21416478676

Committed 27 Jan 2026 10:20PM UTC coverage: 99.423% (+0.01%) from 99.412%

Build # 21416478676

Build Type

push

github

Committed by

BenMorel

Commit Message

Remove deprecated BigRational::simplified()

Coverage Stats

1207 of 1214 relevant lines covered (99.42%)

2597.78 hits per line

Source File
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98.72

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

        // 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 + $b;	7,811✔
62
63	if (is_int($result)) {	7,811✔
64	return (string) $result;	4,322✔
65	}
66
67	if ($a === '0') {	5,144✔
68	return $b;	4,094✔
69	}
70
71	if ($b === '0') {	5,111✔
72	return $a;	×
73	}
74
75	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	5,111✔
76
77	$result = $aNeg === $bNeg ? $this->doAdd($aDig, $bDig) : $this->doSub($aDig, $bDig);	5,111✔
78
79	if ($aNeg) {	5,111✔
80	$result = $this->neg($result);	122✔
81	}
82
83	return $result;	5,111✔
84	}
85
86	#[Override]
87	public function sub(string $a, string $b): string
88	{
89	return $this->add($a, $this->neg($b));	4,715✔
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 * $b;	7,043✔
100
101	if (is_int($result)) {	7,043✔
102	return (string) $result;	4,018✔
103	}
104
105	if ($a === '0' \|\| $b === '0') {	4,259✔
106	return '0';	7✔
107	}
108
109	if ($a === '1') {	4,254✔
110	return $b;	3✔
111	}
112
113	if ($b === '1') {	4,254✔
114	return $a;	×
115	}
116
117	if ($a === '-1') {	4,254✔
118	return $this->neg($b);	12✔
119	}
120
121	if ($b === '-1') {	4,242✔
122	return $this->neg($a);	1✔
123	}
124
125	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	4,241✔
126
127	$result = $this->doMul($aDig, $bDig);	4,241✔
128
129	if ($aNeg !== $bNeg) {	4,241✔
130	$result = $this->neg($result);	100✔
131	}
132
133	return $result;	4,241✔
134	}
135
136	#[Override]
137	public function divQ(string $a, string $b): string
138	{
139	return $this->divQR($a, $b)[0];	6,302✔
140	}
141
142	#[Override]
143	public function divR(string $a, string $b): string
144	{
145	return $this->divQR($a, $b)[1];	1,780✔
146	}
147
148	#[Override]
149	public function divQR(string $a, string $b): array
150	{
151	if ($a === '0') {	9,437✔
152	return ['0', '0'];	112✔
153	}
154
155	if ($a === $b) {	9,401✔
156	return ['1', '0'];	467✔
157	}
158
159	if ($b === '1') {	9,348✔
160	return [$a, '0'];	522✔
161	}
162
163	if ($b === '-1') {	9,319✔
164	return [$this->neg($a), '0'];	285✔
165	}
166
167	/** @var numeric-string $a */
168	$na = $a * 1; // cast to number	9,299✔
169
170	if (is_int($na)) {	9,299✔
171	/** @var numeric-string $b */
172	$nb = $b * 1;	4,898✔
173
174	if (is_int($nb)) {	4,898✔
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);	4,768✔
178	$r = $na % $nb;	4,768✔
179
180	return [	4,768✔
181	(string) $q,	4,768✔
182	(string) $r,	4,768✔
183	];	4,768✔
184	}
185	}
186
187	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	5,931✔
188
189	[$q, $r] = $this->doDiv($aDig, $bDig);	5,931✔
190
191	if ($aNeg !== $bNeg) {	5,931✔
192	$q = $this->neg($q);	750✔
193	}
194
195	if ($aNeg) {	5,931✔
196	$r = $this->neg($r);	867✔
197	}
198
199	return [$q, $r];	5,931✔
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 $mod): string
232	{
233	// special case: the algorithm below fails with 0 power 0 mod 1 (returns 1 instead of 0)
234	if ($base === '0' && $exp === '0' && $mod === '1') {	11✔
235	return '0';	1✔
236	}
237
238	// special case: the algorithm below fails with power 0 mod 1 (returns 1 instead of 0)
239	if ($exp === '0' && $mod === '1') {	10✔
240	return '0';	1✔
241	}
242
243	$x = $base;	9✔
244
245	$res = '1';	9✔
246
247	// numbers are positive, so we can use remainder instead of modulo
248	$x = $this->divR($x, $mod);	9✔
249
250	while ($exp !== '0') {	9✔
251	if (in_array($exp[-1], ['1', '3', '5', '7', '9'])) { // odd	9✔
252	$res = $this->divR($this->mul($res, $x), $mod);	9✔
253	}
254
255	$exp = $this->divQ($exp, '2');	9✔
256	$x = $this->divR($this->mul($x, $x), $mod);	9✔
257	}
258
259	return $res;	9✔
260	}
261
262	/**
263	* Adapted from https://cp-algorithms.com/num_methods/roots_newton.html.
264	*/
265	#[Override]
266	public function sqrt(string $n): string
267	{
268	if ($n === '0') {	5,548✔
269	return '0';	10✔
270	}
271
272	// initial approximation
273	$x = str_repeat('9', intdiv(strlen($n), 2) ?: 1);	5,538✔
274
275	$decreased = false;	5,538✔
276
277	for (; ;) {
278	$nx = $this->divQ($this->add($x, $this->divQ($n, $x)), '2');	5,538✔
279
280	if ($x === $nx \|\| $this->cmp($nx, $x) > 0 && $decreased) {	5,538✔
281	break;	5,538✔
282	}
283
284	$decreased = $this->cmp($nx, $x) < 0;	5,528✔
285	$x = $nx;	5,538✔
286	}
287
288	return $x;	5,538✔
289	}
290
291	/**
292	* Performs the addition of two non-signed large integers.
293	*
294	* @pure
295	*/
296	private function doAdd(string $a, string $b): string
297	{
298	[$a, $b, $length] = $this->pad($a, $b);	4,949✔
299
300	$carry = 0;	4,949✔
301	$result = '';	4,949✔
302
303	for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {	4,949✔
304	$blockLength = $this->maxDigits;	4,949✔
305
306	if ($i < 0) {	4,949✔
307	$blockLength += $i;	4,916✔
308	$i = 0;	4,916✔
309	}
310
311	/** @var numeric-string $blockA */
312	$blockA = substr($a, $i, $blockLength);	4,949✔
313
314	/** @var numeric-string $blockB */
315	$blockB = substr($b, $i, $blockLength);	4,949✔
316
317	$sum = (string) ($blockA + $blockB + $carry);	4,949✔
318	$sumLength = strlen($sum);	4,949✔
319
320	if ($sumLength > $blockLength) {	4,949✔
321	$sum = substr($sum, 1);	4,603✔
322	$carry = 1;	4,603✔
323	} else {
324	if ($sumLength < $blockLength) {	4,949✔
325	$sum = str_repeat('0', $blockLength - $sumLength) . $sum;	4,534✔
326	}
327	$carry = 0;	4,949✔
328	}
329
330	$result = $sum . $result;	4,949✔
331
332	if ($i === 0) {	4,949✔
333	break;	4,949✔
334	}
335	}
336
337	if ($carry === 1) {	4,949✔
338	$result = '1' . $result;	3,112✔
339	}
340
341	return $result;	4,949✔
342	}
343
344	/**
345	* Performs the subtraction of two non-signed large integers.
346	*
347	* @pure
348	*/
349	private function doSub(string $a, string $b): string
350	{
351	if ($a === $b) {	4,167✔
352	return '0';	3,413✔
353	}
354
355	// Ensure that we always subtract to a positive result: biggest minus smallest.
356	$cmp = $this->doCmp($a, $b);	4,159✔
357
358	$invert = ($cmp === -1);	4,159✔
359
360	if ($invert) {	4,159✔
361	$c = $a;	40✔
362	$a = $b;	40✔
363	$b = $c;	40✔
364	}
365
366	[$a, $b, $length] = $this->pad($a, $b);	4,159✔
367
368	$carry = 0;	4,159✔
369	$result = '';	4,159✔
370
371	$complement = 10 ** $this->maxDigits;	4,159✔
372
373	for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {	4,159✔
374	$blockLength = $this->maxDigits;	4,159✔
375
376	if ($i < 0) {	4,159✔
377	$blockLength += $i;	4,158✔
378	$i = 0;	4,158✔
379	}
380
381	/** @var numeric-string $blockA */
382	$blockA = substr($a, $i, $blockLength);	4,159✔
383
384	/** @var numeric-string $blockB */
385	$blockB = substr($b, $i, $blockLength);	4,159✔
386
387	$sum = $blockA - $blockB - $carry;	4,159✔
388
389	if ($sum < 0) {	4,159✔
390	$sum += $complement;	4,111✔
391	$carry = 1;	4,111✔
392	} else {
393	$carry = 0;	4,159✔
394	}
395
396	$sum = (string) $sum;	4,159✔
397	$sumLength = strlen($sum);	4,159✔
398
399	if ($sumLength < $blockLength) {	4,159✔
400	$sum = str_repeat('0', $blockLength - $sumLength) . $sum;	4,125✔
401	}
402
403	$result = $sum . $result;	4,159✔
404
405	if ($i === 0) {	4,159✔
406	break;	4,159✔
407	}
408	}
409
410	// Carry cannot be 1 when the loop ends, as a > b
411	assert($carry === 0);
412
413	$result = ltrim($result, '0');	4,159✔
414
415	if ($invert) {	4,159✔
416	$result = $this->neg($result);	40✔
417	}
418
419	return $result;	4,159✔
420	}
421
422	/**
423	* Performs the multiplication of two non-signed large integers.
424	*
425	* @pure
426	*/
427	private function doMul(string $a, string $b): string
428	{
429	$x = strlen($a);	4,241✔
430	$y = strlen($b);	4,241✔
431
432	$maxDigits = intdiv($this->maxDigits, 2);	4,241✔
433	$complement = 10 ** $maxDigits;	4,241✔
434
435	$result = '0';	4,241✔
436
437	for ($i = $x - $maxDigits; ; $i -= $maxDigits) {	4,241✔
438	$blockALength = $maxDigits;	4,241✔
439
440	if ($i < 0) {	4,241✔
441	$blockALength += $i;	3,959✔
442	$i = 0;	3,959✔
443	}
444
445	$blockA = (int) substr($a, $i, $blockALength);	4,241✔
446
447	$line = '';	4,241✔
448	$carry = 0;	4,241✔
449
450	for ($j = $y - $maxDigits; ; $j -= $maxDigits) {	4,241✔
451	$blockBLength = $maxDigits;	4,241✔
452
453	if ($j < 0) {	4,241✔
454	$blockBLength += $j;	3,987✔
455	$j = 0;	3,987✔
456	}
457
458	$blockB = (int) substr($b, $j, $blockBLength);	4,241✔
459
460	$mul = $blockA * $blockB + $carry;	4,241✔
461	$value = $mul % $complement;	4,241✔
462	$carry = ($mul - $value) / $complement;	4,241✔
463
464	$value = (string) $value;	4,241✔
465	$value = str_pad($value, $maxDigits, '0', STR_PAD_LEFT);	4,241✔
466
467	$line = $value . $line;	4,241✔
468
469	if ($j === 0) {	4,241✔
470	break;	4,241✔
471	}
472	}
473
474	if ($carry !== 0) {	4,241✔
475	$line = $carry . $line;	4,168✔
476	}
477
478	$line = ltrim($line, '0');	4,241✔
479
480	if ($line !== '') {	4,241✔
481	$line .= str_repeat('0', $x - $blockALength - $i);	4,241✔
482	$result = $this->add($result, $line);	4,241✔
483	}
484
485	if ($i === 0) {	4,241✔
486	break;	4,241✔
487	}
488	}
489
490	return $result;	4,241✔
491	}
492
493	/**
494	* Performs the division of two non-signed large integers.
495	*
496	* @return string[] The quotient and remainder.
497	*
498	* @pure
499	*/
500	private function doDiv(string $a, string $b): array
501	{
502	$cmp = $this->doCmp($a, $b);	5,931✔
503
504	if ($cmp === -1) {	5,931✔
505	return ['0', $a];	631✔
506	}
507
508	$x = strlen($a);	5,883✔
509	$y = strlen($b);	5,883✔
510
511	// we now know that a >= b && x >= y
512
513	$q = '0'; // quotient	5,883✔
514	$r = $a; // remainder	5,883✔
515	$z = $y; // focus length, always $y or $y+1	5,883✔
516
517	/** @var numeric-string $b */
518	$nb = $b * 1; // cast to number	5,883✔
519	// performance optimization in cases where the remainder will never cause int overflow
520	if (is_int(($nb - 1) * 10 + 9)) {	5,883✔
521	$r = (int) substr($a, 0, $z - 1);	5,740✔
522
523	for ($i = $z - 1; $i < $x; $i++) {	5,740✔
524	$n = $r * 10 + (int) $a[$i];	5,740✔
525	/** @var int $nb */
526	$q .= intdiv($n, $nb);	5,740✔
527	$r = $n % $nb;	5,740✔
528	}
529
530	return [ltrim($q, '0') ?: '0', (string) $r];	5,740✔
531	}
532
533	for (; ;) {
534	$focus = substr($a, 0, $z);	4,120✔
535
536	$cmp = $this->doCmp($focus, $b);	4,120✔
537
538	if ($cmp === -1) {	4,120✔
539	if ($z === $x) { // remainder < dividend	4,093✔
540	break;	3,952✔
541	}
542
543	$z++;	4,089✔
544	}
545
546	$zeros = str_repeat('0', $x - $z);	4,120✔
547
548	$q = $this->add($q, '1' . $zeros);	4,120✔
549	$a = $this->sub($a, $b . $zeros);	4,120✔
550
551	$r = $a;	4,120✔
552
553	if ($r === '0') { // remainder == 0	4,120✔
554	break;	3,402✔
555	}
556
557	$x = strlen($a);	4,117✔
558
559	if ($x < $y) { // remainder < dividend	4,117✔
560	break;	3,910✔
561	}
562
563	$z = $y;	4,120✔
564	}
565
566	return [$q, $r];	4,120✔
567	}
568
569	/**
570	* Compares two non-signed large numbers.
571	*
572	* @return -1\|0\|1
573	*
574	* @pure
575	*/
576	private function doCmp(string $a, string $b): int
577	{
578	$x = strlen($a);	5,951✔
579	$y = strlen($b);	5,951✔
580
581	$cmp = $x <=> $y;	5,951✔
582
583	if ($cmp !== 0) {	5,951✔
584	return $cmp;	5,921✔
585	}
586
587	return strcmp($a, $b) <=> 0; // enforce -1\|0\|1	4,145✔
588	}
589
590	/**
591	* Pads the left of one of the given numbers with zeros if necessary to make both numbers the same length.
592	*
593	* The numbers must only consist of digits, without leading minus sign.
594	*
595	* @return array{string, string, int}
596	*
597	* @pure
598	*/
599	private function pad(string $a, string $b): array
600	{
601	$x = strlen($a);	5,105✔
602	$y = strlen($b);	5,105✔
603
604	if ($x > $y) {	5,105✔
605	$b = str_repeat('0', $x - $y) . $b;	4,553✔
606
607	return [$a, $b, $x];	4,553✔
608	}
609
610	if ($x < $y) {	4,927✔
611	$a = str_repeat('0', $y - $x) . $a;	4,332✔
612
613	return [$a, $b, $y];	4,332✔
614	}
615
616	return [$a, $b, $x];	4,545✔
617	}
618	}

brick / math / 21416478676

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