1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118

// Copyright 2014-2020 Optimal Computing (NZ) Ltd.
// Licensed under the MIT license.  See LICENSE for details.

#[cfg(feature = "num-traits")]
#[allow(unused_imports)]
use num_traits::float::FloatCore;
use super::Ulps;

/// ApproxEqUlps is a trait for approximate equality comparisons.
/// The associated type Flt is a floating point type which implements Ulps, and is
/// required so that this trait can be implemented for compound types (e.g. vectors),
/// not just for the floats themselves.
pub trait ApproxEqUlps {
    type Flt: Ulps;

    /// This method tests for `self` and `other` values to be approximately equal
    /// within ULPs (Units of Least Precision) floating point representations.
    /// Differing signs are always unequal with this method, and zeroes are only
    /// equal to zeroes. Use approx_eq() from the ApproxEq trait if that is more
    /// appropriate.
    fn approx_eq_ulps(&self, other: &Self, ulps: <Self::Flt as Ulps>::U) -> bool;

    /// This method tests for `self` and `other` values to be not approximately
    /// equal within ULPs (Units of Least Precision) floating point representations.
    /// Differing signs are always unequal with this method, and zeroes are only
    /// equal to zeroes. Use approx_eq() from the ApproxEq trait if that is more
    /// appropriate.
    #[inline]
    fn approx_ne_ulps(&self, other: &Self, ulps: <Self::Flt as Ulps>::U) -> bool {
        !self.approx_eq_ulps(other, ulps)
    }
}

impl ApproxEqUlps for f32 {
    type Flt = f32;

    fn approx_eq_ulps(&self, other: &f32, ulps: i32) -> bool {
        // -0 and +0 are drastically far in ulps terms, so
        // we need a special case for that.
        if *self==*other { return true; }

        // Handle differing signs as a special case, even if
        // they are very close, most people consider them
        // unequal.
        if self.is_sign_positive() != other.is_sign_positive() { return false; }

        let diff: i32 = self.ulps(other);
        diff >= -ulps && diff <= ulps
    }
}

#[test]
fn f32_approx_eq_ulps_test1() {
    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:
    assert!(sum.approx_eq_ulps(&product,1) == true); // But should be close
    assert!(sum.approx_eq_ulps(&product,0) == false);
}
#[test]
fn f32_approx_eq_ulps_test2() {
    let x: f32 = 1000000_f32;
    let y: f32 = 1000000.1_f32;
    assert!(x != y); // Should not be directly equal
    assert!(x.approx_eq_ulps(&y,2) == true);
    assert!(x.approx_eq_ulps(&y,1) == false);
}
#[test]
fn f32_approx_eq_ulps_test_zeroes() {
    let x: f32 = 0.0_f32;
    let y: f32 = -0.0_f32;
    assert!(x.approx_eq_ulps(&y,0) == true);
}

impl ApproxEqUlps for f64 {
    type Flt = f64;

    fn approx_eq_ulps(&self, other: &f64, ulps: i64) -> bool {
        // -0 and +0 are drastically far in ulps terms, so
        // we need a special case for that.
        if *self==*other { return true; }

        // Handle differing signs as a special case, even if
        // they are very close, most people consider them
        // unequal.
        if self.is_sign_positive() != other.is_sign_positive() { return false; }

        let diff: i64 = self.ulps(other);
        diff >= -ulps && diff <= ulps
    }
}

#[test]
fn f64_approx_eq_ulps_test1() {
    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:
    assert!(sum.approx_eq_ulps(&product,1) == true); // But should be close
    assert!(sum.approx_eq_ulps(&product,0) == false);
}
#[test]
fn f64_approx_eq_ulps_test2() {
    let x: f64 = 1000000_f64;
    let y: f64 = 1000000.0000000003_f64;
    assert!(x != y); // Should not be directly equal
    assert!(x.approx_eq_ulps(&y,3) == true);
    assert!(x.approx_eq_ulps(&y,2) == false);
}
#[test]
fn f64_approx_eq_ulps_test_zeroes() {
    let x: f64 = 0.0_f64;
    let y: f64 = -0.0_f64;
    assert!(x.approx_eq_ulps(&y,0) == true);
}