# Qqwy / elixir-rational

Rational number library for Elixir.

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# 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
``````

The normal comparison-operators are optionally overloaded, with associated longhand variants. To enable them, `use Ratio, comparison: true`

``````  iex> 0.1 == (1 <|> 10)
true
iex> 10 < (1 <|> 10)
false
iex> 10 >= (1 <|> 10)
true
``````

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)

Since version 2.4.0, Ratio also accepts Decimals as input, which will be converted to rationals automatically.

## Installation

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

``````    def deps do
[
{:ratio, "~> 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 want to override the Kernel's built-in comparison operators (not overridden by default) use

``````  # Override ==, <, >, <=, >=
use Ratio, comparison: true
``````

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

• 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.
• 2.0.0 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

## 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.

Rational number library for Elixir.