Rev 846 | Rev 1042 | Go to most recent revision | Details | Compare with Previous | Last modification | View Log | RSS feed
| Rev | Author | Line No. | Line |
|---|---|---|---|
| 827 | daniel-mar | 1 | <?php |
| 2 | |||
| 3 | /** |
||
| 4 | * Pure-PHP BigInteger Engine |
||
| 5 | * |
||
| 6 | * PHP version 5 and 7 |
||
| 7 | * |
||
| 874 | daniel-mar | 8 | * @category Math |
| 9 | * @package BigInteger |
||
| 827 | daniel-mar | 10 | * @author Jim Wigginton <terrafrost@php.net> |
| 11 | * @copyright 2017 Jim Wigginton |
||
| 12 | * @license http://www.opensource.org/licenses/mit-license.html MIT License |
||
| 13 | * @link http://pear.php.net/package/Math_BigInteger |
||
| 14 | */ |
||
| 15 | |||
| 16 | namespace phpseclib3\Math\BigInteger\Engines; |
||
| 17 | |||
| 18 | use ParagonIE\ConstantTime\Hex; |
||
| 19 | use phpseclib3\Exception\BadConfigurationException; |
||
| 20 | |||
| 21 | /** |
||
| 22 | * Pure-PHP Engine. |
||
| 23 | * |
||
| 874 | daniel-mar | 24 | * @package PHP |
| 827 | daniel-mar | 25 | * @author Jim Wigginton <terrafrost@php.net> |
| 874 | daniel-mar | 26 | * @access public |
| 827 | daniel-mar | 27 | */ |
| 28 | abstract class PHP extends Engine |
||
| 29 | { |
||
| 30 | /**#@+ |
||
| 31 | * Array constants |
||
| 32 | * |
||
| 33 | * Rather than create a thousands and thousands of new BigInteger objects in repeated function calls to add() and |
||
| 34 | * multiply() or whatever, we'll just work directly on arrays, taking them in as parameters and returning them. |
||
| 35 | * |
||
| 874 | daniel-mar | 36 | * @access protected |
| 827 | daniel-mar | 37 | */ |
| 38 | /** |
||
| 39 | * $result[self::VALUE] contains the value. |
||
| 40 | */ |
||
| 41 | const VALUE = 0; |
||
| 42 | /** |
||
| 43 | * $result[self::SIGN] contains the sign. |
||
| 44 | */ |
||
| 45 | const SIGN = 1; |
||
| 46 | /**#@-*/ |
||
| 47 | |||
| 48 | /** |
||
| 49 | * Karatsuba Cutoff |
||
| 50 | * |
||
| 51 | * At what point do we switch between Karatsuba multiplication and schoolbook long multiplication? |
||
| 52 | * |
||
| 874 | daniel-mar | 53 | * @access private |
| 827 | daniel-mar | 54 | */ |
| 55 | const KARATSUBA_CUTOFF = 25; |
||
| 56 | |||
| 57 | /** |
||
| 58 | * Can Bitwise operations be done fast? |
||
| 59 | * |
||
| 60 | * @see parent::bitwise_leftRotate() |
||
| 61 | * @see parent::bitwise_rightRotate() |
||
| 874 | daniel-mar | 62 | * @access protected |
| 827 | daniel-mar | 63 | */ |
| 64 | const FAST_BITWISE = true; |
||
| 65 | |||
| 66 | /** |
||
| 67 | * Engine Directory |
||
| 68 | * |
||
| 69 | * @see parent::setModExpEngine |
||
| 874 | daniel-mar | 70 | * @access protected |
| 827 | daniel-mar | 71 | */ |
| 72 | const ENGINE_DIR = 'PHP'; |
||
| 73 | |||
| 74 | /** |
||
| 75 | * Default constructor |
||
| 76 | * |
||
| 77 | * @param mixed $x integer Base-10 number or base-$base number if $base set. |
||
| 78 | * @param int $base |
||
| 79 | * @return PHP |
||
| 80 | * @see parent::__construct() |
||
| 81 | */ |
||
| 82 | public function __construct($x = 0, $base = 10) |
||
| 83 | { |
||
| 84 | if (!isset(static::$isValidEngine[static::class])) { |
||
| 85 | static::$isValidEngine[static::class] = static::isValidEngine(); |
||
| 86 | } |
||
| 87 | if (!static::$isValidEngine[static::class]) { |
||
| 88 | throw new BadConfigurationException(static::class . ' is not setup correctly on this system'); |
||
| 89 | } |
||
| 90 | |||
| 91 | $this->value = []; |
||
| 92 | parent::__construct($x, $base); |
||
| 93 | } |
||
| 94 | |||
| 95 | /** |
||
| 96 | * Initialize a PHP BigInteger Engine instance |
||
| 97 | * |
||
| 98 | * @param int $base |
||
| 99 | * @see parent::__construct() |
||
| 100 | */ |
||
| 101 | protected function initialize($base) |
||
| 102 | { |
||
| 103 | switch (abs($base)) { |
||
| 104 | case 16: |
||
| 105 | $x = (strlen($this->value) & 1) ? '0' . $this->value : $this->value; |
||
| 106 | $temp = new static(Hex::decode($x), 256); |
||
| 107 | $this->value = $temp->value; |
||
| 108 | break; |
||
| 109 | case 10: |
||
| 110 | $temp = new static(); |
||
| 111 | |||
| 112 | $multiplier = new static(); |
||
| 113 | $multiplier->value = [static::MAX10]; |
||
| 114 | |||
| 115 | $x = $this->value; |
||
| 116 | |||
| 117 | if ($x[0] == '-') { |
||
| 118 | $this->is_negative = true; |
||
| 119 | $x = substr($x, 1); |
||
| 120 | } |
||
| 121 | |||
| 122 | $x = str_pad( |
||
| 123 | $x, |
||
| 124 | strlen($x) + ((static::MAX10LEN - 1) * strlen($x)) % static::MAX10LEN, |
||
| 125 | 0, |
||
| 126 | STR_PAD_LEFT |
||
| 127 | ); |
||
| 128 | while (strlen($x)) { |
||
| 129 | $temp = $temp->multiply($multiplier); |
||
| 130 | $temp = $temp->add(new static($this->int2bytes(substr($x, 0, static::MAX10LEN)), 256)); |
||
| 131 | $x = substr($x, static::MAX10LEN); |
||
| 132 | } |
||
| 133 | |||
| 134 | $this->value = $temp->value; |
||
| 135 | } |
||
| 136 | } |
||
| 137 | |||
| 138 | /** |
||
| 139 | * Pads strings so that unpack may be used on them |
||
| 140 | * |
||
| 141 | * @param string $str |
||
| 142 | * @return string |
||
| 143 | */ |
||
| 144 | protected function pad($str) |
||
| 145 | { |
||
| 146 | $length = strlen($str); |
||
| 147 | |||
| 148 | $pad = 4 - (strlen($str) % 4); |
||
| 149 | |||
| 150 | return str_pad($str, $length + $pad, "\0", STR_PAD_LEFT); |
||
| 151 | } |
||
| 152 | |||
| 153 | /** |
||
| 154 | * Converts a BigInteger to a base-10 number. |
||
| 155 | * |
||
| 156 | * @return string |
||
| 157 | */ |
||
| 158 | public function toString() |
||
| 159 | { |
||
| 160 | if (!count($this->value)) { |
||
| 161 | return '0'; |
||
| 162 | } |
||
| 163 | |||
| 164 | $temp = clone $this; |
||
| 165 | $temp->bitmask = false; |
||
| 166 | $temp->is_negative = false; |
||
| 167 | |||
| 168 | $divisor = new static(); |
||
| 169 | $divisor->value = [static::MAX10]; |
||
| 170 | $result = ''; |
||
| 171 | while (count($temp->value)) { |
||
| 172 | list($temp, $mod) = $temp->divide($divisor); |
||
| 173 | $result = str_pad( |
||
| 174 | isset($mod->value[0]) ? $mod->value[0] : '', |
||
| 175 | static::MAX10LEN, |
||
| 176 | '0', |
||
| 177 | STR_PAD_LEFT |
||
| 178 | ) . $result; |
||
| 179 | } |
||
| 180 | $result = ltrim($result, '0'); |
||
| 181 | if (empty($result)) { |
||
| 182 | $result = '0'; |
||
| 183 | } |
||
| 184 | |||
| 185 | if ($this->is_negative) { |
||
| 186 | $result = '-' . $result; |
||
| 187 | } |
||
| 188 | |||
| 189 | return $result; |
||
| 190 | } |
||
| 191 | |||
| 192 | /** |
||
| 193 | * Converts a BigInteger to a byte string (eg. base-256). |
||
| 194 | * |
||
| 195 | * @param bool $twos_compliment |
||
| 196 | * @return string |
||
| 197 | */ |
||
| 198 | public function toBytes($twos_compliment = false) |
||
| 199 | { |
||
| 200 | if ($twos_compliment) { |
||
| 201 | return $this->toBytesHelper(); |
||
| 202 | } |
||
| 203 | |||
| 204 | if (!count($this->value)) { |
||
| 205 | return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : ''; |
||
| 206 | } |
||
| 207 | |||
| 208 | $result = $this->bitwise_small_split(8); |
||
| 209 | $result = implode('', array_map('chr', $result)); |
||
| 210 | |||
| 211 | return $this->precision > 0 ? |
||
| 212 | str_pad( |
||
| 213 | substr($result, -(($this->precision + 7) >> 3)), |
||
| 214 | ($this->precision + 7) >> 3, |
||
| 215 | chr(0), |
||
| 216 | STR_PAD_LEFT |
||
| 217 | ) : |
||
| 218 | $result; |
||
| 219 | } |
||
| 220 | |||
| 221 | /** |
||
| 222 | * Performs addition. |
||
| 223 | * |
||
| 224 | * @param array $x_value |
||
| 225 | * @param bool $x_negative |
||
| 226 | * @param array $y_value |
||
| 227 | * @param bool $y_negative |
||
| 228 | * @return array |
||
| 229 | */ |
||
| 230 | protected static function addHelper(array $x_value, $x_negative, array $y_value, $y_negative) |
||
| 231 | { |
||
| 232 | $x_size = count($x_value); |
||
| 233 | $y_size = count($y_value); |
||
| 234 | |||
| 235 | if ($x_size == 0) { |
||
| 236 | return [ |
||
| 237 | self::VALUE => $y_value, |
||
| 238 | self::SIGN => $y_negative |
||
| 239 | ]; |
||
| 240 | } elseif ($y_size == 0) { |
||
| 241 | return [ |
||
| 242 | self::VALUE => $x_value, |
||
| 243 | self::SIGN => $x_negative |
||
| 244 | ]; |
||
| 245 | } |
||
| 246 | |||
| 247 | // subtract, if appropriate |
||
| 248 | if ($x_negative != $y_negative) { |
||
| 249 | if ($x_value == $y_value) { |
||
| 250 | return [ |
||
| 251 | self::VALUE => [], |
||
| 252 | self::SIGN => false |
||
| 253 | ]; |
||
| 254 | } |
||
| 255 | |||
| 256 | $temp = self::subtractHelper($x_value, false, $y_value, false); |
||
| 257 | $temp[self::SIGN] = self::compareHelper($x_value, false, $y_value, false) > 0 ? |
||
| 258 | $x_negative : $y_negative; |
||
| 259 | |||
| 260 | return $temp; |
||
| 261 | } |
||
| 262 | |||
| 263 | if ($x_size < $y_size) { |
||
| 264 | $size = $x_size; |
||
| 265 | $value = $y_value; |
||
| 266 | } else { |
||
| 267 | $size = $y_size; |
||
| 268 | $value = $x_value; |
||
| 269 | } |
||
| 270 | |||
| 271 | $value[count($value)] = 0; // just in case the carry adds an extra digit |
||
| 272 | |||
| 273 | $carry = 0; |
||
| 274 | for ($i = 0, $j = 1; $j < $size; $i += 2, $j += 2) { |
||
| 275 | //$sum = $x_value[$j] * static::BASE_FULL + $x_value[$i] + $y_value[$j] * static::BASE_FULL + $y_value[$i] + $carry; |
||
| 276 | $sum = ($x_value[$j] + $y_value[$j]) * static::BASE_FULL + $x_value[$i] + $y_value[$i] + $carry; |
||
| 277 | $carry = $sum >= static::MAX_DIGIT2; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1 |
||
| 278 | $sum = $carry ? $sum - static::MAX_DIGIT2 : $sum; |
||
| 279 | |||
| 280 | $temp = static::BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31); |
||
| 281 | |||
| 282 | $value[$i] = (int)($sum - static::BASE_FULL * $temp); // eg. a faster alternative to fmod($sum, 0x4000000) |
||
| 283 | $value[$j] = $temp; |
||
| 284 | } |
||
| 285 | |||
| 286 | if ($j == $size) { // ie. if $y_size is odd |
||
| 287 | $sum = $x_value[$i] + $y_value[$i] + $carry; |
||
| 288 | $carry = $sum >= static::BASE_FULL; |
||
| 289 | $value[$i] = $carry ? $sum - static::BASE_FULL : $sum; |
||
| 290 | ++$i; // ie. let $i = $j since we've just done $value[$i] |
||
| 291 | } |
||
| 292 | |||
| 293 | if ($carry) { |
||
| 294 | for (; $value[$i] == static::MAX_DIGIT; ++$i) { |
||
| 295 | $value[$i] = 0; |
||
| 296 | } |
||
| 297 | ++$value[$i]; |
||
| 298 | } |
||
| 299 | |||
| 300 | return [ |
||
| 301 | self::VALUE => self::trim($value), |
||
| 302 | self::SIGN => $x_negative |
||
| 303 | ]; |
||
| 304 | } |
||
| 305 | |||
| 306 | /** |
||
| 307 | * Performs subtraction. |
||
| 308 | * |
||
| 309 | * @param array $x_value |
||
| 310 | * @param bool $x_negative |
||
| 311 | * @param array $y_value |
||
| 312 | * @param bool $y_negative |
||
| 313 | * @return array |
||
| 314 | */ |
||
| 315 | public static function subtractHelper(array $x_value, $x_negative, array $y_value, $y_negative) |
||
| 316 | { |
||
| 317 | $x_size = count($x_value); |
||
| 318 | $y_size = count($y_value); |
||
| 319 | |||
| 320 | if ($x_size == 0) { |
||
| 321 | return [ |
||
| 322 | self::VALUE => $y_value, |
||
| 323 | self::SIGN => !$y_negative |
||
| 324 | ]; |
||
| 325 | } elseif ($y_size == 0) { |
||
| 326 | return [ |
||
| 327 | self::VALUE => $x_value, |
||
| 328 | self::SIGN => $x_negative |
||
| 329 | ]; |
||
| 330 | } |
||
| 331 | |||
| 332 | // add, if appropriate (ie. -$x - +$y or +$x - -$y) |
||
| 333 | if ($x_negative != $y_negative) { |
||
| 334 | $temp = self::addHelper($x_value, false, $y_value, false); |
||
| 335 | $temp[self::SIGN] = $x_negative; |
||
| 336 | |||
| 337 | return $temp; |
||
| 338 | } |
||
| 339 | |||
| 340 | $diff = self::compareHelper($x_value, $x_negative, $y_value, $y_negative); |
||
| 341 | |||
| 342 | if (!$diff) { |
||
| 343 | return [ |
||
| 344 | self::VALUE => [], |
||
| 345 | self::SIGN => false |
||
| 346 | ]; |
||
| 347 | } |
||
| 348 | |||
| 349 | // switch $x and $y around, if appropriate. |
||
| 350 | if ((!$x_negative && $diff < 0) || ($x_negative && $diff > 0)) { |
||
| 351 | $temp = $x_value; |
||
| 352 | $x_value = $y_value; |
||
| 353 | $y_value = $temp; |
||
| 354 | |||
| 355 | $x_negative = !$x_negative; |
||
| 356 | |||
| 357 | $x_size = count($x_value); |
||
| 358 | $y_size = count($y_value); |
||
| 359 | } |
||
| 360 | |||
| 361 | // at this point, $x_value should be at least as big as - if not bigger than - $y_value |
||
| 362 | |||
| 363 | $carry = 0; |
||
| 364 | for ($i = 0, $j = 1; $j < $y_size; $i += 2, $j += 2) { |
||
| 365 | $sum = ($x_value[$j] - $y_value[$j]) * static::BASE_FULL + $x_value[$i] - $y_value[$i] - $carry; |
||
| 366 | |||
| 367 | $carry = $sum < 0; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1 |
||
| 368 | $sum = $carry ? $sum + static::MAX_DIGIT2 : $sum; |
||
| 369 | |||
| 370 | $temp = static::BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31); |
||
| 371 | |||
| 372 | $x_value[$i] = (int)($sum - static::BASE_FULL * $temp); |
||
| 373 | $x_value[$j] = $temp; |
||
| 374 | } |
||
| 375 | |||
| 376 | if ($j == $y_size) { // ie. if $y_size is odd |
||
| 377 | $sum = $x_value[$i] - $y_value[$i] - $carry; |
||
| 378 | $carry = $sum < 0; |
||
| 379 | $x_value[$i] = $carry ? $sum + static::BASE_FULL : $sum; |
||
| 380 | ++$i; |
||
| 381 | } |
||
| 382 | |||
| 383 | if ($carry) { |
||
| 384 | for (; !$x_value[$i]; ++$i) { |
||
| 385 | $x_value[$i] = static::MAX_DIGIT; |
||
| 386 | } |
||
| 387 | --$x_value[$i]; |
||
| 388 | } |
||
| 389 | |||
| 390 | return [ |
||
| 391 | self::VALUE => self::trim($x_value), |
||
| 392 | self::SIGN => $x_negative |
||
| 393 | ]; |
||
| 394 | } |
||
| 395 | |||
| 396 | /** |
||
| 397 | * Performs multiplication. |
||
| 398 | * |
||
| 399 | * @param array $x_value |
||
| 400 | * @param bool $x_negative |
||
| 401 | * @param array $y_value |
||
| 402 | * @param bool $y_negative |
||
| 403 | * @return array |
||
| 404 | */ |
||
| 405 | protected static function multiplyHelper(array $x_value, $x_negative, array $y_value, $y_negative) |
||
| 406 | { |
||
| 407 | //if ( $x_value == $y_value ) { |
||
| 408 | // return [ |
||
| 409 | // self::VALUE => self::square($x_value), |
||
| 410 | // self::SIGN => $x_sign != $y_value |
||
| 411 | // ]; |
||
| 412 | //} |
||
| 413 | |||
| 414 | $x_length = count($x_value); |
||
| 415 | $y_length = count($y_value); |
||
| 416 | |||
| 417 | if (!$x_length || !$y_length) { // a 0 is being multiplied |
||
| 418 | return [ |
||
| 419 | self::VALUE => [], |
||
| 420 | self::SIGN => false |
||
| 421 | ]; |
||
| 422 | } |
||
| 423 | |||
| 424 | return [ |
||
| 425 | self::VALUE => min($x_length, $y_length) < 2 * self::KARATSUBA_CUTOFF ? |
||
| 426 | self::trim(self::regularMultiply($x_value, $y_value)) : |
||
| 427 | self::trim(self::karatsuba($x_value, $y_value)), |
||
| 428 | self::SIGN => $x_negative != $y_negative |
||
| 429 | ]; |
||
| 430 | } |
||
| 431 | |||
| 432 | /** |
||
| 433 | * Performs Karatsuba multiplication on two BigIntegers |
||
| 434 | * |
||
| 435 | * See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm Karatsuba algorithm} and |
||
| 436 | * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=120 MPM 5.2.3}. |
||
| 437 | * |
||
| 438 | * @param array $x_value |
||
| 439 | * @param array $y_value |
||
| 440 | * @return array |
||
| 441 | */ |
||
| 442 | private static function karatsuba(array $x_value, array $y_value) |
||
| 443 | { |
||
| 444 | $m = min(count($x_value) >> 1, count($y_value) >> 1); |
||
| 445 | |||
| 446 | if ($m < self::KARATSUBA_CUTOFF) { |
||
| 447 | return self::regularMultiply($x_value, $y_value); |
||
| 448 | } |
||
| 449 | |||
| 450 | $x1 = array_slice($x_value, $m); |
||
| 451 | $x0 = array_slice($x_value, 0, $m); |
||
| 452 | $y1 = array_slice($y_value, $m); |
||
| 453 | $y0 = array_slice($y_value, 0, $m); |
||
| 454 | |||
| 455 | $z2 = self::karatsuba($x1, $y1); |
||
| 456 | $z0 = self::karatsuba($x0, $y0); |
||
| 457 | |||
| 458 | $z1 = self::addHelper($x1, false, $x0, false); |
||
| 459 | $temp = self::addHelper($y1, false, $y0, false); |
||
| 460 | $z1 = self::karatsuba($z1[self::VALUE], $temp[self::VALUE]); |
||
| 461 | $temp = self::addHelper($z2, false, $z0, false); |
||
| 462 | $z1 = self::subtractHelper($z1, false, $temp[self::VALUE], false); |
||
| 463 | |||
| 464 | $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2); |
||
| 465 | $z1[self::VALUE] = array_merge(array_fill(0, $m, 0), $z1[self::VALUE]); |
||
| 466 | |||
| 467 | $xy = self::addHelper($z2, false, $z1[self::VALUE], $z1[self::SIGN]); |
||
| 468 | $xy = self::addHelper($xy[self::VALUE], $xy[self::SIGN], $z0, false); |
||
| 469 | |||
| 470 | return $xy[self::VALUE]; |
||
| 471 | } |
||
| 472 | |||
| 473 | /** |
||
| 474 | * Performs long multiplication on two BigIntegers |
||
| 475 | * |
||
| 476 | * Modeled after 'multiply' in MutableBigInteger.java. |
||
| 477 | * |
||
| 478 | * @param array $x_value |
||
| 479 | * @param array $y_value |
||
| 480 | * @return array |
||
| 481 | */ |
||
| 482 | protected static function regularMultiply(array $x_value, array $y_value) |
||
| 483 | { |
||
| 484 | $x_length = count($x_value); |
||
| 485 | $y_length = count($y_value); |
||
| 486 | |||
| 487 | if (!$x_length || !$y_length) { // a 0 is being multiplied |
||
| 488 | return []; |
||
| 489 | } |
||
| 490 | |||
| 491 | $product_value = self::array_repeat(0, $x_length + $y_length); |
||
| 492 | |||
| 493 | // the following for loop could be removed if the for loop following it |
||
| 494 | // (the one with nested for loops) initially set $i to 0, but |
||
| 495 | // doing so would also make the result in one set of unnecessary adds, |
||
| 496 | // since on the outermost loops first pass, $product->value[$k] is going |
||
| 497 | // to always be 0 |
||
| 498 | |||
| 499 | $carry = 0; |
||
| 500 | for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0 |
||
| 501 | $temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0 |
||
| 502 | $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); |
||
| 503 | $product_value[$j] = (int)($temp - static::BASE_FULL * $carry); |
||
| 504 | } |
||
| 505 | |||
| 506 | $product_value[$j] = $carry; |
||
| 507 | |||
| 508 | // the above for loop is what the previous comment was talking about. the |
||
| 509 | // following for loop is the "one with nested for loops" |
||
| 510 | for ($i = 1; $i < $y_length; ++$i) { |
||
| 511 | $carry = 0; |
||
| 512 | |||
| 513 | for ($j = 0, $k = $i; $j < $x_length; ++$j, ++$k) { |
||
| 514 | $temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry; |
||
| 515 | $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); |
||
| 516 | $product_value[$k] = (int)($temp - static::BASE_FULL * $carry); |
||
| 517 | } |
||
| 518 | |||
| 519 | $product_value[$k] = $carry; |
||
| 520 | } |
||
| 521 | |||
| 522 | return $product_value; |
||
| 523 | } |
||
| 524 | |||
| 525 | /** |
||
| 526 | * Divides two BigIntegers. |
||
| 527 | * |
||
| 528 | * Returns an array whose first element contains the quotient and whose second element contains the |
||
| 529 | * "common residue". If the remainder would be positive, the "common residue" and the remainder are the |
||
| 530 | * same. If the remainder would be negative, the "common residue" is equal to the sum of the remainder |
||
| 531 | * and the divisor (basically, the "common residue" is the first positive modulo). |
||
| 532 | * |
||
| 533 | * @return array{static, static} |
||
| 534 | * @internal This function is based off of |
||
| 535 | * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=9 HAC 14.20}. |
||
| 536 | */ |
||
| 537 | protected function divideHelper(PHP $y) |
||
| 538 | { |
||
| 539 | if (count($y->value) == 1) { |
||
| 540 | list($q, $r) = $this->divide_digit($this->value, $y->value[0]); |
||
| 541 | $quotient = new static(); |
||
| 542 | $remainder = new static(); |
||
| 543 | $quotient->value = $q; |
||
| 544 | $remainder->value = [$r]; |
||
| 545 | $quotient->is_negative = $this->is_negative != $y->is_negative; |
||
| 546 | return [$this->normalize($quotient), $this->normalize($remainder)]; |
||
| 547 | } |
||
| 548 | |||
| 549 | $x = clone $this; |
||
| 550 | $y = clone $y; |
||
| 551 | |||
| 552 | $x_sign = $x->is_negative; |
||
| 553 | $y_sign = $y->is_negative; |
||
| 554 | |||
| 555 | $x->is_negative = $y->is_negative = false; |
||
| 556 | |||
| 557 | $diff = $x->compare($y); |
||
| 558 | |||
| 559 | if (!$diff) { |
||
| 560 | $temp = new static(); |
||
| 561 | $temp->value = [1]; |
||
| 562 | $temp->is_negative = $x_sign != $y_sign; |
||
| 563 | return [$this->normalize($temp), $this->normalize(static::$zero[static::class])]; |
||
| 564 | } |
||
| 565 | |||
| 566 | if ($diff < 0) { |
||
| 567 | // if $x is negative, "add" $y. |
||
| 568 | if ($x_sign) { |
||
| 569 | $x = $y->subtract($x); |
||
| 570 | } |
||
| 571 | return [$this->normalize(static::$zero[static::class]), $this->normalize($x)]; |
||
| 572 | } |
||
| 573 | |||
| 574 | // normalize $x and $y as described in HAC 14.23 / 14.24 |
||
| 575 | $msb = $y->value[count($y->value) - 1]; |
||
| 576 | for ($shift = 0; !($msb & static::MSB); ++$shift) { |
||
| 577 | $msb <<= 1; |
||
| 578 | } |
||
| 579 | $x->lshift($shift); |
||
| 580 | $y->lshift($shift); |
||
| 581 | $y_value = &$y->value; |
||
| 582 | |||
| 583 | $x_max = count($x->value) - 1; |
||
| 584 | $y_max = count($y->value) - 1; |
||
| 585 | |||
| 586 | $quotient = new static(); |
||
| 587 | $quotient_value = &$quotient->value; |
||
| 588 | $quotient_value = self::array_repeat(0, $x_max - $y_max + 1); |
||
| 589 | |||
| 590 | static $temp, $lhs, $rhs; |
||
| 591 | if (!isset($temp)) { |
||
| 592 | $temp = new static(); |
||
| 593 | $lhs = new static(); |
||
| 594 | $rhs = new static(); |
||
| 595 | } |
||
| 596 | if (static::class != get_class($temp)) { |
||
| 597 | $temp = new static(); |
||
| 598 | $lhs = new static(); |
||
| 599 | $rhs = new static(); |
||
| 600 | } |
||
| 601 | $temp_value = &$temp->value; |
||
| 602 | $rhs_value = &$rhs->value; |
||
| 603 | |||
| 604 | // $temp = $y << ($x_max - $y_max-1) in base 2**26 |
||
| 605 | $temp_value = array_merge(self::array_repeat(0, $x_max - $y_max), $y_value); |
||
| 606 | |||
| 607 | while ($x->compare($temp) >= 0) { |
||
| 608 | // calculate the "common residue" |
||
| 609 | ++$quotient_value[$x_max - $y_max]; |
||
| 610 | $x = $x->subtract($temp); |
||
| 611 | $x_max = count($x->value) - 1; |
||
| 612 | } |
||
| 613 | |||
| 614 | for ($i = $x_max; $i >= $y_max + 1; --$i) { |
||
| 615 | $x_value = &$x->value; |
||
| 616 | $x_window = [ |
||
| 617 | isset($x_value[$i]) ? $x_value[$i] : 0, |
||
| 618 | isset($x_value[$i - 1]) ? $x_value[$i - 1] : 0, |
||
| 619 | isset($x_value[$i - 2]) ? $x_value[$i - 2] : 0 |
||
| 620 | ]; |
||
| 621 | $y_window = [ |
||
| 622 | $y_value[$y_max], |
||
| 623 | ($y_max > 0) ? $y_value[$y_max - 1] : 0 |
||
| 624 | ]; |
||
| 625 | |||
| 626 | $q_index = $i - $y_max - 1; |
||
| 627 | if ($x_window[0] == $y_window[0]) { |
||
| 628 | $quotient_value[$q_index] = static::MAX_DIGIT; |
||
| 629 | } else { |
||
| 630 | $quotient_value[$q_index] = self::safe_divide( |
||
| 631 | $x_window[0] * static::BASE_FULL + $x_window[1], |
||
| 632 | $y_window[0] |
||
| 633 | ); |
||
| 634 | } |
||
| 635 | |||
| 636 | $temp_value = [$y_window[1], $y_window[0]]; |
||
| 637 | |||
| 638 | $lhs->value = [$quotient_value[$q_index]]; |
||
| 639 | $lhs = $lhs->multiply($temp); |
||
| 640 | |||
| 641 | $rhs_value = [$x_window[2], $x_window[1], $x_window[0]]; |
||
| 642 | |||
| 643 | while ($lhs->compare($rhs) > 0) { |
||
| 644 | --$quotient_value[$q_index]; |
||
| 645 | |||
| 646 | $lhs->value = [$quotient_value[$q_index]]; |
||
| 647 | $lhs = $lhs->multiply($temp); |
||
| 648 | } |
||
| 649 | |||
| 650 | $adjust = self::array_repeat(0, $q_index); |
||
| 651 | $temp_value = [$quotient_value[$q_index]]; |
||
| 652 | $temp = $temp->multiply($y); |
||
| 653 | $temp_value = &$temp->value; |
||
| 654 | if (count($temp_value)) { |
||
| 655 | $temp_value = array_merge($adjust, $temp_value); |
||
| 656 | } |
||
| 657 | |||
| 658 | $x = $x->subtract($temp); |
||
| 659 | |||
| 660 | if ($x->compare(static::$zero[static::class]) < 0) { |
||
| 661 | $temp_value = array_merge($adjust, $y_value); |
||
| 662 | $x = $x->add($temp); |
||
| 663 | |||
| 664 | --$quotient_value[$q_index]; |
||
| 665 | } |
||
| 666 | |||
| 667 | $x_max = count($x_value) - 1; |
||
| 668 | } |
||
| 669 | |||
| 670 | // unnormalize the remainder |
||
| 671 | $x->rshift($shift); |
||
| 672 | |||
| 673 | $quotient->is_negative = $x_sign != $y_sign; |
||
| 674 | |||
| 675 | // calculate the "common residue", if appropriate |
||
| 676 | if ($x_sign) { |
||
| 677 | $y->rshift($shift); |
||
| 678 | $x = $y->subtract($x); |
||
| 679 | } |
||
| 680 | |||
| 681 | return [$this->normalize($quotient), $this->normalize($x)]; |
||
| 682 | } |
||
| 683 | |||
| 684 | /** |
||
| 685 | * Divides a BigInteger by a regular integer |
||
| 686 | * |
||
| 687 | * abc / x = a00 / x + b0 / x + c / x |
||
| 688 | * |
||
| 689 | * @param array $dividend |
||
| 690 | * @param int $divisor |
||
| 691 | * @return array |
||
| 692 | */ |
||
| 693 | private static function divide_digit(array $dividend, $divisor) |
||
| 694 | { |
||
| 695 | $carry = 0; |
||
| 696 | $result = []; |
||
| 697 | |||
| 698 | for ($i = count($dividend) - 1; $i >= 0; --$i) { |
||
| 699 | $temp = static::BASE_FULL * $carry + $dividend[$i]; |
||
| 700 | $result[$i] = self::safe_divide($temp, $divisor); |
||
| 701 | $carry = (int)($temp - $divisor * $result[$i]); |
||
| 702 | } |
||
| 703 | |||
| 704 | return [$result, $carry]; |
||
| 705 | } |
||
| 706 | |||
| 707 | /** |
||
| 708 | * Single digit division |
||
| 709 | * |
||
| 710 | * Even if int64 is being used the division operator will return a float64 value |
||
| 711 | * if the dividend is not evenly divisible by the divisor. Since a float64 doesn't |
||
| 712 | * have the precision of int64 this is a problem so, when int64 is being used, |
||
| 713 | * we'll guarantee that the dividend is divisible by first subtracting the remainder. |
||
| 714 | * |
||
| 715 | * @param int $x |
||
| 716 | * @param int $y |
||
| 717 | * @return int |
||
| 718 | */ |
||
| 719 | private static function safe_divide($x, $y) |
||
| 720 | { |
||
| 721 | if (static::BASE === 26) { |
||
| 722 | return (int)($x / $y); |
||
| 723 | } |
||
| 724 | |||
| 725 | // static::BASE === 31 |
||
| 726 | /** @var int */ |
||
| 727 | return ($x - ($x % $y)) / $y; |
||
| 728 | } |
||
| 729 | |||
| 730 | /** |
||
| 731 | * Convert an array / boolean to a PHP BigInteger object |
||
| 732 | * |
||
| 733 | * @param array $arr |
||
| 734 | * @return static |
||
| 735 | */ |
||
| 736 | protected function convertToObj(array $arr) |
||
| 737 | { |
||
| 738 | $result = new static(); |
||
| 739 | $result->value = $arr[self::VALUE]; |
||
| 740 | $result->is_negative = $arr[self::SIGN]; |
||
| 741 | |||
| 742 | return $this->normalize($result); |
||
| 743 | } |
||
| 744 | |||
| 745 | /** |
||
| 746 | * Normalize |
||
| 747 | * |
||
| 748 | * Removes leading zeros and truncates (if necessary) to maintain the appropriate precision |
||
| 749 | * |
||
| 750 | * @param PHP $result |
||
| 751 | * @return static |
||
| 752 | */ |
||
| 753 | protected function normalize(PHP $result) |
||
| 754 | { |
||
| 755 | $result->precision = $this->precision; |
||
| 756 | $result->bitmask = $this->bitmask; |
||
| 757 | |||
| 758 | $value = &$result->value; |
||
| 759 | |||
| 760 | if (!count($value)) { |
||
| 761 | $result->is_negative = false; |
||
| 762 | return $result; |
||
| 763 | } |
||
| 764 | |||
| 765 | $value = static::trim($value); |
||
| 766 | |||
| 767 | if (!empty($result->bitmask->value)) { |
||
| 768 | $length = min(count($value), count($result->bitmask->value)); |
||
| 769 | $value = array_slice($value, 0, $length); |
||
| 770 | |||
| 771 | for ($i = 0; $i < $length; ++$i) { |
||
| 772 | $value[$i] = $value[$i] & $result->bitmask->value[$i]; |
||
| 773 | } |
||
| 774 | |||
| 775 | $value = static::trim($value); |
||
| 776 | } |
||
| 777 | |||
| 778 | return $result; |
||
| 779 | } |
||
| 780 | |||
| 781 | /** |
||
| 782 | * Compares two numbers. |
||
| 783 | * |
||
| 784 | * @param array $x_value |
||
| 785 | * @param bool $x_negative |
||
| 786 | * @param array $y_value |
||
| 787 | * @param bool $y_negative |
||
| 788 | * @return int |
||
| 789 | * @see static::compare() |
||
| 790 | */ |
||
| 791 | protected static function compareHelper(array $x_value, $x_negative, array $y_value, $y_negative) |
||
| 792 | { |
||
| 793 | if ($x_negative != $y_negative) { |
||
| 794 | return (!$x_negative && $y_negative) ? 1 : -1; |
||
| 795 | } |
||
| 796 | |||
| 797 | $result = $x_negative ? -1 : 1; |
||
| 798 | |||
| 799 | if (count($x_value) != count($y_value)) { |
||
| 800 | return (count($x_value) > count($y_value)) ? $result : -$result; |
||
| 801 | } |
||
| 802 | $size = max(count($x_value), count($y_value)); |
||
| 803 | |||
| 804 | $x_value = array_pad($x_value, $size, 0); |
||
| 805 | $y_value = array_pad($y_value, $size, 0); |
||
| 806 | |||
| 807 | for ($i = count($x_value) - 1; $i >= 0; --$i) { |
||
| 808 | if ($x_value[$i] != $y_value[$i]) { |
||
| 809 | return ($x_value[$i] > $y_value[$i]) ? $result : -$result; |
||
| 810 | } |
||
| 811 | } |
||
| 812 | |||
| 813 | return 0; |
||
| 814 | } |
||
| 815 | |||
| 816 | /** |
||
| 817 | * Absolute value. |
||
| 818 | * |
||
| 819 | * @return PHP |
||
| 820 | */ |
||
| 821 | public function abs() |
||
| 822 | { |
||
| 823 | $temp = new static(); |
||
| 824 | $temp->value = $this->value; |
||
| 825 | |||
| 826 | return $temp; |
||
| 827 | } |
||
| 828 | |||
| 829 | /** |
||
| 830 | * Trim |
||
| 831 | * |
||
| 832 | * Removes leading zeros |
||
| 833 | * |
||
| 834 | * @param list<static> $value |
||
| 835 | * @return list<static> |
||
| 836 | */ |
||
| 837 | protected static function trim(array $value) |
||
| 838 | { |
||
| 839 | for ($i = count($value) - 1; $i >= 0; --$i) { |
||
| 840 | if ($value[$i]) { |
||
| 841 | break; |
||
| 842 | } |
||
| 843 | unset($value[$i]); |
||
| 844 | } |
||
| 845 | |||
| 846 | return $value; |
||
| 847 | } |
||
| 848 | |||
| 849 | /** |
||
| 850 | * Logical Right Shift |
||
| 851 | * |
||
| 852 | * Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift. |
||
| 853 | * |
||
| 854 | * @param int $shift |
||
| 855 | * @return PHP |
||
| 856 | */ |
||
| 857 | public function bitwise_rightShift($shift) |
||
| 858 | { |
||
| 859 | $temp = new static(); |
||
| 860 | |||
| 861 | // could just replace lshift with this, but then all lshift() calls would need to be rewritten |
||
| 862 | // and I don't want to do that... |
||
| 863 | $temp->value = $this->value; |
||
| 864 | $temp->rshift($shift); |
||
| 865 | |||
| 866 | return $this->normalize($temp); |
||
| 867 | } |
||
| 868 | |||
| 869 | /** |
||
| 870 | * Logical Left Shift |
||
| 871 | * |
||
| 872 | * Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift. |
||
| 873 | * |
||
| 874 | * @param int $shift |
||
| 875 | * @return PHP |
||
| 876 | */ |
||
| 877 | public function bitwise_leftShift($shift) |
||
| 878 | { |
||
| 879 | $temp = new static(); |
||
| 880 | // could just replace _rshift with this, but then all _lshift() calls would need to be rewritten |
||
| 881 | // and I don't want to do that... |
||
| 882 | $temp->value = $this->value; |
||
| 883 | $temp->lshift($shift); |
||
| 884 | |||
| 885 | return $this->normalize($temp); |
||
| 886 | } |
||
| 887 | |||
| 888 | /** |
||
| 889 | * Converts 32-bit integers to bytes. |
||
| 890 | * |
||
| 891 | * @param int $x |
||
| 892 | * @return string |
||
| 893 | */ |
||
| 894 | private static function int2bytes($x) |
||
| 895 | { |
||
| 896 | return ltrim(pack('N', $x), chr(0)); |
||
| 897 | } |
||
| 898 | |||
| 899 | /** |
||
| 900 | * Array Repeat |
||
| 901 | * |
||
| 902 | * @param int $input |
||
| 903 | * @param int $multiplier |
||
| 904 | * @return array |
||
| 905 | */ |
||
| 906 | protected static function array_repeat($input, $multiplier) |
||
| 907 | { |
||
| 908 | return $multiplier ? array_fill(0, $multiplier, $input) : []; |
||
| 909 | } |
||
| 910 | |||
| 911 | /** |
||
| 912 | * Logical Left Shift |
||
| 913 | * |
||
| 914 | * Shifts BigInteger's by $shift bits. |
||
| 915 | * |
||
| 916 | * @param int $shift |
||
| 917 | */ |
||
| 918 | protected function lshift($shift) |
||
| 919 | { |
||
| 920 | if ($shift == 0) { |
||
| 921 | return; |
||
| 922 | } |
||
| 923 | |||
| 924 | $num_digits = (int)($shift / static::BASE); |
||
| 925 | $shift %= static::BASE; |
||
| 926 | $shift = 1 << $shift; |
||
| 927 | |||
| 928 | $carry = 0; |
||
| 929 | |||
| 930 | for ($i = 0; $i < count($this->value); ++$i) { |
||
| 931 | $temp = $this->value[$i] * $shift + $carry; |
||
| 932 | $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); |
||
| 933 | $this->value[$i] = (int)($temp - $carry * static::BASE_FULL); |
||
| 934 | } |
||
| 935 | |||
| 936 | if ($carry) { |
||
| 937 | $this->value[count($this->value)] = $carry; |
||
| 938 | } |
||
| 939 | |||
| 940 | while ($num_digits--) { |
||
| 941 | array_unshift($this->value, 0); |
||
| 942 | } |
||
| 943 | } |
||
| 944 | |||
| 945 | /** |
||
| 946 | * Logical Right Shift |
||
| 947 | * |
||
| 948 | * Shifts BigInteger's by $shift bits. |
||
| 949 | * |
||
| 950 | * @param int $shift |
||
| 951 | */ |
||
| 952 | protected function rshift($shift) |
||
| 953 | { |
||
| 954 | if ($shift == 0) { |
||
| 955 | return; |
||
| 956 | } |
||
| 957 | |||
| 958 | $num_digits = (int)($shift / static::BASE); |
||
| 959 | $shift %= static::BASE; |
||
| 960 | $carry_shift = static::BASE - $shift; |
||
| 961 | $carry_mask = (1 << $shift) - 1; |
||
| 962 | |||
| 963 | if ($num_digits) { |
||
| 964 | $this->value = array_slice($this->value, $num_digits); |
||
| 965 | } |
||
| 966 | |||
| 967 | $carry = 0; |
||
| 968 | |||
| 969 | for ($i = count($this->value) - 1; $i >= 0; --$i) { |
||
| 970 | $temp = $this->value[$i] >> $shift | $carry; |
||
| 971 | $carry = ($this->value[$i] & $carry_mask) << $carry_shift; |
||
| 972 | $this->value[$i] = $temp; |
||
| 973 | } |
||
| 974 | |||
| 975 | $this->value = static::trim($this->value); |
||
| 976 | } |
||
| 977 | |||
| 978 | /** |
||
| 979 | * Performs modular exponentiation. |
||
| 980 | * |
||
| 981 | * @param PHP $e |
||
| 982 | * @param PHP $n |
||
| 983 | * @return PHP |
||
| 984 | */ |
||
| 985 | protected function powModInner(PHP $e, PHP $n) |
||
| 986 | { |
||
| 987 | try { |
||
| 988 | $class = static::$modexpEngine[static::class]; |
||
| 989 | return $class::powModHelper($this, $e, $n, static::class); |
||
| 990 | } catch (\Exception $err) { |
||
| 991 | return PHP\DefaultEngine::powModHelper($this, $e, $n, static::class); |
||
| 992 | } |
||
| 993 | } |
||
| 994 | |||
| 995 | /** |
||
| 996 | * Performs squaring |
||
| 997 | * |
||
| 998 | * @param list<static> $x |
||
| 999 | * @return list<static> |
||
| 1000 | */ |
||
| 1001 | protected static function square(array $x) |
||
| 1002 | { |
||
| 1003 | return count($x) < 2 * self::KARATSUBA_CUTOFF ? |
||
| 1004 | self::trim(self::baseSquare($x)) : |
||
| 1005 | self::trim(self::karatsubaSquare($x)); |
||
| 1006 | } |
||
| 1007 | |||
| 1008 | /** |
||
| 1009 | * Performs traditional squaring on two BigIntegers |
||
| 1010 | * |
||
| 1011 | * Squaring can be done faster than multiplying a number by itself can be. See |
||
| 1012 | * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=7 HAC 14.2.4} / |
||
| 1013 | * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=141 MPM 5.3} for more information. |
||
| 1014 | * |
||
| 1015 | * @param array $value |
||
| 1016 | * @return array |
||
| 1017 | */ |
||
| 1018 | protected static function baseSquare(array $value) |
||
| 1019 | { |
||
| 1020 | if (empty($value)) { |
||
| 1021 | return []; |
||
| 1022 | } |
||
| 1023 | $square_value = self::array_repeat(0, 2 * count($value)); |
||
| 1024 | |||
| 1025 | for ($i = 0, $max_index = count($value) - 1; $i <= $max_index; ++$i) { |
||
| 1026 | $i2 = $i << 1; |
||
| 1027 | |||
| 1028 | $temp = $square_value[$i2] + $value[$i] * $value[$i]; |
||
| 1029 | $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); |
||
| 1030 | $square_value[$i2] = (int)($temp - static::BASE_FULL * $carry); |
||
| 1031 | |||
| 1032 | // note how we start from $i+1 instead of 0 as we do in multiplication. |
||
| 1033 | for ($j = $i + 1, $k = $i2 + 1; $j <= $max_index; ++$j, ++$k) { |
||
| 1034 | $temp = $square_value[$k] + 2 * $value[$j] * $value[$i] + $carry; |
||
| 1035 | $carry = static::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31); |
||
| 1036 | $square_value[$k] = (int)($temp - static::BASE_FULL * $carry); |
||
| 1037 | } |
||
| 1038 | |||
| 1039 | // the following line can yield values larger 2**15. at this point, PHP should switch |
||
| 1040 | // over to floats. |
||
| 1041 | $square_value[$i + $max_index + 1] = $carry; |
||
| 1042 | } |
||
| 1043 | |||
| 1044 | return $square_value; |
||
| 1045 | } |
||
| 1046 | |||
| 1047 | /** |
||
| 1048 | * Performs Karatsuba "squaring" on two BigIntegers |
||
| 1049 | * |
||
| 1050 | * See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm Karatsuba algorithm} and |
||
| 1051 | * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=151 MPM 5.3.4}. |
||
| 1052 | * |
||
| 1053 | * @param array $value |
||
| 1054 | * @return array |
||
| 1055 | */ |
||
| 1056 | protected static function karatsubaSquare(array $value) |
||
| 1057 | { |
||
| 1058 | $m = count($value) >> 1; |
||
| 1059 | |||
| 1060 | if ($m < self::KARATSUBA_CUTOFF) { |
||
| 1061 | return self::baseSquare($value); |
||
| 1062 | } |
||
| 1063 | |||
| 1064 | $x1 = array_slice($value, $m); |
||
| 1065 | $x0 = array_slice($value, 0, $m); |
||
| 1066 | |||
| 1067 | $z2 = self::karatsubaSquare($x1); |
||
| 1068 | $z0 = self::karatsubaSquare($x0); |
||
| 1069 | |||
| 1070 | $z1 = self::addHelper($x1, false, $x0, false); |
||
| 1071 | $z1 = self::karatsubaSquare($z1[self::VALUE]); |
||
| 1072 | $temp = self::addHelper($z2, false, $z0, false); |
||
| 1073 | $z1 = self::subtractHelper($z1, false, $temp[self::VALUE], false); |
||
| 1074 | |||
| 1075 | $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2); |
||
| 1076 | $z1[self::VALUE] = array_merge(array_fill(0, $m, 0), $z1[self::VALUE]); |
||
| 1077 | |||
| 1078 | $xx = self::addHelper($z2, false, $z1[self::VALUE], $z1[self::SIGN]); |
||
| 1079 | $xx = self::addHelper($xx[self::VALUE], $xx[self::SIGN], $z0, false); |
||
| 1080 | |||
| 1081 | return $xx[self::VALUE]; |
||
| 1082 | } |
||
| 1083 | |||
| 1084 | /** |
||
| 1085 | * Make the current number odd |
||
| 1086 | * |
||
| 1087 | * If the current number is odd it'll be unchanged. If it's even, one will be added to it. |
||
| 1088 | * |
||
| 1089 | * @see self::randomPrime() |
||
| 1090 | */ |
||
| 1091 | protected function make_odd() |
||
| 1092 | { |
||
| 1093 | $this->value[0] |= 1; |
||
| 1094 | } |
||
| 1095 | |||
| 1096 | /** |
||
| 1097 | * Test the number against small primes. |
||
| 1098 | * |
||
| 1099 | * @see self::isPrime() |
||
| 1100 | */ |
||
| 1101 | protected function testSmallPrimes() |
||
| 1102 | { |
||
| 1103 | if ($this->value == [1]) { |
||
| 1104 | return false; |
||
| 1105 | } |
||
| 1106 | if ($this->value == [2]) { |
||
| 1107 | return true; |
||
| 1108 | } |
||
| 1109 | if (~$this->value[0] & 1) { |
||
| 1110 | return false; |
||
| 1111 | } |
||
| 1112 | |||
| 1113 | $value = $this->value; |
||
| 1114 | foreach (static::PRIMES as $prime) { |
||
| 1115 | list(, $r) = self::divide_digit($value, $prime); |
||
| 1116 | if (!$r) { |
||
| 1117 | return count($value) == 1 && $value[0] == $prime; |
||
| 1118 | } |
||
| 1119 | } |
||
| 1120 | |||
| 1121 | return true; |
||
| 1122 | } |
||
| 1123 | |||
| 1124 | /** |
||
| 1125 | * Scan for 1 and right shift by that amount |
||
| 1126 | * |
||
| 1127 | * ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s)); |
||
| 1128 | * |
||
| 1129 | * @param PHP $r |
||
| 1130 | * @return int |
||
| 1131 | * @see self::isPrime() |
||
| 1132 | */ |
||
| 1133 | public static function scan1divide(PHP $r) |
||
| 1134 | { |
||
| 1135 | $r_value = &$r->value; |
||
| 1136 | for ($i = 0, $r_length = count($r_value); $i < $r_length; ++$i) { |
||
| 1137 | $temp = ~$r_value[$i] & static::MAX_DIGIT; |
||
| 1138 | for ($j = 1; ($temp >> $j) & 1; ++$j) { |
||
| 1139 | } |
||
| 1140 | if ($j <= static::BASE) { |
||
| 1141 | break; |
||
| 1142 | } |
||
| 1143 | } |
||
| 1144 | $s = static::BASE * $i + $j; |
||
| 1145 | $r->rshift($s); |
||
| 1146 | return $s; |
||
| 1147 | } |
||
| 1148 | |||
| 1149 | /** |
||
| 1150 | * Performs exponentiation. |
||
| 1151 | * |
||
| 1152 | * @param PHP $n |
||
| 1153 | * @return PHP |
||
| 1154 | */ |
||
| 1155 | protected function powHelper(PHP $n) |
||
| 1156 | { |
||
| 1157 | if ($n->compare(static::$zero[static::class]) == 0) { |
||
| 1158 | return new static(1); |
||
| 1159 | } // n^0 = 1 |
||
| 1160 | |||
| 1161 | $temp = clone $this; |
||
| 1162 | while (!$n->equals(static::$one[static::class])) { |
||
| 1163 | $temp = $temp->multiply($this); |
||
| 1164 | $n = $n->subtract(static::$one[static::class]); |
||
| 1165 | } |
||
| 1166 | |||
| 1167 | return $temp; |
||
| 1168 | } |
||
| 1169 | |||
| 1170 | /** |
||
| 1171 | * Is Odd? |
||
| 1172 | * |
||
| 1173 | * @return bool |
||
| 1174 | */ |
||
| 1175 | public function isOdd() |
||
| 1176 | { |
||
| 1177 | return (bool)($this->value[0] & 1); |
||
| 1178 | } |
||
| 1179 | |||
| 1180 | /** |
||
| 1181 | * Tests if a bit is set |
||
| 1182 | * |
||
| 1183 | * @return bool |
||
| 1184 | */ |
||
| 1185 | public function testBit($x) |
||
| 1186 | { |
||
| 1187 | $digit = (int) floor($x / static::BASE); |
||
| 1188 | $bit = $x % static::BASE; |
||
| 1189 | |||
| 1190 | if (!isset($this->value[$digit])) { |
||
| 1191 | return false; |
||
| 1192 | } |
||
| 1193 | |||
| 1194 | return (bool)($this->value[$digit] & (1 << $bit)); |
||
| 1195 | } |
||
| 1196 | |||
| 1197 | /** |
||
| 1198 | * Is Negative? |
||
| 1199 | * |
||
| 1200 | * @return bool |
||
| 1201 | */ |
||
| 1202 | public function isNegative() |
||
| 1203 | { |
||
| 1204 | return $this->is_negative; |
||
| 1205 | } |
||
| 1206 | |||
| 1207 | /** |
||
| 1208 | * Negate |
||
| 1209 | * |
||
| 1210 | * Given $k, returns -$k |
||
| 1211 | * |
||
| 1212 | * @return static |
||
| 1213 | */ |
||
| 1214 | public function negate() |
||
| 1215 | { |
||
| 1216 | $temp = clone $this; |
||
| 1217 | $temp->is_negative = !$temp->is_negative; |
||
| 1218 | |||
| 1219 | return $temp; |
||
| 1220 | } |
||
| 1221 | |||
| 1222 | /** |
||
| 1223 | * Bitwise Split |
||
| 1224 | * |
||
| 1225 | * Splits BigInteger's into chunks of $split bits |
||
| 1226 | * |
||
| 1227 | * @param int $split |
||
| 1228 | * @return list<static> |
||
| 1229 | */ |
||
| 1230 | public function bitwise_split($split) |
||
| 1231 | { |
||
| 1232 | if ($split < 1) { |
||
| 1233 | throw new \RuntimeException('Offset must be greater than 1'); |
||
| 1234 | } |
||
| 1235 | |||
| 1236 | $width = (int)($split / static::BASE); |
||
| 1237 | if (!$width) { |
||
| 1238 | $arr = $this->bitwise_small_split($split); |
||
| 1239 | return array_map(function ($digit) { |
||
| 1240 | $temp = new static(); |
||
| 1241 | $temp->value = $digit != 0 ? [$digit] : []; |
||
| 1242 | return $temp; |
||
| 1243 | }, $arr); |
||
| 1244 | } |
||
| 1245 | |||
| 1246 | $vals = []; |
||
| 1247 | $val = $this->value; |
||
| 1248 | |||
| 1249 | $i = $overflow = 0; |
||
| 1250 | $len = count($val); |
||
| 1251 | while ($i < $len) { |
||
| 1252 | $digit = []; |
||
| 1253 | if (!$overflow) { |
||
| 1254 | $digit = array_slice($val, $i, $width); |
||
| 1255 | $i += $width; |
||
| 1256 | $overflow = $split % static::BASE; |
||
| 1257 | if ($overflow) { |
||
| 1258 | $mask = (1 << $overflow) - 1; |
||
| 1259 | $temp = isset($val[$i]) ? $val[$i] : 0; |
||
| 1260 | $digit[] = $temp & $mask; |
||
| 1261 | } |
||
| 1262 | } else { |
||
| 1263 | $remaining = static::BASE - $overflow; |
||
| 1264 | $tempsplit = $split - $remaining; |
||
| 1265 | $tempwidth = (int)($tempsplit / static::BASE + 1); |
||
| 1266 | $digit = array_slice($val, $i, $tempwidth); |
||
| 1267 | $i += $tempwidth; |
||
| 1268 | $tempoverflow = $tempsplit % static::BASE; |
||
| 1269 | if ($tempoverflow) { |
||
| 1270 | $tempmask = (1 << $tempoverflow) - 1; |
||
| 1271 | $temp = isset($val[$i]) ? $val[$i] : 0; |
||
| 1272 | $digit[] = $temp & $tempmask; |
||
| 1273 | } |
||
| 1274 | $newbits = 0; |
||
| 1275 | for ($j = count($digit) - 1; $j >= 0; $j--) { |
||
| 1276 | $temp = $digit[$j] & $mask; |
||
| 1277 | $digit[$j] = ($digit[$j] >> $overflow) | ($newbits << $remaining); |
||
| 1278 | $newbits = $temp; |
||
| 1279 | } |
||
| 1280 | $overflow = $tempoverflow; |
||
| 1281 | $mask = $tempmask; |
||
| 1282 | } |
||
| 1283 | $temp = new static(); |
||
| 1284 | $temp->value = static::trim($digit); |
||
| 1285 | $vals[] = $temp; |
||
| 1286 | } |
||
| 1287 | |||
| 1288 | return array_reverse($vals); |
||
| 1289 | } |
||
| 1290 | |||
| 1291 | /** |
||
| 1292 | * Bitwise Split where $split < static::BASE |
||
| 1293 | * |
||
| 1294 | * @param int $split |
||
| 1295 | * @return list<int> |
||
| 1296 | */ |
||
| 1297 | private function bitwise_small_split($split) |
||
| 1298 | { |
||
| 1299 | $vals = []; |
||
| 1300 | $val = $this->value; |
||
| 1301 | |||
| 1302 | $mask = (1 << $split) - 1; |
||
| 1303 | |||
| 1304 | $i = $overflow = 0; |
||
| 1305 | $len = count($val); |
||
| 1306 | $val[] = 0; |
||
| 1307 | $remaining = static::BASE; |
||
| 1308 | while ($i != $len) { |
||
| 1309 | $digit = $val[$i] & $mask; |
||
| 1310 | $val[$i] >>= $split; |
||
| 1311 | if (!$overflow) { |
||
| 1312 | $remaining -= $split; |
||
| 1313 | $overflow = $split <= $remaining ? 0 : $split - $remaining; |
||
| 1314 | |||
| 1315 | if (!$remaining) { |
||
| 1316 | $i++; |
||
| 1317 | $remaining = static::BASE; |
||
| 1318 | $overflow = 0; |
||
| 1319 | } |
||
| 1320 | } elseif (++$i != $len) { |
||
| 1321 | $tempmask = (1 << $overflow) - 1; |
||
| 1322 | $digit |= ($val[$i] & $tempmask) << $remaining; |
||
| 1323 | $val[$i] >>= $overflow; |
||
| 1324 | $remaining = static::BASE - $overflow; |
||
| 1325 | $overflow = $split <= $remaining ? 0 : $split - $remaining; |
||
| 1326 | } |
||
| 1327 | |||
| 1328 | $vals[] = $digit; |
||
| 1329 | } |
||
| 1330 | |||
| 1331 | while ($vals[count($vals) - 1] == 0) { |
||
| 1332 | unset($vals[count($vals) - 1]); |
||
| 1333 | } |
||
| 1334 | |||
| 1335 | return array_reverse($vals); |
||
| 1336 | } |
||
| 1337 | } |