changelog.rst +++ b/doc/source/changelog.rst @@ -3,8 +3,18 @@ Changelog ========= -v0.37.1 -------- +v0.37.2 - 6/2/2018 +------------------ + +* After joining the Bladeburners division, there is now a button to go to the Bladeburner content + in the 'City' page +* You now start with $250m in BitNode-8 (increased from $100m) +* Bug Fix: You can now no longer directly edit Hacknet Node values through NetscriptJS (hopefully) +* Bug Fix: Bladeburners is no longer accessible in BN-8 +* Bug Fix: getBitNodeMultipliers() Netscript function now returns a copy rather than the original object + +v0.37.1 - 5/22/2018 +------------------- * You now earn money from successfully completing Bladeburner contracts. The amount you earn is based on the difficulty of the contract. * Completing Field Analysis in Bladeburner now grants 0.1 rank diff --git a/netscript.js b/netscript.js index d42b2bcb82..88fd9a03bb 100644 --- a/netscript.js +++ b/netscript.js @@ -103,7 +103,7 @@ var NetscriptHighlightRules = function(options) { "JSON|Math|" + // Other "this|arguments|prototype|window|document" , // Pseudo "keyword": - "const|yield|import|get|set|async|await|foop|" + + "const|yield|import|get|set|async|await|" + "break|case|catch|continue|default|delete|do|else|finally|for|function|" + "if|in|of|instanceof|new|return|switch|throw|try|typeof|let|var|while|with|debugger|" + "__parent__|__count__|escape|unescape|with|__proto__|" + diff --git a/package-lock.json b/package-lock.json index 2798aa85df..f491032025 100644 --- a/package-lock.json +++ b/package-lock.json @@ -7432,6 +7432,11 @@ "resolved": "https://registry.npmjs.org/decamelize/-/decamelize-1.2.0.tgz", "integrity": "sha1-9lNNFRSCabIDUue+4m9QH5oZEpA=" }, + "decimal.js": { + "version": "7.2.3", + "resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-7.2.3.tgz", + "integrity": "sha512-AoFI37QS0S87Ft0r3Bdz4q9xSpm1Paa9lSeKLXgMPk/u/+QPIM5Gy4DHcZQS1seqPJH4gHLauPGn347z0HbsrA==" + }, "decode-uri-component": { "version": "0.2.0", "resolved": "https://registry.npmjs.org/decode-uri-component/-/decode-uri-component-0.2.0.tgz", diff --git a/package.json b/package.json index 6d39d7f22a..a8487b3d44 100644 --- a/package.json +++ b/package.json @@ -13,6 +13,7 @@ "async": "^2.1.2", "bluebird": "^3.5.1", "brace": "^0.11.1", + "decimal.js": "7.2.3", "enhanced-resolve": "^3.4.0", "escope": "^3.6.0", "file-saver": "^1.3.3", diff --git a/src/Bladeburner.js b/src/Bladeburner.js index 312363f8bb..daca05e914 100644 --- a/src/Bladeburner.js +++ b/src/Bladeburner.js @@ -3185,7 +3185,7 @@ function initBladeburner() { Skills[SkillNames.Overclock] = new Skill({ name:SkillNames.Overclock, desc:"Each level of this skill decreases the time it takes " + - "to attempt a contract or operation by 1% (Max Level: 99)", + "to attempt a contract or operation by 1% (Max Level: 95)", baseCost:5, costInc:1, maxLvl:95, actionTime:1 }); diff --git a/src/CompanyManagement.js b/src/CompanyManagement.js index 6f4a3925b0..9414d65300 100644 --- a/src/CompanyManagement.js +++ b/src/CompanyManagement.js @@ -5,7 +5,7 @@ import {showLiterature} from "./Literature.js"; import {Locations} from "./Location.js"; import {Player} from "./Player.js"; -import Decimal from '../utils/decimal.js'; +import Decimal from "decimal.js"; import {dialogBoxCreate} from "../utils/DialogBox.js"; import {getRandomInt, removeElementById, createElement, createAccordionElement, diff --git a/src/Constants.js b/src/Constants.js index 87274b7f01..3e665a6635 100644 --- a/src/Constants.js +++ b/src/Constants.js @@ -1,5 +1,5 @@ let CONSTANTS = { - Version: "0.37.1", + Version: "0.37.2", //Max level for any skill, assuming no multipliers. Determined by max numerical value in javascript for experience //and the skill level formula in Player.js. Note that all this means it that when experience hits MAX_INT, then @@ -484,16 +484,13 @@ let CONSTANTS = { "World Stock Exchange account and TIX API Access
        ", LatestUpdate: - "v0.37.1
        " + - "* You now earn money from successfully completing Bladeburner contracts. The amount you earn is based " + - "on the difficulty of the contract.
        " + - "* Completing Field Analysis in Bladeburner now grants 0.1 rank
        " + - "* The maximum RAM you can get on a purchased server is now 1,048,576GB (2^20)
        " + - "* Bug Fix: Fixed Netscript syntax highlighting issues with the new NetscriptJS
        " + - "* Bug Fix: Netscript Functions now properly incur RAM costs in NetscriptJS
        " + - "* Bug Fix: deleteServer() now fails if its called on the server you are currently connected to
        " + - "* Removed in-game Netscript documentation, since it was outdated and difficult to maintain.
        " + - "* Bug Fix: Updated the gymWorkout() Singularity function with the new exp/cost values for gyms
        " + "v0.37.2
        " + + "* After joining the Bladeburners division, there is now a button to go to the Bladeburner content " + + "in the 'City' page
        " + + "* You now start with $250m in BitNode-8 (increased from $100m)
        " + + "* Bug Fix: You can now no longer directly edit Hacknet Node values through NetscriptJS (hopefully)
        " + + "* Bug Fix: Bladeburners is no longer accessible in BN-8
        " + + "* Bug Fix: getBitNodeMultipliers() Netscript function now returns a copy rather than the original object
        " } export {CONSTANTS}; diff --git a/src/HacknetNode.js b/src/HacknetNode.js index 4c7597b735..8461dd58a2 100644 --- a/src/HacknetNode.js +++ b/src/HacknetNode.js @@ -56,6 +56,7 @@ function HacknetNode(name) { this.moneyGainRatePerSecond = 0; } + HacknetNode.prototype.updateMoneyGainRate = function() { //How much extra $/s is gained per level var gainPerLevel = CONSTANTS.HacknetNodeMoneyGainPerLevel; @@ -180,6 +181,36 @@ HacknetNode.fromJSON = function(value) { Reviver.constructors.HacknetNode = HacknetNode; +var HacknetNodeWrapper = function(hacknetNodeObj) { + var _node = hacknetNodeObj; + return { + name : _node.name, + level : _node.level, + ram : _node.ram, + cores : _node.cores, + totalMoneyGenerated : _node.totalMoneyGenerated, + onlineTimeSeconds : _node.onlineTimeSeconds, + moneyGainRatePerSecond : _node.moneyGainRatePerSecond, + upgradeLevel : function(n) { + return _node.upgradeLevel(n); + }, + upgradeRam : function() { + return _node.upgradeRam(); + }, + upgradeCore : function() { + return _node.upgradeCore(); + }, + getLevelUpgradeCost : function(n) { + return _node.getLevelUpgradeCost(n); + }, + getRamUpgradeCost : function() { + return _node.getRamUpgradeCost(); + }, + getCoreUpgradeCost : function() { + return _node.getCoreUpgradeCost(); + } + } +} function purchaseHacknet() { /* INTERACTIVE TUTORIAL */ @@ -469,8 +500,31 @@ function updateHacknetNodeDomElement(nodeObj) { } } +function createPlayerHacknetNodeWrappers() { + Player.hacknetNodeWrappers.length = Player.hacknetNodes.length; + for (var i = 0; i < Player.hacknetNodes.length; ++i) { + Player.hacknetNodeWrappers[i] = new HacknetNodeWrapper(Player.hacknetNodes[i]); + } +} + +function updatePlayerHacknetNodeWrappers() { + if (Player.hacknetNodeWrappers.length !== Player.hacknetNodes.length) { + return createPlayerHacknetNodeWrappers(); + } + for (var i = 0; i < Player.hacknetNodeWrappers.length; ++i) { + if (!(Player.hacknetNodeWrappers[i] instanceof HacknetNodeWrapper)) {return createPlayerHacknetNodeWrappers();} + Player.hacknetNodeWrappers[i].level = Player.hacknetNodes[i].level; + Player.hacknetNodeWrappers[i].ram = Player.hacknetNodes[i].ram; + Player.hacknetNodeWrappers[i].cores = Player.hacknetNodes[i].cores; + Player.hacknetNodeWrappers[i].totalMoneyGenerated = Player.hacknetNodes[i].totalMoneyGenerated; + Player.hacknetNodeWrappers[i].onlineTimeSeconds = Player.hacknetNodes[i].onlineTimeSeconds; + Player.hacknetNodeWrappers[i].moneyGainRatePerSecond = Player.hacknetNodes[i].moneyGainRatePerSecond; + } +} + function processAllHacknetNodeEarnings(numCycles) { var total = 0; + updatePlayerHacknetNodeWrappers(); for (var i = 0; i < Player.hacknetNodes.length; ++i) { total += processSingleHacknetNodeEarnings(numCycles, Player.hacknetNodes[i]); } @@ -503,4 +557,4 @@ function getHacknetNode(name) { export {hacknetNodesInit, HacknetNode, purchaseHacknet, updateTotalHacknetProduction, getCostOfNextHacknetNode, updateHacknetNodesMultiplierButtons, getMaxNumberLevelUpgrades, displayHacknetNodesContent, updateHacknetNodesContent, processAllHacknetNodeEarnings, - getHacknetNode}; + getHacknetNode, createPlayerHacknetNodeWrappers}; diff --git a/src/Location.js b/src/Location.js index 65ad38c67b..30e8bdf1ca 100644 --- a/src/Location.js +++ b/src/Location.js @@ -726,6 +726,7 @@ function displayLocationContent() { securityJob.style.display = "block"; agentJob.style.display = "block"; if (Player.bitNodeN === 6 || hasBladeburnerSF === true) { + if (Player.bitNodeN === 8) {break;} if (Player.bladeburner instanceof Bladeburner) { //Note: Can't infiltrate NSA when part of bladeburner nsaBladeburner.innerText = "Enter Bladeburner Headquarters"; diff --git a/src/NetscriptFunctions.js b/src/NetscriptFunctions.js index c5f5c7ffa9..6e40dddbb4 100644 --- a/src/NetscriptFunctions.js +++ b/src/NetscriptFunctions.js @@ -58,7 +58,7 @@ import {makeRuntimeRejectMsg, netscriptDelay, runScriptFromScript, import {Environment} from "./NetscriptEnvironment.js"; import {NetscriptPort} from "./NetscriptPort.js"; -import Decimal from '../utils/decimal.js'; +import Decimal from "decimal.js"; import {dialogBoxCreate} from "../utils/DialogBox.js"; import {printArray, powerOfTwo} from "../utils/HelperFunctions.js"; import {createRandomIp} from "../utils/IPAddress.js"; @@ -151,7 +151,7 @@ function NetscriptFunctions(workerScript) { Math : Math, Date : Date, Number : Number, - hacknetnodes : Player.hacknetNodes, + hacknetnodes : Player.hacknetNodeWrappers, sprintf : sprintf, vsprintf: vsprintf, scan : function(ip=workerScript.serverIp, hostnames=true){ @@ -1118,7 +1118,8 @@ function NetscriptFunctions(workerScript) { if (!hasAISF) { throw makeRuntimeRejectMsg(workerScript, "Cannot run getBitNodeMultipliers(). It requires Source-File 5 to run."); } - return BitNodeMultipliers; + let copy = Object.assign({}, BitNodeMultipliers); + return copy; }, getServerMoneyAvailable : function(ip){ if (workerScript.checkingRam) { diff --git a/src/Player.js b/src/Player.js index f3883e8b60..4d76c79de1 100644 --- a/src/Player.js +++ b/src/Player.js @@ -19,7 +19,7 @@ import {AllServers, Server, AddToAllServers} from "./Server.js"; import {SpecialServerIps, SpecialServerNames} from "./SpecialServerIps.js"; import {SourceFiles, applySourceFile} from "./SourceFile.js"; -import Decimal from '../utils/decimal.js'; +import Decimal from "decimal.js"; import {dialogBoxCreate} from "../utils/DialogBox.js"; import {clearEventListeners} from "../utils/HelperFunctions.js"; import {createRandomIp} from "../utils/IPAddress.js"; @@ -99,6 +99,7 @@ function PlayerObject() { this.currentServer = ""; //IP address of Server currently being accessed through terminal this.purchasedServers = []; //IP Addresses of purchased servers this.hacknetNodes = []; + this.hacknetNodeWrappers = []; this.totalHacknetNodeProduction = 0; //Factions @@ -390,16 +391,8 @@ PlayerObject.prototype.prestigeSourceFile = function() { if (this.bitNodeN === 3) {this.money = new Decimal(150e9);} this.corporation = 0; - //Reset Bladeburner this.bladeburner = 0; - //BitNode 8: Ghost of Wall Street - if (this.bitNodeN === 8) {this.money = new Decimal(100000000);} - if (this.bitNodeN === 8 || hasWallStreetSF) { - this.hasWseAccount = true; - this.hasTixApiAccess = true; - } - this.playtimeSinceLastAug = 0; this.scriptProdSinceLastAug = 0; } diff --git a/src/Prestige.js b/src/Prestige.js index ceaf6e56a5..51ba473552 100644 --- a/src/Prestige.js +++ b/src/Prestige.js @@ -27,13 +27,15 @@ import {initStockMarket, initSymbolToStockMap, stockMarketContentCreated, setStockMarketContentCreated} from "./StockMarket.js"; import {Terminal, postNetburnerText} from "./Terminal.js"; -import Decimal from '../utils/decimal.js'; +import Decimal from "decimal.js"; import {dialogBoxCreate} from "../utils/DialogBox.js"; import {createPopup, createElement, removeElementById, exceptionAlert} from "../utils/HelperFunctions.js"; import {yesNoBoxCreate, yesNoBoxGetYesButton, yesNoBoxGetNoButton, yesNoBoxClose} from "../utils/YesNoBox.js"; +let BitNode8StartingMoney = 250e6; + //Prestige by purchasing augmentation function prestigeAugmentation() { initBitNodeMultipliers(); @@ -127,7 +129,7 @@ function prestigeAugmentation() { Player.bladeburner = null; //BitNode 8: Ghost of Wall Street - if (Player.bitNodeN === 8) {Player.money = new Decimal(100e6);} + if (Player.bitNodeN === 8) {Player.money = new Decimal(BitNode8StartingMoney);} if (Player.bitNodeN === 8 || hasWallStreetSF) { Player.hasWseAccount = true; Player.hasTixApiAccess = true; @@ -305,6 +307,13 @@ function prestigeSourceFile() { } + //BitNode 8: Ghost of Wall Street + if (Player.bitNodeN === 8) {Player.money = new Decimal(BitNode8StartingMoney);} + if (Player.bitNodeN === 8 || hasWallStreetSF) { + Player.hasWseAccount = true; + Player.hasTixApiAccess = true; + } + //Gain int exp Player.gainIntelligenceExp(5); } diff --git a/src/SaveObject.js b/src/SaveObject.js index 020ecca3ab..244c8820c7 100644 --- a/src/SaveObject.js +++ b/src/SaveObject.js @@ -8,7 +8,8 @@ import {loadFactions, Factions, processPassiveFactionRepGain} from "./Faction.js"; import {FconfSettings, loadFconf} from "./Fconf.js"; import {loadAllGangs, AllGangs} from "./Gang.js"; -import {processAllHacknetNodeEarnings} from "./HacknetNode.js"; +import {processAllHacknetNodeEarnings, + createPlayerHacknetNodeWrappers} from "./HacknetNode.js"; import {loadMessages, initMessages, Messages} from "./Message.js"; import {Player, loadPlayer} from "./Player.js"; import {loadAllRunningScripts} from "./Script.js"; @@ -24,7 +25,7 @@ import {Reviver, Generic_toJSON, Generic_fromJSON} from "../utils/JSONReviver.js"; import {formatNumber} from "../utils/StringHelperFunctions.js"; -import Decimal from '../utils/decimal.js'; +import Decimal from "decimal.js"; /* SaveObject.js * Defines the object used to save/load games @@ -227,6 +228,8 @@ function loadGame(saveString) { } } + //Re-initialize Hacknet Node Wrappers + createPlayerHacknetNodeWrappers(); return true; } @@ -443,6 +446,9 @@ function loadImportedGame(saveObj, saveString) { } } + //Re-initialize Hacknet Node Wrappers + createPlayerHacknetNodeWrappers(); + var popupId = "import-game-restart-game-notice"; var txt = createElement("p", { innerText:"Imported game! I would suggest saving the game and then reloading the page " + diff --git a/src/StockMarket.js b/src/StockMarket.js index 7a060111ad..9c9a6b6b3a 100644 --- a/src/StockMarket.js +++ b/src/StockMarket.js @@ -702,6 +702,9 @@ function displayStockMarketContent() { wseAccountButton.innerText = "Buy WSE Account - $" + formatNumber(CONSTANTS.WSEAccountCost, 2).toString(); if (!Player.hasWseAccount && Player.money.gte(CONSTANTS.WSEAccountCost)) { wseAccountButton.setAttribute("class", "a-link-button"); + } else if (Player.hasWseAccount){ + wseAccountButton.innerText = "WSE Account - Purchased"; + wseAccountButton.setAttribute("class", "a-link-button-bought"); } else { wseAccountButton.setAttribute("class", "a-link-button-inactive"); } @@ -720,6 +723,9 @@ function displayStockMarketContent() { formatNumber(CONSTANTS.TIXAPICost, 2).toString(); if (!Player.hasTixApiAccess && Player.money.gte(CONSTANTS.TIXAPICost)) { tixApiAccessButton.setAttribute("class", "a-link-button"); + } else if(Player.hasTixApiAccess) { + tixApiAccessButton.innerText = "Trade Information eXchange (TIX) API Access - Purchased" + tixApiAccessButton.setAttribute("class", "a-link-button-bought"); } else { tixApiAccessButton.setAttribute("class", "a-link-button-inactive"); } diff --git a/src/engine.js b/src/engine.js index 809405e2ff..d913f39522 100644 --- a/src/engine.js +++ b/src/engine.js @@ -650,6 +650,7 @@ let Engine = { //Generic Locations (common to every city): // World Stock Exchange // Corporation (if applicable) + // Bladeburner HQ (if applicable); var genericLocationsList = document.getElementById("generic-locations-list"); genericLocationsList.style.display = "inline"; removeChildrenFromElement(genericLocationsList); @@ -676,6 +677,18 @@ let Engine = { })); genericLocationsList.appendChild(li); } + + if (Player.bladeburner instanceof Bladeburner) { + var li = createElement("li"); + li.appendChild(createElement("a", { + innerText:"Bladeburner Headquarters", class:"a-link-button", + clickListener:()=>{ + Engine.loadBladeburnerContent(); + return false; + } + })); + genericLocationsList.appendChild(li); + } }, displayFactionsInfo: function() { @@ -738,9 +751,9 @@ let Engine = { clickListener:()=>{ joinFaction(Factions[factionName]); for (var i = 0; i < Player.factionInvitations.length; ++i) { - if (Player.factionInvitations[i] == factionName) { + if (Player.factionInvitations[i] == factionName || Factions[Player.factionInvitations[i]].isBanned) { Player.factionInvitations.splice(i, 1); - break; + i--; } } Engine.displayFactionsInfo(); diff --git a/utils/decimal.js b/utils/decimal.js deleted file mode 100644 index deca2957e1..0000000000 --- a/utils/decimal.js +++ /dev/null @@ -1,4812 +0,0 @@ -/*! decimal.js v7.2.3 https://github.com/MikeMcl/decimal.js/LICENCE */ -;(function (globalScope) { - 'use strict'; - - - /* - * decimal.js v7.2.3 - * An arbitrary-precision Decimal type for JavaScript. - * https://github.com/MikeMcl/decimal.js - * Copyright (c) 2017 Michael Mclaughlin - * MIT Licence - */ - - - // ----------------------------------- EDITABLE DEFAULTS ------------------------------------ // - - - // The maximum exponent magnitude. - // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`. - var EXP_LIMIT = 9e15, // 0 to 9e15 - - // The limit on the value of `precision`, and on the value of the first argument to - // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`. - MAX_DIGITS = 1e9, // 0 to 1e9 - - // Base conversion alphabet. - NUMERALS = '0123456789abcdef', - // The natural logarithm of 10 (1025 digits). - LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058', - - // Pi (1025 digits). - PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789', - - - // The initial configuration properties of the Decimal constructor. - Decimal = { - - // These values must be integers within the stated ranges (inclusive). - // Most of these values can be changed at run-time using the `Decimal.config` method. - - // The maximum number of significant digits of the result of a calculation or base conversion. - // E.g. `Decimal.config({ precision: 20 });` - precision: 20, // 1 to MAX_DIGITS - - // The rounding mode used when rounding to `precision`. - // - // ROUND_UP 0 Away from zero. - // ROUND_DOWN 1 Towards zero. - // ROUND_CEIL 2 Towards +Infinity. - // ROUND_FLOOR 3 Towards -Infinity. - // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up. - // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. - // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. - // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. - // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. - // - // E.g. - // `Decimal.rounding = 4;` - // `Decimal.rounding = Decimal.ROUND_HALF_UP;` - rounding: 4, // 0 to 8 - - // The modulo mode used when calculating the modulus: a mod n. - // The quotient (q = a / n) is calculated according to the corresponding rounding mode. - // The remainder (r) is calculated as: r = a - n * q. - // - // UP 0 The remainder is positive if the dividend is negative, else is negative. - // DOWN 1 The remainder has the same sign as the dividend (JavaScript %). - // FLOOR 3 The remainder has the same sign as the divisor (Python %). - // HALF_EVEN 6 The IEEE 754 remainder function. - // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive. - // - // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian - // division (9) are commonly used for the modulus operation. The other rounding modes can also - // be used, but they may not give useful results. - modulo: 1, // 0 to 9 - - // The exponent value at and beneath which `toString` returns exponential notation. - // JavaScript numbers: -7 - toExpNeg: -7, // 0 to -EXP_LIMIT - - // The exponent value at and above which `toString` returns exponential notation. - // JavaScript numbers: 21 - toExpPos: 21, // 0 to EXP_LIMIT - - // The minimum exponent value, beneath which underflow to zero occurs. - // JavaScript numbers: -324 (5e-324) - minE: -EXP_LIMIT, // -1 to -EXP_LIMIT - - // The maximum exponent value, above which overflow to Infinity occurs. - // JavaScript numbers: 308 (1.7976931348623157e+308) - maxE: EXP_LIMIT, // 1 to EXP_LIMIT - - // Whether to use cryptographically-secure random number generation, if available. - crypto: false // true/false - }, - - - // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- // - - - inexact, noConflict, quadrant, - external = true, - - decimalError = '[DecimalError] ', - invalidArgument = decimalError + 'Invalid argument: ', - precisionLimitExceeded = decimalError + 'Precision limit exceeded', - cryptoUnavailable = decimalError + 'crypto unavailable', - - mathfloor = Math.floor, - mathpow = Math.pow, - - isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i, - isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i, - isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i, - isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, - - BASE = 1e7, - LOG_BASE = 7, - MAX_SAFE_INTEGER = 9007199254740991, - - LN10_PRECISION = LN10.length - 1, - PI_PRECISION = PI.length - 1, - - // Decimal.prototype object - P = {}; - - - // Decimal prototype methods - - - /* - * absoluteValue abs - * ceil - * comparedTo cmp - * cosine cos - * cubeRoot cbrt - * decimalPlaces dp - * dividedBy div - * dividedToIntegerBy divToInt - * equals eq - * floor - * greaterThan gt - * greaterThanOrEqualTo gte - * hyperbolicCosine cosh - * hyperbolicSine sinh - * hyperbolicTangent tanh - * inverseCosine acos - * inverseHyperbolicCosine acosh - * inverseHyperbolicSine asinh - * inverseHyperbolicTangent atanh - * inverseSine asin - * inverseTangent atan - * isFinite - * isInteger isInt - * isNaN - * isNegative isNeg - * isPositive isPos - * isZero - * lessThan lt - * lessThanOrEqualTo lte - * logarithm log - * [maximum] [max] - * [minimum] [min] - * minus sub - * modulo mod - * naturalExponential exp - * naturalLogarithm ln - * negated neg - * plus add - * precision sd - * round - * sine sin - * squareRoot sqrt - * tangent tan - * times mul - * toBinary - * toDecimalPlaces toDP - * toExponential - * toFixed - * toFraction - * toHexadecimal toHex - * toNearest - * toNumber - * toOctal - * toPower pow - * toPrecision - * toSignificantDigits toSD - * toString - * truncated trunc - * valueOf toJSON - */ - - - /* - * Return a new Decimal whose value is the absolute value of this Decimal. - * - */ - P.absoluteValue = P.abs = function () { - var x = new this.constructor(this); - if (x.s < 0) x.s = 1; - return finalise(x); - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of positive Infinity. - * - */ - P.ceil = function () { - return finalise(new this.constructor(this), this.e + 1, 2); - }; - - - /* - * Return - * 1 if the value of this Decimal is greater than the value of `y`, - * -1 if the value of this Decimal is less than the value of `y`, - * 0 if they have the same value, - * NaN if the value of either Decimal is NaN. - * - */ - P.comparedTo = P.cmp = function (y) { - var i, j, xdL, ydL, - x = this, - xd = x.d, - yd = (y = new x.constructor(y)).d, - xs = x.s, - ys = y.s; - - // Either NaN or ±Infinity? - if (!xd || !yd) { - return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1; - } - - // Either zero? - if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0; - - // Signs differ? - if (xs !== ys) return xs; - - // Compare exponents. - if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1; - - xdL = xd.length; - ydL = yd.length; - - // Compare digit by digit. - for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) { - if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1; - } - - // Compare lengths. - return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1; - }; - - - /* - * Return a new Decimal whose value is the cosine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * cos(0) = 1 - * cos(-0) = 1 - * cos(Infinity) = NaN - * cos(-Infinity) = NaN - * cos(NaN) = NaN - * - */ - P.cosine = P.cos = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.d) return new Ctor(NaN); - - // cos(0) = cos(-0) = 1 - if (!x.d[0]) return new Ctor(1); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; - - x = cosine(Ctor, toLessThanHalfPi(Ctor, x)); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true); - }; - - - /* - * - * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * cbrt(0) = 0 - * cbrt(-0) = -0 - * cbrt(1) = 1 - * cbrt(-1) = -1 - * cbrt(N) = N - * cbrt(-I) = -I - * cbrt(I) = I - * - * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3)) - * - */ - P.cubeRoot = P.cbrt = function () { - var e, m, n, r, rep, s, sd, t, t3, t3plusx, - x = this, - Ctor = x.constructor; - - if (!x.isFinite() || x.isZero()) return new Ctor(x); - external = false; - - // Initial estimate. - s = x.s * Math.pow(x.s * x, 1 / 3); - - // Math.cbrt underflow/overflow? - // Pass x to Math.pow as integer, then adjust the exponent of the result. - if (!s || Math.abs(s) == 1 / 0) { - n = digitsToString(x.d); - e = x.e; - - // Adjust n exponent so it is a multiple of 3 away from x exponent. - if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00'); - s = Math.pow(n, 1 / 3); - - // Rarely, e may be one less than the result exponent value. - e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2)); - - if (s == 1 / 0) { - n = '5e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } - - r = new Ctor(n); - r.s = x.s; - } else { - r = new Ctor(s.toString()); - } - - sd = (e = Ctor.precision) + 3; - - // Halley's method. - // TODO? Compare Newton's method. - for (;;) { - t = r; - t3 = t.times(t).times(t); - t3plusx = t3.plus(x); - r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1); - - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); - - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999 - // , i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { - - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); - - if (t.times(t).times(t).eq(x)) { - r = t; - break; - } - } - - sd += 4; - rep = 1; - } else { - - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).times(r).eq(x); - } - - break; - } - } - } - - external = true; - - return finalise(r, e, Ctor.rounding, m); - }; - - - /* - * Return the number of decimal places of the value of this Decimal. - * - */ - P.decimalPlaces = P.dp = function () { - var w, - d = this.d, - n = NaN; - - if (d) { - w = d.length - 1; - n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE; - - // Subtract the number of trailing zeros of the last word. - w = d[w]; - if (w) for (; w % 10 == 0; w /= 10) n--; - if (n < 0) n = 0; - } - - return n; - }; - - - /* - * n / 0 = I - * n / N = N - * n / I = 0 - * 0 / n = 0 - * 0 / 0 = N - * 0 / N = N - * 0 / I = 0 - * N / n = N - * N / 0 = N - * N / N = N - * N / I = N - * I / n = I - * I / 0 = I - * I / N = N - * I / I = N - * - * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedBy = P.div = function (y) { - return divide(this, new this.constructor(y)); - }; - - - /* - * Return a new Decimal whose value is the integer part of dividing the value of this Decimal - * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedToIntegerBy = P.divToInt = function (y) { - var x = this, - Ctor = x.constructor; - return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding); - }; - - - /* - * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false. - * - */ - P.equals = P.eq = function (y) { - return this.cmp(y) === 0; - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of negative Infinity. - * - */ - P.floor = function () { - return finalise(new this.constructor(this), this.e + 1, 3); - }; - - - /* - * Return true if the value of this Decimal is greater than the value of `y`, otherwise return - * false. - * - */ - P.greaterThan = P.gt = function (y) { - return this.cmp(y) > 0; - }; - - - /* - * Return true if the value of this Decimal is greater than or equal to the value of `y`, - * otherwise return false. - * - */ - P.greaterThanOrEqualTo = P.gte = function (y) { - var k = this.cmp(y); - return k == 1 || k === 0; - }; - - - /* - * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [1, Infinity] - * - * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ... - * - * cosh(0) = 1 - * cosh(-0) = 1 - * cosh(Infinity) = Infinity - * cosh(-Infinity) = Infinity - * cosh(NaN) = NaN - * - * x time taken (ms) result - * 1000 9 9.8503555700852349694e+433 - * 10000 25 4.4034091128314607936e+4342 - * 100000 171 1.4033316802130615897e+43429 - * 1000000 3817 1.5166076984010437725e+434294 - * 10000000 abandoned after 2 minute wait - * - * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x)) - * - */ - P.hyperbolicCosine = P.cosh = function () { - var k, n, pr, rm, len, - x = this, - Ctor = x.constructor, - one = new Ctor(1); - - if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN); - if (x.isZero()) return one; - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; - - // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1 - // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4)) - - // Estimate the optimum number of times to use the argument reduction. - // TODO? Estimation reused from cosine() and may not be optimal here. - if (len < 32) { - k = Math.ceil(len / 3); - n = Math.pow(4, -k).toString(); - } else { - k = 16; - n = '2.3283064365386962890625e-10'; - } - - x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true); - - // Reverse argument reduction - var cosh2_x, - i = k, - d8 = new Ctor(8); - for (; i--;) { - cosh2_x = x.times(x); - x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8)))); - } - - return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true); - }; - - - /* - * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ... - * - * sinh(0) = 0 - * sinh(-0) = -0 - * sinh(Infinity) = Infinity - * sinh(-Infinity) = -Infinity - * sinh(NaN) = NaN - * - * x time taken (ms) - * 10 2 ms - * 100 5 ms - * 1000 14 ms - * 10000 82 ms - * 100000 886 ms 1.4033316802130615897e+43429 - * 200000 2613 ms - * 300000 5407 ms - * 400000 8824 ms - * 500000 13026 ms 8.7080643612718084129e+217146 - * 1000000 48543 ms - * - * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x)) - * - */ - P.hyperbolicSine = P.sinh = function () { - var k, pr, rm, len, - x = this, - Ctor = x.constructor; - - if (!x.isFinite() || x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; - - if (len < 3) { - x = taylorSeries(Ctor, 2, x, x, true); - } else { - - // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x)) - // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3)) - // 3 multiplications and 1 addition - - // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x))) - // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5))) - // 4 multiplications and 2 additions - - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; - - x = x.times(Math.pow(5, -k)); - - x = taylorSeries(Ctor, 2, x, x, true); - - // Reverse argument reduction - var sinh2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sinh2_x = x.times(x); - x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20)))); - } - } - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(x, pr, rm, true); - }; - - - /* - * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * tanh(x) = sinh(x) / cosh(x) - * - * tanh(0) = 0 - * tanh(-0) = -0 - * tanh(Infinity) = 1 - * tanh(-Infinity) = -1 - * tanh(NaN) = NaN - * - */ - P.hyperbolicTangent = P.tanh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(x.s); - if (x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 7; - Ctor.rounding = 1; - - return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm); - }; - - - /* - * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of - * this Decimal. - * - * Domain: [-1, 1] - * Range: [0, pi] - * - * acos(x) = pi/2 - asin(x) - * - * acos(0) = pi/2 - * acos(-0) = pi/2 - * acos(1) = 0 - * acos(-1) = pi - * acos(1/2) = pi/3 - * acos(-1/2) = 2*pi/3 - * acos(|x| > 1) = NaN - * acos(NaN) = NaN - * - */ - P.inverseCosine = P.acos = function () { - var halfPi, - x = this, - Ctor = x.constructor, - k = x.abs().cmp(1), - pr = Ctor.precision, - rm = Ctor.rounding; - - if (k !== -1) { - return k === 0 - // |x| is 1 - ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) - // |x| > 1 or x is NaN - : new Ctor(NaN); - } - - if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5); - - // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3 - - Ctor.precision = pr + 6; - Ctor.rounding = 1; - - x = x.asin(); - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return halfPi.minus(x); - }; - - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the - * value of this Decimal. - * - * Domain: [1, Infinity] - * Range: [0, Infinity] - * - * acosh(x) = ln(x + sqrt(x^2 - 1)) - * - * acosh(x < 1) = NaN - * acosh(NaN) = NaN - * acosh(Infinity) = Infinity - * acosh(-Infinity) = NaN - * acosh(0) = NaN - * acosh(-0) = NaN - * acosh(1) = 0 - * acosh(-1) = NaN - * - */ - P.inverseHyperbolicCosine = P.acosh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN); - if (!x.isFinite()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4; - Ctor.rounding = 1; - external = false; - - x = x.times(x).minus(1).sqrt().plus(x); - - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.ln(); - }; - - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * asinh(x) = ln(x + sqrt(x^2 + 1)) - * - * asinh(NaN) = NaN - * asinh(Infinity) = Infinity - * asinh(-Infinity) = -Infinity - * asinh(0) = 0 - * asinh(-0) = -0 - * - */ - P.inverseHyperbolicSine = P.asinh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite() || x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6; - Ctor.rounding = 1; - external = false; - - x = x.times(x).plus(1).sqrt().plus(x); - - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.ln(); - }; - - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the - * value of this Decimal. - * - * Domain: [-1, 1] - * Range: [-Infinity, Infinity] - * - * atanh(x) = 0.5 * ln((1 + x) / (1 - x)) - * - * atanh(|x| > 1) = NaN - * atanh(NaN) = NaN - * atanh(Infinity) = NaN - * atanh(-Infinity) = NaN - * atanh(0) = 0 - * atanh(-0) = -0 - * atanh(1) = Infinity - * atanh(-1) = -Infinity - * - */ - P.inverseHyperbolicTangent = P.atanh = function () { - var pr, rm, wpr, xsd, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(NaN); - if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN); - - pr = Ctor.precision; - rm = Ctor.rounding; - xsd = x.sd(); - - if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true); - - Ctor.precision = wpr = xsd - x.e; - - x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1); - - Ctor.precision = pr + 4; - Ctor.rounding = 1; - - x = x.ln(); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.times(0.5); - }; - - - /* - * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2))) - * - * asin(0) = 0 - * asin(-0) = -0 - * asin(1/2) = pi/6 - * asin(-1/2) = -pi/6 - * asin(1) = pi/2 - * asin(-1) = -pi/2 - * asin(|x| > 1) = NaN - * asin(NaN) = NaN - * - * TODO? Compare performance of Taylor series. - * - */ - P.inverseSine = P.asin = function () { - var halfPi, k, - pr, rm, - x = this, - Ctor = x.constructor; - - if (x.isZero()) return new Ctor(x); - - k = x.abs().cmp(1); - pr = Ctor.precision; - rm = Ctor.rounding; - - if (k !== -1) { - - // |x| is 1 - if (k === 0) { - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); - halfPi.s = x.s; - return halfPi; - } - - // |x| > 1 or x is NaN - return new Ctor(NaN); - } - - // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6 - - Ctor.precision = pr + 6; - Ctor.rounding = 1; - - x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan(); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.times(2); - }; - - - /* - * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - * - * atan(0) = 0 - * atan(-0) = -0 - * atan(1) = pi/4 - * atan(-1) = -pi/4 - * atan(Infinity) = pi/2 - * atan(-Infinity) = -pi/2 - * atan(NaN) = NaN - * - */ - P.inverseTangent = P.atan = function () { - var i, j, k, n, px, t, r, wpr, x2, - x = this, - Ctor = x.constructor, - pr = Ctor.precision, - rm = Ctor.rounding; - - if (!x.isFinite()) { - if (!x.s) return new Ctor(NaN); - if (pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.5); - r.s = x.s; - return r; - } - } else if (x.isZero()) { - return new Ctor(x); - } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.25); - r.s = x.s; - return r; - } - - Ctor.precision = wpr = pr + 10; - Ctor.rounding = 1; - - // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x); - - // Argument reduction - // Ensure |x| < 0.42 - // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2))) - - k = Math.min(28, wpr / LOG_BASE + 2 | 0); - - for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1)); - - external = false; - - j = Math.ceil(wpr / LOG_BASE); - n = 1; - x2 = x.times(x); - r = new Ctor(x); - px = x; - - // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - for (; i !== -1;) { - px = px.times(x2); - t = r.minus(px.div(n += 2)); - - px = px.times(x2); - r = t.plus(px.div(n += 2)); - - if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;); - } - - if (k) r = r.times(2 << (k - 1)); - - external = true; - - return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true); - }; - - - /* - * Return true if the value of this Decimal is a finite number, otherwise return false. - * - */ - P.isFinite = function () { - return !!this.d; - }; - - - /* - * Return true if the value of this Decimal is an integer, otherwise return false. - * - */ - P.isInteger = P.isInt = function () { - return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2; - }; - - - /* - * Return true if the value of this Decimal is NaN, otherwise return false. - * - */ - P.isNaN = function () { - return !this.s; - }; - - - /* - * Return true if the value of this Decimal is negative, otherwise return false. - * - */ - P.isNegative = P.isNeg = function () { - return this.s < 0; - }; - - - /* - * Return true if the value of this Decimal is positive, otherwise return false. - * - */ - P.isPositive = P.isPos = function () { - return this.s > 0; - }; - - - /* - * Return true if the value of this Decimal is 0 or -0, otherwise return false. - * - */ - P.isZero = function () { - return !!this.d && this.d[0] === 0; - }; - - - /* - * Return true if the value of this Decimal is less than `y`, otherwise return false. - * - */ - P.lessThan = P.lt = function (y) { - return this.cmp(y) < 0; - }; - - - /* - * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false. - * - */ - P.lessThanOrEqualTo = P.lte = function (y) { - return this.cmp(y) < 1; - }; - - - /* - * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * If no base is specified, return log[10](arg). - * - * log[base](arg) = ln(arg) / ln(base) - * - * The result will always be correctly rounded if the base of the log is 10, and 'almost always' - * otherwise: - * - * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen - * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error - * between the result and the correctly rounded result will be one ulp (unit in the last place). - * - * log[-b](a) = NaN - * log[0](a) = NaN - * log[1](a) = NaN - * log[NaN](a) = NaN - * log[Infinity](a) = NaN - * log[b](0) = -Infinity - * log[b](-0) = -Infinity - * log[b](-a) = NaN - * log[b](1) = 0 - * log[b](Infinity) = Infinity - * log[b](NaN) = NaN - * - * [base] {number|string|Decimal} The base of the logarithm. - * - */ - P.logarithm = P.log = function (base) { - var isBase10, d, denominator, k, inf, num, sd, r, - arg = this, - Ctor = arg.constructor, - pr = Ctor.precision, - rm = Ctor.rounding, - guard = 5; - - // Default base is 10. - if (base == null) { - base = new Ctor(10); - isBase10 = true; - } else { - base = new Ctor(base); - d = base.d; - - // Return NaN if base is negative, or non-finite, or is 0 or 1. - if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN); - - isBase10 = base.eq(10); - } - - d = arg.d; - - // Is arg negative, non-finite, 0 or 1? - if (arg.s < 0 || !d || !d[0] || arg.eq(1)) { - return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0); - } - - // The result will have a non-terminating decimal expansion if base is 10 and arg is not an - // integer power of 10. - if (isBase10) { - if (d.length > 1) { - inf = true; - } else { - for (k = d[0]; k % 10 === 0;) k /= 10; - inf = k !== 1; - } - } - - external = false; - sd = pr + guard; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - - // The result will have 5 rounding digits. - r = divide(num, denominator, sd, 1); - - // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000, - // calculate 10 further digits. - // - // If the result is known to have an infinite decimal expansion, repeat this until it is clear - // that the result is above or below the boundary. Otherwise, if after calculating the 10 - // further digits, the last 14 are nines, round up and assume the result is exact. - // Also assume the result is exact if the last 14 are zero. - // - // Example of a result that will be incorrectly rounded: - // log[1048576](4503599627370502) = 2.60000000000000009610279511444746... - // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it - // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so - // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal - // place is still 2.6. - if (checkRoundingDigits(r.d, k = pr, rm)) { - - do { - sd += 10; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - r = divide(num, denominator, sd, 1); - - if (!inf) { - - // Check for 14 nines from the 2nd rounding digit, as the first may be 4. - if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } - - break; - } - } while (checkRoundingDigits(r.d, k += 10, rm)); - } - - external = true; - - return finalise(r, pr, rm); - }; - - - /* - * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.max = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'lt'); - }; - */ - - - /* - * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.min = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'gt'); - }; - */ - - - /* - * n - 0 = n - * n - N = N - * n - I = -I - * 0 - n = -n - * 0 - 0 = 0 - * 0 - N = N - * 0 - I = -I - * N - n = N - * N - 0 = N - * N - N = N - * N - I = N - * I - n = I - * I - 0 = I - * I - N = N - * I - I = N - * - * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.minus = P.sub = function (y) { - var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd, - x = this, - Ctor = x.constructor; - - y = new Ctor(y); - - // If either is not finite... - if (!x.d || !y.d) { - - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); - - // Return y negated if x is finite and y is ±Infinity. - else if (x.d) y.s = -y.s; - - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with different signs. - // Return NaN if both are ±Infinity with the same sign. - else y = new Ctor(y.d || x.s !== y.s ? x : NaN); - - return y; - } - - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.plus(y); - } - - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; - - // If either is zero... - if (!xd[0] || !yd[0]) { - - // Return y negated if x is zero and y is non-zero. - if (yd[0]) y.s = -y.s; - - // Return x if y is zero and x is non-zero. - else if (xd[0]) y = new Ctor(x); - - // Return zero if both are zero. - // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity. - else return new Ctor(rm === 3 ? -0 : 0); - - return external ? finalise(y, pr, rm) : y; - } - - // x and y are finite, non-zero numbers with the same sign. - - // Calculate base 1e7 exponents. - e = mathfloor(y.e / LOG_BASE); - xe = mathfloor(x.e / LOG_BASE); - - xd = xd.slice(); - k = xe - e; - - // If base 1e7 exponents differ... - if (k) { - xLTy = k < 0; - - if (xLTy) { - d = xd; - k = -k; - len = yd.length; - } else { - d = yd; - e = xe; - len = xd.length; - } - - // Numbers with massively different exponents would result in a very high number of - // zeros needing to be prepended, but this can be avoided while still ensuring correct - // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`. - i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2; - - if (k > i) { - k = i; - d.length = 1; - } - - // Prepend zeros to equalise exponents. - d.reverse(); - for (i = k; i--;) d.push(0); - d.reverse(); - - // Base 1e7 exponents equal. - } else { - - // Check digits to determine which is the bigger number. - - i = xd.length; - len = yd.length; - xLTy = i < len; - if (xLTy) len = i; - - for (i = 0; i < len; i++) { - if (xd[i] != yd[i]) { - xLTy = xd[i] < yd[i]; - break; - } - } - - k = 0; - } - - if (xLTy) { - d = xd; - xd = yd; - yd = d; - y.s = -y.s; - } - - len = xd.length; - - // Append zeros to `xd` if shorter. - // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length. - for (i = yd.length - len; i > 0; --i) xd[len++] = 0; - - // Subtract yd from xd. - for (i = yd.length; i > k;) { - - if (xd[--i] < yd[i]) { - for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1; - --xd[j]; - xd[i] += BASE; - } - - xd[i] -= yd[i]; - } - - // Remove trailing zeros. - for (; xd[--len] === 0;) xd.pop(); - - // Remove leading zeros and adjust exponent accordingly. - for (; xd[0] === 0; xd.shift()) --e; - - // Zero? - if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0); - - y.d = xd; - y.e = getBase10Exponent(xd, e); - - return external ? finalise(y, pr, rm) : y; - }; - - - /* - * n % 0 = N - * n % N = N - * n % I = n - * 0 % n = 0 - * -0 % n = -0 - * 0 % 0 = N - * 0 % N = N - * 0 % I = 0 - * N % n = N - * N % 0 = N - * N % N = N - * N % I = N - * I % n = N - * I % 0 = N - * I % N = N - * I % I = N - * - * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * The result depends on the modulo mode. - * - */ - P.modulo = P.mod = function (y) { - var q, - x = this, - Ctor = x.constructor; - - y = new Ctor(y); - - // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0. - if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN); - - // Return x if y is ±Infinity or x is ±0. - if (!y.d || x.d && !x.d[0]) { - return finalise(new Ctor(x), Ctor.precision, Ctor.rounding); - } - - // Prevent rounding of intermediate calculations. - external = false; - - if (Ctor.modulo == 9) { - - // Euclidian division: q = sign(y) * floor(x / abs(y)) - // result = x - q * y where 0 <= result < abs(y) - q = divide(x, y.abs(), 0, 3, 1); - q.s *= y.s; - } else { - q = divide(x, y, 0, Ctor.modulo, 1); - } - - q = q.times(y); - - external = true; - - return x.minus(q); - }; - - - /* - * Return a new Decimal whose value is the natural exponential of the value of this Decimal, - * i.e. the base e raised to the power the value of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.naturalExponential = P.exp = function () { - return naturalExponential(this); - }; - - - /* - * Return a new Decimal whose value is the natural logarithm of the value of this Decimal, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.naturalLogarithm = P.ln = function () { - return naturalLogarithm(this); - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by - * -1. - * - */ - P.negated = P.neg = function () { - var x = new this.constructor(this); - x.s = -x.s; - return finalise(x); - }; - - - /* - * n + 0 = n - * n + N = N - * n + I = I - * 0 + n = n - * 0 + 0 = 0 - * 0 + N = N - * 0 + I = I - * N + n = N - * N + 0 = N - * N + N = N - * N + I = N - * I + n = I - * I + 0 = I - * I + N = N - * I + I = I - * - * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.plus = P.add = function (y) { - var carry, d, e, i, k, len, pr, rm, xd, yd, - x = this, - Ctor = x.constructor; - - y = new Ctor(y); - - // If either is not finite... - if (!x.d || !y.d) { - - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); - - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with the same sign. - // Return NaN if both are ±Infinity with different signs. - // Return y if x is finite and y is ±Infinity. - else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN); - - return y; - } - - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.minus(y); - } - - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; - - // If either is zero... - if (!xd[0] || !yd[0]) { - - // Return x if y is zero. - // Return y if y is non-zero. - if (!yd[0]) y = new Ctor(x); - - return external ? finalise(y, pr, rm) : y; - } - - // x and y are finite, non-zero numbers with the same sign. - - // Calculate base 1e7 exponents. - k = mathfloor(x.e / LOG_BASE); - e = mathfloor(y.e / LOG_BASE); - - xd = xd.slice(); - i = k - e; - - // If base 1e7 exponents differ... - if (i) { - - if (i < 0) { - d = xd; - i = -i; - len = yd.length; - } else { - d = yd; - e = k; - len = xd.length; - } - - // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1. - k = Math.ceil(pr / LOG_BASE); - len = k > len ? k + 1 : len + 1; - - if (i > len) { - i = len; - d.length = 1; - } - - // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts. - d.reverse(); - for (; i--;) d.push(0); - d.reverse(); - } - - len = xd.length; - i = yd.length; - - // If yd is longer than xd, swap xd and yd so xd points to the longer array. - if (len - i < 0) { - i = len; - d = yd; - yd = xd; - xd = d; - } - - // Only start adding at yd.length - 1 as the further digits of xd can be left as they are. - for (carry = 0; i;) { - carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0; - xd[i] %= BASE; - } - - if (carry) { - xd.unshift(carry); - ++e; - } - - // Remove trailing zeros. - // No need to check for zero, as +x + +y != 0 && -x + -y != 0 - for (len = xd.length; xd[--len] == 0;) xd.pop(); - - y.d = xd; - y.e = getBase10Exponent(xd, e); - - return external ? finalise(y, pr, rm) : y; - }; - - - /* - * Return the number of significant digits of the value of this Decimal. - * - * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0. - * - */ - P.precision = P.sd = function (z) { - var k, - x = this; - - if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z); - - if (x.d) { - k = getPrecision(x.d); - if (z && x.e + 1 > k) k = x.e + 1; - } else { - k = NaN; - } - - return k; - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using - * rounding mode `rounding`. - * - */ - P.round = function () { - var x = this, - Ctor = x.constructor; - - return finalise(new Ctor(x), x.e + 1, Ctor.rounding); - }; - - - /* - * Return a new Decimal whose value is the sine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * sin(x) = x - x^3/3! + x^5/5! - ... - * - * sin(0) = 0 - * sin(-0) = -0 - * sin(Infinity) = NaN - * sin(-Infinity) = NaN - * sin(NaN) = NaN - * - */ - P.sine = P.sin = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; - - x = sine(Ctor, toLessThanHalfPi(Ctor, x)); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true); - }; - - - /* - * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * sqrt(-n) = N - * sqrt(N) = N - * sqrt(-I) = N - * sqrt(I) = I - * sqrt(0) = 0 - * sqrt(-0) = -0 - * - */ - P.squareRoot = P.sqrt = function () { - var m, n, sd, r, rep, t, - x = this, - d = x.d, - e = x.e, - s = x.s, - Ctor = x.constructor; - - // Negative/NaN/Infinity/zero? - if (s !== 1 || !d || !d[0]) { - return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0); - } - - external = false; - - // Initial estimate. - s = Math.sqrt(+x); - - // Math.sqrt underflow/overflow? - // Pass x to Math.sqrt as integer, then adjust the exponent of the result. - if (s == 0 || s == 1 / 0) { - n = digitsToString(d); - - if ((n.length + e) % 2 == 0) n += '0'; - s = Math.sqrt(n); - e = mathfloor((e + 1) / 2) - (e < 0 || e % 2); - - if (s == 1 / 0) { - n = '1e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } - - r = new Ctor(n); - } else { - r = new Ctor(s.toString()); - } - - sd = (e = Ctor.precision) + 3; - - // Newton-Raphson iteration. - for (;;) { - t = r; - r = t.plus(divide(x, t, sd + 2, 1)).times(0.5); - - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); - - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or - // 4999, i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { - - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); - - if (t.times(t).eq(x)) { - r = t; - break; - } - } - - sd += 4; - rep = 1; - } else { - - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).eq(x); - } - - break; - } - } - } - - external = true; - - return finalise(r, e, Ctor.rounding, m); - }; - - - /* - * Return a new Decimal whose value is the tangent of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * tan(0) = 0 - * tan(-0) = -0 - * tan(Infinity) = NaN - * tan(-Infinity) = NaN - * tan(NaN) = NaN - * - */ - P.tangent = P.tan = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 10; - Ctor.rounding = 1; - - x = x.sin(); - x.s = 1; - x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true); - }; - - - /* - * n * 0 = 0 - * n * N = N - * n * I = I - * 0 * n = 0 - * 0 * 0 = 0 - * 0 * N = N - * 0 * I = N - * N * n = N - * N * 0 = N - * N * N = N - * N * I = N - * I * n = I - * I * 0 = N - * I * N = N - * I * I = I - * - * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - */ - P.times = P.mul = function (y) { - var carry, e, i, k, r, rL, t, xdL, ydL, - x = this, - Ctor = x.constructor, - xd = x.d, - yd = (y = new Ctor(y)).d; - - y.s *= x.s; - - // If either is NaN, ±Infinity or ±0... - if (!xd || !xd[0] || !yd || !yd[0]) { - - return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd - - // Return NaN if either is NaN. - // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity. - ? NaN - - // Return ±Infinity if either is ±Infinity. - // Return ±0 if either is ±0. - : !xd || !yd ? y.s / 0 : y.s * 0); - } - - e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE); - xdL = xd.length; - ydL = yd.length; - - // Ensure xd points to the longer array. - if (xdL < ydL) { - r = xd; - xd = yd; - yd = r; - rL = xdL; - xdL = ydL; - ydL = rL; - } - - // Initialise the result array with zeros. - r = []; - rL = xdL + ydL; - for (i = rL; i--;) r.push(0); - - // Multiply! - for (i = ydL; --i >= 0;) { - carry = 0; - for (k = xdL + i; k > i;) { - t = r[k] + yd[i] * xd[k - i - 1] + carry; - r[k--] = t % BASE | 0; - carry = t / BASE | 0; - } - - r[k] = (r[k] + carry) % BASE | 0; - } - - // Remove trailing zeros. - for (; !r[--rL];) r.pop(); - - if (carry) ++e; - else r.shift(); - - y.d = r; - y.e = getBase10Exponent(r, e); - - return external ? finalise(y, Ctor.precision, Ctor.rounding) : y; - }; - - - /* - * Return a string representing the value of this Decimal in base 2, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toBinary = function (sd, rm) { - return toStringBinary(this, 2, sd, rm); - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp` - * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted. - * - * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toDecimalPlaces = P.toDP = function (dp, rm) { - var x = this, - Ctor = x.constructor; - - x = new Ctor(x); - if (dp === void 0) return x; - - checkInt32(dp, 0, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - - return finalise(x, dp + x.e + 1, rm); - }; - - - /* - * Return a string representing the value of this Decimal in exponential notation rounded to - * `dp` fixed decimal places using rounding mode `rounding`. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toExponential = function (dp, rm) { - var str, - x = this, - Ctor = x.constructor; - - if (dp === void 0) { - str = finiteToString(x, true); - } else { - checkInt32(dp, 0, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - - x = finalise(new Ctor(x), dp + 1, rm); - str = finiteToString(x, true, dp + 1); - } - - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; - - - /* - * Return a string representing the value of this Decimal in normal (fixed-point) notation to - * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is - * omitted. - * - * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'. - * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'. - * (-0).toFixed(3) is '0.000'. - * (-0.5).toFixed(0) is '-0'. - * - */ - P.toFixed = function (dp, rm) { - var str, y, - x = this, - Ctor = x.constructor; - - if (dp === void 0) { - str = finiteToString(x); - } else { - checkInt32(dp, 0, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - - y = finalise(new Ctor(x), dp + x.e + 1, rm); - str = finiteToString(y, false, dp + y.e + 1); - } - - // To determine whether to add the minus sign look at the value before it was rounded, - // i.e. look at `x` rather than `y`. - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; - - - /* - * Return an array representing the value of this Decimal as a simple fraction with an integer - * numerator and an integer denominator. - * - * The denominator will be a positive non-zero value less than or equal to the specified maximum - * denominator. If a maximum denominator is not specified, the denominator will be the lowest - * value necessary to represent the number exactly. - * - * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity. - * - */ - P.toFraction = function (maxD) { - var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r, - x = this, - xd = x.d, - Ctor = x.constructor; - - if (!xd) return new Ctor(x); - - n1 = d0 = new Ctor(1); - d1 = n0 = new Ctor(0); - - d = new Ctor(d1); - e = d.e = getPrecision(xd) - x.e - 1; - k = e % LOG_BASE; - d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k); - - if (maxD == null) { - - // d is 10**e, the minimum max-denominator needed. - maxD = e > 0 ? d : n1; - } else { - n = new Ctor(maxD); - if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n); - maxD = n.gt(d) ? (e > 0 ? d : n1) : n; - } - - external = false; - n = new Ctor(digitsToString(xd)); - pr = Ctor.precision; - Ctor.precision = e = xd.length * LOG_BASE * 2; - - for (;;) { - q = divide(n, d, 0, 1, 1); - d2 = d0.plus(q.times(d1)); - if (d2.cmp(maxD) == 1) break; - d0 = d1; - d1 = d2; - d2 = n1; - n1 = n0.plus(q.times(d2)); - n0 = d2; - d2 = d; - d = n.minus(q.times(d2)); - n = d2; - } - - d2 = divide(maxD.minus(d0), d1, 0, 1, 1); - n0 = n0.plus(d2.times(n1)); - d0 = d0.plus(d2.times(d1)); - n0.s = n1.s = x.s; - - // Determine which fraction is closer to x, n0/d0 or n1/d1? - r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 - ? [n1, d1] : [n0, d0]; - - Ctor.precision = pr; - external = true; - - return r; - }; - - - /* - * Return a string representing the value of this Decimal in base 16, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toHexadecimal = P.toHex = function (sd, rm) { - return toStringBinary(this, 16, sd, rm); - }; - - - - /* - * Returns a new Decimal whose value is the nearest multiple of the magnitude of `y` to the value - * of this Decimal. - * - * If the value of this Decimal is equidistant from two multiples of `y`, the rounding mode `rm`, - * or `Decimal.rounding` if `rm` is omitted, determines the direction of the nearest multiple. - * - * In the context of this method, rounding mode 4 (ROUND_HALF_UP) is the same as rounding mode 0 - * (ROUND_UP), and so on. - * - * The return value will always have the same sign as this Decimal, unless either this Decimal - * or `y` is NaN, in which case the return value will be also be NaN. - * - * The return value is not affected by the value of `precision`. - * - * y {number|string|Decimal} The magnitude to round to a multiple of. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toNearest() rounding mode not an integer: {rm}' - * 'toNearest() rounding mode out of range: {rm}' - * - */ - P.toNearest = function (y, rm) { - var x = this, - Ctor = x.constructor; - - x = new Ctor(x); - - if (y == null) { - - // If x is not finite, return x. - if (!x.d) return x; - - y = new Ctor(1); - rm = Ctor.rounding; - } else { - y = new Ctor(y); - if (rm !== void 0) checkInt32(rm, 0, 8); - - // If x is not finite, return x if y is not NaN, else NaN. - if (!x.d) return y.s ? x : y; - - // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN. - if (!y.d) { - if (y.s) y.s = x.s; - return y; - } - } - - // If y is not zero, calculate the nearest multiple of y to x. - if (y.d[0]) { - external = false; - if (rm < 4) rm = [4, 5, 7, 8][rm]; - x = divide(x, y, 0, rm, 1).times(y); - external = true; - finalise(x); - - // If y is zero, return zero with the sign of x. - } else { - y.s = x.s; - x = y; - } - - return x; - }; - - - /* - * Return the value of this Decimal converted to a number primitive. - * Zero keeps its sign. - * - */ - P.toNumber = function () { - return +this; - }; - - - /* - * Return a string representing the value of this Decimal in base 8, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toOctal = function (sd, rm) { - return toStringBinary(this, 8, sd, rm); - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded - * to `precision` significant digits using rounding mode `rounding`. - * - * ECMAScript compliant. - * - * pow(x, NaN) = NaN - * pow(x, ±0) = 1 - - * pow(NaN, non-zero) = NaN - * pow(abs(x) > 1, +Infinity) = +Infinity - * pow(abs(x) > 1, -Infinity) = +0 - * pow(abs(x) == 1, ±Infinity) = NaN - * pow(abs(x) < 1, +Infinity) = +0 - * pow(abs(x) < 1, -Infinity) = +Infinity - * pow(+Infinity, y > 0) = +Infinity - * pow(+Infinity, y < 0) = +0 - * pow(-Infinity, odd integer > 0) = -Infinity - * pow(-Infinity, even integer > 0) = +Infinity - * pow(-Infinity, odd integer < 0) = -0 - * pow(-Infinity, even integer < 0) = +0 - * pow(+0, y > 0) = +0 - * pow(+0, y < 0) = +Infinity - * pow(-0, odd integer > 0) = -0 - * pow(-0, even integer > 0) = +0 - * pow(-0, odd integer < 0) = -Infinity - * pow(-0, even integer < 0) = +Infinity - * pow(finite x < 0, finite non-integer) = NaN - * - * For non-integer or very large exponents pow(x, y) is calculated using - * - * x^y = exp(y*ln(x)) - * - * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the - * probability of an incorrectly rounded result - * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14 - * i.e. 1 in 250,000,000,000,000 - * - * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place). - * - * y {number|string|Decimal} The power to which to raise this Decimal. - * - */ - P.toPower = P.pow = function (y) { - var e, k, pr, r, rm, s, - x = this, - Ctor = x.constructor, - yn = +(y = new Ctor(y)); - - // Either ±Infinity, NaN or ±0? - if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn)); - - x = new Ctor(x); - - if (x.eq(1)) return x; - - pr = Ctor.precision; - rm = Ctor.rounding; - - if (y.eq(1)) return finalise(x, pr, rm); - - // y exponent - e = mathfloor(y.e / LOG_BASE); - - // If y is a small integer use the 'exponentiation by squaring' algorithm. - if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) { - r = intPow(Ctor, x, k, pr); - return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm); - } - - s = x.s; - - // if x is negative - if (s < 0) { - - // if y is not an integer - if (e < y.d.length - 1) return new Ctor(NaN); - - // Result is positive if x is negative and the last digit of integer y is even. - if ((y.d[e] & 1) == 0) s = 1; - - // if x.eq(-1) - if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) { - x.s = s; - return x; - } - } - - // Estimate result exponent. - // x^y = 10^e, where e = y * log10(x) - // log10(x) = log10(x_significand) + x_exponent - // log10(x_significand) = ln(x_significand) / ln(10) - k = mathpow(+x, yn); - e = k == 0 || !isFinite(k) - ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) - : new Ctor(k + '').e; - - // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1. - - // Overflow/underflow? - if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0); - - external = false; - Ctor.rounding = x.s = 1; - - // Estimate the extra guard digits needed to ensure five correct rounding digits from - // naturalLogarithm(x). Example of failure without these extra digits (precision: 10): - // new Decimal(2.32456).pow('2087987436534566.46411') - // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815 - k = Math.min(12, (e + '').length); - - // r = x^y = exp(y*ln(x)) - r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr); - - // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40) - if (r.d) { - - // Truncate to the required precision plus five rounding digits. - r = finalise(r, pr + 5, 1); - - // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate - // the result. - if (checkRoundingDigits(r.d, pr, rm)) { - e = pr + 10; - - // Truncate to the increased precision plus five rounding digits. - r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1); - - // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9). - if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } - } - } - - r.s = s; - external = true; - Ctor.rounding = rm; - - return finalise(r, pr, rm); - }; - - - /* - * Return a string representing the value of this Decimal rounded to `sd` significant digits - * using rounding mode `rounding`. - * - * Return exponential notation if `sd` is less than the number of digits necessary to represent - * the integer part of the value in normal notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toPrecision = function (sd, rm) { - var str, - x = this, - Ctor = x.constructor; - - if (sd === void 0) { - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - } else { - checkInt32(sd, 1, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - - x = finalise(new Ctor(x), sd, rm); - str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd); - } - - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd` - * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if - * omitted. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toSD() digits out of range: {sd}' - * 'toSD() digits not an integer: {sd}' - * 'toSD() rounding mode not an integer: {rm}' - * 'toSD() rounding mode out of range: {rm}' - * - */ - P.toSignificantDigits = P.toSD = function (sd, rm) { - var x = this, - Ctor = x.constructor; - - if (sd === void 0) { - sd = Ctor.precision; - rm = Ctor.rounding; - } else { - checkInt32(sd, 1, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - } - - return finalise(new Ctor(x), sd, rm); - }; - - - /* - * Return a string representing the value of this Decimal. - * - * Return exponential notation if this Decimal has a positive exponent equal to or greater than - * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`. - * - */ - P.toString = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - - return x.isNeg() && !x.isZero() ? '-' + str : str; - }; - - - /* - * Return a new Decimal whose value is the value of this Decimal truncated to a whole number. - * - */ - P.truncated = P.trunc = function () { - return finalise(new this.constructor(this), this.e + 1, 1); - }; - - - /* - * Return a string representing the value of this Decimal. - * Unlike `toString`, negative zero will include the minus sign. - * - */ - P.valueOf = P.toJSON = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - - return x.isNeg() ? '-' + str : str; - }; - - - /* - // Add aliases to match BigDecimal method names. - // P.add = P.plus; - P.subtract = P.minus; - P.multiply = P.times; - P.divide = P.div; - P.remainder = P.mod; - P.compareTo = P.cmp; - P.negate = P.neg; - */ - - - // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers. - - - /* - * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower, - * finiteToString, naturalExponential, naturalLogarithm - * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest, - * P.toPrecision, P.toSignificantDigits, toStringBinary, random - * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm - * convertBase toStringBinary, parseOther - * cos P.cos - * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy, - * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction, - * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm, - * taylorSeries, atan2, parseOther - * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh, - * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus, - * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot, - * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed, - * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits, - * P.truncated, divide, getLn10, getPi, naturalExponential, - * naturalLogarithm, ceil, floor, round, trunc - * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf, - * toStringBinary - * getBase10Exponent P.minus, P.plus, P.times, parseOther - * getLn10 P.logarithm, naturalLogarithm - * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2 - * getPrecision P.precision, P.toFraction - * getZeroString digitsToString, finiteToString - * intPow P.toPower, parseOther - * isOdd toLessThanHalfPi - * maxOrMin max, min - * naturalExponential P.naturalExponential, P.toPower - * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm, - * P.toPower, naturalExponential - * nonFiniteToString finiteToString, toStringBinary - * parseDecimal Decimal - * parseOther Decimal - * sin P.sin - * taylorSeries P.cosh, P.sinh, cos, sin - * toLessThanHalfPi P.cos, P.sin - * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal - * truncate intPow - * - * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi, - * naturalLogarithm, config, parseOther, random, Decimal - */ - - - function digitsToString(d) { - var i, k, ws, - indexOfLastWord = d.length - 1, - str = '', - w = d[0]; - - if (indexOfLastWord > 0) { - str += w; - for (i = 1; i < indexOfLastWord; i++) { - ws = d[i] + ''; - k = LOG_BASE - ws.length; - if (k) str += getZeroString(k); - str += ws; - } - - w = d[i]; - ws = w + ''; - k = LOG_BASE - ws.length; - if (k) str += getZeroString(k); - } else if (w === 0) { - return '0'; - } - - // Remove trailing zeros of last w. - for (; w % 10 === 0;) w /= 10; - - return str + w; - } - - - function checkInt32(i, min, max) { - if (i !== ~~i || i < min || i > max) { - throw Error(invalidArgument + i); - } - } - - - /* - * Check 5 rounding digits if `repeating` is null, 4 otherwise. - * `repeating == null` if caller is `log` or `pow`, - * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`. - */ - function checkRoundingDigits(d, i, rm, repeating) { - var di, k, r, rd; - - // Get the length of the first word of the array d. - for (k = d[0]; k >= 10; k /= 10) --i; - - // Is the rounding digit in the first word of d? - if (--i < 0) { - i += LOG_BASE; - di = 0; - } else { - di = Math.ceil((i + 1) / LOG_BASE); - i %= LOG_BASE; - } - - // i is the index (0 - 6) of the rounding digit. - // E.g. if within the word 3487563 the first rounding digit is 5, - // then i = 4, k = 1000, rd = 3487563 % 1000 = 563 - k = mathpow(10, LOG_BASE - i); - rd = d[di] % k | 0; - - if (repeating == null) { - if (i < 3) { - if (i == 0) rd = rd / 100 | 0; - else if (i == 1) rd = rd / 10 | 0; - r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0; - } else { - r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) && - (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 || - (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0; - } - } else { - if (i < 4) { - if (i == 0) rd = rd / 1000 | 0; - else if (i == 1) rd = rd / 100 | 0; - else if (i == 2) rd = rd / 10 | 0; - r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999; - } else { - r = ((repeating || rm < 4) && rd + 1 == k || - (!repeating && rm > 3) && rd + 1 == k / 2) && - (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1; - } - } - - return r; - } - - - // Convert string of `baseIn` to an array of numbers of `baseOut`. - // Eg. convertBase('255', 10, 16) returns [15, 15]. - // Eg. convertBase('ff', 16, 10) returns [2, 5, 5]. - function convertBase(str, baseIn, baseOut) { - var j, - arr = [0], - arrL, - i = 0, - strL = str.length; - - for (; i < strL;) { - for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn; - arr[0] += NUMERALS.indexOf(str.charAt(i++)); - for (j = 0; j < arr.length; j++) { - if (arr[j] > baseOut - 1) { - if (arr[j + 1] === void 0) arr[j + 1] = 0; - arr[j + 1] += arr[j] / baseOut | 0; - arr[j] %= baseOut; - } - } - } - - return arr.reverse(); - } - - - /* - * cos(x) = 1 - x^2/2! + x^4/4! - ... - * |x| < pi/2 - * - */ - function cosine(Ctor, x) { - var k, y, - len = x.d.length; - - // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1 - // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1 - - // Estimate the optimum number of times to use the argument reduction. - if (len < 32) { - k = Math.ceil(len / 3); - y = Math.pow(4, -k).toString(); - } else { - k = 16; - y = '2.3283064365386962890625e-10'; - } - - Ctor.precision += k; - - x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)); - - // Reverse argument reduction - for (var i = k; i--;) { - var cos2x = x.times(x); - x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1); - } - - Ctor.precision -= k; - - return x; - } - - - /* - * Perform division in the specified base. - */ - var divide = (function () { - - // Assumes non-zero x and k, and hence non-zero result. - function multiplyInteger(x, k, base) { - var temp, - carry = 0, - i = x.length; - - for (x = x.slice(); i--;) { - temp = x[i] * k + carry; - x[i] = temp % base | 0; - carry = temp / base | 0; - } - - if (carry) x.unshift(carry); - - return x; - } - - function compare(a, b, aL, bL) { - var i, r; - - if (aL != bL) { - r = aL > bL ? 1 : -1; - } else { - for (i = r = 0; i < aL; i++) { - if (a[i] != b[i]) { - r = a[i] > b[i] ? 1 : -1; - break; - } - } - } - - return r; - } - - function subtract(a, b, aL, base) { - var i = 0; - - // Subtract b from a. - for (; aL--;) { - a[aL] -= i; - i = a[aL] < b[aL] ? 1 : 0; - a[aL] = i * base + a[aL] - b[aL]; - } - - // Remove leading zeros. - for (; !a[0] && a.length > 1;) a.shift(); - } - - return function (x, y, pr, rm, dp, base) { - var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, - yL, yz, - Ctor = x.constructor, - sign = x.s == y.s ? 1 : -1, - xd = x.d, - yd = y.d; - - // Either NaN, Infinity or 0? - if (!xd || !xd[0] || !yd || !yd[0]) { - - return new Ctor(// Return NaN if either NaN, or both Infinity or 0. - !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN : - - // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0. - xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0); - } - - if (base) { - logBase = 1; - e = x.e - y.e; - } else { - base = BASE; - logBase = LOG_BASE; - e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase); - } - - yL = yd.length; - xL = xd.length; - q = new Ctor(sign); - qd = q.d = []; - - // Result exponent may be one less than e. - // The digit array of a Decimal from toStringBinary may have trailing zeros. - for (i = 0; yd[i] == (xd[i] || 0); i++); - - if (yd[i] > (xd[i] || 0)) e--; - - if (pr == null) { - sd = pr = Ctor.precision; - rm = Ctor.rounding; - } else if (dp) { - sd = pr + (x.e - y.e) + 1; - } else { - sd = pr; - } - - if (sd < 0) { - qd.push(1); - more = true; - } else { - - // Convert precision in number of base 10 digits to base 1e7 digits. - sd = sd / logBase + 2 | 0; - i = 0; - - // divisor < 1e7 - if (yL == 1) { - k = 0; - yd = yd[0]; - sd++; - - // k is the carry. - for (; (i < xL || k) && sd--; i++) { - t = k * base + (xd[i] || 0); - qd[i] = t / yd | 0; - k = t % yd | 0; - } - - more = k || i < xL; - - // divisor >= 1e7 - } else { - - // Normalise xd and yd so highest order digit of yd is >= base/2 - k = base / (yd[0] + 1) | 0; - - if (k > 1) { - yd = multiplyInteger(yd, k, base); - xd = multiplyInteger(xd, k, base); - yL = yd.length; - xL = xd.length; - } - - xi = yL; - rem = xd.slice(0, yL); - remL = rem.length; - - // Add zeros to make remainder as long as divisor. - for (; remL < yL;) rem[remL++] = 0; - - yz = yd.slice(); - yz.unshift(0); - yd0 = yd[0]; - - if (yd[1] >= base / 2) ++yd0; - - do { - k = 0; - - // Compare divisor and remainder. - cmp = compare(yd, rem, yL, remL); - - // If divisor < remainder. - if (cmp < 0) { - - // Calculate trial digit, k. - rem0 = rem[0]; - if (yL != remL) rem0 = rem0 * base + (rem[1] || 0); - - // k will be how many times the divisor goes into the current remainder. - k = rem0 / yd0 | 0; - - // Algorithm: - // 1. product = divisor * trial digit (k) - // 2. if product > remainder: product -= divisor, k-- - // 3. remainder -= product - // 4. if product was < remainder at 2: - // 5. compare new remainder and divisor - // 6. If remainder > divisor: remainder -= divisor, k++ - - if (k > 1) { - if (k >= base) k = base - 1; - - // product = divisor * trial digit. - prod = multiplyInteger(yd, k, base); - prodL = prod.length; - remL = rem.length; - - // Compare product and remainder. - cmp = compare(prod, rem, prodL, remL); - - // product > remainder. - if (cmp == 1) { - k--; - - // Subtract divisor from product. - subtract(prod, yL < prodL ? yz : yd, prodL, base); - } - } else { - - // cmp is -1. - // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1 - // to avoid it. If k is 1 there is a need to compare yd and rem again below. - if (k == 0) cmp = k = 1; - prod = yd.slice(); - } - - prodL = prod.length; - if (prodL < remL) prod.unshift(0); - - // Subtract product from remainder. - subtract(rem, prod, remL, base); - - // If product was < previous remainder. - if (cmp == -1) { - remL = rem.length; - - // Compare divisor and new remainder. - cmp = compare(yd, rem, yL, remL); - - // If divisor < new remainder, subtract divisor from remainder. - if (cmp < 1) { - k++; - - // Subtract divisor from remainder. - subtract(rem, yL < remL ? yz : yd, remL, base); - } - } - - remL = rem.length; - } else if (cmp === 0) { - k++; - rem = [0]; - } // if cmp === 1, k will be 0 - - // Add the next digit, k, to the result array. - qd[i++] = k; - - // Update the remainder. - if (cmp && rem[0]) { - rem[remL++] = xd[xi] || 0; - } else { - rem = [xd[xi]]; - remL = 1; - } - - } while ((xi++ < xL || rem[0] !== void 0) && sd--); - - more = rem[0] !== void 0; - } - - // Leading zero? - if (!qd[0]) qd.shift(); - } - - // logBase is 1 when divide is being used for base conversion. - if (logBase == 1) { - q.e = e; - inexact = more; - } else { - - // To calculate q.e, first get the number of digits of qd[0]. - for (i = 1, k = qd[0]; k >= 10; k /= 10) i++; - q.e = i + e * logBase - 1; - - finalise(q, dp ? pr + q.e + 1 : pr, rm, more); - } - - return q; - }; - })(); - - - /* - * Round `x` to `sd` significant digits using rounding mode `rm`. - * Check for over/under-flow. - */ - function finalise(x, sd, rm, isTruncated) { - var digits, i, j, k, rd, roundUp, w, xd, xdi, - Ctor = x.constructor; - - // Don't round if sd is null or undefined. - out: if (sd != null) { - xd = x.d; - - // Infinity/NaN. - if (!xd) return x; - - // rd: the rounding digit, i.e. the digit after the digit that may be rounded up. - // w: the word of xd containing rd, a base 1e7 number. - // xdi: the index of w within xd. - // digits: the number of digits of w. - // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if - // they had leading zeros) - // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero). - - // Get the length of the first word of the digits array xd. - for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++; - i = sd - digits; - - // Is the rounding digit in the first word of xd? - if (i < 0) { - i += LOG_BASE; - j = sd; - w = xd[xdi = 0]; - - // Get the rounding digit at index j of w. - rd = w / mathpow(10, digits - j - 1) % 10 | 0; - } else { - xdi = Math.ceil((i + 1) / LOG_BASE); - k = xd.length; - if (xdi >= k) { - if (isTruncated) { - - // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`. - for (; k++ <= xdi;) xd.push(0); - w = rd = 0; - digits = 1; - i %= LOG_BASE; - j = i - LOG_BASE + 1; - } else { - break out; - } - } else { - w = k = xd[xdi]; - - // Get the number of digits of w. - for (digits = 1; k >= 10; k /= 10) digits++; - - // Get the index of rd within w. - i %= LOG_BASE; - - // Get the index of rd within w, adjusted for leading zeros. - // The number of leading zeros of w is given by LOG_BASE - digits. - j = i - LOG_BASE + digits; - - // Get the rounding digit at index j of w. - rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0; - } - } - - // Are there any non-zero digits after the rounding digit? - isTruncated = isTruncated || sd < 0 || - xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)); - - // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right - // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression - // will give 714. - - roundUp = rm < 4 - ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) - : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 && - - // Check whether the digit to the left of the rounding digit is odd. - ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 || - rm == (x.s < 0 ? 8 : 7)); - - if (sd < 1 || !xd[0]) { - xd.length = 0; - if (roundUp) { - - // Convert sd to decimal places. - sd -= x.e + 1; - - // 1, 0.1, 0.01, 0.001, 0.0001 etc. - xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE); - x.e = -sd || 0; - } else { - - // Zero. - xd[0] = x.e = 0; - } - - return x; - } - - // Remove excess digits. - if (i == 0) { - xd.length = xdi; - k = 1; - xdi--; - } else { - xd.length = xdi + 1; - k = mathpow(10, LOG_BASE - i); - - // E.g. 56700 becomes 56000 if 7 is the rounding digit. - // j > 0 means i > number of leading zeros of w. - xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0; - } - - if (roundUp) { - for (;;) { - - // Is the digit to be rounded up in the first word of xd? - if (xdi == 0) { - - // i will be the length of xd[0] before k is added. - for (i = 1, j = xd[0]; j >= 10; j /= 10) i++; - j = xd[0] += k; - for (k = 1; j >= 10; j /= 10) k++; - - // if i != k the length has increased. - if (i != k) { - x.e++; - if (xd[0] == BASE) xd[0] = 1; - } - - break; - } else { - xd[xdi] += k; - if (xd[xdi] != BASE) break; - xd[xdi--] = 0; - k = 1; - } - } - } - - // Remove trailing zeros. - for (i = xd.length; xd[--i] === 0;) xd.pop(); - } - - if (external) { - - // Overflow? - if (x.e > Ctor.maxE) { - - // Infinity. - x.d = null; - x.e = NaN; - - // Underflow? - } else if (x.e < Ctor.minE) { - - // Zero. - x.e = 0; - x.d = [0]; - // Ctor.underflow = true; - } // else Ctor.underflow = false; - } - - return x; - } - - - function finiteToString(x, isExp, sd) { - if (!x.isFinite()) return nonFiniteToString(x); - var k, - e = x.e, - str = digitsToString(x.d), - len = str.length; - - if (isExp) { - if (sd && (k = sd - len) > 0) { - str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k); - } else if (len > 1) { - str = str.charAt(0) + '.' + str.slice(1); - } - - str = str + (x.e < 0 ? 'e' : 'e+') + x.e; - } else if (e < 0) { - str = '0.' + getZeroString(-e - 1) + str; - if (sd && (k = sd - len) > 0) str += getZeroString(k); - } else if (e >= len) { - str += getZeroString(e + 1 - len); - if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k); - } else { - if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k); - if (sd && (k = sd - len) > 0) { - if (e + 1 === len) str += '.'; - str += getZeroString(k); - } - } - - return str; - } - - - // Calculate the base 10 exponent from the base 1e7 exponent. - function getBase10Exponent(digits, e) { - var w = digits[0]; - - // Add the number of digits of the first word of the digits array. - for ( e *= LOG_BASE; w >= 10; w /= 10) e++; - return e; - } - - - function getLn10(Ctor, sd, pr) { - if (sd > LN10_PRECISION) { - - // Reset global state in case the exception is caught. - external = true; - if (pr) Ctor.precision = pr; - throw Error(precisionLimitExceeded); - } - return finalise(new Ctor(LN10), sd, 1, true); - } - - - function getPi(Ctor, sd, rm) { - if (sd > PI_PRECISION) throw Error(precisionLimitExceeded); - return finalise(new Ctor(PI), sd, rm, true); - } - - - function getPrecision(digits) { - var w = digits.length - 1, - len = w * LOG_BASE + 1; - - w = digits[w]; - - // If non-zero... - if (w) { - - // Subtract the number of trailing zeros of the last word. - for (; w % 10 == 0; w /= 10) len--; - - // Add the number of digits of the first word. - for (w = digits[0]; w >= 10; w /= 10) len++; - } - - return len; - } - - - function getZeroString(k) { - var zs = ''; - for (; k--;) zs += '0'; - return zs; - } - - - /* - * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an - * integer of type number. - * - * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`. - * - */ - function intPow(Ctor, x, n, pr) { - var isTruncated, - r = new Ctor(1), - - // Max n of 9007199254740991 takes 53 loop iterations. - // Maximum digits array length; leaves [28, 34] guard digits. - k = Math.ceil(pr / LOG_BASE + 4); - - external = false; - - for (;;) { - if (n % 2) { - r = r.times(x); - if (truncate(r.d, k)) isTruncated = true; - } - - n = mathfloor(n / 2); - if (n === 0) { - - // To ensure correct rounding when r.d is truncated, increment the last word if it is zero. - n = r.d.length - 1; - if (isTruncated && r.d[n] === 0) ++r.d[n]; - break; - } - - x = x.times(x); - truncate(x.d, k); - } - - external = true; - - return r; - } - - - function isOdd(n) { - return n.d[n.d.length - 1] & 1; - } - - - /* - * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'. - */ - function maxOrMin(Ctor, args, ltgt) { - var y, - x = new Ctor(args[0]), - i = 0; - - for (; ++i < args.length;) { - y = new Ctor(args[i]); - if (!y.s) { - x = y; - break; - } else if (x[ltgt](y)) { - x = y; - } - } - - return x; - } - - - /* - * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant - * digits. - * - * Taylor/Maclaurin series. - * - * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ... - * - * Argument reduction: - * Repeat x = x / 32, k += 5, until |x| < 0.1 - * exp(x) = exp(x / 2^k)^(2^k) - * - * Previously, the argument was initially reduced by - * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10) - * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was - * found to be slower than just dividing repeatedly by 32 as above. - * - * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000 - * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000 - * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324) - * - * exp(Infinity) = Infinity - * exp(-Infinity) = 0 - * exp(NaN) = NaN - * exp(±0) = 1 - * - * exp(x) is non-terminating for any finite, non-zero x. - * - * The result will always be correctly rounded. - * - */ - function naturalExponential(x, sd) { - var denominator, guard, j, pow, sum, t, wpr, - rep = 0, - i = 0, - k = 0, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; - - // 0/NaN/Infinity? - if (!x.d || !x.d[0] || x.e > 17) { - - return new Ctor(x.d - ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0 - : x.s ? x.s < 0 ? 0 : x : 0 / 0); - } - - if (sd == null) { - external = false; - wpr = pr; - } else { - wpr = sd; - } - - t = new Ctor(0.03125); - - // while abs(x) >= 0.1 - while (x.e > -2) { - - // x = x / 2^5 - x = x.times(t); - k += 5; - } - - // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision - // necessary to ensure the first 4 rounding digits are correct. - guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0; - wpr += guard; - denominator = pow = sum = new Ctor(1); - Ctor.precision = wpr; - - for (;;) { - pow = finalise(pow.times(x), wpr, 1); - denominator = denominator.times(++i); - t = sum.plus(divide(pow, denominator, wpr, 1)); - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - j = k; - while (j--) sum = finalise(sum.times(sum), wpr, 1); - - // Check to see if the first 4 rounding digits are [49]999. - // If so, repeat the summation with a higher precision, otherwise - // e.g. with precision: 18, rounding: 1 - // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123) - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - - if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += 10; - denominator = pow = t = new Ctor(1); - i = 0; - rep++; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } - } else { - Ctor.precision = pr; - return sum; - } - } - - sum = t; - } - } - - - /* - * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant - * digits. - * - * ln(-n) = NaN - * ln(0) = -Infinity - * ln(-0) = -Infinity - * ln(1) = 0 - * ln(Infinity) = Infinity - * ln(-Infinity) = NaN - * ln(NaN) = NaN - * - * ln(n) (n != 1) is non-terminating. - * - */ - function naturalLogarithm(y, sd) { - var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2, - n = 1, - guard = 10, - x = y, - xd = x.d, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; - - // Is x negative or Infinity, NaN, 0 or 1? - if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) { - return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x); - } - - if (sd == null) { - external = false; - wpr = pr; - } else { - wpr = sd; - } - - Ctor.precision = wpr += guard; - c = digitsToString(xd); - c0 = c.charAt(0); - - if (Math.abs(e = x.e) < 1.5e15) { - - // Argument reduction. - // The series converges faster the closer the argument is to 1, so using - // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b - // multiply the argument by itself until the leading digits of the significand are 7, 8, 9, - // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can - // later be divided by this number, then separate out the power of 10 using - // ln(a*10^b) = ln(a) + b*ln(10). - - // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14). - //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) { - // max n is 6 (gives 0.7 - 1.3) - while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) { - x = x.times(y); - c = digitsToString(x.d); - c0 = c.charAt(0); - n++; - } - - e = x.e; - - if (c0 > 1) { - x = new Ctor('0.' + c); - e++; - } else { - x = new Ctor(c0 + '.' + c.slice(1)); - } - } else { - - // The argument reduction method above may result in overflow if the argument y is a massive - // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this - // function using ln(x*10^e) = ln(x) + e*ln(10). - t = getLn10(Ctor, wpr + 2, pr).times(e + ''); - x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t); - Ctor.precision = pr; - - return sd == null ? finalise(x, pr, rm, external = true) : x; - } - - // x1 is x reduced to a value near 1. - x1 = x; - - // Taylor series. - // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...) - // where x = (y - 1)/(y + 1) (|x| < 1) - sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = 3; - - for (;;) { - numerator = finalise(numerator.times(x2), wpr, 1); - t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1)); - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - sum = sum.times(2); - - // Reverse the argument reduction. Check that e is not 0 because, besides preventing an - // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0. - if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + '')); - sum = divide(sum, new Ctor(n), wpr, 1); - - // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has - // been repeated previously) and the first 4 rounding digits 9999? - // If so, restart the summation with a higher precision, otherwise - // e.g. with precision: 12, rounding: 1 - // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463. - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += guard; - t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = rep = 1; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } - } else { - Ctor.precision = pr; - return sum; - } - } - - sum = t; - denominator += 2; - } - } - - - // ±Infinity, NaN. - function nonFiniteToString(x) { - // Unsigned. - return String(x.s * x.s / 0); - } - - - /* - * Parse the value of a new Decimal `x` from string `str`. - */ - function parseDecimal(x, str) { - var e, i, len; - - // Decimal point? - if ((e = str.indexOf('.')) > -1) str = str.replace('.', ''); - - // Exponential form? - if ((i = str.search(/e/i)) > 0) { - - // Determine exponent. - if (e < 0) e = i; - e += +str.slice(i + 1); - str = str.substring(0, i); - } else if (e < 0) { - - // Integer. - e = str.length; - } - - // Determine leading zeros. - for (i = 0; str.charCodeAt(i) === 48; i++); - - // Determine trailing zeros. - for (len = str.length; str.charCodeAt(len - 1) === 48; --len); - str = str.slice(i, len); - - if (str) { - len -= i; - x.e = e = e - i - 1; - x.d = []; - - // Transform base - - // e is the base 10 exponent. - // i is where to slice str to get the first word of the digits array. - i = (e + 1) % LOG_BASE; - if (e < 0) i += LOG_BASE; - - if (i < len) { - if (i) x.d.push(+str.slice(0, i)); - for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE)); - str = str.slice(i); - i = LOG_BASE - str.length; - } else { - i -= len; - } - - for (; i--;) str += '0'; - x.d.push(+str); - - if (external) { - - // Overflow? - if (x.e > x.constructor.maxE) { - - // Infinity. - x.d = null; - x.e = NaN; - - // Underflow? - } else if (x.e < x.constructor.minE) { - - // Zero. - x.e = 0; - x.d = [0]; - // x.constructor.underflow = true; - } // else x.constructor.underflow = false; - } - } else { - - // Zero. - x.e = 0; - x.d = [0]; - } - - return x; - } - - - /* - * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value. - */ - function parseOther(x, str) { - var base, Ctor, divisor, i, isFloat, len, p, xd, xe; - - if (str === 'Infinity' || str === 'NaN') { - if (!+str) x.s = NaN; - x.e = NaN; - x.d = null; - return x; - } - - if (isHex.test(str)) { - base = 16; - str = str.toLowerCase(); - } else if (isBinary.test(str)) { - base = 2; - } else if (isOctal.test(str)) { - base = 8; - } else { - throw Error(invalidArgument + str); - } - - // Is there a binary exponent part? - i = str.search(/p/i); - - if (i > 0) { - p = +str.slice(i + 1); - str = str.substring(2, i); - } else { - str = str.slice(2); - } - - // Convert `str` as an integer then divide the result by `base` raised to a power such that the - // fraction part will be restored. - i = str.indexOf('.'); - isFloat = i >= 0; - Ctor = x.constructor; - - if (isFloat) { - str = str.replace('.', ''); - len = str.length; - i = len - i; - - // log[10](16) = 1.2041... , log[10](88) = 1.9444.... - divisor = intPow(Ctor, new Ctor(base), i, i * 2); - } - - xd = convertBase(str, base, BASE); - xe = xd.length - 1; - - // Remove trailing zeros. - for (i = xe; xd[i] === 0; --i) xd.pop(); - if (i < 0) return new Ctor(x.s * 0); - x.e = getBase10Exponent(xd, xe); - x.d = xd; - external = false; - - // At what precision to perform the division to ensure exact conversion? - // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount) - // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412 - // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits. - // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount - // Therefore using 4 * the number of digits of str will always be enough. - if (isFloat) x = divide(x, divisor, len * 4); - - // Multiply by the binary exponent part if present. - if (p) x = x.times(Math.abs(p) < 54 ? Math.pow(2, p) : Decimal.pow(2, p)); - external = true; - - return x; - } - - - /* - * sin(x) = x - x^3/3! + x^5/5! - ... - * |x| < pi/2 - * - */ - function sine(Ctor, x) { - var k, - len = x.d.length; - - if (len < 3) return taylorSeries(Ctor, 2, x, x); - - // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x) - // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5) - // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20)) - - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; - - // Max k before Math.pow precision loss is 22 - x = x.times(Math.pow(5, -k)); - x = taylorSeries(Ctor, 2, x, x); - - // Reverse argument reduction - var sin2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sin2_x = x.times(x); - x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20)))); - } - - return x; - } - - - // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`. - function taylorSeries(Ctor, n, x, y, isHyperbolic) { - var j, t, u, x2, - i = 1, - pr = Ctor.precision, - k = Math.ceil(pr / LOG_BASE); - - external = false; - x2 = x.times(x); - u = new Ctor(y); - - for (;;) { - t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1); - u = isHyperbolic ? y.plus(t) : y.minus(t); - y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1); - t = u.plus(y); - - if (t.d[k] !== void 0) { - for (j = k; t.d[j] === u.d[j] && j--;); - if (j == -1) break; - } - - j = u; - u = y; - y = t; - t = j; - i++; - } - - external = true; - t.d.length = k + 1; - - return t; - } - - - // Return the absolute value of `x` reduced to less than or equal to half pi. - function toLessThanHalfPi(Ctor, x) { - var t, - isNeg = x.s < 0, - pi = getPi(Ctor, Ctor.precision, 1), - halfPi = pi.times(0.5); - - x = x.abs(); - - if (x.lte(halfPi)) { - quadrant = isNeg ? 4 : 1; - return x; - } - - t = x.divToInt(pi); - - if (t.isZero()) { - quadrant = isNeg ? 3 : 2; - } else { - x = x.minus(t.times(pi)); - - // 0 <= x < pi - if (x.lte(halfPi)) { - quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1); - return x; - } - - quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2); - } - - return x.minus(pi).abs(); - } - - - /* - * Return the value of Decimal `x` as a string in base `baseOut`. - * - * If the optional `sd` argument is present include a binary exponent suffix. - */ - function toStringBinary(x, baseOut, sd, rm) { - var base, e, i, k, len, roundUp, str, xd, y, - Ctor = x.constructor, - isExp = sd !== void 0; - - if (isExp) { - checkInt32(sd, 1, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - } else { - sd = Ctor.precision; - rm = Ctor.rounding; - } - - if (!x.isFinite()) { - str = nonFiniteToString(x); - } else { - str = finiteToString(x); - i = str.indexOf('.'); - - // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required: - // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10)) - // minBinaryExponent = floor(decimalExponent * log[2](10)) - // log[2](10) = 3.321928094887362347870319429489390175864 - - if (isExp) { - base = 2; - if (baseOut == 16) { - sd = sd * 4 - 3; - } else if (baseOut == 8) { - sd = sd * 3 - 2; - } - } else { - base = baseOut; - } - - // Convert the number as an integer then divide the result by its base raised to a power such - // that the fraction part will be restored. - - // Non-integer. - if (i >= 0) { - str = str.replace('.', ''); - y = new Ctor(1); - y.e = str.length - i; - y.d = convertBase(finiteToString(y), 10, base); - y.e = y.d.length; - } - - xd = convertBase(str, 10, base); - e = len = xd.length; - - // Remove trailing zeros. - for (; xd[--len] == 0;) xd.pop(); - - if (!xd[0]) { - str = isExp ? '0p+0' : '0'; - } else { - if (i < 0) { - e--; - } else { - x = new Ctor(x); - x.d = xd; - x.e = e; - x = divide(x, y, sd, rm, 0, base); - xd = x.d; - e = x.e; - roundUp = inexact; - } - - // The rounding digit, i.e. the digit after the digit that may be rounded up. - i = xd[sd]; - k = base / 2; - roundUp = roundUp || xd[sd + 1] !== void 0; - - roundUp = rm < 4 - ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) - : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 || - rm === (x.s < 0 ? 8 : 7)); - - xd.length = sd; - - if (roundUp) { - - // Rounding up may mean the previous digit has to be rounded up and so on. - for (; ++xd[--sd] > base - 1;) { - xd[sd] = 0; - if (!sd) { - ++e; - xd.unshift(1); - } - } - } - - // Determine trailing zeros. - for (len = xd.length; !xd[len - 1]; --len); - - // E.g. [4, 11, 15] becomes 4bf. - for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]); - - // Add binary exponent suffix? - if (isExp) { - if (len > 1) { - if (baseOut == 16 || baseOut == 8) { - i = baseOut == 16 ? 4 : 3; - for (--len; len % i; len++) str += '0'; - xd = convertBase(str, base, baseOut); - for (len = xd.length; !xd[len - 1]; --len); - - // xd[0] will always be be 1 - for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]); - } else { - str = str.charAt(0) + '.' + str.slice(1); - } - } - - str = str + (e < 0 ? 'p' : 'p+') + e; - } else if (e < 0) { - for (; ++e;) str = '0' + str; - str = '0.' + str; - } else { - if (++e > len) for (e -= len; e-- ;) str += '0'; - else if (e < len) str = str.slice(0, e) + '.' + str.slice(e); - } - } - - str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str; - } - - return x.s < 0 ? '-' + str : str; - } - - - // Does not strip trailing zeros. - function truncate(arr, len) { - if (arr.length > len) { - arr.length = len; - return true; - } - } - - - // Decimal methods - - - /* - * abs - * acos - * acosh - * add - * asin - * asinh - * atan - * atanh - * atan2 - * cbrt - * ceil - * clone - * config - * cos - * cosh - * div - * exp - * floor - * hypot - * ln - * log - * log2 - * log10 - * max - * min - * mod - * mul - * pow - * random - * round - * set - * sign - * sin - * sinh - * sqrt - * sub - * tan - * tanh - * trunc - */ - - - /* - * Return a new Decimal whose value is the absolute value of `x`. - * - * x {number|string|Decimal} - * - */ - function abs(x) { - return new this(x).abs(); - } - - - /* - * Return a new Decimal whose value is the arccosine in radians of `x`. - * - * x {number|string|Decimal} - * - */ - function acos(x) { - return new this(x).acos(); - } - - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function acosh(x) { - return new this(x).acosh(); - } - - - /* - * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function add(x, y) { - return new this(x).plus(y); - } - - - /* - * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function asin(x) { - return new this(x).asin(); - } - - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function asinh(x) { - return new this(x).asinh(); - } - - - /* - * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function atan(x) { - return new this(x).atan(); - } - - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function atanh(x) { - return new this(x).atanh(); - } - - - /* - * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi - * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi, pi] - * - * y {number|string|Decimal} The y-coordinate. - * x {number|string|Decimal} The x-coordinate. - * - * atan2(±0, -0) = ±pi - * atan2(±0, +0) = ±0 - * atan2(±0, -x) = ±pi for x > 0 - * atan2(±0, x) = ±0 for x > 0 - * atan2(-y, ±0) = -pi/2 for y > 0 - * atan2(y, ±0) = pi/2 for y > 0 - * atan2(±y, -Infinity) = ±pi for finite y > 0 - * atan2(±y, +Infinity) = ±0 for finite y > 0 - * atan2(±Infinity, x) = ±pi/2 for finite x - * atan2(±Infinity, -Infinity) = ±3*pi/4 - * atan2(±Infinity, +Infinity) = ±pi/4 - * atan2(NaN, x) = NaN - * atan2(y, NaN) = NaN - * - */ - function atan2(y, x) { - y = new this(y); - x = new this(x); - var r, - pr = this.precision, - rm = this.rounding, - wpr = pr + 4; - - // Either NaN - if (!y.s || !x.s) { - r = new this(NaN); - - // Both ±Infinity - } else if (!y.d && !x.d) { - r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75); - r.s = y.s; - - // x is ±Infinity or y is ±0 - } else if (!x.d || y.isZero()) { - r = x.s < 0 ? getPi(this, pr, rm) : new this(0); - r.s = y.s; - - // y is ±Infinity or x is ±0 - } else if (!y.d || x.isZero()) { - r = getPi(this, wpr, 1).times(0.5); - r.s = y.s; - - // Both non-zero and finite - } else if (x.s < 0) { - this.precision = wpr; - this.rounding = 1; - r = this.atan(divide(y, x, wpr, 1)); - x = getPi(this, wpr, 1); - this.precision = pr; - this.rounding = rm; - r = y.s < 0 ? r.minus(x) : r.plus(x); - } else { - r = this.atan(divide(y, x, wpr, 1)); - } - - return r; - } - - - /* - * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function cbrt(x) { - return new this(x).cbrt(); - } - - - /* - * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`. - * - * x {number|string|Decimal} - * - */ - function ceil(x) { - return finalise(x = new this(x), x.e + 1, 2); - } - - - /* - * Configure global settings for a Decimal constructor. - * - * `obj` is an object with one or more of the following properties, - * - * precision {number} - * rounding {number} - * toExpNeg {number} - * toExpPos {number} - * maxE {number} - * minE {number} - * modulo {number} - * crypto {boolean|number} - * - * E.g. Decimal.config({ precision: 20, rounding: 4 }) - * - */ - function config(obj) { - if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected'); - var i, p, v, - ps = [ - 'precision', 1, MAX_DIGITS, - 'rounding', 0, 8, - 'toExpNeg', -EXP_LIMIT, 0, - 'toExpPos', 0, EXP_LIMIT, - 'maxE', 0, EXP_LIMIT, - 'minE', -EXP_LIMIT, 0, - 'modulo', 0, 9 - ]; - - for (i = 0; i < ps.length; i += 3) { - if ((v = obj[p = ps[i]]) !== void 0) { - if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v; - else throw Error(invalidArgument + p + ': ' + v); - } - } - - if ((v = obj[p = 'crypto']) !== void 0) { - if (v === true || v === false || v === 0 || v === 1) { - if (v) { - if (typeof crypto != 'undefined' && crypto && - (crypto.getRandomValues || crypto.randomBytes)) { - this[p] = true; - } else { - throw Error(cryptoUnavailable); - } - } else { - this[p] = false; - } - } else { - throw Error(invalidArgument + p + ': ' + v); - } - } - - return this; - } - - - /* - * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cos(x) { - return new this(x).cos(); - } - - - /* - * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cosh(x) { - return new this(x).cosh(); - } - - - /* - * Create and return a Decimal constructor with the same configuration properties as this Decimal - * constructor. - * - */ - function clone(obj) { - var i, p, ps; - - /* - * The Decimal constructor and exported function. - * Return a new Decimal instance. - * - * v {number|string|Decimal} A numeric value. - * - */ - function Decimal(v) { - var e, i, t, - x = this; - - // Decimal called without new. - if (!(x instanceof Decimal)) return new Decimal(v); - - // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor - // which points to Object. - x.constructor = Decimal; - - // Duplicate. - if (v instanceof Decimal) { - x.s = v.s; - x.e = v.e; - x.d = (v = v.d) ? v.slice() : v; - return; - } - - t = typeof v; - - if (t === 'number') { - if (v === 0) { - x.s = 1 / v < 0 ? -1 : 1; - x.e = 0; - x.d = [0]; - return; - } - - if (v < 0) { - v = -v; - x.s = -1; - } else { - x.s = 1; - } - - // Fast path for small integers. - if (v === ~~v && v < 1e7) { - for (e = 0, i = v; i >= 10; i /= 10) e++; - x.e = e; - x.d = [v]; - return; - - // Infinity, NaN. - } else if (v * 0 !== 0) { - if (!v) x.s = NaN; - x.e = NaN; - x.d = null; - return; - } - - return parseDecimal(x, v.toString()); - - } else if (t !== 'string') { - throw Error(invalidArgument + v); - } - - // Minus sign? - if (v.charCodeAt(0) === 45) { - v = v.slice(1); - x.s = -1; - } else { - x.s = 1; - } - - return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v); - } - - Decimal.prototype = P; - - Decimal.ROUND_UP = 0; - Decimal.ROUND_DOWN = 1; - Decimal.ROUND_CEIL = 2; - Decimal.ROUND_FLOOR = 3; - Decimal.ROUND_HALF_UP = 4; - Decimal.ROUND_HALF_DOWN = 5; - Decimal.ROUND_HALF_EVEN = 6; - Decimal.ROUND_HALF_CEIL = 7; - Decimal.ROUND_HALF_FLOOR = 8; - Decimal.EUCLID = 9; - - Decimal.config = Decimal.set = config; - Decimal.clone = clone; - - Decimal.abs = abs; - Decimal.acos = acos; - Decimal.acosh = acosh; // ES6 - Decimal.add = add; - Decimal.asin = asin; - Decimal.asinh = asinh; // ES6 - Decimal.atan = atan; - Decimal.atanh = atanh; // ES6 - Decimal.atan2 = atan2; - Decimal.cbrt = cbrt; // ES6 - Decimal.ceil = ceil; - Decimal.cos = cos; - Decimal.cosh = cosh; // ES6 - Decimal.div = div; - Decimal.exp = exp; - Decimal.floor = floor; - Decimal.hypot = hypot; // ES6 - Decimal.ln = ln; - Decimal.log = log; - Decimal.log10 = log10; // ES6 - Decimal.log2 = log2; // ES6 - Decimal.max = max; - Decimal.min = min; - Decimal.mod = mod; - Decimal.mul = mul; - Decimal.pow = pow; - Decimal.random = random; - Decimal.round = round; - Decimal.sign = sign; // ES6 - Decimal.sin = sin; - Decimal.sinh = sinh; // ES6 - Decimal.sqrt = sqrt; - Decimal.sub = sub; - Decimal.tan = tan; - Decimal.tanh = tanh; // ES6 - Decimal.trunc = trunc; // ES6 - - if (obj === void 0) obj = {}; - if (obj) { - ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto']; - for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p]; - } - - Decimal.config(obj); - - return Decimal; - } - - - /* - * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function div(x, y) { - return new this(x).div(y); - } - - - /* - * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The power to which to raise the base of the natural log. - * - */ - function exp(x) { - return new this(x).exp(); - } - - - /* - * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`. - * - * x {number|string|Decimal} - * - */ - function floor(x) { - return finalise(x = new this(x), x.e + 1, 3); - } - - - /* - * Return a new Decimal whose value is the square root of the sum of the squares of the arguments, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...) - * - */ - function hypot() { - var i, n, - t = new this(0); - - external = false; - - for (i = 0; i < arguments.length;) { - n = new this(arguments[i++]); - if (!n.d) { - if (n.s) { - external = true; - return new this(1 / 0); - } - t = n; - } else if (t.d) { - t = t.plus(n.times(n)); - } - } - - external = true; - - return t.sqrt(); - } - - - /* - * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function ln(x) { - return new this(x).ln(); - } - - - /* - * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base - * is specified, rounded to `precision` significant digits using rounding mode `rounding`. - * - * log[y](x) - * - * x {number|string|Decimal} The argument of the logarithm. - * y {number|string|Decimal} The base of the logarithm. - * - */ - function log(x, y) { - return new this(x).log(y); - } - - - /* - * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log2(x) { - return new this(x).log(2); - } - - - /* - * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log10(x) { - return new this(x).log(10); - } - - - /* - * Return a new Decimal whose value is the maximum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function max() { - return maxOrMin(this, arguments, 'lt'); - } - - - /* - * Return a new Decimal whose value is the minimum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function min() { - return maxOrMin(this, arguments, 'gt'); - } - - - /* - * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mod(x, y) { - return new this(x).mod(y); - } - - - /* - * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mul(x, y) { - return new this(x).mul(y); - } - - - /* - * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The base. - * y {number|string|Decimal} The exponent. - * - */ - function pow(x, y) { - return new this(x).pow(y); - } - - - /* - * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with - * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros - * are produced). - * - * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive. - * - */ - function random(sd) { - var d, e, k, n, - i = 0, - r = new this(1), - rd = []; - - if (sd === void 0) sd = this.precision; - else checkInt32(sd, 1, MAX_DIGITS); - - k = Math.ceil(sd / LOG_BASE); - - if (!this.crypto) { - for (; i < k;) rd[i++] = Math.random() * 1e7 | 0; - - // Browsers supporting crypto.getRandomValues. - } else if (crypto.getRandomValues) { - d = crypto.getRandomValues(new Uint32Array(k)); - - for (; i < k;) { - n = d[i]; - - // 0 <= n < 4294967296 - // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865). - if (n >= 4.29e9) { - d[i] = crypto.getRandomValues(new Uint32Array(1))[0]; - } else { - - // 0 <= n <= 4289999999 - // 0 <= (n % 1e7) <= 9999999 - rd[i++] = n % 1e7; - } - } - - // Node.js supporting crypto.randomBytes. - } else if (crypto.randomBytes) { - - // buffer - d = crypto.randomBytes(k *= 4); - - for (; i < k;) { - - // 0 <= n < 2147483648 - n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24); - - // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286). - if (n >= 2.14e9) { - crypto.randomBytes(4).copy(d, i); - } else { - - // 0 <= n <= 2139999999 - // 0 <= (n % 1e7) <= 9999999 - rd.push(n % 1e7); - i += 4; - } - } - - i = k / 4; - } else { - throw Error(cryptoUnavailable); - } - - k = rd[--i]; - sd %= LOG_BASE; - - // Convert trailing digits to zeros according to sd. - if (k && sd) { - n = mathpow(10, LOG_BASE - sd); - rd[i] = (k / n | 0) * n; - } - - // Remove trailing words which are zero. - for (; rd[i] === 0; i--) rd.pop(); - - // Zero? - if (i < 0) { - e = 0; - rd = [0]; - } else { - e = -1; - - // Remove leading words which are zero and adjust exponent accordingly. - for (; rd[0] === 0; e -= LOG_BASE) rd.shift(); - - // Count the digits of the first word of rd to determine leading zeros. - for (k = 1, n = rd[0]; n >= 10; n /= 10) k++; - - // Adjust the exponent for leading zeros of the first word of rd. - if (k < LOG_BASE) e -= LOG_BASE - k; - } - - r.e = e; - r.d = rd; - - return r; - } - - - /* - * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`. - * - * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL). - * - * x {number|string|Decimal} - * - */ - function round(x) { - return finalise(x = new this(x), x.e + 1, this.rounding); - } - - - /* - * Return - * 1 if x > 0, - * -1 if x < 0, - * 0 if x is 0, - * -0 if x is -0, - * NaN otherwise - * - */ - function sign(x) { - x = new this(x); - return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN; - } - - - /* - * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sin(x) { - return new this(x).sin(); - } - - - /* - * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sinh(x) { - return new this(x).sinh(); - } - - - /* - * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function sqrt(x) { - return new this(x).sqrt(); - } - - - /* - * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function sub(x, y) { - return new this(x).sub(y); - } - - - /* - * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tan(x) { - return new this(x).tan(); - } - - - /* - * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tanh(x) { - return new this(x).tanh(); - } - - - /* - * Return a new Decimal whose value is `x` truncated to an integer. - * - * x {number|string|Decimal} - * - */ - function trunc(x) { - return finalise(x = new this(x), x.e + 1, 1); - } - - - // Create and configure initial Decimal constructor. - Decimal = clone(Decimal); - - // Create the internal constants from their string values. - LN10 = new Decimal(LN10); - PI = new Decimal(PI); - - - // Export. - - - // AMD. - if (typeof define == 'function' && define.amd) { - define(function () { - return Decimal; - }); - - // Node and other environments that support module.exports. - } else if (typeof module != 'undefined' && module.exports) { - module.exports = Decimal['default'] = Decimal.Decimal = Decimal; - - // Browser. - } else { - if (!globalScope) { - globalScope = typeof self != 'undefined' && self && self.self == self - ? self : Function('return this')(); - } - - noConflict = globalScope.Decimal; - Decimal.noConflict = function () { - globalScope.Decimal = noConflict; - return Decimal; - }; - - globalScope.Decimal = Decimal; - } -})(this);