Class: Math_BigInteger

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:

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:

Parameters:

Instead of the top x bits being dropped they're appended to the shifted bit string.

Parameters:

Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift.

Parameters:

Parameters:

Instead of the bottom x bits being dropped they're prepended to the shifted bit string.

Parameters:

Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift.

Parameters:

Parameters:

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:

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 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:

If you need to see if one number is greater than or less than another number, use Math_BigInteger::compare()

Parameters:

Say you have 693 and 609. The GCD is 21. Bézout's identity states that there exist integers x and y such that 693*x + 609*y == 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:

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:

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:

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:

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:

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:

Alias for Math_BigInteger::modPow()

Parameters:

Parameters:

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:

Some bitwise operations give different results depending on the precision being used. Examples include left shift, not, and rotates.

Parameters:

$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:

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:

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:

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:

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:

Here's an example:

 <?php

    include('Math/BigInteger.php');
 
    $a = new Math_BigInteger('50');
 
    echo $a->toString(); // outputs 50
 ?>

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.

Will be called, automatically, when serialize() is called on a Math_BigInteger object.

Will be called, automatically, if you're supporting just PHP5. If you're supporting PHP4, you'll need to call toString().

Will be called, automatically, when unserialize() is called on a Math_BigInteger object.