libm/math/fmaf.rs
1/* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */
2/*-
3 * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28use core::f32;
29use core::ptr::read_volatile;
30
31use super::fenv::{
32 FE_INEXACT, FE_TONEAREST, FE_UNDERFLOW, feclearexcept, fegetround, feraiseexcept, fetestexcept,
33};
34
35/*
36 * Fused multiply-add: Compute x * y + z with a single rounding error.
37 *
38 * A double has more than twice as much precision than a float, so
39 * direct double-precision arithmetic suffices, except where double
40 * rounding occurs.
41 */
42
43/// Floating multiply add (f32)
44///
45/// Computes `(x*y)+z`, rounded as one ternary operation:
46/// Computes the value (as if) to infinite precision and rounds once to the result format,
47/// according to the rounding mode characterized by the value of FLT_ROUNDS.
48#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
49pub fn fmaf(x: f32, y: f32, mut z: f32) -> f32 {
50 let xy: f64;
51 let mut result: f64;
52 let mut ui: u64;
53 let e: i32;
54
55 xy = x as f64 * y as f64;
56 result = xy + z as f64;
57 ui = result.to_bits();
58 e = (ui >> 52) as i32 & 0x7ff;
59 /* Common case: The double precision result is fine. */
60 if (
61 /* not a halfway case */
62 ui & 0x1fffffff) != 0x10000000 ||
63 /* NaN */
64 e == 0x7ff ||
65 /* exact */
66 (result - xy == z as f64 && result - z as f64 == xy) ||
67 /* not round-to-nearest */
68 fegetround() != FE_TONEAREST
69 {
70 /*
71 underflow may not be raised correctly, example:
72 fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f)
73 */
74 if e < 0x3ff - 126 && e >= 0x3ff - 149 && fetestexcept(FE_INEXACT) != 0 {
75 feclearexcept(FE_INEXACT);
76 // prevent `xy + vz` from being CSE'd with `xy + z` above
77 let vz: f32 = unsafe { read_volatile(&z) };
78 result = xy + vz as f64;
79 if fetestexcept(FE_INEXACT) != 0 {
80 feraiseexcept(FE_UNDERFLOW);
81 } else {
82 feraiseexcept(FE_INEXACT);
83 }
84 }
85 z = result as f32;
86 return z;
87 }
88
89 /*
90 * If result is inexact, and exactly halfway between two float values,
91 * we need to adjust the low-order bit in the direction of the error.
92 */
93 let neg = ui >> 63 != 0;
94 let err = if neg == (z as f64 > xy) { xy - result + z as f64 } else { z as f64 - result + xy };
95 if neg == (err < 0.0) {
96 ui += 1;
97 } else {
98 ui -= 1;
99 }
100 f64::from_bits(ui) as f32
101}
102
103#[cfg(test)]
104mod tests {
105 #[test]
106 fn issue_263() {
107 let a = f32::from_bits(1266679807);
108 let b = f32::from_bits(1300234242);
109 let c = f32::from_bits(1115553792);
110 let expected = f32::from_bits(1501560833);
111 assert_eq!(super::fmaf(a, b, c), expected);
112 }
113}