# struct BigRational

## Overview

Rational numbers are represented as the quotient of arbitrarily large numerators and denominators. Rationals are canonicalized such that the denominator and the numerator have no common factors, and that the denominator is positive. Zero has the unique representation 0/1.

NOTE To use `BigRational`, you must explicitly import it with `require "big"`

``````require "big"

r = BigRational.new(7.to_big_i, 3.to_big_i)
r.to_s # => "7/3"

r = BigRational.new(3, -9)
r.to_s # => "-1/3"``````

It is implemented under the hood with GMP.

## Defined in:

big.cr
big/big_decimal.cr
big/big_rational.cr
big/number.cr

## Constructor Detail

def self.new(numerator : Int, denominator : Int) #

Creates a new `BigRational`.

If denominator is 0, this will raise an exception.

def self.new(num : Int) #

Creates a new `BigRational` with num as the numerator and 1 for denominator.

def self.new(num : Float::Primitive) #

Creates an exact representation of float as rational.

Raises `ArgumentError` if num is not finite.

def self.new(num : BigFloat) #

Creates an exact representation of float as rational.

def self.new(num : BigRational) #

Creates a `BigRational` from the given num.

def self.new(num : BigDecimal) #

Creates a `BigRational` from the given num.

## Instance Method Detail

def %(other : BigRational) : BigRational #

def %(other : Int) : BigRational #

def *(other : BigRational) : BigRational #

def *(other : Int) : BigRational #

def **(other : Int) : BigRational #

Raises the rational to the otherth power

This will raise `DivisionByZeroError` if rational is 0 and other is negative.

``````require "big"

BigRational.new(2, 3) ** 2  # => 4/9
BigRational.new(2, 3) ** -1 # => 3/2``````

def +(other : BigRational) : BigRational #

def +(other : Int) : BigRational #

def -(other : BigRational) : BigRational #

def -(other : Int) : BigRational #

def - : BigRational #

def /(other : BigRational) : BigRational #

def /(other : BigInt) : BigRational #

def /(other : BigFloat) : BigRational #

def /(other : BigDecimal) : BigRational #

def /(other : Int8) : BigRational #

def /(other : UInt8) : BigRational #

def /(other : Int16) : BigRational #

def /(other : UInt16) : BigRational #

def /(other : Int32) : BigRational #

def /(other : UInt32) : BigRational #

def /(other : Int64) : BigRational #

def /(other : UInt64) : BigRational #

def /(other : Int128) : BigRational #

def /(other : UInt128) : BigRational #

def /(other : Float32) : BigRational #

def /(other : Float64) : BigRational #

def //(other : BigRational) : BigRational #

def //(other : Int) : BigRational #

def <<(other : Int) : BigRational #

Multiplies the rational by (2 ** other)

``````require "big"

BigRational.new(2, 3) << 2 # => 8/3``````

def <=>(other : BigRational) #

def <=>(other : Float::Primitive) #

def <=>(other : BigFloat) #

def <=>(other : BigInt) #

def <=>(other : Int) #

def <=>(other : BigDecimal) #
Description copied from module Comparable(BigDecimal)

The comparison operator. Returns `0` if the two objects are equal, a negative number if this object is considered less than other, a positive number if this object is considered greater than other, or `nil` if the two objects are not comparable.

Subclasses define this method to provide class-specific ordering.

The comparison operator is usually used to sort values:

``````# Sort in a descending way:
[3, 1, 2].sort { |x, y| y <=> x } # => [3, 2, 1]

# Sort in an ascending way:
[3, 1, 2].sort { |x, y| x <=> y } # => [1, 2, 3]``````

def ==(other : BigRational) : Bool #

def >>(other : Int) : BigRational #

Divides the rational by (2 ** other)

``````require "big"

BigRational.new(2, 3) >> 2 # => 1/6``````

def abs : BigRational #
Description copied from struct Number

Returns the absolute value of this number.

``````123.abs  # => 123
-123.abs # => 123``````

def ceil : BigRational #

def clone #

def denominator : BigInt #

def floor : BigRational #

def format(io : IO, separator = '.', delimiter = ',', decimal_places : Int | Nil = nil, *, group : Int = 3, only_significant : Bool = false) : Nil #

Prints this number as a `String` using a customizable format.

separator is used as decimal separator, delimiter as thousands delimiter between batches of group digits.

If decimal_places is `nil`, all significant decimal places are printed (similar to `#to_s`). If the argument has a numeric value, the number of visible decimal places will be fixed to that amount.

Trailing zeros are omitted if only_significant is `true`.

``````123_456.789.format                                            # => "123,456.789"
123_456.789.format(',', '.')                                  # => "123.456,789"
123_456.789.format(decimal_places: 2)                         # => "123,456.79"
123_456.789.format(decimal_places: 6)                         # => "123,456.789000"
123_456.789.format(decimal_places: 6, only_significant: true) # => "123,456.789"``````

def inspect(io : IO) : Nil #
Description copied from class Object

Prints to io an unambiguous and information-rich string representation of this object, typically intended for developers.

It is similar to `#to_s(IO)`, but often provides more information. Ideally, it should contain sufficient information to be able to recreate an object with the same value (given an identical environment).

For types that don't provide a custom implementation of this method, default implementation delegates to `#to_s(IO)`. This said, it is advisable to have an appropriate `#inspect` implementation on every type. Default implementations are provided by `Struct#inspect` and `Reference#inspect`.

`::p` and `::p!` use this method to print an object in `STDOUT`.

def inspect : String #
Description copied from class Object

Returns an unambiguous and information-rich string representation of this object, typically intended for developers.

This method should usually not be overridden. It delegates to `#inspect(IO)` which can be overridden for custom implementations.

Also see `#to_s`.

def integer? : Bool #

Returns `true` if `self` is an integer.

Non-integer types may return `true` as long as `self` denotes a finite value without any fractional parts.

``````1.integer?       # => true
1.0.integer?     # => true
1.2.integer?     # => false
(1 / 0).integer? # => false
(0 / 0).integer? # => false``````

def inv : BigRational #

Returns a new `BigRational` as 1/r.

This will raise an exception if rational is 0.

def numerator : BigInt #

def remainder(other : BigRational) : BigRational #

def remainder(other : Int) : BigRational #

def round_away : BigRational #

def round_even : BigRational #

def tdiv(other : BigRational) : BigRational #

def tdiv(other : Int) : BigRational #

def to_big_d : BigDecimal #

Converts `self` to `BigDecimal`.

def to_big_f : BigFloat #

def to_big_i : BigInt #

def to_big_r : BigRational #

Returns `self`.

``````require "big"

BigRational.new(4, 5).to_big_r # => 4/5``````

def to_f : Float64 #

Returns the `Float64` representing this rational.

def to_f! : Float64 #

def to_f32 : Float32 #

def to_f32! : Float32 #

def to_f64 : Float64 #

def to_f64! : Float64 #

def to_i16(*args, **options) #

def to_i16(*args, **options, &) #

def to_i32(*args, **options) #

def to_i32(*args, **options, &) #

def to_i64(*args, **options) #

def to_i64(*args, **options, &) #

def to_i8(*args, **options) #

def to_i8(*args, **options, &) #

def to_s(base : Int = 10) : String #

Returns the string representing this rational.

Optionally takes a radix base (2 through 36).

``````require "big"

r = BigRational.new(8243243, 562828882)
r.to_s     # => "8243243/562828882"
r.to_s(16) # => "7dc82b/218c1652"
r.to_s(36) # => "4woiz/9b3djm"``````

def to_s(io : IO, base : Int = 10) : Nil #
Description copied from class Object

Prints a nicely readable and concise string representation of this object, typically intended for users, to io.

This method is called when an object is interpolated in a string literal:

``"foo #{bar} baz" # calls bar.to_io with the builder for this string``

`IO#<<` calls this method to append an object to itself:

``io << bar # calls bar.to_s(io)``

Thus implementations must not interpolate `self` in a string literal or call `io << self` which both would lead to an endless loop.

Also see `#inspect(IO)`.

def to_u16(*args, **options) #

def to_u16(*args, **options, &) #

def to_u32(*args, **options) #

def to_u32(*args, **options, &) #

def to_u64(*args, **options) #

def to_u64(*args, **options, &) #

def to_u8(*args, **options) #

def to_u8(*args, **options, &) #

def to_unsafe #

def trunc : BigRational #