aboutsummaryrefslogtreecommitdiffstats
path: root/vendor/brick/math/src/Internal/Calculator.php
blob: 44795acbb3a9e68eb6c9a0ab6a0a392610567c52 (plain) (blame)
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
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
<?php

declare(strict_types=1);

namespace Brick\Math\Internal;

use Brick\Math\Exception\RoundingNecessaryException;
use Brick\Math\RoundingMode;

/**
 * Performs basic operations on arbitrary size integers.
 *
 * Unless otherwise specified, all parameters must be validated as non-empty strings of digits,
 * without leading zero, and with an optional leading minus sign if the number is not zero.
 *
 * Any other parameter format will lead to undefined behaviour.
 * All methods must return strings respecting this format, unless specified otherwise.
 *
 * @internal
 *
 * @psalm-immutable
 */
abstract class Calculator
{
    /**
     * The maximum exponent value allowed for the pow() method.
     */
    public const MAX_POWER = 1000000;

    /**
     * The alphabet for converting from and to base 2 to 36, lowercase.
     */
    public const ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';

    /**
     * The Calculator instance in use.
     *
     * @var Calculator|null
     */
    private static $instance;

    /**
     * Sets the Calculator instance to use.
     *
     * An instance is typically set only in unit tests: the autodetect is usually the best option.
     *
     * @param Calculator|null $calculator The calculator instance, or NULL to revert to autodetect.
     *
     * @return void
     */
    final public static function set(?Calculator $calculator) : void
    {
        self::$instance = $calculator;
    }

    /**
     * Returns the Calculator instance to use.
     *
     * If none has been explicitly set, the fastest available implementation will be returned.
     *
     * @return Calculator
     *
     * @psalm-pure
     * @psalm-suppress ImpureStaticProperty
     */
    final public static function get() : Calculator
    {
        if (self::$instance === null) {
            /** @psalm-suppress ImpureMethodCall */
            self::$instance = self::detect();
        }

        return self::$instance;
    }

    /**
     * Returns the fastest available Calculator implementation.
     *
     * @codeCoverageIgnore
     *
     * @return Calculator
     */
    private static function detect() : Calculator
    {
        if (\extension_loaded('gmp')) {
            return new Calculator\GmpCalculator();
        }

        if (\extension_loaded('bcmath')) {
            return new Calculator\BcMathCalculator();
        }

        return new Calculator\NativeCalculator();
    }

    /**
     * Extracts the sign & digits of the operands.
     *
     * @param string $a The first operand.
     * @param string $b The second operand.
     *
     * @return array{0: bool, 1: bool, 2: string, 3: string} Whether $a and $b are negative, followed by their digits.
     */
    final protected function init(string $a, string $b) : array
    {
        return [
            $aNeg = ($a[0] === '-'),
            $bNeg = ($b[0] === '-'),

            $aNeg ? \substr($a, 1) : $a,
            $bNeg ? \substr($b, 1) : $b,
        ];
    }

    /**
     * Returns the absolute value of a number.
     *
     * @param string $n The number.
     *
     * @return string The absolute value.
     */
    final public function abs(string $n) : string
    {
        return ($n[0] === '-') ? \substr($n, 1) : $n;
    }

    /**
     * Negates a number.
     *
     * @param string $n The number.
     *
     * @return string The negated value.
     */
    final public function neg(string $n) : string
    {
        if ($n === '0') {
            return '0';
        }

        if ($n[0] === '-') {
            return \substr($n, 1);
        }

        return '-' . $n;
    }

    /**
     * Compares two numbers.
     *
     * @param string $a The first number.
     * @param string $b The second number.
     *
     * @return int [-1, 0, 1] If the first number is less than, equal to, or greater than the second number.
     */
    final public function cmp(string $a, string $b) : int
    {
        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);

        if ($aNeg && ! $bNeg) {
            return -1;
        }

        if ($bNeg && ! $aNeg) {
            return 1;
        }

        $aLen = \strlen($aDig);
        $bLen = \strlen($bDig);

        if ($aLen < $bLen) {
            $result = -1;
        } elseif ($aLen > $bLen) {
            $result = 1;
        } else {
            $result = $aDig <=> $bDig;
        }

        return $aNeg ? -$result : $result;
    }

    /**
     * Adds two numbers.
     *
     * @param string $a The augend.
     * @param string $b The addend.
     *
     * @return string The sum.
     */
    abstract public function add(string $a, string $b) : string;

    /**
     * Subtracts two numbers.
     *
     * @param string $a The minuend.
     * @param string $b The subtrahend.
     *
     * @return string The difference.
     */
    abstract public function sub(string $a, string $b) : string;

    /**
     * Multiplies two numbers.
     *
     * @param string $a The multiplicand.
     * @param string $b The multiplier.
     *
     * @return string The product.
     */
    abstract public function mul(string $a, string $b) : string;

    /**
     * Returns the quotient of the division of two numbers.
     *
     * @param string $a The dividend.
     * @param string $b The divisor, must not be zero.
     *
     * @return string The quotient.
     */
    abstract public function divQ(string $a, string $b) : string;

    /**
     * Returns the remainder of the division of two numbers.
     *
     * @param string $a The dividend.
     * @param string $b The divisor, must not be zero.
     *
     * @return string The remainder.
     */
    abstract public function divR(string $a, string $b) : string;

    /**
     * Returns the quotient and remainder of the division of two numbers.
     *
     * @param string $a The dividend.
     * @param string $b The divisor, must not be zero.
     *
     * @return string[] An array containing the quotient and remainder.
     */
    abstract public function divQR(string $a, string $b) : array;

    /**
     * Exponentiates a number.
     *
     * @param string $a The base number.
     * @param int    $e The exponent, validated as an integer between 0 and MAX_POWER.
     *
     * @return string The power.
     */
    abstract public function pow(string $a, int $e) : string;

    /**
     * @param string $a
     * @param string $b The modulus; must not be zero.
     *
     * @return string
     */
    public function mod(string $a, string $b) : string
    {
        return $this->divR($this->add($this->divR($a, $b), $b), $b);
    }

    /**
     * Returns the modular multiplicative inverse of $x modulo $m.
     *
     * If $x has no multiplicative inverse mod m, this method must return null.
     *
     * This method can be overridden by the concrete implementation if the underlying library has built-in support.
     *
     * @param string $x
     * @param string $m The modulus; must not be negative or zero.
     *
     * @return string|null
     */
    public function modInverse(string $x, string $m) : ?string
    {
        if ($m === '1') {
            return '0';
        }

        $modVal = $x;

        if ($x[0] === '-' || ($this->cmp($this->abs($x), $m) >= 0)) {
            $modVal = $this->mod($x, $m);
        }

        $x = '0';
        $y = '0';
        $g = $this->gcdExtended($modVal, $m, $x, $y);

        if ($g !== '1') {
            return null;
        }

        return $this->mod($this->add($this->mod($x, $m), $m), $m);
    }

    /**
     * Raises a number into power with modulo.
     *
     * @param string $base The base number; must be positive or zero.
     * @param string $exp  The exponent; must be positive or zero.
     * @param string $mod  The modulus; must be strictly positive.
     *
     * @return string The power.
     */
    abstract public function modPow(string $base, string $exp, string $mod) : string;

    /**
     * Returns the greatest common divisor of the two numbers.
     *
     * This method can be overridden by the concrete implementation if the underlying library
     * has built-in support for GCD calculations.
     *
     * @param string $a The first number.
     * @param string $b The second number.
     *
     * @return string The GCD, always positive, or zero if both arguments are zero.
     */
    public function gcd(string $a, string $b) : string
    {
        if ($a === '0') {
            return $this->abs($b);
        }

        if ($b === '0') {
            return $this->abs($a);
        }

        return $this->gcd($b, $this->divR($a, $b));
    }

    private function gcdExtended(string $a, string $b, string &$x, string &$y) : string
    {
        if ($a === '0') {
            $x = '0';
            $y = '1';

            return $b;
        }

        $x1 = '0';
        $y1 = '0';

        $gcd = $this->gcdExtended($this->mod($b, $a), $a, $x1, $y1);

        $x = $this->sub($y1, $this->mul($this->divQ($b, $a), $x1));
        $y = $x1;

        return $gcd;
    }

    /**
     * Returns the square root of the given number, rounded down.
     *
     * The result is the largest x such that x² ≤ n.
     * The input MUST NOT be negative.
     *
     * @param string $n The number.
     *
     * @return string The square root.
     */
    abstract public function sqrt(string $n) : string;

    /**
     * Converts a number from an arbitrary base.
     *
     * This method can be overridden by the concrete implementation if the underlying library
     * has built-in support for base conversion.
     *
     * @param string $number The number, positive or zero, non-empty, case-insensitively validated for the given base.
     * @param int    $base   The base of the number, validated from 2 to 36.
     *
     * @return string The converted number, following the Calculator conventions.
     */
    public function fromBase(string $number, int $base) : string
    {
        return $this->fromArbitraryBase(\strtolower($number), self::ALPHABET, $base);
    }

    /**
     * Converts a number to an arbitrary base.
     *
     * This method can be overridden by the concrete implementation if the underlying library
     * has built-in support for base conversion.
     *
     * @param string $number The number to convert, following the Calculator conventions.
     * @param int    $base   The base to convert to, validated from 2 to 36.
     *
     * @return string The converted number, lowercase.
     */
    public function toBase(string $number, int $base) : string
    {
        $negative = ($number[0] === '-');

        if ($negative) {
            $number = \substr($number, 1);
        }

        $number = $this->toArbitraryBase($number, self::ALPHABET, $base);

        if ($negative) {
            return '-' . $number;
        }

        return $number;
    }

    /**
     * Converts a non-negative number in an arbitrary base using a custom alphabet, to base 10.
     *
     * @param string $number   The number to convert, validated as a non-empty string,
     *                         containing only chars in the given alphabet/base.
     * @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum.
     * @param int    $base     The base of the number, validated from 2 to alphabet length.
     *
     * @return string The number in base 10, following the Calculator conventions.
     */
    final public function fromArbitraryBase(string $number, string $alphabet, int $base) : string
    {
        // remove leading "zeros"
        $number = \ltrim($number, $alphabet[0]);

        if ($number === '') {
            return '0';
        }

        // optimize for "one"
        if ($number === $alphabet[1]) {
            return '1';
        }

        $result = '0';
        $power = '1';

        $base = (string) $base;

        for ($i = \strlen($number) - 1; $i >= 0; $i--) {
            $index = \strpos($alphabet, $number[$i]);

            if ($index !== 0) {
                $result = $this->add($result, ($index === 1)
                    ? $power
                    : $this->mul($power, (string) $index)
                );
            }

            if ($i !== 0) {
                $power = $this->mul($power, $base);
            }
        }

        return $result;
    }

    /**
     * Converts a non-negative number to an arbitrary base using a custom alphabet.
     *
     * @param string $number   The number to convert, positive or zero, following the Calculator conventions.
     * @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum.
     * @param int    $base     The base to convert to, validated from 2 to alphabet length.
     *
     * @return string The converted number in the given alphabet.
     */
    final public function toArbitraryBase(string $number, string $alphabet, int $base) : string
    {
        if ($number === '0') {
            return $alphabet[0];
        }

        $base = (string) $base;
        $result = '';

        while ($number !== '0') {
            [$number, $remainder] = $this->divQR($number, $base);
            $remainder = (int) $remainder;

            $result .= $alphabet[$remainder];
        }

        return \strrev($result);
    }

    /**
     * Performs a rounded division.
     *
     * Rounding is performed when the remainder of the division is not zero.
     *
     * @param string $a            The dividend.
     * @param string $b            The divisor, must not be zero.
     * @param int    $roundingMode The rounding mode.
     *
     * @return string
     *
     * @throws \InvalidArgumentException  If the rounding mode is invalid.
     * @throws RoundingNecessaryException If RoundingMode::UNNECESSARY is provided but rounding is necessary.
     */
    final public function divRound(string $a, string $b, int $roundingMode) : string
    {
        [$quotient, $remainder] = $this->divQR($a, $b);

        $hasDiscardedFraction = ($remainder !== '0');
        $isPositiveOrZero = ($a[0] === '-') === ($b[0] === '-');

        $discardedFractionSign = function() use ($remainder, $b) : int {
            $r = $this->abs($this->mul($remainder, '2'));
            $b = $this->abs($b);

            return $this->cmp($r, $b);
        };

        $increment = false;

        switch ($roundingMode) {
            case RoundingMode::UNNECESSARY:
                if ($hasDiscardedFraction) {
                    throw RoundingNecessaryException::roundingNecessary();
                }
                break;

            case RoundingMode::UP:
                $increment = $hasDiscardedFraction;
                break;

            case RoundingMode::DOWN:
                break;

            case RoundingMode::CEILING:
                $increment = $hasDiscardedFraction && $isPositiveOrZero;
                break;

            case RoundingMode::FLOOR:
                $increment = $hasDiscardedFraction && ! $isPositiveOrZero;
                break;

            case RoundingMode::HALF_UP:
                $increment = $discardedFractionSign() >= 0;
                break;

            case RoundingMode::HALF_DOWN:
                $increment = $discardedFractionSign() > 0;
                break;

            case RoundingMode::HALF_CEILING:
                $increment = $isPositiveOrZero ? $discardedFractionSign() >= 0 : $discardedFractionSign() > 0;
                break;

            case RoundingMode::HALF_FLOOR:
                $increment = $isPositiveOrZero ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0;
                break;

            case RoundingMode::HALF_EVEN:
                $lastDigit = (int) $quotient[-1];
                $lastDigitIsEven = ($lastDigit % 2 === 0);
                $increment = $lastDigitIsEven ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0;
                break;

            default:
                throw new \InvalidArgumentException('Invalid rounding mode.');
        }

        if ($increment) {
            return $this->add($quotient, $isPositiveOrZero ? '1' : '-1');
        }

        return $quotient;
    }

    /**
     * Calculates bitwise AND of two numbers.
     *
     * This method can be overridden by the concrete implementation if the underlying library
     * has built-in support for bitwise operations.
     *
     * @param string $a
     * @param string $b
     *
     * @return string
     */
    public function and(string $a, string $b) : string
    {
        return $this->bitwise('and', $a, $b);
    }

    /**
     * Calculates bitwise OR of two numbers.
     *
     * This method can be overridden by the concrete implementation if the underlying library
     * has built-in support for bitwise operations.
     *
     * @param string $a
     * @param string $b
     *
     * @return string
     */
    public function or(string $a, string $b) : string
    {
        return $this->bitwise('or', $a, $b);
    }

    /**
     * Calculates bitwise XOR of two numbers.
     *
     * This method can be overridden by the concrete implementation if the underlying library
     * has built-in support for bitwise operations.
     *
     * @param string $a
     * @param string $b
     *
     * @return string
     */
    public function xor(string $a, string $b) : string
    {
        return $this->bitwise('xor', $a, $b);
    }

    /**
     * Performs a bitwise operation on a decimal number.
     *
     * @param string $operator The operator to use, must be "and", "or" or "xor".
     * @param string $a        The left operand.
     * @param string $b        The right operand.
     *
     * @return string
     */
    private function bitwise(string $operator, string $a, string $b) : string
    {
        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);

        $aBin = $this->toBinary($aDig);
        $bBin = $this->toBinary($bDig);

        $aLen = \strlen($aBin);
        $bLen = \strlen($bBin);

        if ($aLen > $bLen) {
            $bBin = \str_repeat("\x00", $aLen - $bLen) . $bBin;
        } elseif ($bLen > $aLen) {
            $aBin = \str_repeat("\x00", $bLen - $aLen) . $aBin;
        }

        if ($aNeg) {
            $aBin = $this->twosComplement($aBin);
        }
        if ($bNeg) {
            $bBin = $this->twosComplement($bBin);
        }

        switch ($operator) {
            case 'and':
                $value = $aBin & $bBin;
                $negative = ($aNeg and $bNeg);
                break;

            case 'or':
                $value = $aBin | $bBin;
                $negative = ($aNeg or $bNeg);
                break;

            case 'xor':
                $value = $aBin ^ $bBin;
                $negative = ($aNeg xor $bNeg);
                break;

            // @codeCoverageIgnoreStart
            default:
                throw new \InvalidArgumentException('Invalid bitwise operator.');
            // @codeCoverageIgnoreEnd
        }

        if ($negative) {
            $value = $this->twosComplement($value);
        }

        $result = $this->toDecimal($value);

        return $negative ? $this->neg($result) : $result;
    }

    /**
     * @param string $number A positive, binary number.
     *
     * @return string
     */
    private function twosComplement(string $number) : string
    {
        $xor = \str_repeat("\xff", \strlen($number));

        $number = $number ^ $xor;

        for ($i = \strlen($number) - 1; $i >= 0; $i--) {
            $byte = \ord($number[$i]);

            if (++$byte !== 256) {
                $number[$i] = \chr($byte);
                break;
            }

            $number[$i] = "\x00";

            if ($i === 0) {
                $number = "\x01" . $number;
            }
        }

        return $number;
    }

    /**
     * Converts a decimal number to a binary string.
     *
     * @param string $number The number to convert, positive or zero, only digits.
     *
     * @return string
     */
    private function toBinary(string $number) : string
    {
        $result = '';

        while ($number !== '0') {
            [$number, $remainder] = $this->divQR($number, '256');
            $result .= \chr((int) $remainder);
        }

        return \strrev($result);
    }

    /**
     * Returns the positive decimal representation of a binary number.
     *
     * @param string $bytes The bytes representing the number.
     *
     * @return string
     */
    private function toDecimal(string $bytes) : string
    {
        $result = '0';
        $power = '1';

        for ($i = \strlen($bytes) - 1; $i >= 0; $i--) {
            $index = \ord($bytes[$i]);

            if ($index !== 0) {
                $result = $this->add($result, ($index === 1)
                    ? $power
                    : $this->mul($power, (string) $index)
                );
            }

            if ($i !== 0) {
                $power = $this->mul($power, '256');
            }
        }

        return $result;
    }
}