0,0 → 1,668 |
<?php |
|
/* |
* PHP GMP-Supplement implemented using BCMath |
* Copyright 2020 Daniel Marschall, ViaThinkSoft |
* Version 2020-02-27 |
* |
* Licensed under the Apache License, Version 2.0 (the "License"); |
* you may not use this file except in compliance with the License. |
* You may obtain a copy of the License at |
* |
* http://www.apache.org/licenses/LICENSE-2.0 |
* |
* Unless required by applicable law or agreed to in writing, software |
* distributed under the License is distributed on an "AS IS" BASIS, |
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
* See the License for the specific language governing permissions and |
* limitations under the License. |
*/ |
|
if (function_exists('bcadd')) { |
// ----------------- Implementation of GMP functions using BCMath ----------------- |
|
if (!function_exists('gmp_init') ) { |
define('GMP_ROUND_ZERO', 0); |
define('GMP_ROUND_PLUSINF', 1); |
define('GMP_ROUND_MINUSINF', 2); |
define('GMP_MSW_FIRST', 1); |
define('GMP_LSW_FIRST', 2); |
define('GMP_LITTLE_ENDIAN', 4); |
define('GMP_BIG_ENDIAN', 8); |
define('GMP_NATIVE_ENDIAN', 16); |
define('GMP_VERSION', '6.0.0'); |
|
// gmp_abs ( GMP $a ) : GMP |
// Absolute value |
function gmp_abs($a) { |
bcscale(0); |
if (bccomp($a, "0") == 1) { |
return $a; |
} else { |
return bcmul($a, "-1"); |
} |
} |
|
// gmp_add ( GMP $a , GMP $b ) : GMP |
// Add numbers |
function gmp_add($a, $b) { |
bcscale(0); |
|
// bcadd ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string |
return bcadd($a, $b); |
} |
|
// gmp_and ( GMP $a , GMP $b ) : GMP |
// Bitwise AND |
function gmp_and($a, $b) { |
bcscale(0); |
// Convert $a and $b to a binary string |
$ab = bc_dec2bin($a); |
$bb = bc_dec2bin($b); |
$length = max(strlen($ab), strlen($bb)); |
$ab = str_pad($ab, $length, "0", STR_PAD_LEFT); |
$bb = str_pad($bb, $length, "0", STR_PAD_LEFT); |
|
// Do the bitwise binary operation |
$cb = ''; |
for ($i=0; $i<$length; $i++) { |
$cb .= (($ab[$i] == 1) and ($bb[$i] == 1)) ? '1' : '0'; |
} |
|
// Convert back to a decimal number |
return bc_bin2dec($cb); |
} |
|
// gmp_binomial ( mixed $n , int $k ) : GMP |
// Calculates binomial coefficient |
function gmp_binomial($n, $k) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_clrbit ( GMP $a , int $index ) : void |
// Clear bit |
function gmp_clrbit($a, $index) { |
bcscale(0); |
return gmp_setbit($a, $index, false); |
} |
|
// gmp_cmp ( GMP $a , GMP $b ) : int |
// Compare numbers |
function gmp_cmp($a, $b) { |
bcscale(0); |
|
// bccomp ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : int |
return bccomp($a, $b); |
} |
|
// gmp_com ( GMP $a ) : GMP |
// Calculates one's complement |
function gmp_com($a) { |
bcscale(0); |
// Convert $a and $b to a binary string |
$ab = bc_dec2bin($a); |
|
// Swap every bit |
for ($i=0; $i<strlen($ab); $i++) { |
$ab[$i] = ($ab[$i] == '1' ? '0' : '1'); |
} |
|
// Convert back to a decimal number |
return bc_bin2dec($ab); |
} |
|
// gmp_div_q ( GMP $a , GMP $b [, int $round = GMP_ROUND_ZERO ] ) : GMP |
// Divide numbers |
function gmp_div_q($a, $b, $round = GMP_ROUND_ZERO/*not implemented*/) { |
bcscale(0); |
|
// bcdiv ( string $dividend , string $divisor [, int $scale = 0 ] ) : string |
return bcdiv($a, $b); |
} |
|
// Divide numbers and get quotient and remainder |
// gmp_div_qr ( GMP $n , GMP $d [, int $round = GMP_ROUND_ZERO ] ) : array |
function gmp_div_qr($n, $d, $round = GMP_ROUND_ZERO/*not implemented*/) { |
bcscale(0); |
return array( |
gmp_div_q($n, $d, $round), |
gmp_div_r($n, $d, $round) |
); |
} |
|
// Remainder of the division of numbers |
// gmp_div_r ( GMP $n , GMP $d [, int $round = GMP_ROUND_ZERO ] ) : GMP |
function gmp_div_r($n, $d, $round = GMP_ROUND_ZERO/*not implemented*/) { |
bcscale(0); |
// The remainder operator can be used with negative integers. The rule is: |
// - Perform the operation as if both operands were positive. |
// - If the left operand is negative, then make the result negative. |
// - If the left operand is positive, then make the result positive. |
// - Ignore the sign of the right operand in all cases. |
$r = bcmod($n, $d); |
if (bccomp($n, "0") < 0) $r = bcmul($r, "-1"); |
return $r; |
} |
|
// gmp_div ( GMP $a , GMP $b [, int $round = GMP_ROUND_ZERO ] ) : GMP |
// Divide numbers |
function gmp_div($a, $b, $round = GMP_ROUND_ZERO/*not implemented*/) { |
bcscale(0); |
return gmp_div_q($a, $b, $round); // Alias von gmp_div_q |
} |
|
// gmp_divexact ( GMP $n , GMP $d ) : GMP |
// Exact division of numbers |
function gmp_divexact($n, $d) { |
bcscale(0); |
return bcdiv($a, $b); |
} |
|
// gmp_export ( GMP $gmpnumber [, int $word_size = 1 [, int $options = GMP_MSW_FIRST | GMP_NATIVE_ENDIAN ]] ) : string |
// Export to a binary string |
function gmp_export($gmpnumber, $word_size = 1, $options = GMP_MSW_FIRST | GMP_NATIVE_ENDIAN) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_fact ( mixed $a ) : GMP |
// Factorial |
function gmp_fact($a) { |
bcscale(0); |
return bcfact($a); |
} |
|
// gmp_gcd ( GMP $a , GMP $b ) : GMP |
// Calculate GCD |
function gmp_gcd($a, $b) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_gcdext ( GMP $a , GMP $b ) : array |
// Calculate GCD and multipliers |
function gmp_gcdext($a, $b) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_hamdist ( GMP $a , GMP $b ) : int |
// Hamming distance |
function gmp_hamdist($a, $b) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_import ( string $data [, int $word_size = 1 [, int $options = GMP_MSW_FIRST | GMP_NATIVE_ENDIAN ]] ) : GMP |
// Import from a binary string |
function gmp_import($data, $word_size=1, $options=GMP_MSW_FIRST | GMP_NATIVE_ENDIAN) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_init ( mixed $number [, int $base = 0 ] ) : GMP |
// Create GMP number |
function gmp_init($number, $base=0) { |
bcscale(0); |
if ($base == 0) { |
// If base is 0 (default value), the actual base is determined from the leading characters: |
// if the first two characters are 0x or 0X, hexadecimal is assumed, |
// otherwise if the first character is "0", octal is assumed, |
// otherwise decimal is assumed. |
if (strtoupper(substr($number, 0, 2)) == '0X') { |
$base = 16; |
} else if (strtoupper(substr($number, 0, 1)) == '0') { |
$base = 8; |
} else { |
$base = 10; |
} |
} |
|
if ($base == 10) { |
return $number; |
} else { |
return base_convert_bigint($number, $base, 10); |
} |
} |
|
// gmp_intval ( GMP $gmpnumber ) : int |
// Convert GMP number to integer |
function gmp_intval($gmpnumber) { |
bcscale(0); |
return (int)$gmpnumber; |
} |
|
// gmp_invert ( GMP $a , GMP $b ) : GMP |
// Inverse by modulo |
function gmp_invert($a, $b) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_jacobi ( GMP $a , GMP $p ) : int |
// Jacobi symbol |
function gmp_jacobi($a, $p) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_kronecker ( mixed $a , mixed $b ) : int |
// Kronecker symbol |
function gmp_kronecker($a, $b) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_lcm ( mixed $a , mixed $b ) : GMP |
// Calculate LCM |
function gmp_lcm($a, $b) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_legendre ( GMP $a , GMP $p ) : int |
// Legendre symbol |
function gmp_legendre($a, $p) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_mod ( GMP $n , GMP $d ) : GMP |
// Modulo operation |
function gmp_mod($n, $d) { |
bcscale(0); |
|
// bcmod ( string $dividend , string $divisor [, int $scale = 0 ] ) : string |
return bcmod($n, $d); |
} |
|
// gmp_mul ( GMP $a , GMP $b ) : GMP |
// Multiply numbers |
function gmp_mul($a, $b) { |
bcscale(0); |
|
// bcmul ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string |
return bcmul($a, $b); |
} |
|
// gmp_neg ( GMP $a ) : GMP |
// Negate number |
function gmp_neg($a) { |
bcscale(0); |
return bcmul($a, "-1"); |
} |
|
// gmp_nextprime ( int $a ) : GMP |
// Find next prime number |
function gmp_nextprime($a) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_or ( GMP $a , GMP $b ) : GMP |
// Bitwise OR |
function gmp_or($a, $b) { |
bcscale(0); |
// Convert $a and $b to a binary string |
$ab = bc_dec2bin($a); |
$bb = bc_dec2bin($b); |
$length = max(strlen($ab), strlen($bb)); |
$ab = str_pad($ab, $length, "0", STR_PAD_LEFT); |
$bb = str_pad($bb, $length, "0", STR_PAD_LEFT); |
|
// Do the bitwise binary operation |
$cb = ''; |
for ($i=0; $i<$length; $i++) { |
$cb .= (($ab[$i] == 1) or ($bb[$i] == 1)) ? '1' : '0'; |
} |
|
// Convert back to a decimal number |
return bc_bin2dec($cb); |
} |
|
// gmp_perfect_power ( mixed $a ) : bool |
// Perfect power check |
function gmp_perfect_power($a) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_perfect_square ( GMP $a ) : bool |
// Perfect square check |
function gmp_perfect_square($a) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_popcount ( GMP $a ) : int |
// Population count |
function gmp_popcount($a) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_pow ( GMP $base , int $exp ) : GMP |
// Raise number into power |
function gmp_pow($base, $exp) { |
bcscale(0); |
|
// bcpow ( string $base , string $exponent [, int $scale = 0 ] ) : string |
return bcpow($base, $exp); |
} |
|
// gmp_powm ( GMP $base , GMP $exp , GMP $mod ) : GMP |
// Raise number into power with modulo |
function gmp_powm($base, $exp, $mod) { |
bcscale(0); |
|
// bcpowmod ( string $base , string $exponent , string $modulus [, int $scale = 0 ] ) : string |
return bcpowmod($base, $exp, $mod); |
} |
|
// gmp_prob_prime ( GMP $a [, int $reps = 10 ] ) : int |
// Check if number is "probably prime" |
function gmp_prob_prime($a, $reps=10) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_random_bits ( int $bits ) : GMP |
// Random number |
function gmp_random_bits($bits) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_random_range ( GMP $min , GMP $max ) : GMP |
// Random number |
function gmp_random_range($min, $max) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_random_seed ( mixed $seed ) : void |
// Sets the RNG seed |
function gmp_random_seed($seed) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_random ([ int $limiter = 20 ] ) : GMP |
// Random number (deprecated) |
function gmp_random($limiter=20) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_root ( GMP $a , int $nth ) : GMP |
// Take the integer part of nth root |
function gmp_root($a, $nth) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_rootrem ( GMP $a , int $nth ) : array |
// Take the integer part and remainder of nth root |
function gmp_rootrem($a, $nth) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_scan0 ( GMP $a , int $start ) : int |
// Scan for 0 |
function gmp_scan0($a, $start) { |
bcscale(0); |
|
$ab = bc_dec2bin($a); |
|
if ($start < 0) throw new Exception("Starting index must be greater than or equal to zero"); |
if ($start >= strlen($ab)) return $start; |
|
for ($i=$start; $i<strlen($ab); $i++) { |
if ($ab[strlen($ab)-1-$i] == '0') { |
return $i; |
} |
} |
|
return false; |
} |
|
// gmp_scan1 ( GMP $a , int $start ) : int |
// Scan for 1 |
function gmp_scan1($a, $start) { |
bcscale(0); |
|
$ab = bc_dec2bin($a); |
|
if ($start < 0) throw new Exception("Starting index must be greater than or equal to zero"); |
if ($start >= strlen($ab)) return -1; |
|
for ($i=$start; $i<strlen($ab); $i++) { |
if ($ab[strlen($ab)-1-$i] == '1') { |
return $i; |
} |
} |
|
return false; |
} |
|
// gmp_setbit ( GMP $a , int $index [, bool $bit_on = TRUE ] ) : void |
// Set bit |
function gmp_setbit($a, $index, $bit_on=TRUE) { |
bcscale(0); |
$ab = bc_dec2bin($a); |
|
if ($index < 0) throw new Exception("Invalid index"); |
if ($index >= strlen($ab)) { |
$ab = str_pad($ab, $index+1, '0', STR_PAD_LEFT); |
} |
|
$ab[strlen($ab)-1-$index] = $bit_on ? '1' : '0'; |
|
return bc_bin2dec($ab); |
} |
|
// gmp_sign ( GMP $a ) : int |
// Sign of number |
function gmp_sign($a) { |
bcscale(0); |
return bccomp($a, "0"); |
} |
|
// gmp_sqrt ( GMP $a ) : GMP |
// Calculate square root |
function gmp_sqrt($a) { |
bcscale(0); |
|
// bcsqrt ( string $operand [, int $scale = 0 ] ) : string |
return bcsqrt($a); |
} |
|
// gmp_sqrtrem ( GMP $a ) : array |
// Square root with remainder |
function gmp_sqrtrem($a) { |
bcscale(0); |
throw new Exception("NOT IMPLEMENTED"); |
} |
|
// gmp_strval ( GMP $gmpnumber [, int $base = 10 ] ) : string |
// Convert GMP number to string |
function gmp_strval($gmpnumber, $base=10) { |
bcscale(0); |
if ($base == 10) { |
return $gmpnumber; |
} else { |
return base_convert_bigint($gmpnumber, 10, $base); |
} |
} |
|
// gmp_sub ( GMP $a , GMP $b ) : GMP |
// Subtract numbers |
function gmp_sub($a, $b) { |
bcscale(0); |
|
// bcsub ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string |
return bcsub($a, $b); |
} |
|
// gmp_testbit ( GMP $a , int $index ) : bool |
// Tests if a bit is set |
function gmp_testbit($a, $index) { |
bcscale(0); |
$ab = bc_dec2bin($a); |
|
if ($index < 0) throw new Exception("Invalid index"); |
if ($index >= strlen($ab)) return ('0' == '1'); |
|
return $ab[strlen($ab)-1-$index] == '1'; |
} |
|
// gmp_xor ( GMP $a , GMP $b ) : GMP |
// Bitwise XOR |
function gmp_xor($a, $b) { |
bcscale(0); |
// Convert $a and $b to a binary string |
$ab = bc_dec2bin($a); |
$bb = bc_dec2bin($b); |
$length = max(strlen($ab), strlen($bb)); |
$ab = str_pad($ab, $length, "0", STR_PAD_LEFT); |
$bb = str_pad($bb, $length, "0", STR_PAD_LEFT); |
|
// Do the bitwise binary operation |
$cb = ''; |
for ($i=0; $i<$length; $i++) { |
$cb .= (($ab[$i] == 1) xor ($bb[$i] == 1)) ? '1' : '0'; |
} |
|
// Convert back to a decimal number |
return bc_bin2dec($cb); |
} |
} |
|
// ----------------- Helper functions ----------------- |
|
function base_convert_bigint($numstring, $frombase, $tobase) { |
$frombase_str = ''; |
for ($i=0; $i<$frombase; $i++) { |
$frombase_str .= strtoupper(base_convert($i, 10, 36)); |
} |
|
$tobase_str = ''; |
for ($i=0; $i<$tobase; $i++) { |
$tobase_str .= strtoupper(base_convert($i, 10, 36)); |
} |
|
$length = strlen($numstring); |
$result = ''; |
$number = array(); |
for ($i = 0; $i < $length; $i++) { |
$number[$i] = stripos($frombase_str, $numstring[$i]); |
} |
do { // Loop until whole number is converted |
$divide = 0; |
$newlen = 0; |
for ($i = 0; $i < $length; $i++) { // Perform division manually (which is why this works with big numbers) |
$divide = $divide * $frombase + $number[$i]; |
if ($divide >= $tobase) { |
$number[$newlen++] = (int)($divide / $tobase); |
$divide = $divide % $tobase; |
} else if ($newlen > 0) { |
$number[$newlen++] = 0; |
} |
} |
$length = $newlen; |
$result = $tobase_str[$divide] . $result; // Divide is basically $numstring % $tobase (i.e. the new character) |
} |
while ($newlen != 0); |
|
return $result; |
} |
|
function bc_dec2bin($decimal_i) { |
// https://www.exploringbinary.com/base-conversion-in-php-using-bcmath/ |
|
bcscale(0); |
|
$binary_i = ''; |
do { |
$binary_i = bcmod($decimal_i,'2') . $binary_i; |
$decimal_i = bcdiv($decimal_i,'2'); |
} while (bccomp($decimal_i,'0')); |
|
return $binary_i; |
} |
|
function bc_bin2dec($binary_i) { |
// https://www.exploringbinary.com/base-conversion-in-php-using-bcmath/ |
|
bcscale(0); |
|
$decimal_i = '0'; |
for ($i = 0; $i < strlen($binary_i); $i++) { |
$decimal_i = bcmul($decimal_i,'2'); |
$decimal_i = bcadd($decimal_i,$binary_i[$i]); |
} |
|
return $decimal_i; |
} |
|
// ----------------- New functions ----------------- |
|
// Newly added: gmp_not / bcnot |
function bcnot($a) { |
bcscale(0); |
// Convert $a and $b to a binary string |
$ab = bc_dec2bin($a); |
$bb = bc_dec2bin($b); |
$length = max(strlen($ab), strlen($bb)); |
$ab = str_pad($ab, $length, "0", STR_PAD_LEFT); |
$bb = str_pad($bb, $length, "0", STR_PAD_LEFT); |
|
// Do the bitwise binary operation |
$cb = ''; |
for ($i=0; $i<$length; $i++) { |
if ($ab[$i] == 1) return false; |
} |
|
return true; |
} |
function gmp_not($a) { |
return bcnot($a); |
} |
|
// Newly added: bcshiftl / gmp_shiftl |
function bcshiftl($num, $bits) { |
bcscale(0); |
return bcmul($num, bcpow('2', $bits)); |
} |
function gmp_shiftl($num, $bits) { |
return bcshiftl($num, $bits); |
} |
|
// Newly added: bcshiftr / gmp_shiftr |
function bcshiftr($num, $bits) { |
bcscale(0); |
return bcdiv($num, bcpow('2', $bits)); |
} |
function gmp_shiftr($num, $bits) { |
return bcshiftr($num, $bits); |
} |
|
// Newly added: bcfact (used by gmp_fact) |
function bcfact($a) { |
bcscale(0); |
|
// Source: https://www.php.net/manual/de/book.bc.php#116510 |
|
if (!filter_var($a, FILTER_VALIDATE_INT) || $a <= 0) { |
throw new InvalidArgumentException(sprintf('Argument must be natural number, "%s" given.', $a)); |
} |
|
for ($result = '1'; $a > 0; $a--) { |
$result = bcmul($result, $a); |
} |
|
return $result; |
} |
} |