1// Copyright 2014-2020 Optimal Computing (NZ) Ltd.
2// Licensed under the MIT license. See LICENSE for details.
3
4#[cfg(feature = "num-traits")]
5#[allow(unused_imports)]
6use num_traits::float::FloatCore;
7use super::Ulps;
8
9/// ApproxEqUlps is a trait for approximate equality comparisons.
10/// The associated type Flt is a floating point type which implements Ulps, and is
11/// required so that this trait can be implemented for compound types (e.g. vectors),
12/// not just for the floats themselves.
13pub trait ApproxEqUlps {
14 type Flt: Ulps;
15
16 /// This method tests for `self` and `other` values to be approximately equal
17 /// within ULPs (Units of Least Precision) floating point representations.
18 /// Differing signs are always unequal with this method, and zeroes are only
19 /// equal to zeroes. Use approx_eq() from the ApproxEq trait if that is more
20 /// appropriate.
21 fn approx_eq_ulps(&self, other: &Self, ulps: <Self::Flt as Ulps>::U) -> bool;
22
23 /// This method tests for `self` and `other` values to be not approximately
24 /// equal within ULPs (Units of Least Precision) floating point representations.
25 /// Differing signs are always unequal with this method, and zeroes are only
26 /// equal to zeroes. Use approx_eq() from the ApproxEq trait if that is more
27 /// appropriate.
28 #[inline]
29 fn approx_ne_ulps(&self, other: &Self, ulps: <Self::Flt as Ulps>::U) -> bool {
30 !self.approx_eq_ulps(other, ulps)
31 }
32}
33
34impl ApproxEqUlps for f32 {
35 type Flt = f32;
36
37 fn approx_eq_ulps(&self, other: &f32, ulps: i32) -> bool {
38 // -0 and +0 are drastically far in ulps terms, so
39 // we need a special case for that.
40 if *self==*other { return true; }
41
42 // Handle differing signs as a special case, even if
43 // they are very close, most people consider them
44 // unequal.
45 if self.is_sign_positive() != other.is_sign_positive() { return false; }
46
47 let diff: i32 = self.ulps(other);
48 diff >= -ulps && diff <= ulps
49 }
50}
51
52#[test]
53fn f32_approx_eq_ulps_test1() {
54 let f: f32 = 0.1_f32;
55 let mut sum: f32 = 0.0_f32;
56 for _ in 0_isize..10_isize { sum += f; }
57 let product: f32 = f * 10.0_f32;
58 assert!(sum != product); // Should not be directly equal:
59 assert!(sum.approx_eq_ulps(&product,1) == true); // But should be close
60 assert!(sum.approx_eq_ulps(&product,0) == false);
61}
62#[test]
63fn f32_approx_eq_ulps_test2() {
64 let x: f32 = 1000000_f32;
65 let y: f32 = 1000000.1_f32;
66 assert!(x != y); // Should not be directly equal
67 assert!(x.approx_eq_ulps(&y,2) == true);
68 assert!(x.approx_eq_ulps(&y,1) == false);
69}
70#[test]
71fn f32_approx_eq_ulps_test_zeroes() {
72 let x: f32 = 0.0_f32;
73 let y: f32 = -0.0_f32;
74 assert!(x.approx_eq_ulps(&y,0) == true);
75}
76
77impl ApproxEqUlps for f64 {
78 type Flt = f64;
79
80 fn approx_eq_ulps(&self, other: &f64, ulps: i64) -> bool {
81 // -0 and +0 are drastically far in ulps terms, so
82 // we need a special case for that.
83 if *self==*other { return true; }
84
85 // Handle differing signs as a special case, even if
86 // they are very close, most people consider them
87 // unequal.
88 if self.is_sign_positive() != other.is_sign_positive() { return false; }
89
90 let diff: i64 = self.ulps(other);
91 diff >= -ulps && diff <= ulps
92 }
93}
94
95#[test]
96fn f64_approx_eq_ulps_test1() {
97 let f: f64 = 0.1_f64;
98 let mut sum: f64 = 0.0_f64;
99 for _ in 0_isize..10_isize { sum += f; }
100 let product: f64 = f * 10.0_f64;
101 assert!(sum != product); // Should not be directly equal:
102 assert!(sum.approx_eq_ulps(&product,1) == true); // But should be close
103 assert!(sum.approx_eq_ulps(&product,0) == false);
104}
105#[test]
106fn f64_approx_eq_ulps_test2() {
107 let x: f64 = 1000000_f64;
108 let y: f64 = 1000000.0000000003_f64;
109 assert!(x != y); // Should not be directly equal
110 assert!(x.approx_eq_ulps(&y,3) == true);
111 assert!(x.approx_eq_ulps(&y,2) == false);
112}
113#[test]
114fn f64_approx_eq_ulps_test_zeroes() {
115 let x: f64 = 0.0_f64;
116 let y: f64 = -0.0_f64;
117 assert!(x.approx_eq_ulps(&y,0) == true);
118}
119