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
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151

/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
/// error, yielding a more accurate result than an unfused multiply-add.
///
/// Using `mul_add` can be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction.
///
/// Note that `A` and `B` are `Self` by default, but this is not mandatory.
///
/// # Example
///
/// ```
/// use std::f32;
///
/// let m = 10.0_f32;
/// let x = 4.0_f32;
/// let b = 60.0_f32;
///
/// // 100.0
/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
///
/// assert!(abs_difference <= 100.0 * f32::EPSILON);
/// ```
pub trait MulAdd<A = Self, B = Self> {
    /// The resulting type after applying the fused multiply-add.
    type Output;

    /// Performs the fused multiply-add operation.
    fn mul_add(self, a: A, b: B) -> Self::Output;
}

/// The fused multiply-add assignment operation.
pub trait MulAddAssign<A = Self, B = Self> {
    /// Performs the fused multiply-add operation.
    fn mul_add_assign(&mut self, a: A, b: B);
}

#[cfg(any(feature = "std", feature = "libm"))]
impl MulAdd<f32, f32> for f32 {
    type Output = Self;

    #[inline]
    fn mul_add(self, a: Self, b: Self) -> Self::Output {
        <Self as ::Float>::mul_add(self, a, b)
    }
}

#[cfg(any(feature = "std", feature = "libm"))]
impl MulAdd<f64, f64> for f64 {
    type Output = Self;

    #[inline]
    fn mul_add(self, a: Self, b: Self) -> Self::Output {
        <Self as ::Float>::mul_add(self, a, b)
    }
}

macro_rules! mul_add_impl {
    ($trait_name:ident for $($t:ty)*) => {$(
        impl $trait_name for $t {
            type Output = Self;

            #[inline]
            fn mul_add(self, a: Self, b: Self) -> Self::Output {
                (self * a) + b
            }
        }
    )*}
}

mul_add_impl!(MulAdd for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
#[cfg(has_i128)]
mul_add_impl!(MulAdd for i128 u128);

#[cfg(any(feature = "std", feature = "libm"))]
impl MulAddAssign<f32, f32> for f32 {
    #[inline]
    fn mul_add_assign(&mut self, a: Self, b: Self) {
        *self = <Self as ::Float>::mul_add(*self, a, b)
    }
}

#[cfg(any(feature = "std", feature = "libm"))]
impl MulAddAssign<f64, f64> for f64 {
    #[inline]
    fn mul_add_assign(&mut self, a: Self, b: Self) {
        *self = <Self as ::Float>::mul_add(*self, a, b)
    }
}

macro_rules! mul_add_assign_impl {
    ($trait_name:ident for $($t:ty)*) => {$(
        impl $trait_name for $t {
            #[inline]
            fn mul_add_assign(&mut self, a: Self, b: Self) {
                *self = (*self * a) + b
            }
        }
    )*}
}

mul_add_assign_impl!(MulAddAssign for isize usize i8 u8 i16 u16 i32 u32 i64 u64);
#[cfg(has_i128)]
mul_add_assign_impl!(MulAddAssign for i128 u128);

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn mul_add_integer() {
        macro_rules! test_mul_add {
            ($($t:ident)+) => {
                $(
                    {
                        let m: $t = 2;
                        let x: $t = 3;
                        let b: $t = 4;

                        assert_eq!(MulAdd::mul_add(m, x, b), (m*x + b));
                    }
                )+
            };
        }

        test_mul_add!(usize u8 u16 u32 u64 isize i8 i16 i32 i64);
    }

    #[test]
    #[cfg(feature = "std")]
    fn mul_add_float() {
        macro_rules! test_mul_add {
            ($($t:ident)+) => {
                $(
                    {
                        use core::$t;

                        let m: $t = 12.0;
                        let x: $t = 3.4;
                        let b: $t = 5.6;

                        let abs_difference = (MulAdd::mul_add(m, x, b) - (m*x + b)).abs();

                        assert!(abs_difference <= 46.4 * $t::EPSILON);
                    }
                )+
            };
        }

        test_mul_add!(f32 f64);
    }
}