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 abs_diff_eq!, and panics with a helpful error on failure.
assert_abs_diff_ne	An assertion that delegates to abs_diff_ne!, and panics with a helpful error on failure.
assert_relative_eq	An assertion that delegates to relative_eq!, and panics with a helpful error on failure.
assert_relative_ne	An assertion that delegates to relative_ne!, and panics with a helpful error on failure.
assert_ulps_eq	An assertion that delegates to ulps_eq!, and panics with a helpful error on failure.
assert_ulps_ne	An assertion that delegates to ulps_ne!, and panics with a helpful error on failure.
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.