<?php
/*
* PHP GMP-Supplement implemented using BCMath
* Copyright 2020-2022 Daniel Marschall, ViaThinkSoft
* Version 2021-06-29
*
* 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.
*/
// ----------------- Implementation of GMP functions using BCMath -----------------
define('GMP_ROUND_PLUSINF', 1); define('GMP_ROUND_MINUSINF', 2); define('GMP_LITTLE_ENDIAN', 4); define('GMP_NATIVE_ENDIAN', 16); define('GMP_VERSION', '6.0.0');
// gmp_abs ( GMP $a ) : GMP
// Absolute value
return $a;
} else {
}
}
// gmp_add ( GMP $a , GMP $b ) : GMP
// Add numbers
// bcadd ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string
}
// gmp_and ( GMP $a , GMP $b ) : GMP
// Bitwise AND
// Convert $a and $b to a binary string
$ab = bc_dec2bin($a);
$bb = bc_dec2bin($b);
$ab = str_pad($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) {
throw new Exception("gmp_binomial() NOT IMPLEMENTED");
}
// gmp_clrbit ( GMP $a , int $index ) : void
// Clear bit
}
// gmp_cmp ( GMP $a , GMP $b ) : int
// Compare numbers
// bccomp ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : int
}
// gmp_com ( GMP $a ) : GMP
// Calculates one's complement
// 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, $round = GMP_ROUND_ZERO
/*$round not implemented*/) {
// bcdiv ( string $dividend , string $divisor [, int $scale = 0 ] ) : string
}
// 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, $round = GMP_ROUND_ZERO
/*$round not implemented*/) { );
}
// 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, $round = GMP_ROUND_ZERO
/*$round not implemented*/) { // 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.
return $r;
}
// gmp_div ( GMP $a , GMP $b [, int $round = GMP_ROUND_ZERO ] ) : GMP
// Divide numbers
function gmp_div($a, $b, $round = GMP_ROUND_ZERO
/*$round not implemented*/) { return gmp_div_q($a, $b, $round); // Alias von gmp_div_q }
// gmp_divexact ( GMP $n , GMP $d ) : GMP
// Exact division of numbers
}
// 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, $options = GMP_MSW_FIRST | GMP_NATIVE_ENDIAN) {
if ($word_size != 1) throw new Exception("Word size != 1 not implemented");
if ($options != GMP_MSW_FIRST | GMP_NATIVE_ENDIAN) throw new Exception("Different options not implemented");
$gmpnumber = bcmul($gmpnumber,"1"); // normalize }
// gmp_fact ( mixed $a ) : GMP
// Factorial
return bcfact($a);
}
// gmp_gcd ( GMP $a , GMP $b ) : GMP
// Calculate GCD
}
// gmp_gcdext ( GMP $a , GMP $b ) : array
// Calculate GCD and multipliers
// Source: https://github.com/phpseclib/phpseclib/blob/master/phpseclib/Math/BigInteger/Engines/BCMath.php#L285
// modified to make it fit here and to be compatible with gmp_gcdext
$s = '1';
$t = '0';
$s_ = '0';
$t_ = '1';
while (bccomp($b, '0', 0) != 0) {
$temp = $a;
$a = $b;
$temp = $s;
$s = $s_;
$temp = $t;
$t = $t_;
}
return [
'g' => /*$this->normalize*/($a),
's' => /*$this->normalize*/($s),
't' => /*$this->normalize*/($t)
];
}
// gmp_hamdist ( GMP $a , GMP $b ) : int
// Hamming distance
throw new Exception("gmp_hamdist() 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, $options=GMP_MSW_FIRST | GMP_NATIVE_ENDIAN) {
if ($word_size != 1) throw new Exception("Word size != 1 not implemented");
if ($options != GMP_MSW_FIRST | GMP_NATIVE_ENDIAN) throw new Exception("Different options not implemented");
}
// gmp_init ( mixed $number [, int $base = 0 ] ) : GMP
// Create GMP number
if ($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.
$base = 16;
$base = 8;
} else {
$base = 10;
}
}
if ($base == 10) {
return $number;
} else {
return base_convert_bigint($number, $base, 10);
}
}
// gmp_intval ( GMP $gmpnumber ) : int
// Convert GMP number to integer
return (int)$gmpnumber;
}
// gmp_invert ( GMP $a , GMP $b ) : GMP
// Inverse by modulo
// Source: https://github.com/CityOfZion/neo-php/blob/master/src/Crypto/NumberTheory.php#L246
}
}
$c=$a;
$d=$b;
$uc=1;
$vc=0;
$ud=0;
$vd=1;
$temp1=$c;
$d=$temp1;
$temp2=$uc;
$temp3=$vc;
$ud=$temp2;
$vd=$temp3;
}
$result='';
$result=$ud;
} else {
}
} else {
throw new ErrorException("ERROR: $a and $b are NOT relatively prime.");
}
return $result;
}
// gmp_jacobi ( GMP $a , GMP $p ) : int
// Jacobi symbol
// Source: https://github.com/CityOfZion/neo-php/blob/master/src/Crypto/NumberTheory.php#L136
if ($p>=3 && $p%2==1) {
if ($a == '0') return '0';
if ($a == '1') return '1';
$a1 = $a;
$e = 0;
while (bcmod($a1, '2') == '0') { }
$s = (bcmod($e, '2')=='0' || bcmod($p, '8')=='1' || bcmod($p, '8')=='7') ?
'1' : '-1'; if ($a1 == '1') return $s;
if (bcmod($p, '4')=='3' && bcmod($a1, '4')=='3') $s = -$s; } else {
return false;
}
}
// gmp_kronecker ( mixed $a , mixed $b ) : int
// Kronecker symbol
function gmp_kronecker($a, $b) {
throw new Exception("gmp_kronecker() NOT IMPLEMENTED");
}
// gmp_lcm ( mixed $a , mixed $b ) : GMP
// Calculate LCM
function gmp_lcm($a, $b) {
return '0';
} else {
}
}
// gmp_legendre ( GMP $a , GMP $p ) : int
// Legendre symbol
throw new Exception("gmp_legendre() NOT IMPLEMENTED");
}
// gmp_mod ( GMP $n , GMP $d ) : GMP
// Modulo operation
// bcmod ( string $dividend , string $divisor [, int $scale = 0 ] ) : string
}
// gmp_mul ( GMP $a , GMP $b ) : GMP
// Multiply numbers
// bcmul ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string
}
// gmp_neg ( GMP $a ) : GMP
// Negate number
}
// gmp_nextprime ( int $a ) : GMP
// Find next prime number
// Source: https://github.com/CityOfZion/neo-php/blob/master/src/Crypto/NumberTheory.php#L692
if (bccomp($a, '2') == '-1') { return '2';
}
$result = bcadd($result, '2'); }
return $result;
}
// gmp_or ( GMP $a , GMP $b ) : GMP
// Bitwise OR
// Convert $a and $b to a binary string
$ab = bc_dec2bin($a);
$bb = bc_dec2bin($b);
$ab = str_pad($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) {
throw new Exception("gmp_perfect_power() NOT IMPLEMENTED");
}
// gmp_perfect_square ( GMP $a ) : bool
// Perfect square check
throw new Exception("gmp_perfect_square() NOT IMPLEMENTED");
}
// gmp_popcount ( GMP $a ) : int
// Population count
$ab = bc_dec2bin($a);
}
// gmp_pow ( GMP $base , int $exp ) : GMP
// Raise number into power
// 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
// bcpowmod ( string $base , string $exponent , string $modulus [, int $scale = 0 ] ) : string
}
// gmp_prob_prime ( GMP $a [, int $reps = 10 ] ) : int
// Check if number is "probably prime"
// Source: https://github.com/CityOfZion/neo-php/blob/master/src/Crypto/NumberTheory.php#L655
$t = 40;
$k = 0;
while (bcmod($m, '2') == '0') { }
for ($i=0; $i<$t; $i++) {
$a = bcrand
('1', bcsub($reps, '1')); if ($m < 0) {
return new ErrorException("Negative exponents ($m) not allowed");
} else {
}
if ($b0!=1 && $b0!=bcsub($reps, '1')) { $j = 1;
while ($j<=$k-1 && $b0!=bcsub($reps, '1')) { if ($b0 == 1) {
return false;
}
$j++;
}
if ($b0 != bcsub($reps, '1')) { return false;
}
}
}
return true;
}
// gmp_random_bits ( int $bits ) : GMP
// Random number
function gmp_random_bits($bits) {
$min = 0;
return bcrand($min, $max);
}
// gmp_random_range ( GMP $min , GMP $max ) : GMP
// Random number
function gmp_random_range($min, $max) {
return bcrand($min, $max);
}
// gmp_random_seed ( mixed $seed ) : void
// Sets the RNG seed
function gmp_random_seed($seed) {
bcrand_seed($seed);
}
// gmp_random ([ int $limiter = 20 ] ) : GMP
// Random number (deprecated)
throw new Exception("gmp_random() is deprecated! Please use gmp_random_bits() or gmp_random_range() instead.");
}
// gmp_root ( GMP $a , int $nth ) : GMP
// Take the integer part of nth root
function gmp_root($a, $nth) {
throw new Exception("gmp_root() NOT IMPLEMENTED");
}
// gmp_rootrem ( GMP $a , int $nth ) : array
// Take the integer part and remainder of nth root
function gmp_rootrem($a, $nth) {
throw new Exception("gmp_rootrem() NOT IMPLEMENTED");
}
// gmp_scan0 ( GMP $a , int $start ) : int
// Scan for 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
$ab = bc_dec2bin($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
$ab = bc_dec2bin($a);
if ($index < 0) throw new Exception("Invalid index");
$ab = str_pad($ab, $index+1, '0', STR_PAD_LEFT
); }
$ab[strlen($ab)-1-$index] = $bit_on ?
'1' : '0';
$a = bc_bin2dec($ab);
}
// gmp_sign ( GMP $a ) : int
// Sign of number
}
// gmp_sqrt ( GMP $a ) : GMP
// Calculate square root
// bcsqrt ( string $operand [, int $scale = 0 ] ) : string
}
// gmp_sqrtrem ( GMP $a ) : array
// Square root with remainder
throw new Exception("gmp_sqrtrem() NOT IMPLEMENTED");
}
// gmp_strval ( GMP $gmpnumber [, int $base = 10 ] ) : string
// Convert GMP number to string
if ($base == 10) {
return $gmpnumber;
} else {
return base_convert_bigint($gmpnumber, 10, $base);
}
}
// gmp_sub ( GMP $a , GMP $b ) : GMP
// Subtract numbers
// bcsub ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string
}
// gmp_testbit ( GMP $a , int $index ) : bool
// Tests if a bit is set
function gmp_testbit($a, $index) {
$ab = bc_dec2bin($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
// Convert $a and $b to a binary string
$ab = bc_dec2bin($a);
$bb = bc_dec2bin($b);
$ab = str_pad($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) {
$numstring = "".$numstring;
$frombase_str = '';
for ($i=0; $i<$frombase; $i++) {
}
$tobase_str = '';
for ($i=0; $i<$tobase; $i++) {
}
$result = '';
for ($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/
$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/
$decimal_i = '0';
for ($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) {
// Convert $a to a binary string
$ab = bc_dec2bin($a);
// Do the bitwise binary operation
$cb = '';
for ($i=0; $i<$length; $i++) {
$cb .= ($ab[$i] == 1) ? '0' : '1';
}
// Convert back to a decimal number
return bc_bin2dec($cb);
}
function gmp_not($a) {
return bcnot($a);
}
// Newly added: bcshiftl / gmp_shiftl
function bcshiftl($num, $bits) {
}
function gmp_shiftl($num, $bits) {
return bcshiftl($num, $bits);
}
// Newly added: bcshiftr / gmp_shiftr
function bcshiftr($num, $bits) {
}
function gmp_shiftr($num, $bits) {
return bcshiftr($num, $bits);
}
// Newly added: bcfact (used by gmp_fact)
function bcfact($a) {
// 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 $result;
}
// Newly added (used by gmp_prob_prime, gmp_random_range and gmp_random_bits)
function bcrand($min, $max = false) {
// Source: https://github.com/CityOfZion/neo-php/blob/master/src/Crypto/BCMathUtils.php#L7
// Fixed: https://github.com/CityOfZion/neo-php/issues/16
if (!$max) {
$max = $min;
$min = 0;
}
}
// Newly added (used by gmp_random_seed)
function bcrand_seed($seed) {
}
}