]>
Commit | Line | Data |
---|---|---|
5e908464 | 1 | /* Compute x * y + z as ternary operation. |
2b778ceb | 2 | Copyright (C) 2010-2021 Free Software Foundation, Inc. |
5e908464 | 3 | This file is part of the GNU C Library. |
5e908464 JJ |
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 | |
59ba27a6 | 16 | License along with the GNU C Library; if not, see |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
5e908464 JJ |
18 | |
19 | #include <float.h> | |
20 | #include <math.h> | |
21 | #include <fenv.h> | |
22 | #include <ieee754.h> | |
b4d5b8b0 | 23 | #include <math-barriers.h> |
f85a176f | 24 | #include <libm-alias-double.h> |
5e908464 JJ |
25 | |
26 | /* This implementation uses rounding to odd to avoid problems with | |
27 | double rounding. See a paper by Boldo and Melquiond: | |
28 | http://www.lri.fr/~melquion/doc/08-tc.pdf */ | |
29 | ||
30 | double | |
31 | __fma (double x, double y, double z) | |
32 | { | |
ca121b11 JM |
33 | if (__glibc_unlikely (!isfinite (x) || !isfinite (y))) |
34 | return x * y + z; | |
35 | else if (__glibc_unlikely (!isfinite (z))) | |
36 | /* If z is Inf, but x and y are finite, the result should be z | |
37 | rather than NaN. */ | |
38 | return (z + x) + y; | |
3e692e05 | 39 | |
8ec5b013 | 40 | /* Ensure correct sign of exact 0 + 0. */ |
a1ffb40e | 41 | if (__glibc_unlikely ((x == 0 || y == 0) && z == 0)) |
09245377 L |
42 | { |
43 | x = math_opt_barrier (x); | |
44 | return x * y + z; | |
45 | } | |
8ec5b013 | 46 | |
5b5b04d6 JM |
47 | fenv_t env; |
48 | feholdexcept (&env); | |
49 | fesetround (FE_TONEAREST); | |
50 | ||
5e908464 JJ |
51 | /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ |
52 | #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1) | |
3e692e05 JJ |
53 | long double x1 = (long double) x * C; |
54 | long double y1 = (long double) y * C; | |
55 | long double m1 = (long double) x * y; | |
5e908464 JJ |
56 | x1 = (x - x1) + x1; |
57 | y1 = (y - y1) + y1; | |
58 | long double x2 = x - x1; | |
59 | long double y2 = y - y1; | |
60 | long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; | |
61 | ||
62 | /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ | |
63 | long double a1 = z + m1; | |
64 | long double t1 = a1 - z; | |
65 | long double t2 = a1 - t1; | |
66 | t1 = m1 - t1; | |
67 | t2 = z - t2; | |
68 | long double a2 = t1 + t2; | |
4896f049 RH |
69 | /* Ensure the arithmetic is not scheduled after feclearexcept call. */ |
70 | math_force_eval (m2); | |
71 | math_force_eval (a2); | |
5b5b04d6 JM |
72 | feclearexcept (FE_INEXACT); |
73 | ||
4896f049 | 74 | /* If the result is an exact zero, ensure it has the correct sign. */ |
5b5b04d6 JM |
75 | if (a1 == 0 && m2 == 0) |
76 | { | |
77 | feupdateenv (&env); | |
4896f049 RH |
78 | /* Ensure that round-to-nearest value of z + m1 is not reused. */ |
79 | z = math_opt_barrier (z); | |
5b5b04d6 JM |
80 | return z + m1; |
81 | } | |
5e908464 | 82 | |
5e908464 JJ |
83 | fesetround (FE_TOWARDZERO); |
84 | /* Perform m2 + a2 addition with round to odd. */ | |
85 | a2 = a2 + m2; | |
86 | ||
87 | /* Add that to a1 again using rounding to odd. */ | |
88 | union ieee854_long_double u; | |
89 | u.d = a1 + a2; | |
90 | if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff) | |
91 | u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; | |
92 | feupdateenv (&env); | |
93 | ||
94 | /* Add finally round to double precision. */ | |
95 | return u.d; | |
96 | } | |
97 | #ifndef __fma | |
f85a176f | 98 | libm_alias_double (__fma, fma) |
5e908464 | 99 | #endif |