-
Notifications
You must be signed in to change notification settings - Fork 52
/
big_float.js
503 lines (429 loc) · 12.6 KB
/
big_float.js
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
// big_float.js
// Douglas Crockford
// 2019-06-28
// You can access the big decimal floating point object in your module
// by importing it.
// import big_float from "./big_float.js";
// big_float.eq(
// big_float.add(
// big_float.make("0.1"),
// big_float.make("0.2")
// ),
// big_float.make("0.3")
// ) // true
/*jslint bitwise */
/*property
abs, abs_lt, add, coefficient, create, div, divrem, eq, exponent, fraction,
freeze, integer, isFinite, isSafeInteger, is_big_float, is_big_integer,
is_negative, is_positive, is_zero, length, lt, make, match, mul, neg,
normalize, number, power, repeat, scientific, sign, signum, slice, string,
sub, ten, two, zero
*/
import big_integer from "./big_integer.js";
function is_big_float(big) {
return (
typeof big === "object"
&& big_integer.is_big_integer(big.coefficient)
&& Number.isSafeInteger(big.exponent)
);
}
function is_negative(big) {
return big_integer.is_negative(big.coefficient);
}
function is_positive(big) {
return big_integer.is_positive(big.coefficient);
}
function is_zero(big) {
return big_integer.is_zero(big.coefficient);
}
const zero = Object.create(null);
zero.coefficient = big_integer.zero;
zero.exponent = 0;
Object.freeze(zero);
function make_big_float(coefficient, exponent) {
if (big_integer.is_zero(coefficient)) {
return zero;
}
const new_big_float = Object.create(null);
new_big_float.coefficient = coefficient;
new_big_float.exponent = exponent;
return Object.freeze(new_big_float);
}
const big_integer_ten_million = big_integer.make(10000000);
function number(a) {
const result = (
is_big_float(a)
? (
a.exponent === 0
? big_integer.number(a.coefficient)
: big_integer.number(a.coefficient) * (10 ** a.exponent)
)
: (
typeof a === "number"
? a
: (
big_integer.is_big_integer(a)
? big_integer.number(a)
: Number(a)
)
)
);
return (
Number.isFinite(result)
? result
: undefined
);
}
function neg(a) {
return make_big_float(big_integer.neg(a.coefficient), a.exponent);
}
function abs(a) {
return (
is_negative(a)
? neg(a)
: a
);
}
function conform_op(op) {
return function (a, b) {
const differential = a.exponent - b.exponent;
return (
differential === 0
? make_big_float(op(a.coefficient, b.coefficient), a.exponent)
: (
differential > 0
? make_big_float(
op(
big_integer.mul(
a.coefficient,
big_integer.power(big_integer.ten, differential)
),
b.coefficient
),
b.exponent
)
: make_big_float(
op(
a.coefficient,
big_integer.mul(
b.coefficient,
big_integer.power(big_integer.ten, -differential)
)
),
a.exponent
)
)
);
};
}
const add = conform_op(big_integer.add);
const sub = conform_op(big_integer.sub);
function eq(comparahend, comparator) {
return comparahend === comparator || is_zero(sub(comparahend, comparator));
}
function lt(comparahend, comparator) {
return is_negative(sub(comparahend, comparator));
}
function mul(multiplicand, multiplier) {
return make_big_float(
big_integer.mul(multiplicand.coefficient, multiplier.coefficient),
multiplicand.exponent + multiplier.exponent
);
}
function div(dividend, divisor, precision = -4) {
if (is_zero(dividend)) {
return zero;
}
if (is_zero(divisor)) {
return undefined;
}
let {coefficient, exponent} = dividend;
exponent -= divisor.exponent;
// Scale the coefficient to the desired precision.
if (typeof precision !== "number") {
precision = number(precision);
}
if (exponent > precision) {
coefficient = big_integer.mul(
coefficient,
big_integer.power(big_integer.ten, exponent - precision)
);
exponent = precision;
}
let remainder;
[coefficient, remainder] = big_integer.divrem(
coefficient,
divisor.coefficient
);
// Round the result if necessary.
if (!big_integer.abs_lt(
big_integer.add(remainder, remainder),
divisor.coefficient
)) {
coefficient = big_integer.add(
coefficient,
big_integer.signum(dividend.coefficient)
);
}
return make_big_float(coefficient, exponent);
}
function normalize(a) {
let {coefficient, exponent} = a;
if (coefficient.length < 2) {
return zero;
}
// If the exponent is zero, it is already normal.
if (exponent !== 0) {
// If the exponent is positive, multiply the coefficient by '10 **' exponent.
if (exponent > 0) {
coefficient = big_integer.mul(
coefficient,
big_integer.power(big_integer.ten, exponent)
);
exponent = 0;
} else {
let quotient;
let remainder;
// While the exponent is negative, if the coefficient is divisible by ten,
// then we do the division and add '1' to the exponent.
// To help this go a little faster, we first try units of ten million,
// reducing 7 zeros at a time.
while (exponent <= -7 && (coefficient[1] & 127) === 0) {
[quotient, remainder] = big_integer.divrem(
coefficient,
big_integer_ten_million
);
if (remainder !== big_integer.zero) {
break;
}
coefficient = quotient;
exponent += 7;
}
while (exponent < 0 && (coefficient[1] & 1) === 0) {
[quotient, remainder] = big_integer.divrem(
coefficient,
big_integer.ten
);
if (remainder !== big_integer.zero) {
break;
}
coefficient = quotient;
exponent += 1;
}
}
}
return make_big_float(coefficient, exponent);
}
function integer(a) {
// The integer function is like the normalize function except that it throws
// away significance. It discards the digits after the decimal point.
let {coefficient, exponent} = a;
if (coefficient.length < 2) {
return zero;
}
// If the exponent is zero, it is already an integer.
if (exponent === 0) {
return a;
}
// If the exponent is positive,
// multiply the coefficient by 10 ** exponent.
if (exponent > 0) {
return make_big_float(
big_integer.mul(
coefficient,
big_integer.power(big_integer.ten, exponent)
),
0
);
}
// If the exponent is negative, divide the coefficient by 10 ** -exponent.
// This truncates the unnecessary bits. This might be a zero result.
return make_big_float(
big_integer.div(
coefficient,
big_integer.power(big_integer.ten, -exponent)
),
0
);
}
function fraction(a) {
return sub(a, integer(a));
}
function deconstruct(number) {
// This function deconstructs a number, reducing it to its components:
// a sign, an integer coefficient, and an exponent, such that
// number = sign * coefficient * (2 ** exponent)
let sign = 1;
let coefficient = number;
let exponent = 0;
// Remove the sign from the coefficient.
if (coefficient < 0) {
coefficient = -coefficient;
sign = -1;
}
if (Number.isFinite(number) && number !== 0) {
// Reduce the coefficient: We can obtain the exponent by dividing the number by
// two until it goes to zero. We add the number of divisions to -1128, which is
// the exponent of 'Number.MIN_VALUE' minus the number of bits in the
// significand minus the bonus bit.
exponent = -1128;
let reduction = coefficient;
while (reduction !== 0) {
// This loop is guaranteed to reach zero. Each division will decrement the
// exponent of the reduction. When the exponent is so small that it can not
// be decremented, then the internal subnormal significand will be shifted
// right instead. Ultimately, all of the bits will be shifted out.
exponent += 1;
reduction /= 2;
}
// Reduce the exponent: When the exponent is zero, the number can be viewed
// as an integer. If the exponent is not zero, then adjust to correct the
// coefficient.
reduction = exponent;
while (reduction > 0) {
coefficient /= 2;
reduction -= 1;
}
while (reduction < 0) {
coefficient *= 2;
reduction += 1;
}
}
// Return an object containing the three components and the original number.
return {
sign,
coefficient,
exponent,
number
};
}
const number_pattern = /^(-?\d+)(?:\.(\d*))?(?:e(-?\d+))?$/;
//. Capturing groups
//. [1] int
//. [2] frac
//. [3] exp
function make(a, b) {
//. (big_integer)
//. (big_integer, exponent)
//. (string)
//. (string, radix)
//. (number)
if (big_integer.is_big_integer(a)) {
return make_big_float(a, b || 0);
}
if (typeof a === "string") {
if (Number.isSafeInteger(b)) {
return make(big_integer.make(a, b), 0);
}
let parts = a.match(number_pattern);
if (parts) {
let frac = parts[2] || "";
return make(
big_integer.make(parts[1] + frac),
(Number(parts[3]) || 0) - frac.length
);
}
}
// If 'a' is a number, then we deconstruct it into its basis '2' exponent
// and coefficient, and then reconstruct as a precise big float.
if (typeof a === "number" && Number.isFinite(a)) {
if (a === 0) {
return zero;
}
let {sign, coefficient, exponent} = deconstruct(a);
if (sign < 0) {
coefficient = -coefficient;
}
coefficient = big_integer.make(coefficient);
// If the exponent is negative, then we can divide by '2 ** abs(exponent)'.
if (exponent < 0) {
return normalize(div(
make(coefficient, 0),
make(big_integer.power(big_integer.two, -exponent), 0),
b
));
}
// If the exponent is greater than zero, then we can multiply the coefficient
// by '2 **' exponent.
if (exponent > 0) {
coefficient = big_integer.mul(
coefficient,
big_integer.power(big_integer.two, exponent)
);
exponent = 0;
}
return make(coefficient, exponent);
}
if (is_big_float(a)) {
return a;
}
}
function string(a, radix) {
if (is_zero(a)) {
return "0";
}
if (is_big_float(radix)) {
radix = normalize(radix);
return (
(radix && radix.exponent === 0)
? big_integer.string(integer(a).coefficient, radix.coefficient)
: undefined
);
}
a = normalize(a);
let s = big_integer.string(big_integer.abs(a.coefficient));
if (a.exponent < 0) {
let point = s.length + a.exponent;
if (point <= 0) {
s = "0".repeat(1 - point) + s;
point = 1;
}
s = s.slice(0, point) + "." + s.slice(point);
} else if (a.exponent > 0) {
s += "0".repeat(a.exponent);
}
if (big_integer.is_negative(a.coefficient)) {
s = "-" + s;
}
return s;
}
function scientific(a) {
if (is_zero(a)) {
return "0";
}
a = normalize(a);
let s = big_integer.string(big_integer.abs(a.coefficient));
let e = a.exponent + s.length - 1;
if (s.length > 1) {
s = s.slice(0, 1) + "." + s.slice(1);
}
if (e !== 0) {
s += "e" + e;
}
if (big_integer.is_negative(a.coefficient)) {
s = "-" + s;
}
return s;
}
export default Object.freeze({
abs,
add,
div,
eq,
fraction,
integer,
is_big_float,
is_negative,
is_positive,
is_zero,
lt,
make,
mul,
neg,
normalize,
number,
scientific,
string,
sub,
zero
});