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// Copyright 2015 Brendan Zabarauskas // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. //! A crate that provides traits and macros for testing the approximate equality of //! floating-point types, using either relative difference, or units in the last place (ULPs) //! comparisons. //! //! ```rust //! #[macro_use] //! extern crate approx; //! use std::f64; //! //! # fn main() { //! 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); //! # } //! ``` //! //! ```rust //! #[macro_use] //! extern crate approx; //! use std::f64; //! //! # fn main() { //! 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: //! //! ```rust //! # #[macro_use] //! # extern crate approx; //! # use approx::ApproxEq; //! #[derive(Debug)] //! struct Complex<T> { //! x: T, //! i: T, //! } //! # impl<T: ApproxEq> ApproxEq for Complex<T> { //! # type Epsilon = T::Epsilon; //! # fn default_epsilon() -> T::Epsilon { T::default_epsilon() } //! # fn default_max_relative() -> T::Epsilon { T::default_max_relative() } //! # fn default_max_ulps() -> u32 { T::default_max_ulps() } //! # 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) } //! # 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) } //! # } //! //! # fn main() { //! 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 `ApproxEq` generically in terms of a type parameter that also //! implements `ApproxEq`. This means that we can make comparisons for either `Complex<f32>` or //! `Complex<f64>`: //! //! ```rust //! # use approx::ApproxEq; //! # #[derive(Debug)] //! # struct Complex<T> { x: T, i: T, } //! # //! impl<T: ApproxEq> ApproxEq for Complex<T> { //! type Epsilon = T::Epsilon; //! //! fn default_epsilon() -> T::Epsilon { //! T::default_epsilon() //! } //! //! fn default_max_relative() -> T::Epsilon { //! T::default_max_relative() //! } //! //! fn default_max_ulps() -> u32 { //! T::default_max_ulps() //! } //! //! 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) //! } //! //! 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](http://floating-point-gui.de/errors/comparison/) //! - [What Every Computer Scientist Should Know About Floating-Point Arithmetic] //! (https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html) pub mod macro_support; mod macros; /// Equality comparisons based on floating point tolerances. pub trait ApproxEq: Sized { /// Used for specifying relative comparisons. This is usually a floating point value. type Epsilon: Copy; /// The default tolerance to use when testing values that are close together. /// /// This is used when no `epsilon` value is supplied to the `relative_eq` or `ulps_eq` macros. fn default_epsilon() -> Self::Epsilon; /// The default relative tolerance for testing values that are far-apart. /// /// This is used when no `max_relative` value is supplied to the `relative_eq` macro. fn default_max_relative() -> Self::Epsilon; /// The default ULPs to tolerate when testing values that are far-apart. /// /// This is used when no `max_relative` value is supplied to the `relative_eq` macro. fn default_max_ulps() -> u32; /// A test for equality that uses a relative comparison if the values are far apart. fn relative_eq(&self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon) -> bool; /// The inverse of `ApproxEq::relative_eq`. fn relative_ne(&self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon) -> bool { !Self::relative_eq(self, other, epsilon, max_relative) } /// A test for equality that uses units in the last place (ULP) if the values are far apart. fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool; /// The inverse of `ApproxEq::ulps_eq`. fn ulps_ne(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool { !Self::ulps_eq(self, other, epsilon, max_ulps) } } macro_rules! impl_float_relative_eq { ($T:ident, $U:ident) => { impl ApproxEq for $T { type Epsilon = $T; #[inline] fn default_epsilon() -> $T { std::$T::EPSILON } #[inline] fn default_max_relative() -> $T { std::$T::EPSILON } #[inline] fn default_max_ulps() -> u32 { 4 } fn relative_eq(&self, other: &$T, epsilon: $T, max_relative: $T) -> bool { // Implementation based on: [Comparing Floating Point Numbers, 2012 Edition] // (https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/) // Handle infinities if self == other { return true; } let abs_diff = $T::abs(self - other); // For when the numbers are really close together if abs_diff <= epsilon { return true }; // Use a relative difference comparison let abs_self = $T::abs(*self); let abs_other = $T::abs(*other); let largest = if abs_other > abs_self { abs_other } else { abs_self }; abs_diff <= largest * max_relative } fn ulps_eq(&self, other: &$T, epsilon: $T, max_ulps: u32) -> bool { // Implementation based on: [Comparing Floating Point Numbers, 2012 Edition] // (https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/) // For when the numbers are really close together if $T::abs(self - other) <= epsilon { return true } // Trivial negative sign check if self.signum() != other.signum() { // Handle -0 == +0 return self == other; } let int_self: $U = unsafe { std::mem::transmute(*self) }; let int_other: $U = unsafe { std::mem::transmute(*other) }; // ULPS difference comparison $U::abs(int_self - int_other) < max_ulps as $U } } } } impl_float_relative_eq!(f32, i32); impl_float_relative_eq!(f64, i64); impl<'a, T: ApproxEq> ApproxEq for &'a T { type Epsilon = T::Epsilon; #[inline] fn default_epsilon() -> Self::Epsilon { T::default_epsilon() } #[inline] fn default_max_relative() -> Self::Epsilon { T::default_max_relative() } #[inline] fn default_max_ulps() -> u32 { T::default_max_ulps() } #[inline] fn relative_eq(&self, other: &&'a T, epsilon: T::Epsilon, max_relative: T::Epsilon) -> bool { T::relative_eq(*self, *other, epsilon, max_relative) } #[inline] fn ulps_eq(&self, other: &&'a T, epsilon: T::Epsilon, max_ulps: u32) -> bool { T::ulps_eq(*self, *other, epsilon, max_ulps) } } impl<'a, T: ApproxEq> ApproxEq for &'a mut T { type Epsilon = T::Epsilon; #[inline] fn default_epsilon() -> Self::Epsilon { T::default_epsilon() } #[inline] fn default_max_relative() -> Self::Epsilon { T::default_max_relative() } #[inline] fn default_max_ulps() -> u32 { T::default_max_ulps() } #[inline] fn relative_eq(&self, other: &&'a mut T, epsilon: T::Epsilon, max_relative: T::Epsilon) -> bool { T::relative_eq(*self, *other, epsilon, max_relative) } #[inline] fn ulps_eq(&self, other: &&'a mut T, epsilon: T::Epsilon, max_ulps: u32) -> bool { T::ulps_eq(*self, *other, epsilon, max_ulps) } }