1/**
2 * This file has no copyright assigned and is placed in the Public Domain.
3 * This file is part of the mingw-w64 runtime package.
4 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
5 */
6long double fmal(long double x, long double y, long double z);
7
8#if __SIZEOF_LONG_DOUBLE__ == __SIZEOF_DOUBLE__
9
10double fma(double x, double y, double z);
11
12/* On ARM `long double` is 64 bits. And ARM has hardware FMA. */
13long double fmal(long double x, long double y, long double z){
14 return fma(x, y, z);
15}
16
17#elif defined(_AMD64_) || defined(__x86_64__) || defined(_X86_) || defined(__i386__)
18
19/**
20 * x87-specific software-emulated FMA by LH_Mouse (lh_mouse at 126 dot com).
21 * This file is donated to the mingw-w64 project.
22 * Note: This file requires C99 support to compile.
23 */
24
25#include <math.h>
26#include <stdint.h>
27
28/* See <https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format>.
29 * Note the higher half of the mantissa has fewer significant bits than the lower
30 * half, which reduces rounding errors in the more significant position but increases
31 * them in the other end.
32 */
33typedef union x87reg_ {
34 struct __attribute__((__packed__)) {
35 uint64_t mlo : 33;
36 uint64_t mhi : 31;
37 uint16_t exp : 15;
38 uint16_t sgn : 1;
39 };
40 long double f;
41} x87reg;
42
43static inline void break_down(x87reg *restrict lo, x87reg *restrict hi, long double x) {
44 hi->f = x;
45 /* Erase low-order significant bits. `hi->f` now has only 31 significant bits. */
46 hi->mlo = 0;
47 /* Store the low-order half. It will be normalized by the hardware. */
48 lo->f = x - hi->f;
49 /* Preserve signness in case of zero. */
50 lo->sgn = hi->sgn;
51}
52
53long double fmal(long double x, long double y, long double z) {
54 /*
55 POSIX-2013:
56 1. If x or y are NaN, a NaN shall be returned.
57 2. If x multiplied by y is an exact infinity and z is also an infinity
58 but with the opposite sign, a domain error shall occur, and either a NaN
59 (if supported), or an implementation-defined value shall be returned.
60 3. If one of x and y is infinite, the other is zero, and z is not a NaN,
61 a domain error shall occur, and either a NaN (if supported), or an
62 implementation-defined value shall be returned.
63 4. If one of x and y is infinite, the other is zero, and z is a NaN, a NaN
64 shall be returned and a domain error may occur.
65 5. If x* y is not 0*Inf nor Inf*0 and z is a NaN, a NaN shall be returned.
66 */
67 /* Check whether the result is finite. */
68 long double ret = x * y + z;
69 if(!isfinite(ret)) {
70 return ret; /* If this naive check doesn't yield a finite value, the FMA isn't
71 likely to return one either. Forward the value as is. */
72 }
73 x87reg xlo, xhi, ylo, yhi;
74 break_down(&xlo, &xhi, x);
75 break_down(&ylo, &yhi, y);
76 /* The order of these four statements is essential. Don't move them around. */
77 ret = z;
78 ret += xhi.f * yhi.f; /* The most significant item comes first. */
79 ret += xhi.f * ylo.f + xlo.f * yhi.f; /* They are equally significant. */
80 ret += xlo.f * ylo.f; /* The least significant item comes last. */
81 return ret;
82}
83
84#else
85
86#error Please add FMA implementation for this platform.
87
88#endif