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if ($aNeg && ! $bNeg) { return -1; } if ($bNeg && ! $aNeg) { return 1; } $aLen = \strlen($aDig); $bLen = \strlen($bDig); if ($aLen < $bLen) { $result = -1; } elseif ($aLen > $bLen) { $result = 1; } else { $result = $aDig <=> $bDig; } return $aNeg ? -$result : $result; } /** * Adds two numbers. * * @param string $a The augend. * @param string $b The addend. * * @return string The sum. */ abstract public function add(string $a, string $b) : string; /** * Subtracts two numbers. * * @param string $a The minuend. * @param string $b The subtrahend. * * @return string The difference. */ abstract public function sub(string $a, string $b) : string; /** * Multiplies two numbers. * * @param string $a The multiplicand. * @param string $b The multiplier. * * @return string The product. */ abstract public function mul(string $a, string $b) : string; /** * Returns the quotient of the division of two numbers. * * @param string $a The dividend. * @param string $b The divisor, must not be zero. * * @return string The quotient. */ abstract public function divQ(string $a, string $b) : string; /** * Returns the remainder of the division of two numbers. * * @param string $a The dividend. * @param string $b The divisor, must not be zero. * * @return string The remainder. */ abstract public function divR(string $a, string $b) : string; /** * Returns the quotient and remainder of the division of two numbers. * * @param string $a The dividend. * @param string $b The divisor, must not be zero. * * @return string[] An array containing the quotient and remainder. */ abstract public function divQR(string $a, string $b) : array; /** * Exponentiates a number. * * @param string $a The base number. * @param int $e The exponent, validated as an integer between 0 and MAX_POWER. * * @return string The power. */ abstract public function pow(string $a, int $e) : string; /** * @param string $a * @param string $b The modulus; must not be zero. * * @return string */ public function mod(string $a, string $b) : string { return $this->divR($this->add($this->divR($a, $b), $b), $b); } /** * Returns the modular multiplicative inverse of $x modulo $m. * * If $x has no multiplicative inverse mod m, this method must return null. * * This method can be overridden by the concrete implementation if the underlying library has built-in support. * * @param string $x * @param string $m The modulus; must not be negative or zero. * * @return string|null */ public function modInverse(string $x, string $m) : ?string { if ($m === '1') { return '0'; } $modVal = $x; if ($x[0] === '-' || ($this->cmp($this->abs($x), $m) >= 0)) { $modVal = $this->mod($x, $m); } $x = '0'; $y = '0'; $g = $this->gcdExtended($modVal, $m, $x, $y); if ($g !== '1') { return null; } return $this->mod($this->add($this->mod($x, $m), $m), $m); } /** * Raises a number into power with modulo. * * @param string $base The base number; must be positive or zero. * @param string $exp The exponent; must be positive or zero. * @param string $mod The modulus; must be strictly positive. * * @return string The power. */ abstract public function modPow(string $base, string $exp, string $mod) : string; /** * Returns the greatest common divisor of the two numbers. * * This method can be overridden by the concrete implementation if the underlying library * has built-in support for GCD calculations. * * @param string $a The first number. * @param string $b The second number. * * @return string The GCD, always positive, or zero if both arguments are zero. */ public function gcd(string $a, string $b) : string { if ($a === '0') { return $this->abs($b); } if ($b === '0') { return $this->abs($a); } return $this->gcd($b, $this->divR($a, $b)); } private function gcdExtended(string $a, string $b, string &$x, string &$y) : string { if ($a === '0') { $x = '0'; $y = '1'; return $b; } $x1 = '0'; $y1 = '0'; $gcd = $this->gcdExtended($this->mod($b, $a), $a, $x1, $y1); $x = $this->sub($y1, $this->mul($this->divQ($b, $a), $x1)); $y = $x1; return $gcd; } /** * Returns the square root of the given number, rounded down. * * The result is the largest x such that x² ≤ n. * The input MUST NOT be negative. * * @param string $n The number. * * @return string The square root. */ abstract public function sqrt(string $n) : string; /** * Converts a number from an arbitrary base. * * This method can be overridden by the concrete implementation if the underlying library * has built-in support for base conversion. * * @param string $number The number, positive or zero, non-empty, case-insensitively validated for the given base. * @param int $base The base of the number, validated from 2 to 36. * * @return string The converted number, following the Calculator conventions. */ public function fromBase(string $number, int $base) : string { return $this->fromArbitraryBase(\strtolower($number), self::ALPHABET, $base); } /** * Converts a number to an arbitrary base. * * This method can be overridden by the concrete implementation if the underlying library * has built-in support for base conversion. * * @param string $number The number to convert, following the Calculator conventions. * @param int $base The base to convert to, validated from 2 to 36. * * @return string The converted number, lowercase. */ public function toBase(string $number, int $base) : string { $negative = ($number[0] === '-'); if ($negative) { $number = \substr($number, 1); } $number = $this->toArbitraryBase($number, self::ALPHABET, $base); if ($negative) { return '-' . $number; } return $number; } /** * Converts a non-negative number in an arbitrary base using a custom alphabet, to base 10. * * @param string $number The number to convert, validated as a non-empty string, * containing only chars in the given alphabet/base. * @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum. * @param int $base The base of the number, validated from 2 to alphabet length. * * @return string The number in base 10, following the Calculator conventions. */ final public function fromArbitraryBase(string $number, string $alphabet, int $base) : string { // remove leading "zeros" $number = \ltrim($number, $alphabet[0]); if ($number === '') { return '0'; } // optimize for "one" if ($number === $alphabet[1]) { return '1'; } $result = '0'; $power = '1'; $base = (string) $base; for ($i = \strlen($number) - 1; $i >= 0; $i--) { $index = \strpos($alphabet, $number[$i]); if ($index !== 0) { $result = $this->add($result, ($index === 1) ? $power : $this->mul($power, (string) $index) ); } if ($i !== 0) { $power = $this->mul($power, $base); } } return $result; } /** * Converts a non-negative number to an arbitrary base using a custom alphabet. * * @param string $number The number to convert, positive or zero, following the Calculator conventions. * @param string $alphabet The alphabet that contains every digit, validated as 2 chars minimum. * @param int $base The base to convert to, validated from 2 to alphabet length. * * @return string The converted number in the given alphabet. */ final public function toArbitraryBase(string $number, string $alphabet, int $base) : string { if ($number === '0') { return $alphabet[0]; } $base = (string) $base; $result = ''; while ($number !== '0') { [$number, $remainder] = $this->divQR($number, $base); $remainder = (int) $remainder; $result .= $alphabet[$remainder]; } return \strrev($result); } /** * Performs a rounded division. * * Rounding is performed when the remainder of the division is not zero. * * @param string $a The dividend. * @param string $b The divisor, must not be zero. * @param int $roundingMode The rounding mode. * * @return string * * @throws \InvalidArgumentException If the rounding mode is invalid. * @throws RoundingNecessaryException If RoundingMode::UNNECESSARY is provided but rounding is necessary. */ final public function divRound(string $a, string $b, int $roundingMode) : string { [$quotient, $remainder] = $this->divQR($a, $b); $hasDiscardedFraction = ($remainder !== '0'); $isPositiveOrZero = ($a[0] === '-') === ($b[0] === '-'); $discardedFractionSign = function() use ($remainder, $b) : int { $r = $this->abs($this->mul($remainder, '2')); $b = $this->abs($b); return $this->cmp($r, $b); }; $increment = false; switch ($roundingMode) { case RoundingMode::UNNECESSARY: if ($hasDiscardedFraction) { throw RoundingNecessaryException::roundingNecessary(); } break; case RoundingMode::UP: $increment = $hasDiscardedFraction; break; case RoundingMode::DOWN: break; case RoundingMode::CEILING: $increment = $hasDiscardedFraction && $isPositiveOrZero; break; case RoundingMode::FLOOR: $increment = $hasDiscardedFraction && ! $isPositiveOrZero; break; case RoundingMode::HALF_UP: $increment = $discardedFractionSign() >= 0; break; case RoundingMode::HALF_DOWN: $increment = $discardedFractionSign() > 0; break; case RoundingMode::HALF_CEILING: $increment = $isPositiveOrZero ? $discardedFractionSign() >= 0 : $discardedFractionSign() > 0; break; case RoundingMode::HALF_FLOOR: $increment = $isPositiveOrZero ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0; break; case RoundingMode::HALF_EVEN: $lastDigit = (int) $quotient[-1]; $lastDigitIsEven = ($lastDigit % 2 === 0); $increment = $lastDigitIsEven ? $discardedFractionSign() > 0 : $discardedFractionSign() >= 0; break; default: throw new \InvalidArgumentException('Invalid rounding mode.'); } if ($increment) { return $this->add($quotient, $isPositiveOrZero ? '1' : '-1'); } return $quotient; } /** * Calculates bitwise AND of two numbers. * * This method can be overridden by the concrete implementation if the underlying library * has built-in support for bitwise operations. * * @param string $a * @param string $b * * @return string */ public function and(string $a, string $b) : string { return $this->bitwise('and', $a, $b); } /** * Calculates bitwise OR of two numbers. * * This method can be overridden by the concrete implementation if the underlying library * has built-in support for bitwise operations. * * @param string $a * @param string $b * * @return string */ public function or(string $a, string $b) : string { return $this->bitwise('or', $a, $b); } /** * Calculates bitwise XOR of two numbers. * * This method can be overridden by the concrete implementation if the underlying library * has built-in support for bitwise operations. * * @param string $a * @param string $b * * @return string */ public function xor(string $a, string $b) : string { return $this->bitwise('xor', $a, $b); } /** * Performs a bitwise operation on a decimal number. * * @param string $operator The operator to use, must be "and", "or" or "xor". * @param string $a The left operand. * @param string $b The right operand. * * @return string */ private function bitwise(string $operator, string $a, string $b) : string { [$aNeg, $bNeg, $aDig, $bDig] = $this->init($a, $b); $aBin = $this->toBinary($aDig); $bBin = $this->toBinary($bDig); $aLen = \strlen($aBin); $bLen = \strlen($bBin); if ($aLen > $bLen) { $bBin = \str_repeat("\x00", $aLen - $bLen) . $bBin; } elseif ($bLen > $aLen) { $aBin = \str_repeat("\x00", $bLen - $aLen) . $aBin; } if ($aNeg) { $aBin = $this->twosComplement($aBin); } if ($bNeg) { $bBin = $this->twosComplement($bBin); } switch ($operator) { case 'and': $value = $aBin & $bBin; $negative = ($aNeg and $bNeg); break; case 'or': $value = $aBin | $bBin; $negative = ($aNeg or $bNeg); break; case 'xor': $value = $aBin ^ $bBin; $negative = ($aNeg xor $bNeg); break; // @codeCoverageIgnoreStart default: throw new \InvalidArgumentException('Invalid bitwise operator.'); // @codeCoverageIgnoreEnd } if ($negative) { $value = $this->twosComplement($value); } $result = $this->toDecimal($value); return $negative ? $this->neg($result) : $result; } /** * @param string $number A positive, binary number. * * @return string */ private function twosComplement(string $number) : string { $xor = \str_repeat("\xff", \strlen($number)); $number ^= $xor; for ($i = \strlen($number) - 1; $i >= 0; $i--) { $byte = \ord($number[$i]); if (++$byte !== 256) { $number[$i] = \chr($byte); break; } $number[$i] = "\x00"; if ($i === 0) { $number = "\x01" . $number; } } return $number; } /** * Converts a decimal number to a binary string. * * @param string $number The number to convert, positive or zero, only digits. * * @return string */ private function toBinary(string $number) : string { $result = ''; while ($number !== '0') { [$number, $remainder] = $this->divQR($number, '256'); $result .= \chr((int) $remainder); } return \strrev($result); } /** * Returns the positive decimal representation of a binary number. * * @param string $bytes The bytes representing the number. * * @return string */ private function toDecimal(string $bytes) : string { $result = '0'; $power = '1'; for ($i = \strlen($bytes) - 1; $i >= 0; $i--) { $index = \ord($bytes[$i]); if ($index !== 0) { $result = $this->add($result, ($index === 1) ? $power : $this->mul($power, (string) $index) ); } if ($i !== 0) { $power = $this->mul($power, '256'); } } return $result; } }