This library allows you to use Rational numbers in Elixir, to enable exact calculations with all numbers big and small.

Ratio follows the Numeric behaviour from Numbers, and can therefore be used in combination with any data type that uses Numbers (such as Tensor and ComplexNum).

Ratio defines arithmetic and comparison operations to work with rational numbers.

Rational numbers can be created by using Ratio.new/2, or by calling mathematical operators where one of the two operands is already a rational number.

Since version 4.0, Ratio no longer defines an infix operator to create rational numbers. Instead, rational numbers are made using Ratio.new, and as the output from using an existing Ratio struct with a mathematical operation.

If you do want to use an infix operator such as <~> (supported in all Elixir versions) or <|> (deprecated in Elixir v1.14, the default of older versions of the Ratio library)

you can add the following one-liner to the module(s) in which you want to use it:

defdelegate numerator <~> denominator, to: Ratio, as: :new

Rational numbers can be manipulated using the functions in the Ratio module.

iex> Ratio.mult(Ratio.new(1, 3), Ratio.new(1, 2))
Ratio.new(1, 6)
iex> Ratio.div(Ratio.new(2, 3), Ratio.new(8, 5))
Ratio.new(5, 12)
iex> Ratio.pow(Ratio.new(2), 4)
Ratio.new(16, 1)

The Ratio module also contains:

• a guard-safe is_rational/1 check.
• a compare/2 function for use with e.g. Enum.sort.
• to_float/1 to (lossly) convert a rational into a float.

Ratio interopts with the Numbers library: If you want to overload Elixir's builtin math operators, you can add use Numbers, overload_operators: true to your module.

This also allows you to pass in a rational number as one argument and an integer, float or Decimal (if you have installed the Decimal library), which are then cast to rational numbers whenever necessary:

defmodule IDoAlotOfMathHere do
  defdelegate numerator <~> denominator, to: Ratio, as: :new
  use Numbers, overload_operators: true

  def calculate(input) do
     num = input <~> 2
     result = num * 2 + (3 <~> 4) * 5.0
     result / 2
  end
end

iex> IDoAlotOfMathHere.calculate(42)
Ratio.new(183, 8)

The package can be installed from hex, by adding :ratio to your list of dependencies in mix.exs:

    def deps do
      [
        {:ratio, "~> 4.0"}
      ]
    end

• 4.0.1 -
  • Fix compiler warnings on Elixir v1.16 (c.f. #128). Thank you, @kidq330
• 4.0.0 -
  • Remove infix operator <|> as its usage is deprecated in Elixir v1.14. This is a backwards-incompatible change. If you want to use the old syntax with the new version, add defdelegate num <|> denom, to: Ratio, as: :new to your module. Alternatively, you might want to use the not-deprecated <~> operator for this instead.
  • Switch the Inspect implementation to use the form Ratio.new(10, 20) instead of 10 <|> 20, related to above. This is also a backwards-incompatible change.
  • Remove implementation of String.Chars, as the earlier implementation was not a (non-programmer) human-readable format.
  • Ensure that the right-hand-side operand of calls to Ratio.{add, sub, mult, div}/2 is allowed to be an integer for ease of use and backwards compatibility. Thank you for noticing this problem, @kipcole9 ! (c.f. #111)
• 3.0.2 -
  • Fixes: A bug with <|> when the numerator was a rational and the denuminator an integer. (c.f. #104) Thank you, @varsill!
• 3.0.1 -
  • Fixes:
    • Problem where Ratio.ceil/1 would be off-by-one (c.f. #89). Thank you, @Hajto!
    • Problem where Ratio.pow/2 would return an integer rather than a new Ratio.(c.f. #100). Thank you, @speeddragon!
• 3.0.0 -
  • All operators except <|> are removed from Ratio. Instead, the operators defined by Numbers (which Ratio depends on) can be used, by adding use Numbers, overload_operators: true to your modules. (c.f. #34)
  • All math-based functions expect and return Ratio structs (rather than also working on integers and returning integers sometimes if the output turned out to be a whole number). (c.f. #43) This makes the code more efficient and more clear for users.
    • Ratio structs representing whole numbers are no longer implicitly converted 'back' to integers, as this behaviour was confusing. (c.f. #28)
    • If conversion to/from other number-like types is really desired, use the automatic conversions provided by Ratio.new, <|> or (a bit slower but more general) the math functions exposed by Numbers. Ratio ships with implementations of Coerce.defcoercion for Integer -> Ratio, Float -> Ratio and Decimal -> Ratio.
  • is_rational?/1 is replaced with the guard-safe is_rational/1 (only exported on Erlang versions where :erlang.map_get/2 is available, i.e. >= OTP 21.0.) (c.f. #37)
  • Float.ratio/1 is now used to convert floats into Ratio structs, rather than maintaining a hand-written version of this logic. (c.f #46) Thank you, @marcinwasowicz !
  • A lot of property-based tests have been added to get some level of confidence of the correctness of the library's operations.
• 2.4.2 Uses extra_applications in mix.exs to silence warnings in Elixir 1.11 and onwards.
• 2.4.1 Fixes a bug in the decimal conversion implementation where certain decimals were not converted properly. Thank you, @iterateNZ!
• 2.4.0 Adds optional support for automatic conversion from Decimals. Thank you, @kipcole !
• 2.3.1 Removes spurious printing statement in Rational.FloatConversion that would output a line of text at compile-time. Fixes support for Numbers v5+ which was broken.
• 2.3.0 Adds trunc and to_floor_error functions.
• 2.1.1 Fixes implementation of floor and ceil which was counter-intuitive for negative numbers (it now correctly rounds towards negative infinity).
  • Drops support for Elixir versions older than 1.4, because of use of Integer.floor_div.
  • First version to support new Erlang versions (20 and onward) that have native floor and ceil functions.
• 2.1.0 Adds optional overloaded comparison operators.
• 2.0.0 Breaking change: Brought Ratio.compare/2 in line with Elixir's comparison function guideline, to return :lt | :eq | :gt. (This used to be -1 | 0 | 1).
• 1.2.9 Improved documentation. (Thanks, @morontt!)
• 1.2.8 Adding :numbers to the applications: list, to ensure that no warnings are thrown when building releases on Elixir < 1.4.0.
• 1.2.6, 1.2.7 Improving documentation.
• 1.2.5 added ceil/1 and floor/1.
• 1.2.4 Fixes Elixir 1.4 warnings in the mix.exs file.
• 1.2.3 Upgraded version of the Numbers dependency to 2.0.
• 1.2.2 Added default argument to Ratio.new/2, to follow the Numeric behaviour fully, and added Ratio.minus/1 as alias for Ratio.negate/1 for the same reason.
• 1.2.0 Changed name of Ratio.mul/2 to Ratio.mult/2, to avoid ambiguety, and to allow incorporation with Numbers. Deprecation Warning was added to using Ratio.mul/2.
• 1.1.1 Negative floats are now converted correctly.
• 1.1.0 Elixir 1.3 compliance (Statefree if/else/catch clauses, etc.)
• 1.0.0 Proper __using__ macro, with more readable option names. Stable release.
• 0.6.0 First public release
• 0.0.1 First features

Observant readers might notice that there also is a 'rational' library in Hex.pm. The design idea between that library vs. this one is a bit different: Ratio hides the internal data representation as much as possible, and numbers are therefore only created using Ratio.new/2. This has as mayor advantage that the internal representation is always correct and simplified.

The Ratio library also (optionally) overrides (by virtue of the Numbers library) the built-in math operations +, -, *, /, div, abs so they work with combinations of integers, floats and rationals.

Finally, Ratio follows the Numeric behaviour, which means that it can be used with any data types that follow Numbers.