# [−][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)
}
}```

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)