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
28 use core::f32;
29 use core::ptr::read_volatile;
30
31 use super::fenv::{
32 feclearexcept, fegetround, feraiseexcept, fesetround, fetestexcept, FE_INEXACT, FE_TONEAREST,
33 FE_TOWARDZERO, FE_UNDERFLOW,
34 };
35
36 /*
37 * Fused multiply-add: Compute x * y + z with a single rounding error.
38 *
39 * A double has more than twice as much precision than a float, so
40 * direct double-precision arithmetic suffices, except where double
41 * rounding occurs.
42 */
43
44 /// Floating multiply add (f32)
45 ///
46 /// Computes `(x*y)+z`, rounded as one ternary operation:
47 /// Computes the value (as if) to infinite precision and rounds once to the result format,
48 /// according to the rounding mode characterized by the value of FLT_ROUNDS.
49 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
fmaf(x: f32, y: f32, mut z: f32) -> f3250 pub fn fmaf(x: f32, y: f32, mut z: f32) -> f32 {
51 let xy: f64;
52 let mut result: f64;
53 let mut ui: u64;
54 let e: i32;
55
56 xy = x as f64 * y as f64;
57 result = xy + z as f64;
58 ui = result.to_bits();
59 e = (ui >> 52) as i32 & 0x7ff;
60 /* Common case: The double precision result is fine. */
61 if (
62 /* not a halfway case */
63 ui & 0x1fffffff) != 0x10000000 ||
64 /* NaN */
65 e == 0x7ff ||
66 /* exact */
67 (result - xy == z as f64 && result - z as f64 == xy) ||
68 /* not round-to-nearest */
69 fegetround() != FE_TONEAREST
70 {
71 /*
72 underflow may not be raised correctly, example:
73 fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f)
74 */
75 if e < 0x3ff - 126 && e >= 0x3ff - 149 && fetestexcept(FE_INEXACT) != 0 {
76 feclearexcept(FE_INEXACT);
77 // prevent `xy + vz` from being CSE'd with `xy + z` above
78 let vz: f32 = unsafe { read_volatile(&z) };
79 result = xy + vz as f64;
80 if fetestexcept(FE_INEXACT) != 0 {
81 feraiseexcept(FE_UNDERFLOW);
82 } else {
83 feraiseexcept(FE_INEXACT);
84 }
85 }
86 z = result as f32;
87 return z;
88 }
89
90 /*
91 * If result is inexact, and exactly halfway between two float values,
92 * we need to adjust the low-order bit in the direction of the error.
93 */
94 fesetround(FE_TOWARDZERO);
95 // prevent `vxy + z` from being CSE'd with `xy + z` above
96 let vxy: f64 = unsafe { read_volatile(&xy) };
97 let mut adjusted_result: f64 = vxy + z as f64;
98 fesetround(FE_TONEAREST);
99 if result == adjusted_result {
100 ui = adjusted_result.to_bits();
101 ui += 1;
102 adjusted_result = f64::from_bits(ui);
103 }
104 z = adjusted_result as f32;
105 z
106 }
107