1 /* Compute x * y + z as ternary operation.
2 Copyright (C) 2010 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, write to the Free
18 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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 */
31 __fma (double x
, double y
, double z
)
33 if (__builtin_expect (isinf (z
), 0))
35 /* If z is Inf, but x and y are finite, the result should be
37 if (finite (x
) && finite (y
))
42 /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
43 #define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
44 long double x1
= (long double) x
* C
;
45 long double y1
= (long double) y
* C
;
46 long double m1
= (long double) x
* y
;
49 long double x2
= x
- x1
;
50 long double y2
= y
- y1
;
51 long double m2
= (((x1
* y1
- m1
) + x1
* y2
) + x2
* y1
) + x2
* y2
;
53 /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
54 long double a1
= z
+ m1
;
55 long double t1
= a1
- z
;
56 long double t2
= a1
- t1
;
59 long double a2
= t1
+ t2
;
63 fesetround (FE_TOWARDZERO
);
64 /* Perform m2 + a2 addition with round to odd. */
67 /* Add that to a1 again using rounding to odd. */
68 union ieee854_long_double u
;
70 if ((u
.ieee
.mantissa1
& 1) == 0 && u
.ieee
.exponent
!= 0x7fff)
71 u
.ieee
.mantissa1
|= fetestexcept (FE_INEXACT
) != 0;
74 /* Add finally round to double precision. */
78 weak_alias (__fma
, fma
)