# Introduction to Zend\\Math

`Zend\Math` namespace provides general mathematical functions. So far the supported functionalities
are:

* `Zend\Math\Rand`, a random number generator;
* `Zend\Math\BigInteger`, a library to manage big integers.

We expect to add more functionalities in the future.

## Random number generator

`Zend\Math\Rand` implements a random number generator that is able to generate random numbers for
general purpose usage and for cryptographic scopes. To generate good random numbers this component
uses different approaches. If PHP 7 is running we used the cryptographically secure pseudo-random
functions [random_bytes](http://php.net/manual/en/function.random-bytes.php) and
[random_int](http://php.net/manual/en/function.random-int.php), otherwise we use the
[Mcrypt](http://it.php.net/manual/en/book.mcrypt.php) extension or /dev/urandom source.
If you don't have a secure random source in your environment the component
will use the library [ircmaxell/RandomLib](https://github.com/ircmaxell/RandomLib) with a
medium strength generator.

The `Zend\Math\Rand` class offers the following methods to generate random values:

* `getBytes($length, $strong = false)` to generate a random set of `$length` bytes;
* `getBoolean($strong = false)` to generate a random boolean value (true or false);
* `getInteger($min, $max, $strong = false)` to generate a random integer between `$min` and `$max`;
* `getFloat($strong = false)` to generate a random float number between 0 and 1;
* `getString($length, $charlist = null, $strong = false)` to generate a random string of $length
characters using the alphabet $charlist (if not provided the default alphabet is the
[Base64](http://en.wikipedia.org/wiki/Base64)).

In all these methods the parameter `$strong` specify the usage of a strong random number generator.
We suggest to set the $strong to true if you need to generate random number for cryptographic and
security implementation.

If `$strong` is set to true and you try to generate random values in a PHP environment without a
secure pseudo-random source the component will throw an Exception.

Below we reported an example on how to generate random data using `Zend\Math\Rand`.

```php
use Zend\Math\Rand;

$bytes = Rand::getBytes(32, true);
printf("Random bytes (in Base64): %s\n", base64_encode($bytes));

$boolean = Rand::getBoolean();
printf("Random boolean: %s\n", $boolean ? 'true' : 'false');

$integer = Rand::getInteger(0,1000);
printf("Random integer in [0-1000]: %d\n", $integer);

$float = Rand::getFloat();
printf("Random float in [0-1): %f\n", $float);

$string = Rand::getString(32, 'abcdefghijklmnopqrstuvwxyz', true);
printf("Random string in latin alphabet: %s\n", $string);
```

## Big integers

`Zend\Math\BigInteger\BigInteger` offers a class to manage arbitrary length integer. PHP supports
integer numbers with a maximum value of `PHP_INT_MAX`. If you need to manage integers bigger than
`PHP_INT_MAX` you have to use external libraries or PHP extensions like
[GMP](http://www.php.net/manual/en/book.gmp.php) or [BC
Math](http://www.php.net/manual/en/book.bc.php).

`Zend\Math\BigInteger\BigInteger` is able to manage big integers using the GMP or the BC Math
extensions as adapters.

The mathematical functions implemented in `Zend\Math\BigInteger\BigInteger` are:

* `add($leftOperand, $rightOperand)`, add two big integers;
* `sub($leftOperand, $rightOperand)`, subtract two big integers;
* `mul($leftOperand, $rightOperand)`, multiply two big integers;
* `div($leftOperand, $rightOperand)`, divide two big integers (this method returns only integer part
of result);
* `pow($operand, $exp)`, raise a big integers to another;
* `sqrt($operand)`, get the square root of a big integer;
* `abs($operand)`, get the absolute value of a big integer;
* `mod($leftOperand, $modulus)`, get modulus of a big integer;
* `powmod($leftOperand, $rightOperand, $modulus)`, raise a big integer to another, reduced by a
specified modulus;
* `comp($leftOperand, $rightOperand)`, compare two big integers, returns < 0 if leftOperand is
less than rightOperand; > 0 if leftOperand is greater than rightOperand, and 0 if they are equal;
* `intToBin($int, $twoc = false)`, convert big integer into it's binary number representation;
* `binToInt($bytes, $twoc = false)`, convert binary number into big integer;
* `baseConvert($operand, $fromBase, $toBase = 10)`, convert a number between arbitrary bases;

Below is reported an example using the BC Math adapter to calculate the sum of two integer random
numbers with 100 digits.

```php
use Zend\Math\BigInteger\BigInteger;
use Zend\Math\Rand;

$bigInt = BigInteger::factory('bcmath');

$x = Rand::getString(100,'0123456789');
$y = Rand::getString(100,'0123456789');

$sum = $bigInt->add($x, $y);
$len = strlen($sum);

printf("%{$len}s +\n%{$len}s =\n%s\n%s\n", $x, $y, str_repeat('-', $len), $sum);
```

As you can see in the code the big integers are managed using strings. Even the result of the sum is
represented as a string.

Below is reported another example using the BC Math adapter to generate the binary representation of
a negative big integer of 100 digits.

```php
use Zend\Math\BigInteger\BigInteger;
use Zend\Math\Rand;

$bigInt = BigInteger::factory('bcmath');

$digit = 100;
$x = '-' . Rand::getString($digit,'0123456789');

$byte = $bigInt->intToBin($x);

printf("The binary representation of the big integer with $digit digit:\n%s\nis (in Base64 format):
%s\n",
       $x, base64_encode($byte));
printf("Length in bytes: %d\n", strlen($byte));

$byte = $bigInt->intToBin($x, true);

printf("The two's complement binary representation of the big integer with $digit digit:\n%s\nis (in
Base64 format): %s\n",
       $x, base64_encode($byte));
printf("Length in bytes: %d\n", strlen($byte));
```

We generated the binary representation of the big integer number using the default binary format and
the [two's complement](http://en.wikipedia.org/wiki/Two%27s_complement) representation (specified
with the `true` parameter in the `intToBin` function).