Ratio

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).

Some Examples

Rationals are constructed using numerator <|> denomerator (or, if you don’t like the infix operator, using Ratio.new(numerator, denomerator))

Notice that Rationals are automatically simplified, and coerced to integers whenever possible.

  iex> use Ratio
  nil
  iex> 1 <|> 2
  1 <|> 2
  iex> 2 <|> 1
  2
  iex> 100 <|> 300
  1 <|> 3
  iex> 1.5 <|> 4
  3 <|> 8

The normal arithmetic-operators are overloaded by Ratio to allow arithmetic with Rationals (as well as normal ints and floats). (If you do not like to overload the infix operators, there are also longhand variants available.)

  iex> 2 + (2 <|> 3)
  5 <|> 5
  iex> 2.3 + 0.3
  13 <|> 5
  iex> (2 <|> 3) - (1 <|> 5)
  7 <|> 15
  iex> (1 <|> 3) / 2
  1 <|> 6
  iex> (2 <|> 3) / (8 <|> 5)
  5 <|> 12

Floats are converted to Rational numbers before performing arithmetic. This allows for more precise results.

  iex> Kernel.-(2.3, 0.3)
  1.9999999999999998
  iex> Kernel.-(2.3, 0.1)
  2.1999999999999997
  iex> use Ratio
  nil
  iex> 2.3 - 0.3
  2
  iex> 2.3 - 0.1
  11 <|> 5

(Of course, when possible, working with integers from the get-go is always more precise than converting floats)

Installation

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

    def deps do
      [
        {:ratio, "~> 1.2.0"}
      ]
    end

To use the module, use use Ratio where you need it.

If you do not want to override the Kernel’s built-in math operators, use

  # Does not override *, /, -, +, div, abs
  use Ratio, override_math: false

If you just do not want to override the Kernel’s built-in inline math operators, use use Ratio, inline_math: false

  # Does not override *, /, -, +
  use Ratio, inline_math: false

If you do not want the new operator <|> to be imported, use

  use Ratio, operator: false

These options can be combined (with override_math taking precedence over inline_math )

Changelog

• 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

Difference with the ‘rational’ library

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 created using Rational.<|>/2 or Ratio.new/2. This has as mayor advantage that the internal representation is always correct and simplified.

The Ratio library also (optionally) overrides 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.