Arbitrary-precision arithmetic library





Fund package maintenance!

Installs: 278 921 574

Dependents: 172

Suggesters: 5

Security: 0

Stars: 1 773

Watchers: 23

Forks: 75

Open Issues: 5



A PHP library to work with arbitrary precision numbers.

Build Status Coverage Status Latest Stable Version Total Downloads License


This library is installable via Composer:

composer require brick/math


This library requires PHP 8.1 or later.

For PHP 8.0 compatibility, you can use version 0.11. For PHP 7.4, you can use version 0.10. For PHP 7.1, 7.2 & 7.3, you can use version 0.9. Note that these PHP versions are EOL and not supported anymore. If you're still using one of these PHP versions, you should consider upgrading as soon as possible.

Although the library can work seamlessly on any PHP installation, it is highly recommended that you install the GMP or BCMath extension to speed up calculations. The fastest available calculator implementation will be automatically selected at runtime.

Project status & release process

While this library is still under development, it is well tested and considered stable enough to use in production environments.

The current releases are numbered 0.x.y. When a non-breaking change is introduced (adding new methods, optimizing existing code, etc.), y is incremented.

When a breaking change is introduced, a new 0.x version cycle is always started.

It is therefore safe to lock your project to a given release cycle, such as ^0.12.

If you need to upgrade to a newer release cycle, check the release history for a list of changes introduced by each further 0.x.0 version.

Package contents

This library provides the following public classes in the Brick\Math namespace:

  • BigNumber: base class for BigInteger, BigDecimal and BigRational
  • BigInteger: represents an arbitrary-precision integer number.
  • BigDecimal: represents an arbitrary-precision decimal number.
  • BigRational: represents an arbitrary-precision rational number (fraction).
  • RoundingMode: enum representing all available rounding modes.

And the following exceptions in the Brick\Math\Exception namespace:



The constructors of the classes are not public, you must use a factory method to obtain an instance.

All classes provide an of() factory method that accepts any of the following types:

  • BigNumber instances
  • int numbers
  • float numbers
  • string representations of integer, decimal and rational numbers




BigRational::of('1.1'); // 11/10

Note that all of() methods accept all the representations above, as long as it can be safely converted to the current type:

BigInteger::of('1.00'); // 1
BigInteger::of('1.01'); // RoundingNecessaryException

BigDecimal::of('1/8'); // 0.125
BigDecimal::of('1/3'); // RoundingNecessaryException

Note about native integers: instantiating from an int is safe as long as you don't exceed the maximum value for your platform (PHP_INT_MAX), in which case it would be transparently converted to float by PHP without notice, and could result in a loss of information. In doubt, prefer instantiating from a string, which supports an unlimited numbers of digits:

echo BigInteger::of(999999999999999999999); // 1000000000000000000000
echo BigInteger::of('999999999999999999999'); // 999999999999999999999

Note about floating-point values: instantiating from a float might be unsafe, as floating-point values are imprecise by design, and could result in a loss of information. Always prefer instantiating from a string, which supports an unlimited number of digits:

echo BigDecimal::of(1.99999999999999999999); // 2
echo BigDecimal::of('1.99999999999999999999'); // 1.99999999999999999999

Immutability & chaining

The BigInteger, BigDecimal and BigRational classes are immutable: their value never changes, so that they can be safely passed around. All methods that return a BigInteger, BigDecimal or BigRational return a new object, leaving the original object unaffected:

$ten = BigInteger::of(10);

echo $ten->plus(5); // 15
echo $ten->multipliedBy(3); // 30

The methods can be chained for better readability:

echo BigInteger::of(10)->plus(5)->multipliedBy(3); // 45

Parameter types

All methods that accept a number: plus(), minus(), multipliedBy(), etc. accept the same types as of(). For example, given the following number:

$integer = BigInteger::of(123);

The following lines are equivalent:


Just like of(), other types of BigNumber are acceptable, as long as they can be safely converted to the current type:

echo BigInteger::of(2)->multipliedBy(BigDecimal::of('2.0')); // 4
echo BigInteger::of(2)->multipliedBy(BigDecimal::of('2.5')); // RoundingNecessaryException
echo BigDecimal::of(2.5)->multipliedBy(BigInteger::of(2)); // 5.0

Division & rounding


By default, dividing a BigInteger returns the exact result of the division, or throws an exception if the remainder of the division is not zero:

echo BigInteger::of(999)->dividedBy(3); // 333
echo BigInteger::of(1000)->dividedBy(3); // RoundingNecessaryException

You can pass an optional rounding mode to round the result, if necessary:

echo BigInteger::of(1000)->dividedBy(3, RoundingMode::DOWN); // 333
echo BigInteger::of(1000)->dividedBy(3, RoundingMode::UP); // 334

If you're into quotients and remainders, there are methods for this, too:

echo BigInteger::of(1000)->quotient(3); // 333
echo BigInteger::of(1000)->remainder(3); // 1

You can even get both at the same time:

[$quotient, $remainder] = BigInteger::of(1000)->quotientAndRemainder(3);

Dividing a BigDecimal always requires a scale to be specified. If the exact result of the division does not fit in the given scale, a rounding mode must be provided.

echo BigDecimal::of(1)->dividedBy('8', 3); // 0.125
echo BigDecimal::of(1)->dividedBy('8', 2); // RoundingNecessaryException
echo BigDecimal::of(1)->dividedBy('8', 2, RoundingMode::HALF_DOWN); // 0.12
echo BigDecimal::of(1)->dividedBy('8', 2, RoundingMode::HALF_UP); // 0.13

If you know that the division yields a finite number of decimals places, you can use exactlyDividedBy(), which will automatically compute the required scale to fit the result, or throw an exception if the division yields an infinite repeating decimal:

echo BigDecimal::of(1)->exactlyDividedBy(256); // 0.00390625
echo BigDecimal::of(1)->exactlyDividedBy(11); // RoundingNecessaryException

The result of the division of a BigRational can always be represented exactly:

echo BigRational::of('123/456')->dividedBy('7'); // 123/3192
echo BigRational::of('123/456')->dividedBy('9/8'); // 984/4104

Bitwise operations

BigInteger supports bitwise operations:

  • and()
  • or()
  • xor()
  • not()

and bit shifting:

  • shiftedLeft()
  • shiftedRight()


BigInteger, BigDecimal and BigRational can be safely serialized on a machine and unserialized on another, even if these machines do not share the same set of PHP extensions.

For example, serializing on a machine with GMP support and unserializing on a machine that does not have this extension installed will still work as expected.