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Added new constant system + imporved BigDouble parsing
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@arguiot
arguiot committed Sep 28, 2022
1 parent 967b27e commit 37d295b
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113 changes: 57 additions & 56 deletions Sources/Euler/BigNumber/BigDouble/BigDouble.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -116,62 +116,66 @@ public struct BigDouble:
}

public init?(_ nStr: String) {
if let bi = BigInt(nStr) {
self.init(bi, over: 1)
} else {
if let exp = nStr.firstIndex(of: "e")?.utf16Offset(in: nStr) {
let beforeExp = String(Array(nStr)[..<exp].filter{ $0 != "." })
var afterExp = String(Array(nStr)[(exp + 1)...])
var sign = false

if let neg = afterExp.firstIndex(of: "-")?.utf16Offset(in: afterExp) {
afterExp = String(Array(afterExp)[(neg + 1)...])
sign = true
}

if sign {
if var safeAfterExp = Int(afterExp) {
if beforeExp.starts(with: "+") || beforeExp.starts(with: "-") {
safeAfterExp = safeAfterExp - beforeExp.count + 2
} else {
safeAfterExp = safeAfterExp - beforeExp.count + 1
}
guard safeAfterExp > 0 else { return nil }
let den = ["1"] + [Character](repeating: "0", count: safeAfterExp)
self.init(beforeExp, over: String(den))
return
}
return nil
} else {
if var safeAfterExp = Int(afterExp) {
if beforeExp.starts(with: "+") || beforeExp.starts(with: "-") {
safeAfterExp = safeAfterExp - beforeExp.count + 2
} else {
safeAfterExp = safeAfterExp - beforeExp.count + 1
}
let num = beforeExp + String([Character](repeating: "0", count: safeAfterExp))
self.init(num, over: "1")
return
}
return nil
}
// Validating the string to be like a number using the following rules:
// 1. The string can't be empty
// 2. The string can't start with a dot
// 3. The string can't have more than one dot
// 4. Plus and minus signs can only be at the beginning of the string and should be followed by a digit
// 5. There should be only one exponent sign (e or E) and it should be followed by a valid integer (positive or negative)
// 6. Valid characters are: 0-9, +, -, ., e, E

guard !nStr.isEmpty else { return nil }
guard !nStr.hasPrefix(".") else { return nil }
guard nStr.filter({ $0 == "." }).count <= 1 else { return nil }
guard nStr.filter({ $0 == "+" || $0 == "-" }).count <= 2 else { return nil }
guard nStr.filter({ $0 == "e" || $0 == "E" }).count <= 1 else { return nil }
guard nStr.filter({ $0.isNumber || $0 == "+" || $0 == "-" || $0 == "." || $0 == "e" || $0 == "E" }).count == nStr.count else { return nil }

// If the string looks like an integer we can use the BigInt initializer
if !nStr.contains(".") {
if let n = BigInt(nStr) {
self.init(n, over: 1)
return
}

if let io = nStr.firstIndex(of: ".") {
let beforePoint = String(nStr[..<io])
let afterPoint = String(nStr[nStr.index(io, offsetBy: 1)...])

if afterPoint == "0" {
self.init(beforePoint, over: "1")
}
else {
let den = ["1"] + [Character](repeating: "0", count: afterPoint.count)
self.init(beforePoint + afterPoint, over: String(den))
}
} else {
return nil
}

// We need to parse the exponent
var exp = 0
let components = nStr.lowercased().components(separatedBy: "e")
if components.count == 2, let e = Int(components[1]) {
exp = e
}

// We need to parse the decimal part
guard let decimal = components.first?.split(separator: ".") else { return nil }
let integerPart = decimal[0]
let decimalPart = decimal.count > 1 ? decimal[1] : ""

// Adjust the exponent
exp -= decimalPart.count

// Numerator
var num = [integerPart, decimalPart]
if exp > 0 {
let upperBound = exp
if upperBound > 0 {
num += Array(repeating: "0", count: upperBound)
} else { // we adjust the exp to shift the decimal point
exp = upperBound
}
}
let numerator = num.joined()

// Denominator
var den = ["1"]
if exp < 0 {
den += Array(repeating: "0", count: abs(exp))
}
let denominator = den.joined()
// We can now create the BigDouble
guard let n = BigInt(numerator) else { return nil }
guard let d = BigInt(denominator) else { return nil }
self.init(n, over: d)
}

/// Create an instance initialized to a string with the value of mathematical numerical system of the specified radix (base).
Expand Down Expand Up @@ -262,9 +266,6 @@ public struct BigDouble:
self.init(value)
}

public init(constant: Constant) {
self.init(constant.rawValue)!
}
//
//
// MARK: - Descriptions
Expand Down
180 changes: 118 additions & 62 deletions Sources/Euler/NumberTheory/Constants.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -12,107 +12,163 @@ import Foundation
/// Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". It is also called Archimedes' constant.
///
public var pi: BigNumber {
return BigNumber("3.141592653589793238")!
return Constant.pi.value
}

/// The mathematical constant
///
/// The number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828, and is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series
///
public var e: BigNumber {
return BigNumber("2.718281828459045235")!
return Constant.e.value
}
/// Exponential function
public func exp(_ r: BigNumber) -> BigNumber {
if let d = r.asDouble() {
return BigDouble(exp(d))
}
let a = BigNumber(constant: .e)
return a ** r
return e ** r
}
/// A list of important mathematical and physical constants
public enum Constant: String {

/// Mathematical constant object
public struct Constant {
/// The name of the constant
public var name: String
/// Quick description of the constant
public var description: String
/// The value of the constant
public var value: BigNumber
}
/// List of mathematical constants
public extension Constant {
/// The mass in `kg` of alpha particles
case alphaParticleMass = "6.64465675e-27"
static let alphaParticleMass = Constant(name: "Alpha Particle Mass", description: "The mass in kg of alpha particles", value: BigNumber("6.64465675e-27")!)
/// The mass in `kg` of an atom (see Wikipedia for more info)
case atomicMass = "1.660538921e-27"
static let atomicMass = Constant(name: "Atomic Mass", description: "The mass in kg of an atom (see Wikipedia for more info)", value: BigNumber("1.660538921e-27")!)
/// Avogadro constant in `mol^(-1)`
case Avogadro = "6.02214129e23"
static let Avogadro = Constant(name: "Avogadro", description: "Avogadro constant in mol^(-1)", value: BigNumber("6.02214129e23")!)
/// Boltzmann constant in `J/K`
case Boltzmann = "1.3806488e-23"
static let Boltzmann = Constant(name: "Boltzmann", description: "Boltzmann constant in J/K", value: BigNumber("1.3806488e-23")!)
/// Quantized unit of electrical conductance in `S`
case conductanceQuantum = "7.7480917346e-5"
static let conductanceQuantum = Constant(name: "Conductance Quantum", description: "Quantized unit of electrical conductance in S", value: BigNumber("7.7480917346e-5")!)
/// The mathematical constant
case e = "2.7182818284590"
static let e = Constant(name: "e", description: "The mathematical constant", value: BigNumber("2.718281828459045235")!)
/// Earth to moon distance in `km`
case earth_moon = "384401"
static let earth_moon = Constant(name: "Earth to Moon", description: "Earth to moon distance in km", value: BigNumber("384401")!)
/// Earth to sun distance in `km`
case earth_sun = "1.496e8"
static let earth_sun = Constant(name: "Earth to Sun", description: "Earth to sun distance in km", value: BigNumber("1.496e8")!)
/// Earth mass in `kg`
case earthMass = "5.974e+24"
static let earthMass = Constant(name: "Earth Mass", description: "Earth mass in kg", value: BigNumber("5.974e+24")!)
/// Earth radius in `km`
case earthRadius = "6371"
static let earthRadius = Constant(name: "Earth Radius", description: "Earth radius in km", value: BigNumber("6371")!)
/// Vacuum permittivity in `F/m`
case electric = "8.854187e-12"
static let electric = Constant(name: "Electric", description: "Vacuum permittivity in F/m", value: BigNumber("8.854187e-12")!)
/// Electron mass in `kg`
case electronMass = "9.10938291e-31"
static let electronMass = Constant(name: "Electron Mass", description: "Electron mass in kg", value: BigNumber("9.10938291e-31")!)
/// Elementary charge in `C`
case elementaryCharge = "1.602176565e-19"
static let elementaryCharge = Constant(name: "Elementary Charge", description: "Elementary charge in C", value: BigNumber("1.602176565e-19")!)
/// Euler–Mascheroni Gamma constant
case EulerGamma = "0.57721566490153286"
static let EulerGamma = Constant(name: "Euler Gamma", description: "Euler–Mascheroni Gamma constant", value: BigNumber("0.57721566490153286")!)
/// Faraday constant in `C/mol`
case Faraday = "96485.3365"
static let Faraday = Constant(name: "Faraday", description: "Faraday constant in C/mol", value: BigNumber("96485.3365")!)
/// Fine structure constant
case fineStructure = "7.2973525698e-3"
static let fineStructure = Constant(name: "Fine Structure", description: "Fine structure constant", value: BigNumber("0.0072973525693")!)
/// Golden ratio
case goldenRatio = "1.61803398874989484820"
/// Standard acceleration due to gravity constant in `m/s^2`
case gravity = "9.80665"
/// Invverse of fine structure constant
case inverseFineStructure = "137.035999074"
static let goldenRatio = Constant(name: "Golden Ratio", description: "Golden ratio", value: BigNumber("1.61803398874989484820")!)
/// Standard gravity in `m/s^2`
static let gravity = Constant(name: "Gravity", description: "Standard gravity in m/s^2", value: BigNumber("9.80665")!)
/// Inverse fine structure constant
static let inverseFineStructure = Constant(name: "Inverse Fine Structure", description: "Inverse fine structure constant", value: BigNumber("137.035999139")!)
/// Vacuum permeability in `H/m`
case magnetic = "1.25663706212e-6"
/// Magnetic flux quantum constant in `Wb`
case magneticFluxQuantum = "2.067833758e-15"
/// Gas constant in `J/K/mol`
case molarGas = "8.3144621"
static let magnetic = Constant(name: "Magnetic", description: "Vacuum permeability in H/m", value: BigNumber("1.2566370614e-6")!)
/// Magnetic flux quantum in `Wb`
static let magneticFluxQuantum = Constant(name: "Magnetic Flux Quantum", description: "Magnetic flux quantum in Wb", value: BigNumber("2.067833831e-15")!)
/// Gas constant in `J/(mol K)`
static let molarGas = Constant(name: "Molar Gas", description: "Gas constant in J/(mol K)", value: BigNumber("8.3144621")!)
/// Mass of the moon in `kg`
case moonMass = "7.348e22"
/// Moon radius in `km`
case moonRadius = "1738"
/// Mass of neutron in `kg`
case neutronMass = "1.674927351e-27"
/// Newton's gravitational constant in `m3⋅kg−1⋅s−2`
case NewtonGravitation = "6.67384e-11"
static let moonMass = Constant(name: "Moon Mass", description: "Mass of the moon in kg", value: BigNumber("7.348e+22")!)
/// Moon's radius in `km`
static let moonRadius = Constant(name: "Moon Radius", description: "Moon's radius in km", value: BigNumber("1737.4")!)
/// Mass of the neutron in `kg`
static let neutronMass = Constant(name: "Neutron Mass", description: "Mass of the neutron in kg", value: BigNumber("1.674927211e-27")!)
/// Newtonian constant of gravitation in `m3⋅kg−1⋅s−2`
static let NewtonianGravitation = Constant(name: "Newtonian Gravitation", description: "Newtonian constant of gravitation in m3⋅kg-1⋅s-2", value: BigNumber("6.67428e-11")!)
/// The mathematical constant
case pi = "3.14159265358979323846"
/// Planck constant in `J s`
case Planck = "6.62606957e-34"
static let pi = Constant(name: "pi", description: "The mathematical constant", value: BigNumber("3.141592653589793238")!)
/// Planck constant in `J⋅s`
static let Planck = Constant(name: "Planck", description: "Planck constant in J⋅s", value: BigNumber("6.62606957e-34")!)
/// Proton mass divided by electron mass
case proton_electronMassRatio = "1836.15267245"
static let protonElectronMassRatio = Constant(name: "Proton Electron Mass Ratio", description: "Proton mass divided by electron mass", value: BigNumber("1836.15267247")!)
/// Proton mass divided by neutron mass
case proton_neutronMassRatio = "0.99862347826"
static let protonNeutronMassRatio = Constant(name: "Proton Neutron Mass Ratio", description: "Proton mass divided by neutron mass", value: BigNumber("0.99862347826")!)
/// Proton mass in `kg`
case protonMass = "1.672621777e-27"
/// Rydberg constant in `m^(-1)`
case Rydberg = "10973731.568539"
static let protonMass = Constant(name: "Proton Mass", description: "Proton mass in kg", value: BigNumber("1.672621777e-27")!)
/// Rydberg constant in `m^-1`
static let Rydberg = Constant(name: "Rydberg", description: "Rydberg constant in m^-1", value: BigNumber("10973731.568539")!)
/// Speed of light in `m/s`
case speedOfLight = "299792458"
static let speedOfLight = Constant(name: "Speed of Light", description: "Speed of light in m/s", value: BigNumber("299792458")!)
/// Speed of sound in `m/s`
case speedOfSound = "340.27"
static let speedOfSound = Constant(name: "Speed of Sound", description: "Speed of sound in m/s", value: BigNumber("340.29")!)
/// The square root of 2
case sqrt2 = "1.41421356237309504880"
/// Stefan-Boltzmann constant in `W m^(-2) K^(-4)`
case Stefan_Boltzmann = "5.670373e-8"
static let sqrt2 = Constant(name: "sqrt(2)", description: "The square root of 2", value: BigNumber("1.41421356237309504880")!)
/// Stefan–Boltzmann constant in `W⋅m−2⋅K−4`
static let StefanBoltzmann = Constant(name: "Stefan Boltzmann", description: "Stefan–Boltzmann constant in W⋅m-2⋅K-4", value: BigNumber("5.670373e-8")!)
/// Mass of the sun in `kg`
case sunMass = "1.989e30"
static let sunMass = Constant(name: "Sun Mass", description: "Mass of the sun in kg", value: BigNumber("1.98892e+30")!)
/// Sun's radius in `km`
case sunRadius = "695500"
/// Dwayne Johnson's mass. Can't mathematician have the sense of humour?
case TheRockMass = "124.73790175"
/// Thomson Cross Section constant in `m^2`
case ThomsonCrossSection = "0.6652458734e-28"
/// The Answer to the Ultimate Question of Life, the Universe, and Everything.
case UltimateAnswer = "42"
/// The coldest temperature in the universe in `C`
case zeroKelvin = "-273.15"
static let sunRadius = Constant(name: "Sun Radius", description: "Sun's radius in km", value: BigNumber("695700")!)
/// Dwayne "The Rock" Johnson's mass in `kg`
static let theRockMass = Constant(name: "The Rock Mass", description: "Dwayne \"The Rock\" Johnson's mass in kg. Can't mathematician have the sense of humour?", value: BigNumber("124.73790175")!)
/// Thomson cross section in `m2`
static let Thomson = Constant(name: "Thomson", description: "Thomson cross section in m2", value: BigNumber("0.6652458734e-28")!)
/// The answer to life, the universe, and everything
static let UltimateAnswer = Constant(name: "Ultimate Answer", description: "The answer to life, the universe, and everything", value: BigNumber("42")!)
/// The coldness of the universe in `C`
static let universeTemperature = Constant(name: "Universe Temperature", description: "The coldness of the universe in C", value: BigNumber("-273.15")!)

/// The list of all constants
static let all: [Constant] = [
.alphaParticleMass,
.atomicMass,
.Avogadro,
.Boltzmann,
.conductanceQuantum,
.e,
.earth_moon,
.earth_sun,
.earthMass,
.earthRadius,
.electric,
.electronMass,
.elementaryCharge,
.EulerGamma,
.Faraday,
.fineStructure,
.goldenRatio,
.gravity,
.inverseFineStructure,
.magnetic,
.magneticFluxQuantum,
.molarGas,
.moonMass,
.moonRadius,
.neutronMass,
.NewtonianGravitation,
.pi,
.Planck,
.protonElectronMassRatio,
.protonNeutronMassRatio,
.protonMass,
.Rydberg,
.speedOfLight,
.speedOfSound,
.sqrt2,
.StefanBoltzmann,
.sunMass,
.sunRadius,
.theRockMass,
.Thomson,
.UltimateAnswer,
.universeTemperature
]
}
2 changes: 1 addition & 1 deletion Sources/Euler/Statistics/Quantile.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,7 @@ public extension Statistics {
guard percentage > 0.0 && percentage < 1.0 else { throw QuantileError.PercentageIssue }
guard self.list.count > 1 else { throw QuantileError.ArrayLength }
var array = self.list
let n = array.removeFirst()
_ = array.removeFirst()
let sorted = array.sorted()
let index = Double(sorted.count - 1) * percentage
let floored = Int(index)
Expand Down
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