Class Math_BigInteger

Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256 numbers.

Package: Math\BigInteger
Copyright: MMVI Jim Wigginton
License: MIT License
Author: Jim Wigginton <terrafrost@php.net>
Version: 1.0.0RC4
Located at vendors/phpseclib/Math/BigInteger.php

Methods summary

`public Math_BigInteger`	# `Math_BigInteger( optional $x = 0, optional $base = 10 )` Converts base-2, base-10, base-16, and binary strings (eg. base-256) to BigIntegers. Converts base-2, base-10, base-16, and binary strings (eg. base-256) to BigIntegers. If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using two's compliment. The sole exception to this is -10, which is treated the same as 10 is. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('0x32', 16); // 50 in base-16 echo $a->toString(); // outputs 50 ?> Parameters `$x` `optional` $x base-10 number or base-$base number if $base set. `$base` `optional` integer $base Returns `Math_BigInteger`
`public String`	# `toBytes( Boolean $twos_compliment = false )` Converts a BigInteger to a byte string (eg. base-256). Converts a BigInteger to a byte string (eg. base-256). Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're saved as two's compliment. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('65'); echo $a->toBytes(); // outputs chr(65) ?> Parameters `$twos_compliment` `Boolean` $twos_compliment Returns `String`
`public String`	# `toHex( Boolean $twos_compliment = false )` Converts a BigInteger to a hex string (eg. base-16)). Converts a BigInteger to a hex string (eg. base-16)). Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're saved as two's compliment. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('65'); echo $a->toHex(); // outputs '41' ?> Parameters `$twos_compliment` `Boolean` $twos_compliment Returns `String`
`public String`	# `toBits( Boolean $twos_compliment = false )` Converts a BigInteger to a bit string (eg. base-2). Converts a BigInteger to a bit string (eg. base-2). Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're saved as two's compliment. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('65'); echo $a->toBits(); // outputs '1000001' ?> Parameters `$twos_compliment` `Boolean` $twos_compliment Returns `String`
`public String`	# `toString( )` Converts a BigInteger to a base-10 number. Converts a BigInteger to a base-10 number. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('50'); echo $a->toString(); // outputs 50 ?> Returns `String`
`public Math_BigInteger`	# `copy( )` Copy an object Copy an object PHP5 passes objects by reference while PHP4 passes by value. As such, we need a function to guarantee that all objects are passed by value, when appropriate. More information can be found here: http://php.net/language.oop5.basic#51624 Returns `Math_BigInteger` See `Math_BigInteger::__clone()`
`public`	# `__toString( )` __toString() magic method __toString() magic method Will be called, automatically, if you're supporting just PHP5. If you're supporting PHP4, you'll need to call toString().
`public Math_BigInteger`	# `__clone( )` __clone() magic method __clone() magic method Although you can call Math_BigInteger::__toString() directly in PHP5, you cannot call Math_BigInteger::__clone() directly in PHP5. You can in PHP4 since it's not a magic method, but in PHP5, you have to call it by using the PHP5 only syntax of $y = clone $x. As such, if you're trying to write an application that works on both PHP4 and PHP5, call Math_BigInteger::copy(), instead. Returns `Math_BigInteger` See `Math_BigInteger::copy()`
`public`	# `__sleep( )` __sleep() magic method __sleep() magic method Will be called, automatically, when serialize() is called on a Math_BigInteger object. See `Math_BigInteger::__wakeup()`
`public`	# `__wakeup( )` __wakeup() magic method __wakeup() magic method Will be called, automatically, when unserialize() is called on a Math_BigInteger object. See `Math_BigInteger::__sleep()`
`public Math_BigInteger`	# `add( Math_BigInteger $y )` Adds two BigIntegers. Adds two BigIntegers. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('10'); $b = new Math_BigInteger('20'); $c = $a->add($b); echo $c->toString(); // outputs 30 ?> Parameters `$y` `Math_BigInteger` $y Returns `Math_BigInteger`
`public Array`	# `_add( Array $x_value, Boolean $x_negative, Array $y_value, Boolean $y_negative )` Performs addition. Performs addition. Parameters `$x_value` `Array` $x_value `$x_negative` `Boolean` $x_negative `$y_value` `Array` $y_value `$y_negative` `Boolean` $y_negative Returns `Array`
`public Math_BigInteger`	# `subtract( Math_BigInteger $y )` Subtracts two BigIntegers. Subtracts two BigIntegers. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('10'); $b = new Math_BigInteger('20'); $c = $a->subtract($b); echo $c->toString(); // outputs -10 ?> Parameters `$y` `Math_BigInteger` $y Returns `Math_BigInteger`
`public Array`	# `_subtract( Array $x_value, Boolean $x_negative, Array $y_value, Boolean $y_negative )` Performs subtraction. Performs subtraction. Parameters `$x_value` `Array` $x_value `$x_negative` `Boolean` $x_negative `$y_value` `Array` $y_value `$y_negative` `Boolean` $y_negative Returns `Array`
`public Math_BigInteger`	# `multiply( Math_BigInteger $x )` Multiplies two BigIntegers Multiplies two BigIntegers Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('10'); $b = new Math_BigInteger('20'); $c = $a->multiply($b); echo $c->toString(); // outputs 200 ?> Parameters `$x` `Math_BigInteger` $x Returns `Math_BigInteger`
`public Array`	# `_multiply( Array $x_value, Boolean $x_negative, Array $y_value, Boolean $y_negative )` Performs multiplication. Performs multiplication. Parameters `$x_value` `Array` $x_value `$x_negative` `Boolean` $x_negative `$y_value` `Array` $y_value `$y_negative` `Boolean` $y_negative Returns `Array`
`public Array`	# `_regularMultiply( Array $x_value, Array $y_value )` Performs long multiplication on two BigIntegers Performs long multiplication on two BigIntegers Modeled after 'multiply' in MutableBigInteger.java. Parameters `$x_value` `Array` $x_value `$y_value` `Array` $y_value Returns `Array`
`public Array`	# `_karatsuba( Array $x_value, Array $y_value )` Performs Karatsuba multiplication on two BigIntegers Performs Karatsuba multiplication on two BigIntegers See Karatsuba algorithm and MPM 5.2.3. Parameters `$x_value` `Array` $x_value `$y_value` `Array` $y_value Returns `Array`
`public Array`	# `_square( Array $x = false )` Performs squaring Performs squaring Parameters `$x` `Array` $x Returns `Array`
`public Array`	# `_baseSquare( Array $value )` Performs traditional squaring on two BigIntegers Performs traditional squaring on two BigIntegers Squaring can be done faster than multiplying a number by itself can be. See HAC 14.2.4 / MPM 5.3 for more information. Parameters `$value` `Array` $value Returns `Array`
`public Array`	# `_karatsubaSquare( Array $value )` Performs Karatsuba "squaring" on two BigIntegers Performs Karatsuba "squaring" on two BigIntegers See Karatsuba algorithm and MPM 5.3.4. Parameters `$value` `Array` $value Returns `Array`
`public Array`	# `divide( Math_BigInteger $y )` Divides two BigIntegers. Divides two BigIntegers. Returns an array whose first element contains the quotient and whose second element contains the "common residue". If the remainder would be positive, the "common residue" and the remainder are the same. If the remainder would be negative, the "common residue" is equal to the sum of the remainder and the divisor (basically, the "common residue" is the first positive modulo). Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('10'); $b = new Math_BigInteger('20'); list($quotient, $remainder) = $a->divide($b); echo $quotient->toString(); // outputs 0 echo "\r\n"; echo $remainder->toString(); // outputs 10 ?> Parameters `$y` `Math_BigInteger` $y Returns `Array`
`public Array`	# `_divide_digit( Array $dividend, Array $divisor )` Divides a BigInteger by a regular integer Divides a BigInteger by a regular integer abc / x = a00 / x + b0 / x + c / x Parameters `$dividend` `Array` $dividend `$divisor` `Array` $divisor Returns `Array`
`public Math_BigInteger`	# `modPow( Math_BigInteger $e, Math_BigInteger $n )` Performs modular exponentiation. Performs modular exponentiation. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger('10'); $b = new Math_BigInteger('20'); $c = new Math_BigInteger('30'); $c = $a->modPow($b, $c); echo $c->toString(); // outputs 10 ?> Parameters `$e` `Math_BigInteger` $e `$n` `Math_BigInteger` $n Returns `Math_BigInteger`
`public Math_BigInteger`	# `powMod( Math_BigInteger $e, Math_BigInteger $n )` Performs modular exponentiation. Performs modular exponentiation. Alias for Math_BigInteger::modPow() Parameters `$e` `Math_BigInteger` $e `$n` `Math_BigInteger` $n Returns `Math_BigInteger`
`public Math_BigInteger`	# `_slidingWindow( Math_BigInteger $e, Math_BigInteger $n, Integer $mode )` Sliding Window k-ary Modular Exponentiation Sliding Window k-ary Modular Exponentiation Based on HAC 14.85 / MPM 7.7. In a departure from those algorithims, however, this function performs a modular reduction after every multiplication and squaring operation. As such, this function has the same preconditions that the reductions being used do. Parameters `$e` `Math_BigInteger` $e `$n` `Math_BigInteger` $n `$mode` `Integer` $mode Returns `Math_BigInteger`
`public Array`	# `_reduce( Array $x, Array $n, Integer $mode )` Modular reduction Modular reduction For most $modes this will return the remainder. Parameters `$x` `Array` $x `$n` `Array` $n `$mode` `Integer` $mode Returns `Array` See `Math_BigInteger::_slidingWindow()`
`public Array`	# `_prepareReduce( Array $x, Array $n, Integer $mode )` Modular reduction preperation Modular reduction preperation Parameters `$x` `Array` $x `$n` `Array` $n `$mode` `Integer` $mode Returns `Array` See `Math_BigInteger::_slidingWindow()`
`public Array`	# `_multiplyReduce( Array $x, Array $y, Array $n, Integer $mode )` Modular multiply Modular multiply Parameters `$x` `Array` $x `$y` `Array` $y `$n` `Array` $n `$mode` `Integer` $mode Returns `Array` See `Math_BigInteger::_slidingWindow()`
`public Array`	# `_squareReduce( Array $x, Array $n, Integer $mode )` Modular square Modular square Parameters `$x` `Array` $x `$n` `Array` $n `$mode` `Integer` $mode Returns `Array` See `Math_BigInteger::_slidingWindow()`
`public Math_BigInteger`	# `_mod2( Math_BigInteger $n )` Modulos for Powers of Two Modulos for Powers of Two Calculates $x%$n, where $n = 2**$e, for some $e. Since this is basically the same as doing $x & ($n-1), we'll just use this function as a wrapper for doing that. Parameters `$n` `Math_BigInteger` Returns `Math_BigInteger` See `Math_BigInteger::_slidingWindow()`
`public Array`	# `_barrett( Array $n, Array $m )` Barrett Modular Reduction Barrett Modular Reduction See HAC 14.3.3 / MPM 6.2.5 for more information. Modified slightly, so as not to require negative numbers (initially, this script didn't support negative numbers). Employs "folding", as described at thesis-149.pdf#page=66. To quote from it, "the idea [behind folding] is to find a value x' such that x (mod m) = x' (mod m), with x' being smaller than x." Unfortunately, the "Barrett Reduction with Folding" algorithm described in thesis-149.pdf is not, as written, all that usable on account of (1) its not using reasonable radix points as discussed in MPM 6.2.2 and (2) the fact that, even with reasonable radix points, it only works when there are an even number of digits in the denominator. The reason for (2) is that (x >> 1) + (x >> 1) != x / 2 + x / 2. If x is even, they're the same, but if x is odd, they're not. See the in-line comments for details. Parameters `$n` `Array` $n `$m` `Array` $m Returns `Array` See `Math_BigInteger::_slidingWindow()`
`public Array`	# `_regularBarrett( Array $x, Array $n )` (Regular) Barrett Modular Reduction (Regular) Barrett Modular Reduction For numbers with more than four digits Math_BigInteger::_barrett() is faster. The difference between that and this is that this function does not fold the denominator into a smaller form. Parameters `$x` `Array` $x `$n` `Array` $n Returns `Array` See `Math_BigInteger::_slidingWindow()`
`public Array`	# `_multiplyLower( Array $x_value, Boolean $x_negative, Array $y_value, Boolean $y_negative, mixed $stop )` Performs long multiplication up to $stop digits Performs long multiplication up to $stop digits If you're going to be doing array_slice($product->value, 0, $stop), some cycles can be saved. Parameters `$x_value` `Array` $x_value `$x_negative` `Boolean` $x_negative `$y_value` `Array` $y_value `$y_negative` `Boolean` $y_negative `$stop` Returns `Array` See `Math_BigInteger::_regularBarrett()`
`public Array`	# `_montgomery( Array $x, Array $n )` Montgomery Modular Reduction Montgomery Modular Reduction ($x->_prepMontgomery($n))->_montgomery($n) yields $x % $n. MPM 6.3 provides insights on how this can be improved upon (basically, by using the comba method). gcd($n, 2) must be equal to one for this function to work correctly. Parameters `$x` `Array` $x `$n` `Array` $n Returns `Array` See `Math_BigInteger::_prepMontgomery()` `Math_BigInteger::_slidingWindow()`
`public Array`	# `_montgomeryMultiply( Array $x, Array $y, Array $m )` Montgomery Multiply Montgomery Multiply Interleaves the montgomery reduction and long multiplication algorithms together as described in HAC 14.36 Parameters `$x` `Array` $x `$y` `Array` $y `$m` `Array` $m Returns `Array` See `Math_BigInteger::_prepMontgomery()` `Math_BigInteger::_montgomery()`
`public Array`	# `_prepMontgomery( Array $x, Array $n )` Prepare a number for use in Montgomery Modular Reductions Prepare a number for use in Montgomery Modular Reductions Parameters `$x` `Array` $x `$n` `Array` $n Returns `Array` See `Math_BigInteger::_montgomery()` `Math_BigInteger::_slidingWindow()`
`public Integer`	# `_modInverse67108864( Array $x )` Modular Inverse of a number mod 226 (eg. 67108864) Modular Inverse of a number mod 226 (eg. 67108864) Based off of the bnpInvDigit function implemented and justified in the following URL: http://www-cs-students.stanford.edu/~tjw/jsbn/jsbn.js The following URL provides more info: http://groups.google.com/group/sci.crypt/msg/7a137205c1be7d85 As for why we do all the bitmasking... strange things can happen when converting from floats to ints. For instance, on some computers, var_dump((int) -4294967297) yields int(-1) and on others, it yields int(-2147483648). To avoid problems stemming from this, we use bitmasks to guarantee that ints aren't auto-converted to floats. The outermost bitmask is present because without it, there's no guarantee that the "residue" returned would be the so-called "common residue". We use fmod, in the last step, because the maximum possible $x is 26 bits and the maximum $result is 16 bits. Thus, we have to be able to handle up to 40 bits, which only 64-bit floating points will support. Thanks to Pedro Gimeno Fortea for input! Parameters `$x` `Array` $x Returns `Integer` See `Math_BigInteger::_montgomery()`
`public mixed`	# `modInverse( Math_BigInteger $n )` Calculates modular inverses. Calculates modular inverses. Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger(30); $b = new Math_BigInteger(17); $c = $a->modInverse($b); echo $c->toString(); // outputs 4 echo "\r\n"; $d = $a->multiply($c); list(, $d) = $d->divide($b); echo $d; // outputs 1 (as per the definition of modular inverse) ?> Parameters `$n` `Math_BigInteger` $n Returns `mixed` false, if no modular inverse exists, Math_BigInteger, otherwise.
`public Math_BigInteger`	# `extendedGCD( Math_BigInteger $n )` Calculates the greatest common divisor and Bézout's identity. Calculates the greatest common divisor and Bézout's identity. Say you have 693 and 609. The GCD is 21. Bézout's identity states that there exist integers x and y such that 693x + 609y == 21. In point of fact, there are actually an infinite number of x and y combinations and which combination is returned is dependant upon which mode is in use. See Bézout's identity - Wikipedia for more information. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger(693); $b = new Math_BigInteger(609); extract($a->extendedGCD($b)); echo $gcd->toString() . "\r\n"; // outputs 21 echo $a->toString() * $x->toString() + $b->toString() * $y->toString(); // outputs 21 ?> Parameters `$n` `Math_BigInteger` $n Returns `Math_BigInteger`
`public Math_BigInteger`	# `gcd( Math_BigInteger $n )` Calculates the greatest common divisor Calculates the greatest common divisor Say you have 693 and 609. The GCD is 21. Here's an example: <?php include('Math/BigInteger.php'); $a = new Math_BigInteger(693); $b = new Math_BigInteger(609); $gcd = a->extendedGCD($b); echo $gcd->toString() . "\r\n"; // outputs 21 ?> Parameters `$n` `Math_BigInteger` $n Returns `Math_BigInteger`
`public Math_BigInteger`	# `abs( )` Absolute value. Absolute value. Returns `Math_BigInteger`
`public Integer`	# `compare( Math_BigInteger $y )` Compares two numbers. Compares two numbers. Although one might think !$x->compare($y) means $x != $y, it, in fact, means the opposite. The reason for this is demonstrated thusly: $x > $y: $x->compare($y) > 0 $x < $y: $x->compare($y) < 0 $x == $y: $x->compare($y) == 0 Note how the same comparison operator is used. If you want to test for equality, use $x->equals($y). Parameters `$y` `Math_BigInteger` $x Returns `Integer` < 0 if $this is less than $x; > 0 if $this is greater than $x, and 0 if they are equal. See `Math_BigInteger::equals()`
`public Integer`	# `_compare( Array $x_value, Boolean $x_negative, Array $y_value, Boolean $y_negative )` Compares two numbers. Compares two numbers. Parameters `$x_value` `Array` $x_value `$x_negative` `Boolean` $x_negative `$y_value` `Array` $y_value `$y_negative` `Boolean` $y_negative Returns `Integer` See `Math_BigInteger::compare()`
`public Boolean`	# `equals( Math_BigInteger $x )` Tests the equality of two numbers. Tests the equality of two numbers. If you need to see if one number is greater than or less than another number, use Math_BigInteger::compare() Parameters `$x` `Math_BigInteger` $x Returns `Boolean` See `Math_BigInteger::compare()`
`public Math_BigInteger`	# `setPrecision( Math_BigInteger $bits )` Set Precision Set Precision Some bitwise operations give different results depending on the precision being used. Examples include left shift, not, and rotates. Parameters `$bits` `Math_BigInteger` $x Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_and( Math_BigInteger $x )` Logical And Logical And Parameters `$x` `Math_BigInteger` $x Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_or( Math_BigInteger $x )` Logical Or Logical Or Parameters `$x` `Math_BigInteger` $x Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_xor( Math_BigInteger $x )` Logical Exclusive-Or Logical Exclusive-Or Parameters `$x` `Math_BigInteger` $x Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_not( )` Logical Not Logical Not Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_rightShift( Integer $shift )` Logical Right Shift Logical Right Shift Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift. Parameters `$shift` `Integer` $shift Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_leftShift( Integer $shift )` Logical Left Shift Logical Left Shift Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift. Parameters `$shift` `Integer` $shift Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_leftRotate( Integer $shift )` Logical Left Rotate Logical Left Rotate Instead of the top x bits being dropped they're appended to the shifted bit string. Parameters `$shift` `Integer` $shift Returns `Math_BigInteger`
`public Math_BigInteger`	# `bitwise_rightRotate( Integer $shift )` Logical Right Rotate Logical Right Rotate Instead of the bottom x bits being dropped they're prepended to the shifted bit string. Parameters `$shift` `Integer` $shift Returns `Math_BigInteger`
`public`	# `setRandomGenerator( optional $generator )` Set random number generator function Set random number generator function $generator should be the name of a random generating function whose first parameter is the minimum value and whose second parameter is the maximum value. If this function needs to be seeded, it should be seeded prior to calling Math_BigInteger::random() or Math_BigInteger::randomPrime() If the random generating function is not explicitly set, it'll be assumed to be mt_rand(). Parameters `$generator` `optional` String $generator See `Math_BigInteger::random()` `Math_BigInteger::randomPrime()`
`public Math_BigInteger`	# `random( optional $min = false, optional $max = false )` Generate a random number Generate a random number Parameters `$min` `optional` Integer $min `$max` `optional` Integer $max Returns `Math_BigInteger`
`public Math_BigInteger`	# `randomPrime( optional $min = false, optional $max = false, optional $timeout = false )` Generate a random prime number. Generate a random prime number. If there's not a prime within the given range, false will be returned. If more than $timeout seconds have elapsed, give up and return false. Parameters `$min` `optional` Integer $min `$max` `optional` Integer $max `$timeout` `optional` Integer $timeout Returns `Math_BigInteger`
`public`	# `_make_odd( )` Make the current number odd Make the current number odd If the current number is odd it'll be unchanged. If it's even, one will be added to it. See `Math_BigInteger::randomPrime()`
`public Boolean`	# `isPrime( optional $t = false )` Checks a numer to see if it's prime Checks a numer to see if it's prime Assuming the $t parameter is not set, this function has an error rate of 2**-80. The main motivation for the $t parameter is distributability. Math_BigInteger::randomPrime() can be distributed accross multiple pageloads on a website instead of just one. Parameters `$t` `optional` Integer $t Returns `Boolean`
`public`	# `_lshift( Integer $shift )` Logical Left Shift Logical Left Shift Shifts BigInteger's by $shift bits. Parameters `$shift` `Integer` $shift
`public`	# `_rshift( Integer $shift )` Logical Right Shift Logical Right Shift Shifts BigInteger's by $shift bits. Parameters `$shift` `Integer` $shift
`public Math_BigInteger`	# `_normalize( Math_BigInteger $result )` Normalize Normalize Removes leading zeros and truncates (if necessary) to maintain the appropriate precision Parameters `$result` `Math_BigInteger` Returns `Math_BigInteger` See `Math_BigInteger::_trim()`
`public Math_BigInteger`	# `_trim( mixed $value )` Trim Trim Removes leading zeros Returns `Math_BigInteger`
`public Array`	# `_array_repeat( mixed $input, mixed $multiplier )` Array Repeat Array Repeat Parameters `$input` `mixed` $input Array `$multiplier` `mixed` $multiplier mixed Returns `Array`
`public String`	# `_base256_lshift( mixed & $x, mixed $shift )` Logical Left Shift Logical Left Shift Shifts binary strings $shift bits, essentially multiplying by 2**$shift. Parameters `$x` `mixed` $x String `$shift` `mixed` $shift Integer Returns `String`
`public String`	# `_base256_rshift( mixed & $x, mixed $shift )` Logical Right Shift Logical Right Shift Shifts binary strings $shift bits, essentially dividing by 2**$shift and returning the remainder. Parameters `$x` `mixed` $x String `$shift` `mixed` $shift Integer Returns `String`
`public String`	# `_int2bytes( Integer $x )` Converts 32-bit integers to bytes. Converts 32-bit integers to bytes. Parameters `$x` `Integer` $x Returns `String`
`public Integer`	# `_bytes2int( String $x )` Converts bytes to 32-bit integers Converts bytes to 32-bit integers Parameters `$x` `String` $x Returns `Integer`

Magic methods summary

Properties summary

`public Array`	`$value`	# Holds the BigInteger's value. Holds the BigInteger's value.
`public Boolean`	`$is_negative`	# Holds the BigInteger's magnitude. Holds the BigInteger's magnitude.
`public string`	`$generator`	# Random number generator function Random number generator function See `Math_BigInteger::setRandomGenerator()`
`public integer`	`$precision`	# Precision Precision See `Math_BigInteger::setPrecision()`
`public boolean`	`$bitmask`	# Precision Bitmask Precision Bitmask See `Math_BigInteger::setPrecision()`
`public String`	`$hex`	# Mode independant value used for serialization. Mode independant value used for serialization. If the bcmath or gmp extensions are installed $this->value will be a non-serializable resource, hence the need for a variable that'll be serializable regardless of whether or not extensions are being used. Unlike $this->value, however, $this->hex is only calculated when $this->__sleep() is called. See `Math_BigInteger::__sleep()` `Math_BigInteger::__wakeup()`

Packages

Classes

Class Math_BigInteger

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