math/README.md

## Brick\Math

<img src="https://raw.githubusercontent.com/brick/brick/master/logo.png" alt="" align="left" height="64">

A library to work with arbitrary precision numbers.

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For a complete list of classes and methods, check the [API documentation](http://brick.io/math/).

### Installation

This library is installable via [Composer](https://getcomposer.org/).
Just define the following requirement in your `composer.json` file:

```json
{
    "require": {
        "brick/math": "0.5.*"
    }
}
```

### Requirements

This library requires PHP 5.6, PHP 7 or [HHVM](http://hhvm.com/).

Although the library can work seamlessly on any PHP installation, it is highly recommended that you install the
[GMP](http://php.net/manual/en/book.gmp.php) or [BCMath](http://php.net/manual/en/book.bc.php) 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 should be 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 `0.5.*`.

If you need to upgrade to a newer release cycle, check the [release history](https://github.com/brick/math/releases)
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](http://brick.io/math/namespace-Brick.Math.html) namespace:

- [BigNumber](http://brick.io/math/class-Brick.Math.BigNumber.html): base class for `BigInteger`, `BigDecimal` and `BigRational`
- [BigInteger](http://brick.io/math/class-Brick.Math.BigInteger.html): represents an arbitrary-precision integer number.
- [BigDecimal](http://brick.io/math/class-Brick.Math.BigDecimal.html): represents an arbitrary-precision decimal number.
- [BigRational](http://brick.io/math/class-Brick.Math.BigRational.html): represents an arbitrary-precision rational number (fraction).
- [RoundingMode](http://brick.io/math/class-Brick.Math.RoundingMode.html): holds constants for the [rounding modes](http://brick.io/math/class-Brick.Math.RoundingMode.html).

And the following exceptions in the [Brick\Math\Exception](http://brick.io/math/namespace-Brick.Math.Exception.html) namespace:

- [ArithmeticException](http://brick.io/math/class-Brick.Math.Exception.ArithmeticException.html): base class for all exceptions
- [DivisionByZeroException](http://brick.io/math/class-Brick.Math.Exception.DivisionByZeroException.html): thrown when a division by zero occurs
- [NumberFormatException](http://brick.io/math/class-Brick.Math.Exception.NumberFormatException.html): thrown when parsing a number string in an invalid format
- [RoundingNecessaryException](http://brick.io/math/class-Brick.Math.Exception.RoundingNecessaryException.html): thrown when the result of the operation cannot be represented without explicit rounding

### 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:

```php
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 of the representations above, *as long as it can be safely converted to
the current type*:

```php
BigInteger::of('1.00'); // 1
BigInteger::of('1.01'); // ArithmeticException

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

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`, since it can store up to 2147483647 digits:

```php
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`, since it can store up to 2147483647 digits:

```php
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:

```php
$ten = BigInteger::of(10);

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

The methods can be chained for better readability:

```php
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:

```php
$integer = BigInteger::of(123);
```

The following lines are equivalent:

```php
$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:

```php
echo BigInteger::of(2)->multipliedBy(BigDecimal::of('2.0')); // 4
echo BigInteger::of(2)->multipliedBy(BigDecimal::of('2.5')); // ArithmeticException
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:

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

You can pass an optional [rounding mode](http://brick.io/math/class-Brick.Math.RoundingMode.html) to round the result, if necessary:

```php
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:

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

You can even get both at the same time:

```php
list ($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](http://brick.io/math/class-Brick.Math.RoundingMode.html) must be provided.

```php
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:

```php
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:

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

#### 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.