1 | /* Compute x * y + z as ternary operation. |
2 | Copyright (C) 2010-2022 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <https://www.gnu.org/licenses/>. */ |
18 | |
19 | #define NO_MATH_REDIRECT |
20 | #include <float.h> |
21 | #define dfmal __hide_dfmal |
22 | #define f32xfmaf64 __hide_f32xfmaf64 |
23 | #include <math.h> |
24 | #undef dfmal |
25 | #undef f32xfmaf64 |
26 | #include <fenv.h> |
27 | #include <ieee754.h> |
28 | #include <math-barriers.h> |
29 | #include <libm-alias-double.h> |
30 | #include <math-narrow-alias.h> |
31 | |
32 | /* This implementation uses rounding to odd to avoid problems with |
33 | double rounding. See a paper by Boldo and Melquiond: |
34 | http://www.lri.fr/~melquion/doc/08-tc.pdf */ |
35 | |
36 | double |
37 | __fma (double x, double y, double z) |
38 | { |
39 | if (__glibc_unlikely (!isfinite (x) || !isfinite (y))) |
40 | return x * y + z; |
41 | else if (__glibc_unlikely (!isfinite (z))) |
42 | /* If z is Inf, but x and y are finite, the result should be z |
43 | rather than NaN. */ |
44 | return (z + x) + y; |
45 | |
46 | /* Ensure correct sign of exact 0 + 0. */ |
47 | if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) |
48 | { |
49 | x = math_opt_barrier (x); |
50 | return x * y + z; |
51 | } |
52 | |
53 | fenv_t env; |
54 | feholdexcept (envp: &env); |
55 | fesetround (FE_TONEAREST); |
56 | |
57 | /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ |
58 | #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1) |
59 | long double x1 = (long double) x * C; |
60 | long double y1 = (long double) y * C; |
61 | long double m1 = (long double) x * y; |
62 | x1 = (x - x1) + x1; |
63 | y1 = (y - y1) + y1; |
64 | long double x2 = x - x1; |
65 | long double y2 = y - y1; |
66 | long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; |
67 | |
68 | /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ |
69 | long double a1 = z + m1; |
70 | long double t1 = a1 - z; |
71 | long double t2 = a1 - t1; |
72 | t1 = m1 - t1; |
73 | t2 = z - t2; |
74 | long double a2 = t1 + t2; |
75 | /* Ensure the arithmetic is not scheduled after feclearexcept call. */ |
76 | math_force_eval (m2); |
77 | math_force_eval (a2); |
78 | feclearexcept (FE_INEXACT); |
79 | |
80 | /* If the result is an exact zero, ensure it has the correct sign. */ |
81 | if (a1 == 0 && m2 == 0) |
82 | { |
83 | feupdateenv (envp: &env); |
84 | /* Ensure that round-to-nearest value of z + m1 is not reused. */ |
85 | z = math_opt_barrier (z); |
86 | return z + m1; |
87 | } |
88 | |
89 | fesetround (FE_TOWARDZERO); |
90 | /* Perform m2 + a2 addition with round to odd. */ |
91 | a2 = a2 + m2; |
92 | |
93 | /* Add that to a1 again using rounding to odd. */ |
94 | union ieee854_long_double u; |
95 | u.d = a1 + a2; |
96 | if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff) |
97 | u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; |
98 | feupdateenv (envp: &env); |
99 | |
100 | /* Add finally round to double precision. */ |
101 | return u.d; |
102 | } |
103 | #ifndef __fma |
104 | libm_alias_double (__fma, fma) |
105 | libm_alias_double_narrow (__fma, fma) |
106 | #endif |
107 | |