# [−][src]Crate approx

A crate that provides facilities for testing the approximate equality of floating-point based types, using either relative difference, or units in the last place (ULPs) comparisons.

You can also use the `approx_{eq, ne}!`

`assert_approx_{eq, ne}!`

macros to test for equality
using a more positional style.

#[macro_use] extern crate approx; use std::f64; abs_diff_eq!(1.0, 1.0); abs_diff_eq!(1.0, 1.0, epsilon = f64::EPSILON); relative_eq!(1.0, 1.0); relative_eq!(1.0, 1.0, epsilon = f64::EPSILON); relative_eq!(1.0, 1.0, max_relative = 1.0); relative_eq!(1.0, 1.0, epsilon = f64::EPSILON, max_relative = 1.0); relative_eq!(1.0, 1.0, max_relative = 1.0, epsilon = f64::EPSILON); ulps_eq!(1.0, 1.0); ulps_eq!(1.0, 1.0, epsilon = f64::EPSILON); ulps_eq!(1.0, 1.0, max_ulps = 4); ulps_eq!(1.0, 1.0, epsilon = f64::EPSILON, max_ulps = 4); ulps_eq!(1.0, 1.0, max_ulps = 4, epsilon = f64::EPSILON);

# Implementing approximate equality for custom types

The `ApproxEq`

trait allows approximate equalities to be implemented on types, based on the
fundamental floating point implementations.

For example, we might want to be able to do approximate assertions on a complex number type:

#[macro_use] extern crate approx; #[derive(Debug, PartialEq)] struct Complex<T> { x: T, i: T, } let x = Complex { x: 1.2, i: 2.3 }; assert_relative_eq!(x, x); assert_ulps_eq!(x, x, max_ulps = 4);

To do this we can implement `AbsDiffEq`

, `RelativeEq`

and `UlpsEq`

generically in terms of a
type parameter that also implements `ApproxEq`

, `RelativeEq`

and `UlpsEq`

respectively. This
means that we can make comparisons for either `Complex<f32>`

or `Complex<f64>`

:

impl<T: AbsDiffEq> AbsDiffEq for Complex<T> where T::Epsilon: Copy, { type Epsilon = T::Epsilon; fn default_epsilon() -> T::Epsilon { T::default_epsilon() } fn abs_diff_eq(&self, other: &Self, epsilon: T::Epsilon) -> bool { T::abs_diff_eq(&self.x, &other.x, epsilon) && T::abs_diff_eq(&self.i, &other.i, epsilon) } } impl<T: RelativeEq> RelativeEq for Complex<T> where T::Epsilon: Copy, { fn default_max_relative() -> T::Epsilon { T::default_max_relative() } fn relative_eq(&self, other: &Self, epsilon: T::Epsilon, max_relative: T::Epsilon) -> bool { T::relative_eq(&self.x, &other.x, epsilon, max_relative) && T::relative_eq(&self.i, &other.i, epsilon, max_relative) } } impl<T: UlpsEq> UlpsEq for Complex<T> where T::Epsilon: Copy, { fn default_max_ulps() -> u32 { T::default_max_ulps() } fn ulps_eq(&self, other: &Self, epsilon: T::Epsilon, max_ulps: u32) -> bool { T::ulps_eq(&self.x, &other.x, epsilon, max_ulps) && T::ulps_eq(&self.i, &other.i, epsilon, max_ulps) } }

# References

Floating point is hard! Thanks goes to these links for helping to make things a *little*
easier to understand:

- [Comparing Floating Point Numbers, 2012 Edition] (https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
- The Floating Point Guide - Comparison
- [What Every Computer Scientist Should Know About Floating-Point Arithmetic] (https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html)

## Macros

abs_diff_eq | Approximate equality of using the absolute difference. |

abs_diff_ne | Approximate inequality of using the absolute difference. |

assert_abs_diff_eq | An assertion that delegates to |

assert_abs_diff_ne | An assertion that delegates to |

assert_relative_eq | An assertion that delegates to |

assert_relative_ne | An assertion that delegates to |

assert_ulps_eq | An assertion that delegates to |

assert_ulps_ne | An assertion that delegates to |

relative_eq | Approximate equality using both the absolute difference and relative based comparisons. |

relative_ne | Approximate inequality using both the absolute difference and relative based comparisons. |

ulps_eq | Approximate equality using both the absolute difference and ULPs (Units in Last Place). |

ulps_ne | Approximate inequality using both the absolute difference and ULPs (Units in Last Place). |

## Structs

AbsDiff | The requisite parameters for testing for approximate equality using a absolute difference based comparison. |

Relative | The requisite parameters for testing for approximate equality using a relative based comparison. |

Ulps | The requisite parameters for testing for approximate equality using an ULPs based comparison. |

## Traits

AbsDiffEq | Equality that is defined using the absolute difference of two numbers. |

RelativeEq | Equality comparisons between two numbers using both the absolute difference and relative based comparisons. |

UlpsEq | Equality comparisons between two numbers using both the absolute difference and ULPs (Units in Last Place) based comparisons. |