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// Copyright 2014-2018 Optimal Computing (NZ) Ltd.
// Licensed under the MIT license. See LICENSE for details.
use std::{f32,f64};
use super::Ulps;
/// ApproxEq is a trait for approximate equality comparisons.
pub trait ApproxEq: Sized {
/// The Margin type defines a margin within which two values are to be
/// considered approximately equal. It must implement Default so that
/// approx_eq() can be called on unknown types.
type Margin: Copy + Default;
/// This method tests for `self` and `other` values to be approximately equal
/// within `margin`.
fn approx_eq<M: Into<Self::Margin>>(self, other: Self, margin: M) -> bool;
/// This method tests for `self` and `other` values to be not approximately
/// equal within `margin`.
fn approx_ne<M: Into<Self::Margin>>(self, other: Self, margin: M) -> bool {
!self.approx_eq(other, margin)
}
}
/// This type defines a margin within two f32s might be considered equal
/// and is intended as the associated type for the `ApproxEq` trait.
///
/// Two methods are used to determine approximate equality.
///
/// First an epsilon method is used, considering them approximately equal if they
/// differ by <= `epsilon`. This will only succeed for very small numbers.
/// Note that it may succeed even if the parameters are of differing signs straddling
/// zero.
///
/// The second method considers how many ULPs (units of least precision, units in
/// the last place, which is the integer number of floating point representations
/// that the parameters are separated by) different the parameters are and considers
/// them approximately equal if this is <= `ulps`. For large floating point numbers,
/// an ULP can be a rather large gap, but this kind of comparison is necessary
/// because floating point operations must round to the nearest representable value
/// and so larger floating point values accumulate larger errors.
#[repr(C)]
#[derive(Debug, Clone, Copy)]
pub struct F32Margin {
pub epsilon: f32,
pub ulps: i32
}
impl Default for F32Margin {
#[inline]
fn default() -> F32Margin {
F32Margin {
epsilon: f32::EPSILON,
ulps: 4
}
}
}
impl F32Margin {
#[inline]
pub fn zero() -> F32Margin {
F32Margin {
epsilon: 0.0,
ulps: 0
}
}
pub fn epsilon(self, epsilon: f32) -> Self {
F32Margin {
epsilon: epsilon,
..self
}
}
pub fn ulps(self, ulps: i32) -> Self {
F32Margin {
ulps: ulps,
..self
}
}
}
impl From<(f32, i32)> for F32Margin {
fn from(m: (f32, i32)) -> F32Margin {
F32Margin {
epsilon: m.0,
ulps: m.1
}
}
}
impl ApproxEq for f32 {
type Margin = F32Margin;
fn approx_eq<M: Into<Self::Margin>>(self, other: f32, margin: M) -> bool {
let margin = margin.into();
// Check for exact equality first. This is often true, and so we get the
// performance benefit of only doing one compare in most cases.
self==other ||
// Perform epsilon comparison next
((self - other).abs() <= margin.epsilon) ||
{
// Perform ulps comparion last
let diff: i32 = self.ulps(&other);
saturating_abs_i32!(diff) <= margin.ulps
}
}
}
#[test]
fn f32_approx_eq_test1() {
let f: f32 = 0.0_f32;
let g: f32 = -0.0000000000000005551115123125783_f32;
assert!(f != g); // Should not be directly equal
assert!(f.approx_eq(g, (f32::EPSILON, 0)) == true);
}
#[test]
fn f32_approx_eq_test2() {
let f: f32 = 0.0_f32;
let g: f32 = -0.0_f32;
assert!(f.approx_eq(g, (f32::EPSILON, 0)) == true);
}
#[test]
fn f32_approx_eq_test3() {
let f: f32 = 0.0_f32;
let g: f32 = 0.00000000000000001_f32;
assert!(f.approx_eq(g, (f32::EPSILON, 0)) == true);
}
#[test]
fn f32_approx_eq_test4() {
let f: f32 = 0.00001_f32;
let g: f32 = 0.00000000000000001_f32;
assert!(f.approx_eq(g, (f32::EPSILON, 0)) == false);
}
#[test]
fn f32_approx_eq_test5() {
let f: f32 = 0.1_f32;
let mut sum: f32 = 0.0_f32;
for _ in 0_isize..10_isize { sum += f; }
let product: f32 = f * 10.0_f32;
assert!(sum != product); // Should not be directly equal:
println!("Ulps Difference: {}",sum.ulps(&product));
assert!(sum.approx_eq(product, (f32::EPSILON, 1)) == true);
assert!(sum.approx_eq(product, F32Margin::zero()) == false);
}
#[test]
fn f32_approx_eq_test6() {
let x: f32 = 1000000_f32;
let y: f32 = 1000000.1_f32;
assert!(x != y); // Should not be directly equal
assert!(x.approx_eq(y, (0.0, 2)) == true); // 2 ulps does it
// epsilon method no good here:
assert!(x.approx_eq(y, (1000.0 * f32::EPSILON, 0)) == false);
}
/// This type defines a margin within two f32s might be considered equal
/// and is intended as the associated type for the `ApproxEq` trait.
///
/// Two methods are used to determine approximate equality.
///
/// First an epsilon method is used, considering them approximately equal if they
/// differ by <= `epsilon`. This will only succeed for very small numbers.
/// Note that it may succeed even if the parameters are of differing signs straddling
/// zero.
///
/// The second method considers how many ULPs (units of least precision, units in
/// the last place, which is the integer number of floating point representations
/// that the parameters are separated by) different the parameters are and considers
/// them approximately equal if this <= `ulps`. For large floating point numbers,
/// an ULP can be a rather large gap, but this kind of comparison is necessary
/// because floating point operations must round to the nearest representable value
/// and so larger floating point values accumulate larger errors.
#[derive(Debug, Clone, Copy)]
pub struct F64Margin {
pub epsilon: f64,
pub ulps: i64
}
impl Default for F64Margin {
#[inline]
fn default() -> F64Margin {
F64Margin {
epsilon: f64::EPSILON,
ulps: 4
}
}
}
impl F64Margin {
#[inline]
pub fn zero() -> F64Margin {
F64Margin {
epsilon: 0.0,
ulps: 0
}
}
pub fn epsilon(self, epsilon: f64) -> Self {
F64Margin {
epsilon: epsilon,
..self
}
}
pub fn ulps(self, ulps: i64) -> Self {
F64Margin {
ulps: ulps,
..self
}
}
}
impl From<(f64, i64)> for F64Margin {
fn from(m: (f64, i64)) -> F64Margin {
F64Margin {
epsilon: m.0,
ulps: m.1
}
}
}
impl ApproxEq for f64 {
type Margin = F64Margin;
fn approx_eq<M: Into<Self::Margin>>(self, other: f64, margin: M) -> bool {
let margin = margin.into();
// Check for exact equality first. This is often true, and so we get the
// performance benefit of only doing one compare in most cases.
self==other ||
// Perform epsilon comparison next
((self - other).abs() <= margin.epsilon) ||
{
// Perform ulps comparion last
let diff: i64 = self.ulps(&other);
saturating_abs_i64!(diff) <= margin.ulps
}
}
}
#[test]
fn f64_approx_eq_test1() {
let f: f64 = 0.0_f64;
let g: f64 = -0.0000000000000005551115123125783_f64;
assert!(f != g); // Should not be directly equal
assert!(f.approx_eq(g, (3.0 * f64::EPSILON, 0)) == true); // 3e is enough
// ulps test wont ever call these equal
}
#[test]
fn f64_approx_eq_test2() {
let f: f64 = 0.0_f64;
let g: f64 = -0.0_f64;
assert!(f.approx_eq(g, (f64::EPSILON, 0)) == true);
}
#[test]
fn f64_approx_eq_test3() {
let f: f64 = 0.0_f64;
let g: f64 = 1e-17_f64;
assert!(f.approx_eq(g, (f64::EPSILON, 0)) == true);
}
#[test]
fn f64_approx_eq_test4() {
let f: f64 = 0.00001_f64;
let g: f64 = 0.00000000000000001_f64;
assert!(f.approx_eq(g, (f64::EPSILON, 0)) == false);
}
#[test]
fn f64_approx_eq_test5() {
let f: f64 = 0.1_f64;
let mut sum: f64 = 0.0_f64;
for _ in 0_isize..10_isize { sum += f; }
let product: f64 = f * 10.0_f64;
assert!(sum != product); // Should not be directly equal:
println!("Ulps Difference: {}",sum.ulps(&product));
assert!(sum.approx_eq(product, (f64::EPSILON, 0)) == true);
assert!(sum.approx_eq(product, (0.0, 1)) == true);
}
#[test]
fn f64_approx_eq_test6() {
let x: f64 = 1000000_f64;
let y: f64 = 1000000.0000000003_f64;
assert!(x != y); // Should not be directly equal
println!("Ulps Difference: {}",x.ulps(&y));
assert!(x.approx_eq(y, (0.0, 3)) == true);
}
#[test]
fn f64_code_triggering_issue_20() {
assert_eq!((-25.0f64).approx_eq(25.0, (0.00390625, 1)), false);
}