21711699273

Committed 05 Feb 2026 12:35PM UTC coverage: 99.361% (+0.08%) from 99.282%

Build # 21711699273

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push

github

Committed by

BenMorel

Commit Message

Remove deprecated BigRational::simplified()

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/src/Internal/Calculator/NativeCalculator.php

<?php

declare(strict_types=1);

namespace Brick\Math\Internal\Calculator;

use Brick\Math\Internal\Calculator;
use Override;

use function assert;
use function in_array;
use function intdiv;
use function is_int;
use function ltrim;
use function str_pad;
use function str_repeat;
use function strcmp;
use function strlen;
use function substr;

use const PHP_INT_SIZE;
use const STR_PAD_LEFT;

/**
 * Calculator implementation using only native PHP code.
 *
 * @internal
 */
final readonly class NativeCalculator extends Calculator
{
    /**
     * The max number of digits the platform can natively add, subtract, multiply or divide without overflow.
     * For multiplication, this represents the max sum of the lengths of both operands.
     *
     * In addition, it is assumed that an extra digit can hold a carry (1) without overflowing.
     * Example: 32-bit: max number 1,999,999,999 (9 digits + carry)
     *          64-bit: max number 1,999,999,999,999,999,999 (18 digits + carry)
     */
    private int $maxDigits;

    /**
     * @pure
     *
     * @codeCoverageIgnore
     */
    public function __construct()
    {
        $this->maxDigits = match (PHP_INT_SIZE) {
            4 => 9,
            8 => 18,
        };
    }

    #[Override]
    public function add(string $a, string $b): string
    {
        /**
         * @var numeric-string $a
         * @var numeric-string $b
         */
        $result = $a + $b;

        if (is_int($result)) {
            return (string) $result;
        }

        if ($a === '0') {
            return $b;
        }

        if ($b === '0') {
            return $a;
        }

        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);

        $result = $aNeg === $bNeg ? $this->doAdd($aDig, $bDig) : $this->doSub($aDig, $bDig);

        if ($aNeg) {
            $result = $this->neg($result);
        }

        return $result;
    }

    #[Override]
    public function sub(string $a, string $b): string
    {
        return $this->add($a, $this->neg($b));
    }

    #[Override]
    public function mul(string $a, string $b): string
    {
        /**
         * @var numeric-string $a
         * @var numeric-string $b
         */
        $result = $a * $b;

        if (is_int($result)) {
            return (string) $result;
        }

        if ($a === '0' || $b === '0') {
            return '0';
        }

        if ($a === '1') {
            return $b;
        }

        if ($b === '1') {
            return $a;
        }

        if ($a === '-1') {
            return $this->neg($b);
        }

        if ($b === '-1') {
            return $this->neg($a);
        }

        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);

        $result = $this->doMul($aDig, $bDig);

        if ($aNeg !== $bNeg) {
            $result = $this->neg($result);
        }

        return $result;
    }

    #[Override]
    public function divQ(string $a, string $b): string
    {
        return $this->divQR($a, $b)[0];
    }

    #[Override]
    public function divR(string $a, string $b): string
    {
        return $this->divQR($a, $b)[1];
    }

    #[Override]
    public function divQR(string $a, string $b): array
    {
        if ($a === '0') {
            return ['0', '0'];
        }

        if ($a === $b) {
            return ['1', '0'];
        }

        if ($b === '1') {
            return [$a, '0'];
        }

        if ($b === '-1') {
            return [$this->neg($a), '0'];
        }

        /** @var numeric-string $a */
        $na = $a * 1; // cast to number

        if (is_int($na)) {
            /** @var numeric-string $b */
            $nb = $b * 1;

            if (is_int($nb)) {
                // the only division that may overflow is PHP_INT_MIN / -1,
                // which cannot happen here as we've already handled a divisor of -1 above.
                $q = intdiv($na, $nb);
                $r = $na % $nb;

                return [
                    (string) $q,
                    (string) $r,
                ];
            }
        }

        [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);

        [$q, $r] = $this->doDiv($aDig, $bDig);

        if ($aNeg !== $bNeg) {
            $q = $this->neg($q);
        }

        if ($aNeg) {
            $r = $this->neg($r);
        }

        return [$q, $r];
    }

    #[Override]
    public function pow(string $a, int $e): string
    {
        if ($e === 0) {
            return '1';
        }

        if ($e === 1) {
            return $a;
        }

        $odd = $e % 2;
        $e -= $odd;

        $aa = $this->mul($a, $a);

        $result = $this->pow($aa, $e / 2);

        if ($odd === 1) {
            $result = $this->mul($result, $a);
        }

        return $result;
    }

    /**
     * Algorithm from: https://www.geeksforgeeks.org/modular-exponentiation-power-in-modular-arithmetic/.
     */
    #[Override]
    public function modPow(string $base, string $exp, string $mod): string
    {
        // normalize to Euclidean representative so modPow() stays consistent with mod()
        $base = $this->mod($base, $mod);

        // special case: the algorithm below fails with power 0 mod 1 (returns 1 instead of 0)
        if ($exp === '0' && $mod === '1') {
            return '0';
        }

        $x = $base;

        $res = '1';

        // numbers are positive, so we can use remainder instead of modulo
        $x = $this->divR($x, $mod);

        while ($exp !== '0') {
            if (in_array($exp[-1], ['1', '3', '5', '7', '9'])) { // odd
                $res = $this->divR($this->mul($res, $x), $mod);
            }

            $exp = $this->divQ($exp, '2');
            $x = $this->divR($this->mul($x, $x), $mod);
        }

        return $res;
    }

    /**
     * Adapted from https://cp-algorithms.com/num_methods/roots_newton.html.
     */
    #[Override]
    public function sqrt(string $n): string
    {
        if ($n === '0') {
            return '0';
        }

        // initial approximation
        $x = str_repeat('9', intdiv(strlen($n), 2) ?: 1);

        $decreased = false;

        for (; ;) {
            $nx = $this->divQ($this->add($x, $this->divQ($n, $x)), '2');

            if ($x === $nx || $this->cmp($nx, $x) > 0 && $decreased) {
                break;
            }

            $decreased = $this->cmp($nx, $x) < 0;
            $x = $nx;
        }

        return $x;
    }

    /**
     * Performs the addition of two non-signed large integers.
     *
     * @pure
     */
    private function doAdd(string $a, string $b): string
    {
        [$a, $b, $length] = $this->pad($a, $b);

        $carry = 0;
        $result = '';

        for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {
            $blockLength = $this->maxDigits;

            if ($i < 0) {
                $blockLength += $i;
                $i = 0;
            }

            /** @var numeric-string $blockA */
            $blockA = substr($a, $i, $blockLength);

            /** @var numeric-string $blockB */
            $blockB = substr($b, $i, $blockLength);

            $sum = (string) ($blockA + $blockB + $carry);
            $sumLength = strlen($sum);

            if ($sumLength > $blockLength) {
                $sum = substr($sum, 1);
                $carry = 1;
            } else {
                if ($sumLength < $blockLength) {
                    $sum = str_repeat('0', $blockLength - $sumLength) . $sum;
                }
                $carry = 0;
            }

            $result = $sum . $result;

            if ($i === 0) {
                break;
            }
        }

        if ($carry === 1) {
            $result = '1' . $result;
        }

        return $result;
    }

    /**
     * Performs the subtraction of two non-signed large integers.
     *
     * @pure
     */
    private function doSub(string $a, string $b): string
    {
        if ($a === $b) {
            return '0';
        }

        // Ensure that we always subtract to a positive result: biggest minus smallest.
        $cmp = $this->doCmp($a, $b);

        $invert = ($cmp === -1);

        if ($invert) {
            $c = $a;
            $a = $b;
            $b = $c;
        }

        [$a, $b, $length] = $this->pad($a, $b);

        $carry = 0;
        $result = '';

        $complement = 10 ** $this->maxDigits;

        for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {
            $blockLength = $this->maxDigits;

            if ($i < 0) {
                $blockLength += $i;
                $i = 0;
            }

            /** @var numeric-string $blockA */
            $blockA = substr($a, $i, $blockLength);

            /** @var numeric-string $blockB */
            $blockB = substr($b, $i, $blockLength);

            $sum = $blockA - $blockB - $carry;

            if ($sum < 0) {
                $sum += $complement;
                $carry = 1;
            } else {
                $carry = 0;
            }

            $sum = (string) $sum;
            $sumLength = strlen($sum);

            if ($sumLength < $blockLength) {
                $sum = str_repeat('0', $blockLength - $sumLength) . $sum;
            }

            $result = $sum . $result;

            if ($i === 0) {
                break;
            }
        }

        // Carry cannot be 1 when the loop ends, as a > b
        assert($carry === 0);

        $result = ltrim($result, '0');

        if ($invert) {
            $result = $this->neg($result);
        }

        return $result;
    }

    /**
     * Performs the multiplication of two non-signed large integers.
     *
     * @pure
     */
    private function doMul(string $a, string $b): string
    {
        $x = strlen($a);
        $y = strlen($b);

        $maxDigits = intdiv($this->maxDigits, 2);
        $complement = 10 ** $maxDigits;

        $result = '0';

        for ($i = $x - $maxDigits; ; $i -= $maxDigits) {
            $blockALength = $maxDigits;

            if ($i < 0) {
                $blockALength += $i;
                $i = 0;
            }

            $blockA = (int) substr($a, $i, $blockALength);

            $line = '';
            $carry = 0;

            for ($j = $y - $maxDigits; ; $j -= $maxDigits) {
                $blockBLength = $maxDigits;

                if ($j < 0) {
                    $blockBLength += $j;
                    $j = 0;
                }

                $blockB = (int) substr($b, $j, $blockBLength);

                $mul = $blockA * $blockB + $carry;
                $value = $mul % $complement;
                $carry = ($mul - $value) / $complement;

                $value = (string) $value;
                $value = str_pad($value, $maxDigits, '0', STR_PAD_LEFT);

                $line = $value . $line;

                if ($j === 0) {
                    break;
                }
            }

            if ($carry !== 0) {
                $line = $carry . $line;
            }

            $line = ltrim($line, '0');

            if ($line !== '') {
                $line .= str_repeat('0', $x - $blockALength - $i);
                $result = $this->add($result, $line);
            }

            if ($i === 0) {
                break;
            }
        }

        return $result;
    }

    /**
     * Performs the division of two non-signed large integers.
     *
     * @return string[] The quotient and remainder.
     *
     * @pure
     */
    private function doDiv(string $a, string $b): array
    {
        $cmp = $this->doCmp($a, $b);

        if ($cmp === -1) {
            return ['0', $a];
        }

        $x = strlen($a);
        $y = strlen($b);

        // we now know that a >= b && x >= y

        $q = '0'; // quotient
        $r = $a; // remainder
        $z = $y; // focus length, always $y or $y+1

        /** @var numeric-string $b */
        $nb = $b * 1; // cast to number
        // performance optimization in cases where the remainder will never cause int overflow
        if (is_int(($nb - 1) * 10 + 9)) {
            $r = (int) substr($a, 0, $z - 1);

            for ($i = $z - 1; $i < $x; $i++) {
                $n = $r * 10 + (int) $a[$i];
                /** @var int $nb */
                $q .= intdiv($n, $nb);
                $r = $n % $nb;
            }

            return [ltrim($q, '0') ?: '0', (string) $r];
        }

        for (; ;) {
            $focus = substr($a, 0, $z);

            $cmp = $this->doCmp($focus, $b);

            if ($cmp === -1) {
                if ($z === $x) { // remainder < dividend
                    break;
                }

                $z++;
            }

            $zeros = str_repeat('0', $x - $z);

            $q = $this->add($q, '1' . $zeros);
            $a = $this->sub($a, $b . $zeros);

            $r = $a;

            if ($r === '0') { // remainder == 0
                break;
            }

            $x = strlen($a);

            if ($x < $y) { // remainder < dividend
                break;
            }

            $z = $y;
        }

        return [$q, $r];
    }

    /**
     * Compares two non-signed large numbers.
     *
     * @return -1|0|1
     *
     * @pure
     */
    private function doCmp(string $a, string $b): int
    {
        $x = strlen($a);
        $y = strlen($b);

        $cmp = $x <=> $y;

        if ($cmp !== 0) {
            return $cmp;
        }

        return strcmp($a, $b) <=> 0; // enforce -1|0|1
    }

    /**
     * Pads the left of one of the given numbers with zeros if necessary to make both numbers the same length.
     *
     * The numbers must only consist of digits, without leading minus sign.
     *
     * @return array{string, string, int}
     *
     * @pure
     */
    private function pad(string $a, string $b): array
    {
        $x = strlen($a);
        $y = strlen($b);

        if ($x > $y) {
            $b = str_repeat('0', $x - $y) . $b;

            return [$a, $b, $x];
        }

        if ($x < $y) {
            $a = str_repeat('0', $y - $x) . $a;

            return [$a, $b, $y];
        }

        return [$a, $b, $x];
    }
}

1	<?php
2
3	declare(strict_types=1);
4
5	namespace Brick\Math\Internal\Calculator;
6
7	use Brick\Math\Internal\Calculator;
8	use Override;
9
10	use function assert;
11	use function in_array;
12	use function intdiv;
13	use function is_int;
14	use function ltrim;
15	use function str_pad;
16	use function str_repeat;
17	use function strcmp;
18	use function strlen;
19	use function substr;
20
21	use const PHP_INT_SIZE;
22	use const STR_PAD_LEFT;
23
24	/**
25	* Calculator implementation using only native PHP code.
26	*
27	* @internal
28	*/
29	final readonly class NativeCalculator extends Calculator
30	{
31	/**
32	* The max number of digits the platform can natively add, subtract, multiply or divide without overflow.
33	* For multiplication, this represents the max sum of the lengths of both operands.
34	*
35	* In addition, it is assumed that an extra digit can hold a carry (1) without overflowing.
36	* Example: 32-bit: max number 1,999,999,999 (9 digits + carry)
37	* 64-bit: max number 1,999,999,999,999,999,999 (18 digits + carry)
38	*/
39	private int $maxDigits;
40
41	/**
42	* @pure
43	*
44	* @codeCoverageIgnore
45	*/
46	public function __construct()
47	{
48	$this->maxDigits = match (PHP_INT_SIZE) {
49	4 => 9,
50	8 => 18,
51	};
52	}
53
54	#[Override]
55	public function add(string $a, string $b): string
56	{
57	/**
58	* @var numeric-string $a
59	* @var numeric-string $b
60	*/
61	$result = $a + $b;	7,887✔
62
63	if (is_int($result)) {	7,887✔
64	return (string) $result;	4,363✔
65	}
66
67	if ($a === '0') {	5,189✔
68	return $b;	4,137✔
69	}
70
71	if ($b === '0') {	5,146✔
72	return $a;	×
73	}
74
75	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	5,146✔
76
77	$result = $aNeg === $bNeg ? $this->doAdd($aDig, $bDig) : $this->doSub($aDig, $bDig);	5,146✔
78
79	if ($aNeg) {	5,146✔
80	$result = $this->neg($result);	127✔
81	}
82
83	return $result;	5,146✔
84	}
85
86	#[Override]
87	public function sub(string $a, string $b): string
88	{
89	return $this->add($a, $this->neg($b));	4,743✔
90	}
91
92	#[Override]
93	public function mul(string $a, string $b): string
94	{
95	/**
96	* @var numeric-string $a
97	* @var numeric-string $b
98	*/
99	$result = $a * $b;	7,290✔
100
101	if (is_int($result)) {	7,290✔
102	return (string) $result;	4,229✔
103	}
104
105	if ($a === '0' \|\| $b === '0') {	4,298✔
106	return '0';	7✔
107	}
108
109	if ($a === '1') {	4,293✔
110	return $b;	6✔
111	}
112
113	if ($b === '1') {	4,293✔
114	return $a;	×
115	}
116
117	if ($a === '-1') {	4,293✔
118	return $this->neg($b);	12✔
119	}
120
121	if ($b === '-1') {	4,281✔
122	return $this->neg($a);	1✔
123	}
124
125	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	4,280✔
126
127	$result = $this->doMul($aDig, $bDig);	4,280✔
128
129	if ($aNeg !== $bNeg) {	4,280✔
130	$result = $this->neg($result);	117✔
131	}
132
133	return $result;	4,280✔
134	}
135
136	#[Override]
137	public function divQ(string $a, string $b): string
138	{
139	return $this->divQR($a, $b)[0];	6,527✔
140	}
141
142	#[Override]
143	public function divR(string $a, string $b): string
144	{
145	return $this->divQR($a, $b)[1];	1,989✔
146	}
147
148	#[Override]
149	public function divQR(string $a, string $b): array
150	{
151	if ($a === '0') {	9,665✔
152	return ['0', '0'];	123✔
153	}
154
155	if ($a === $b) {	9,628✔
156	return ['1', '0'];	519✔
157	}
158
159	if ($b === '1') {	9,566✔
160	return [$a, '0'];	631✔
161	}
162
163	if ($b === '-1') {	9,520✔
164	return [$this->neg($a), '0'];	286✔
165	}
166
167	/** @var numeric-string $a */
168	$na = $a * 1; // cast to number	9,493✔
169
170	if (is_int($na)) {	9,493✔
171	/** @var numeric-string $b */
172	$nb = $b * 1;	5,077✔
173
174	if (is_int($nb)) {	5,077✔
175	// the only division that may overflow is PHP_INT_MIN / -1,
176	// which cannot happen here as we've already handled a divisor of -1 above.
177	$q = intdiv($na, $nb);	4,940✔
178	$r = $na % $nb;	4,940✔
179
180	return [	4,940✔
181	(string) $q,	4,940✔
182	(string) $r,	4,940✔
183	];	4,940✔
184	}
185	}
186
187	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	5,962✔
188
189	[$q, $r] = $this->doDiv($aDig, $bDig);	5,962✔
190
191	if ($aNeg !== $bNeg) {	5,962✔
192	$q = $this->neg($q);	764✔
193	}
194
195	if ($aNeg) {	5,962✔
196	$r = $this->neg($r);	702✔
197	}
198
199	return [$q, $r];	5,962✔
200	}
201
202	#[Override]
203	public function pow(string $a, int $e): string
204	{
205	if ($e === 0) {	560✔
206	return '1';	×
207	}
208
209	if ($e === 1) {	560✔
210	return $a;	560✔
211	}
212
213	$odd = $e % 2;	560✔
214	$e -= $odd;	560✔
215
216	$aa = $this->mul($a, $a);	560✔
217
218	$result = $this->pow($aa, $e / 2);	560✔
219
220	if ($odd === 1) {	560✔
221	$result = $this->mul($result, $a);	449✔
222	}
223
224	return $result;	560✔
225	}
226
227	/**
228	* Algorithm from: https://www.geeksforgeeks.org/modular-exponentiation-power-in-modular-arithmetic/.
229	*/
230	#[Override]
231	public function modPow(string $base, string $exp, string $mod): string
232	{
233	// normalize to Euclidean representative so modPow() stays consistent with mod()
234	$base = $this->mod($base, $mod);	58✔
235
236	// special case: the algorithm below fails with power 0 mod 1 (returns 1 instead of 0)
237	if ($exp === '0' && $mod === '1') {	58✔
238	return '0';	3✔
239	}
240
241	$x = $base;	55✔
242
243	$res = '1';	55✔
244
245	// numbers are positive, so we can use remainder instead of modulo
246	$x = $this->divR($x, $mod);	55✔
247
248	while ($exp !== '0') {	55✔
249	if (in_array($exp[-1], ['1', '3', '5', '7', '9'])) { // odd	53✔
250	$res = $this->divR($this->mul($res, $x), $mod);	53✔
251	}
252
253	$exp = $this->divQ($exp, '2');	53✔
254	$x = $this->divR($this->mul($x, $x), $mod);	53✔
255	}
256
257	return $res;	55✔
258	}
259
260	/**
261	* Adapted from https://cp-algorithms.com/num_methods/roots_newton.html.
262	*/
263	#[Override]
264	public function sqrt(string $n): string
265	{
266	if ($n === '0') {	5,548✔
267	return '0';	10✔
268	}
269
270	// initial approximation
271	$x = str_repeat('9', intdiv(strlen($n), 2) ?: 1);	5,538✔
272
273	$decreased = false;	5,538✔
274
275	for (; ;) {
276	$nx = $this->divQ($this->add($x, $this->divQ($n, $x)), '2');	5,538✔
277
278	if ($x === $nx \|\| $this->cmp($nx, $x) > 0 && $decreased) {	5,538✔
279	break;	5,538✔
280	}
281
282	$decreased = $this->cmp($nx, $x) < 0;	5,528✔
283	$x = $nx;	5,538✔
284	}
285
286	return $x;	5,538✔
287	}
288
289	/**
290	* Performs the addition of two non-signed large integers.
291	*
292	* @pure
293	*/
294	private function doAdd(string $a, string $b): string
295	{
296	[$a, $b, $length] = $this->pad($a, $b);	4,979✔
297
298	$carry = 0;	4,979✔
299	$result = '';	4,979✔
300
301	for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {	4,979✔
302	$blockLength = $this->maxDigits;	4,979✔
303
304	if ($i < 0) {	4,979✔
305	$blockLength += $i;	4,946✔
306	$i = 0;	4,946✔
307	}
308
309	/** @var numeric-string $blockA */
310	$blockA = substr($a, $i, $blockLength);	4,979✔
311
312	/** @var numeric-string $blockB */
313	$blockB = substr($b, $i, $blockLength);	4,979✔
314
315	$sum = (string) ($blockA + $blockB + $carry);	4,979✔
316	$sumLength = strlen($sum);	4,979✔
317
318	if ($sumLength > $blockLength) {	4,979✔
319	$sum = substr($sum, 1);	4,611✔
320	$carry = 1;	4,611✔
321	} else {
322	if ($sumLength < $blockLength) {	4,979✔
323	$sum = str_repeat('0', $blockLength - $sumLength) . $sum;	4,553✔
324	}
325	$carry = 0;	4,979✔
326	}
327
328	$result = $sum . $result;	4,979✔
329
330	if ($i === 0) {	4,979✔
331	break;	4,979✔
332	}
333	}
334
335	if ($carry === 1) {	4,979✔
336	$result = '1' . $result;	3,114✔
337	}
338
339	return $result;	4,979✔
340	}
341
342	/**
343	* Performs the subtraction of two non-signed large integers.
344	*
345	* @pure
346	*/
347	private function doSub(string $a, string $b): string
348	{
349	if ($a === $b) {	4,188✔
350	return '0';	3,420✔
351	}
352
353	// Ensure that we always subtract to a positive result: biggest minus smallest.
354	$cmp = $this->doCmp($a, $b);	4,173✔
355
356	$invert = ($cmp === -1);	4,173✔
357
358	if ($invert) {	4,173✔
359	$c = $a;	40✔
360	$a = $b;	40✔
361	$b = $c;	40✔
362	}
363
364	[$a, $b, $length] = $this->pad($a, $b);	4,173✔
365
366	$carry = 0;	4,173✔
367	$result = '';	4,173✔
368
369	$complement = 10 ** $this->maxDigits;	4,173✔
370
371	for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {	4,173✔
372	$blockLength = $this->maxDigits;	4,173✔
373
374	if ($i < 0) {	4,173✔
375	$blockLength += $i;	4,172✔
376	$i = 0;	4,172✔
377	}
378
379	/** @var numeric-string $blockA */
380	$blockA = substr($a, $i, $blockLength);	4,173✔
381
382	/** @var numeric-string $blockB */
383	$blockB = substr($b, $i, $blockLength);	4,173✔
384
385	$sum = $blockA - $blockB - $carry;	4,173✔
386
387	if ($sum < 0) {	4,173✔
388	$sum += $complement;	4,126✔
389	$carry = 1;	4,126✔
390	} else {
391	$carry = 0;	4,173✔
392	}
393
394	$sum = (string) $sum;	4,173✔
395	$sumLength = strlen($sum);	4,173✔
396
397	if ($sumLength < $blockLength) {	4,173✔
398	$sum = str_repeat('0', $blockLength - $sumLength) . $sum;	4,140✔
399	}
400
401	$result = $sum . $result;	4,173✔
402
403	if ($i === 0) {	4,173✔
404	break;	4,173✔
405	}
406	}
407
408	// Carry cannot be 1 when the loop ends, as a > b
409	assert($carry === 0);
410
411	$result = ltrim($result, '0');	4,173✔
412
413	if ($invert) {	4,173✔
414	$result = $this->neg($result);	40✔
415	}
416
417	return $result;	4,173✔
418	}
419
420	/**
421	* Performs the multiplication of two non-signed large integers.
422	*
423	* @pure
424	*/
425	private function doMul(string $a, string $b): string
426	{
427	$x = strlen($a);	4,280✔
428	$y = strlen($b);	4,280✔
429
430	$maxDigits = intdiv($this->maxDigits, 2);	4,280✔
431	$complement = 10 ** $maxDigits;	4,280✔
432
433	$result = '0';	4,280✔
434
435	for ($i = $x - $maxDigits; ; $i -= $maxDigits) {	4,280✔
436	$blockALength = $maxDigits;	4,280✔
437
438	if ($i < 0) {	4,280✔
439	$blockALength += $i;	3,994✔
440	$i = 0;	3,994✔
441	}
442
443	$blockA = (int) substr($a, $i, $blockALength);	4,280✔
444
445	$line = '';	4,280✔
446	$carry = 0;	4,280✔
447
448	for ($j = $y - $maxDigits; ; $j -= $maxDigits) {	4,280✔
449	$blockBLength = $maxDigits;	4,280✔
450
451	if ($j < 0) {	4,280✔
452	$blockBLength += $j;	4,026✔
453	$j = 0;	4,026✔
454	}
455
456	$blockB = (int) substr($b, $j, $blockBLength);	4,280✔
457
458	$mul = $blockA * $blockB + $carry;	4,280✔
459	$value = $mul % $complement;	4,280✔
460	$carry = ($mul - $value) / $complement;	4,280✔
461
462	$value = (string) $value;	4,280✔
463	$value = str_pad($value, $maxDigits, '0', STR_PAD_LEFT);	4,280✔
464
465	$line = $value . $line;	4,280✔
466
467	if ($j === 0) {	4,280✔
468	break;	4,280✔
469	}
470	}
471
472	if ($carry !== 0) {	4,280✔
473	$line = $carry . $line;	4,191✔
474	}
475
476	$line = ltrim($line, '0');	4,280✔
477
478	if ($line !== '') {	4,280✔
479	$line .= str_repeat('0', $x - $blockALength - $i);	4,280✔
480	$result = $this->add($result, $line);	4,280✔
481	}
482
483	if ($i === 0) {	4,280✔
484	break;	4,280✔
485	}
486	}
487
488	return $result;	4,280✔
489	}
490
491	/**
492	* Performs the division of two non-signed large integers.
493	*
494	* @return string[] The quotient and remainder.
495	*
496	* @pure
497	*/
498	private function doDiv(string $a, string $b): array
499	{
500	$cmp = $this->doCmp($a, $b);	5,962✔
501
502	if ($cmp === -1) {	5,962✔
503	return ['0', $a];	645✔
504	}
505
506	$x = strlen($a);	5,909✔
507	$y = strlen($b);	5,909✔
508
509	// we now know that a >= b && x >= y
510
511	$q = '0'; // quotient	5,909✔
512	$r = $a; // remainder	5,909✔
513	$z = $y; // focus length, always $y or $y+1	5,909✔
514
515	/** @var numeric-string $b */
516	$nb = $b * 1; // cast to number	5,909✔
517	// performance optimization in cases where the remainder will never cause int overflow
518	if (is_int(($nb - 1) * 10 + 9)) {	5,909✔
519	$r = (int) substr($a, 0, $z - 1);	5,748✔
520
521	for ($i = $z - 1; $i < $x; $i++) {	5,748✔
522	$n = $r * 10 + (int) $a[$i];	5,748✔
523	/** @var int $nb */
524	$q .= intdiv($n, $nb);	5,748✔
525	$r = $n % $nb;	5,748✔
526	}
527
528	return [ltrim($q, '0') ?: '0', (string) $r];	5,748✔
529	}
530
531	for (; ;) {
532	$focus = substr($a, 0, $z);	4,139✔
533
534	$cmp = $this->doCmp($focus, $b);	4,139✔
535
536	if ($cmp === -1) {	4,139✔
537	if ($z === $x) { // remainder < dividend	4,105✔
538	break;	3,954✔
539	}
540
541	$z++;	4,102✔
542	}
543
544	$zeros = str_repeat('0', $x - $z);	4,139✔
545
546	$q = $this->add($q, '1' . $zeros);	4,139✔
547	$a = $this->sub($a, $b . $zeros);	4,139✔
548
549	$r = $a;	4,139✔
550
551	if ($r === '0') { // remainder == 0	4,139✔
552	break;	3,406✔
553	}
554
555	$x = strlen($a);	4,132✔
556
557	if ($x < $y) { // remainder < dividend	4,132✔
558	break;	3,923✔
559	}
560
561	$z = $y;	4,139✔
562	}
563
564	return [$q, $r];	4,139✔
565	}
566
567	/**
568	* Compares two non-signed large numbers.
569	*
570	* @return -1\|0\|1
571	*
572	* @pure
573	*/
574	private function doCmp(string $a, string $b): int
575	{
576	$x = strlen($a);	5,982✔
577	$y = strlen($b);	5,982✔
578
579	$cmp = $x <=> $y;	5,982✔
580
581	if ($cmp !== 0) {	5,982✔
582	return $cmp;	5,953✔
583	}
584
585	return strcmp($a, $b) <=> 0; // enforce -1\|0\|1	4,163✔
586	}
587
588	/**
589	* Pads the left of one of the given numbers with zeros if necessary to make both numbers the same length.
590	*
591	* The numbers must only consist of digits, without leading minus sign.
592	*
593	* @return array{string, string, int}
594	*
595	* @pure
596	*/
597	private function pad(string $a, string $b): array
598	{
599	$x = strlen($a);	5,135✔
600	$y = strlen($b);	5,135✔
601
602	if ($x > $y) {	5,135✔
603	$b = str_repeat('0', $x - $y) . $b;	4,571✔
604
605	return [$a, $b, $x];	4,571✔
606	}
607
608	if ($x < $y) {	4,953✔
609	$a = str_repeat('0', $y - $x) . $a;	4,357✔
610
611	return [$a, $b, $y];	4,357✔
612	}
613
614	return [$a, $b, $x];	4,557✔
615	}
616	}

brick / math / 21711699273

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