21598325800

Committed 02 Feb 2026 04:26PM UTC coverage: 99.287% (-0.08%) from 99.363%

Build # 21598325800

Build Type

push

github

Committed by

BenMorel

Commit Message

Minor documentation tweaks

Run Details

1253 of 1262 relevant lines covered (99.29%)

2507.0 hits per line

Source File
Press 'n' to go to next uncovered line, 'b' for previous

98.31

/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 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 + $b;	7,857✔
62
63	if (is_int($result)) {	7,857✔
64	return (string) $result;	4,353✔
65	}
66
67	if ($a === '0') {	5,161✔
68	return $b;	4,113✔
69	}
70
71	if ($b === '0') {	5,120✔
72	return $a;	×
73	}
74
75	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	5,120✔
76
77	$result = $aNeg === $bNeg ? $this->doAdd($aDig, $bDig) : $this->doSub($aDig, $bDig);	5,120✔
78
79	if ($aNeg) {	5,120✔
80	$result = $this->neg($result);	121✔
81	}
82
83	return $result;	5,120✔
84	}
85
86	#[Override]
87	public function sub(string $a, string $b): string
88	{
89	return $this->add($a, $this->neg($b));	4,721✔
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 * $b;	7,264✔
100
101	if (is_int($result)) {	7,264✔
102	return (string) $result;	4,221✔
103	}
104
105	if ($a === '0' \|\| $b === '0') {	4,280✔
106	return '0';	7✔
107	}
108
109	if ($a === '1') {	4,275✔
110	return $b;	6✔
111	}
112
113	if ($b === '1') {	4,275✔
114	return $a;	×
115	}
116
117	if ($a === '-1') {	4,275✔
118	return $this->neg($b);	12✔
119	}
120
121	if ($b === '-1') {	4,263✔
122	return $this->neg($a);	1✔
123	}
124
125	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	4,262✔
126
127	$result = $this->doMul($aDig, $bDig);	4,262✔
128
129	if ($aNeg !== $bNeg) {	4,262✔
130	$result = $this->neg($result);	108✔
131	}
132
133	return $result;	4,262✔
134	}
135
136	#[Override]
137	public function divQ(string $a, string $b): string
138	{
139	return $this->divQR($a, $b)[0];	6,523✔
140	}
141
142	#[Override]
143	public function divR(string $a, string $b): string
144	{
145	return $this->divQR($a, $b)[1];	1,964✔
146	}
147
148	#[Override]
149	public function divQR(string $a, string $b): array
150	{
151	if ($a === '0') {	9,622✔
152	return ['0', '0'];	123✔
153	}
154
155	if ($a === $b) {	9,585✔
156	return ['1', '0'];	519✔
157	}
158
159	if ($b === '1') {	9,523✔
160	return [$a, '0'];	615✔
161	}
162
163	if ($b === '-1') {	9,487✔
164	return [$this->neg($a), '0'];	281✔
165	}
166
167	/** @var numeric-string $a */
168	$na = $a * 1; // cast to number	9,460✔
169
170	if (is_int($na)) {	9,460✔
171	/** @var numeric-string $b */
172	$nb = $b * 1;	5,062✔
173
174	if (is_int($nb)) {	5,062✔
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);	4,933✔
178	$r = $na % $nb;	4,933✔
179
180	return [	4,933✔
181	(string) $q,	4,933✔
182	(string) $r,	4,933✔
183	];	4,933✔
184	}
185	}
186
187	[$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b);	5,932✔
188
189	[$q, $r] = $this->doDiv($aDig, $bDig);	5,932✔
190
191	if ($aNeg !== $bNeg) {	5,932✔
192	$q = $this->neg($q);	749✔
193	}
194
195	if ($aNeg) {	5,932✔
196	$r = $this->neg($r);	687✔
197	}
198
199	return [$q, $r];	5,932✔
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, $mod);	58✔
235
236	// special case: the algorithm below fails with 0 power 0 mod 1 (returns 1 instead of 0)
237	if ($base === '0' && $exp === '0' && $mod === '1') {	58✔
238	return '0';	3✔
239	}
240
241	// special case: the algorithm below fails with power 0 mod 1 (returns 1 instead of 0)
242	if ($exp === '0' && $mod === '1') {	55✔
243	return '0';	×
244	}
245
246	$x = $base;	55✔
247
248	$res = '1';	55✔
249
250	// numbers are positive, so we can use remainder instead of modulo
251	$x = $this->divR($x, $mod);	55✔
252
253	while ($exp !== '0') {	55✔
254	if (in_array($exp[-1], ['1', '3', '5', '7', '9'])) { // odd	53✔
255	$res = $this->divR($this->mul($res, $x), $mod);	53✔
256	}
257
258	$exp = $this->divQ($exp, '2');	53✔
259	$x = $this->divR($this->mul($x, $x), $mod);	53✔
260	}
261
262	return $res;	55✔
263	}
264
265	/**
266	* Adapted from https://cp-algorithms.com/num_methods/roots_newton.html.
267	*/
268	#[Override]
269	public function sqrt(string $n): string
270	{
271	if ($n === '0') {	5,548✔
272	return '0';	10✔
273	}
274
275	// initial approximation
276	$x = str_repeat('9', intdiv(strlen($n), 2) ?: 1);	5,538✔
277
278	$decreased = false;	5,538✔
279
280	for (; ;) {
281	$nx = $this->divQ($this->add($x, $this->divQ($n, $x)), '2');	5,538✔
282
283	if ($x === $nx \|\| $this->cmp($nx, $x) > 0 && $decreased) {	5,538✔
284	break;	5,538✔
285	}
286
287	$decreased = $this->cmp($nx, $x) < 0;	5,528✔
288	$x = $nx;	5,538✔
289	}
290
291	return $x;	5,538✔
292	}
293
294	/**
295	* Performs the addition of two non-signed large integers.
296	*
297	* @pure
298	*/
299	private function doAdd(string $a, string $b): string
300	{
301	[$a, $b, $length] = $this->pad($a, $b);	4,961✔
302
303	$carry = 0;	4,961✔
304	$result = '';	4,961✔
305
306	for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {	4,961✔
307	$blockLength = $this->maxDigits;	4,961✔
308
309	if ($i < 0) {	4,961✔
310	$blockLength += $i;	4,928✔
311	$i = 0;	4,928✔
312	}
313
314	/** @var numeric-string $blockA */
315	$blockA = substr($a, $i, $blockLength);	4,961✔
316
317	/** @var numeric-string $blockB */
318	$blockB = substr($b, $i, $blockLength);	4,961✔
319
320	$sum = (string) ($blockA + $blockB + $carry);	4,961✔
321	$sumLength = strlen($sum);	4,961✔
322
323	if ($sumLength > $blockLength) {	4,961✔
324	$sum = substr($sum, 1);	4,607✔
325	$carry = 1;	4,607✔
326	} else {
327	if ($sumLength < $blockLength) {	4,961✔
328	$sum = str_repeat('0', $blockLength - $sumLength) . $sum;	4,537✔
329	}
330	$carry = 0;	4,961✔
331	}
332
333	$result = $sum . $result;	4,961✔
334
335	if ($i === 0) {	4,961✔
336	break;	4,961✔
337	}
338	}
339
340	if ($carry === 1) {	4,961✔
341	$result = '1' . $result;	3,112✔
342	}
343
344	return $result;	4,961✔
345	}
346
347	/**
348	* Performs the subtraction of two non-signed large integers.
349	*
350	* @pure
351	*/
352	private function doSub(string $a, string $b): string
353	{
354	if ($a === $b) {	4,168✔
355	return '0';	3,415✔
356	}
357
358	// Ensure that we always subtract to a positive result: biggest minus smallest.
359	$cmp = $this->doCmp($a, $b);	4,158✔
360
361	$invert = ($cmp === -1);	4,158✔
362
363	if ($invert) {	4,158✔
364	$c = $a;	40✔
365	$a = $b;	40✔
366	$b = $c;	40✔
367	}
368
369	[$a, $b, $length] = $this->pad($a, $b);	4,158✔
370
371	$carry = 0;	4,158✔
372	$result = '';	4,158✔
373
374	$complement = 10 ** $this->maxDigits;	4,158✔
375
376	for ($i = $length - $this->maxDigits; ; $i -= $this->maxDigits) {	4,158✔
377	$blockLength = $this->maxDigits;	4,158✔
378
379	if ($i < 0) {	4,158✔
380	$blockLength += $i;	4,157✔
381	$i = 0;	4,157✔
382	}
383
384	/** @var numeric-string $blockA */
385	$blockA = substr($a, $i, $blockLength);	4,158✔
386
387	/** @var numeric-string $blockB */
388	$blockB = substr($b, $i, $blockLength);	4,158✔
389
390	$sum = $blockA - $blockB - $carry;	4,158✔
391
392	if ($sum < 0) {	4,158✔
393	$sum += $complement;	4,112✔
394	$carry = 1;	4,112✔
395	} else {
396	$carry = 0;	4,158✔
397	}
398
399	$sum = (string) $sum;	4,158✔
400	$sumLength = strlen($sum);	4,158✔
401
402	if ($sumLength < $blockLength) {	4,158✔
403	$sum = str_repeat('0', $blockLength - $sumLength) . $sum;	4,125✔
404	}
405
406	$result = $sum . $result;	4,158✔
407
408	if ($i === 0) {	4,158✔
409	break;	4,158✔
410	}
411	}
412
413	// Carry cannot be 1 when the loop ends, as a > b
414	assert($carry === 0);
415
416	$result = ltrim($result, '0');	4,158✔
417
418	if ($invert) {	4,158✔
419	$result = $this->neg($result);	40✔
420	}
421
422	return $result;	4,158✔
423	}
424
425	/**
426	* Performs the multiplication of two non-signed large integers.
427	*
428	* @pure
429	*/
430	private function doMul(string $a, string $b): string
431	{
432	$x = strlen($a);	4,262✔
433	$y = strlen($b);	4,262✔
434
435	$maxDigits = intdiv($this->maxDigits, 2);	4,262✔
436	$complement = 10 ** $maxDigits;	4,262✔
437
438	$result = '0';	4,262✔
439
440	for ($i = $x - $maxDigits; ; $i -= $maxDigits) {	4,262✔
441	$blockALength = $maxDigits;	4,262✔
442
443	if ($i < 0) {	4,262✔
444	$blockALength += $i;	3,980✔
445	$i = 0;	3,980✔
446	}
447
448	$blockA = (int) substr($a, $i, $blockALength);	4,262✔
449
450	$line = '';	4,262✔
451	$carry = 0;	4,262✔
452
453	for ($j = $y - $maxDigits; ; $j -= $maxDigits) {	4,262✔
454	$blockBLength = $maxDigits;	4,262✔
455
456	if ($j < 0) {	4,262✔
457	$blockBLength += $j;	4,008✔
458	$j = 0;	4,008✔
459	}
460
461	$blockB = (int) substr($b, $j, $blockBLength);	4,262✔
462
463	$mul = $blockA * $blockB + $carry;	4,262✔
464	$value = $mul % $complement;	4,262✔
465	$carry = ($mul - $value) / $complement;	4,262✔
466
467	$value = (string) $value;	4,262✔
468	$value = str_pad($value, $maxDigits, '0', STR_PAD_LEFT);	4,262✔
469
470	$line = $value . $line;	4,262✔
471
472	if ($j === 0) {	4,262✔
473	break;	4,262✔
474	}
475	}
476
477	if ($carry !== 0) {	4,262✔
478	$line = $carry . $line;	4,181✔
479	}
480
481	$line = ltrim($line, '0');	4,262✔
482
483	if ($line !== '') {	4,262✔
484	$line .= str_repeat('0', $x - $blockALength - $i);	4,262✔
485	$result = $this->add($result, $line);	4,262✔
486	}
487
488	if ($i === 0) {	4,262✔
489	break;	4,262✔
490	}
491	}
492
493	return $result;	4,262✔
494	}
495
496	/**
497	* Performs the division of two non-signed large integers.
498	*
499	* @return string[] The quotient and remainder.
500	*
501	* @pure
502	*/
503	private function doDiv(string $a, string $b): array
504	{
505	$cmp = $this->doCmp($a, $b);	5,932✔
506
507	if ($cmp === -1) {	5,932✔
508	return ['0', $a];	631✔
509	}
510
511	$x = strlen($a);	5,885✔
512	$y = strlen($b);	5,885✔
513
514	// we now know that a >= b && x >= y
515
516	$q = '0'; // quotient	5,885✔
517	$r = $a; // remainder	5,885✔
518	$z = $y; // focus length, always $y or $y+1	5,885✔
519
520	/** @var numeric-string $b */
521	$nb = $b * 1; // cast to number	5,885✔
522	// performance optimization in cases where the remainder will never cause int overflow
523	if (is_int(($nb - 1) * 10 + 9)) {	5,885✔
524	$r = (int) substr($a, 0, $z - 1);	5,742✔
525
526	for ($i = $z - 1; $i < $x; $i++) {	5,742✔
527	$n = $r * 10 + (int) $a[$i];	5,742✔
528	/** @var int $nb */
529	$q .= intdiv($n, $nb);	5,742✔
530	$r = $n % $nb;	5,742✔
531	}
532
533	return [ltrim($q, '0') ?: '0', (string) $r];	5,742✔
534	}
535
536	for (; ;) {
537	$focus = substr($a, 0, $z);	4,121✔
538
539	$cmp = $this->doCmp($focus, $b);	4,121✔
540
541	if ($cmp === -1) {	4,121✔
542	if ($z === $x) { // remainder < dividend	4,091✔
543	break;	3,950✔
544	}
545
546	$z++;	4,088✔
547	}
548
549	$zeros = str_repeat('0', $x - $z);	4,121✔
550
551	$q = $this->add($q, '1' . $zeros);	4,121✔
552	$a = $this->sub($a, $b . $zeros);	4,121✔
553
554	$r = $a;	4,121✔
555
556	if ($r === '0') { // remainder == 0	4,121✔
557	break;	3,402✔
558	}
559
560	$x = strlen($a);	4,118✔
561
562	if ($x < $y) { // remainder < dividend	4,118✔
563	break;	3,913✔
564	}
565
566	$z = $y;	4,121✔
567	}
568
569	return [$q, $r];	4,121✔
570	}
571
572	/**
573	* Compares two non-signed large numbers.
574	*
575	* @return -1\|0\|1
576	*
577	* @pure
578	*/
579	private function doCmp(string $a, string $b): int
580	{
581	$x = strlen($a);	5,951✔
582	$y = strlen($b);	5,951✔
583
584	$cmp = $x <=> $y;	5,951✔
585
586	if ($cmp !== 0) {	5,951✔
587	return $cmp;	5,923✔
588	}
589
590	return strcmp($a, $b) <=> 0; // enforce -1\|0\|1	4,144✔
591	}
592
593	/**
594	* Pads the left of one of the given numbers with zeros if necessary to make both numbers the same length.
595	*
596	* The numbers must only consist of digits, without leading minus sign.
597	*
598	* @return array{string, string, int}
599	*
600	* @pure
601	*/
602	private function pad(string $a, string $b): array
603	{
604	$x = strlen($a);	5,114✔
605	$y = strlen($b);	5,114✔
606
607	if ($x > $y) {	5,114✔
608	$b = str_repeat('0', $x - $y) . $b;	4,555✔
609
610	return [$a, $b, $x];	4,555✔
611	}
612
613	if ($x < $y) {	4,936✔
614	$a = str_repeat('0', $y - $x) . $a;	4,345✔
615
616	return [$a, $b, $y];	4,345✔
617	}
618
619	return [$a, $b, $x];	4,544✔
620	}
621	}

brick / math / 21598325800

Source File Press 'n' to go to next uncovered line, 'b' for previous

Source File
Press 'n' to go to next uncovered line, 'b' for previous