A library providing math and statistics operations for numbers of arbitrary size.

Fund package maintenance!

v2.1.1 2021-06-30 01:08 UTC


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This project is unit tested against 8.0, and merges are not accepted unless the tests pass.


To install, simply require the package using composer:

composer require "samsara/fermat:^2.0"

Or include it in your composer.json file:

    "require": {
        "samsara/fermat": "^2.0"

The project namespace is Samsara\Fermat\*. You can view the project on Packagist.


Modules for Fermat provide additional functionality, as many of these features would be unused by most people. NOTE: Prior to v2.0, much of this functionality was included in this package:

  • Algebra Expressions: Provides support for algebraic expressions such as polynomials and functions.
  • Complex Numbers: Provides complex numbers and enables additional features in Decimal instances.
  • Coordinate Systems: Provides coordinate systems for cartesian, spherical, polar, and cylindrical coordinates.
  • Matrices & Vectors: Provides support for matrix math and vector math.
  • Statistics: Provides support for statistical operations and distributions.

To require the entire library, including all available modules, use:

composer require samsara/fermat-all "^1.0"

Or in your composer.json file:

    "require": {
        "samsara/fermat-all": "^1.0"


The Samsara\Fermat\Numbers factory class provides a way to use the Value classes in Fermat without being as specific as those classes may require. Consider the following code:


use Samsara\Fermat\Numbers;

$five = Numbers::make(Numbers::IMMUTABLE, 5);
$ten = Numbers::make(Numbers::IMMUTABLE, '10');

echo $five->add($ten); // Prints: "15"

Note that the make() method allows you to provide both an int and a string as the value. In fact, it also allows you to provide a float. The first argument is the specific class that will be used for the value, the second argument is the value itself. The third and fourth arguments are optional and represent the scale (in number of decimal places) and the base of the number respectively. The scale and base arguments will only accept integer values.

If you do not specify a scale value, and you are using the default values, it automatically has a scale of either 10, or the string length of the input value, whichever is greater.

Here is an example of using the factory method to make a value that is in a base other than base10:


use Samsara\Fermat\Numbers;

$five = Numbers::make(Numbers::IMMUTABLE, '10', null, 5); // Value in base5
$ten = Numbers::make(Numbers::IMMUTABLE, '10'); // Value in base10

echo $ten->add($five); // Prints: "15" (The sum in base10)
echo $five->add($ten); // Prints: "30" (The sum in base5)

You can also use a Fraction and Number together:


use Samsara\Fermat\Values\ImmutableDecimal;
use Samsara\Fermat\Values\ImmutableFraction;

$five = new ImmutableDecimal(5);
$oneQuarter = new ImmutableFraction(1, 4);

echo $five->add($oneQuarter); // Prints: "5.25"
// The asDecimal() method is called on $oneQuarter

echo $oneQuarter->add($five); // Prints: "21/4"
// Calls getValue() on $five and instantiates a new ImmutableFraction

You can read the full documentation for Fermat here.


Please ensure that pull requests meet the following guidelines:

  • New files created in the pull request must have a corresponding unit test file, or must be covered within an existing test file.
  • Your merge may not drop the project's test coverage below 70%.
  • Your merge may not drop the project's test coverage by MORE than 5%.
  • Your merge must pass Scrutinizer-CI build tests for PHP 8.X.

For more information, please see the section on Contributing