Brick\Math
A PHP library to work with arbitrary precision numbers.
Installation
This library is installable via Composer:
composer require brick/math
Requirements
This library requires PHP 8.1 or later.
For PHP 8.0 compatibility, you can use version 0.12
. 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 nonbreaking 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
andBigRational
 BigInteger: represents an arbitraryprecision integer number.
 BigDecimal: represents an arbitraryprecision decimal number.
 BigRational: represents an arbitraryprecision rational number (fraction).
 RoundingMode: enum representing all available rounding modes.
And the following exceptions in the Brick\Math\Exception
namespace:
 MathException: base class for all exceptions
 DivisionByZeroException: thrown when a division by zero occurs

IntegerOverflowException: thrown when attempting to convert a too large
BigInteger
toint
 NumberFormatException: thrown when parsing a number string in an invalid format
 RoundingNecessaryException: thrown when the result of the operation cannot be represented without explicit rounding
 NegativeNumberException: thrown when attempting to calculate the square root of a negative number
Overview
Instantiation
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
Example:
BigInteger::of(123546);
BigInteger::of('9999999999999999999999999999999999999999999');
BigDecimal::of(1.2);
BigDecimal::of('9.99999999999999999999999999999999999999999999');
BigRational::of('2/3');
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 floatingpoint values: instantiating from a float
might be unsafe, as floatingpoint 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:
$integer>multipliedBy(123);
$integer>multipliedBy('123');
$integer>multipliedBy($integer);
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
BigInteger
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);
BigDecimal
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
BigRational
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()
Serialization
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.