Crate approx[−][src]
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 *_{eq, ne}!
and assert_*_{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 *Eq
traits allow 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 AbsDiffEq
, 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:
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. |