1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
|
/* mpfr_fma -- Floating multiply-add
Copyright 2001, 2002 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute
it and/or modify it under the terms of the GNU Lesser
General Public License as published by the Free Software
Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will
be useful, but WITHOUT ANY WARRANTY; without even the
implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser
General Public License along with the MPFR Library; see
the file COPYING.LIB. If not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of fma of x y and u is done by
fma(s,x,y,z)= z + x*y = s
*/
int
mpfr_fma (mpfr_ptr s, mpfr_srcptr x, mpfr_srcptr y, mpfr_srcptr z,
mp_rnd_t rnd_mode)
{
int inexact = 0;
/* Flag calcul exacte */
int not_exact = 0;
/* particular cases */
if (MPFR_IS_NAN(x) || MPFR_IS_NAN(y) || MPFR_IS_NAN(z))
{
MPFR_SET_NAN(s);
MPFR_RET_NAN;
}
if (MPFR_IS_INF(x) || MPFR_IS_INF(y))
{
/* cases Inf*0+z, 0*Inf+z, Inf-Inf */
if ((MPFR_IS_FP(y) && MPFR_IS_ZERO(y)) ||
(MPFR_IS_FP(x) && MPFR_IS_ZERO(x)) ||
(MPFR_IS_INF(z) && ((MPFR_SIGN(x) * MPFR_SIGN(y)) != MPFR_SIGN(z))))
{
MPFR_SET_NAN(s);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(s);
if (MPFR_IS_INF(z)) /* case Inf-Inf already checked above */
{
MPFR_SET_INF(s);
MPFR_SET_SAME_SIGN(s, z);
MPFR_RET(0);
}
else /* z is finite */
{
MPFR_SET_INF(s);
if (MPFR_SIGN(s) != (MPFR_SIGN(x) * MPFR_SIGN(y)))
MPFR_CHANGE_SIGN(s);
MPFR_RET(0);
}
}
MPFR_CLEAR_NAN(s);
/* now x and y are finite */
if (MPFR_IS_INF(z))
{
MPFR_SET_INF(s);
MPFR_SET_SAME_SIGN(s, z);
MPFR_RET(0);
}
MPFR_CLEAR_INF(s);
if (MPFR_IS_ZERO(x) || MPFR_IS_ZERO(y))
{
if (MPFR_IS_ZERO(z))
{
int sign_p, sign_z;
sign_p = MPFR_SIGN(x) * MPFR_SIGN(y);
sign_z = MPFR_SIGN(z);
if (MPFR_SIGN(s) !=
(rnd_mode != GMP_RNDD ?
((sign_p < 0 && sign_z < 0) ? -1 : 1) :
((sign_p > 0 && sign_z > 0) ? 1 : -1)))
{
MPFR_CHANGE_SIGN(s);
}
MPFR_SET_ZERO(s);
MPFR_RET(0);
}
else
return mpfr_set (s, z, rnd_mode);
}
if (MPFR_IS_ZERO(z))
return mpfr_mul (s, x, y, rnd_mode);
/* General case */
/* Detail of the compute */
/* u <- x*y */
/* t <- z+u */
{
/* Declaration of the intermediary variable */
mpfr_t t, u;
int d;
int accu = 0;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nz = MPFR_PREC(z); /* Precision of input variable */
mp_prec_t Ns = MPFR_PREC(s); /* Precision of output variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
unsigned int first_pass = 0; /* temporary precision */
/* compute the precision of intermediary variable */
Nt = MAX(MAX(Nx,Ny),Nz);
/* the optimal number of bits is MPFR_EXP(u)-MPFR_EXP(v)+1 */
/* but u and v are not yet compute, also we take in account */
/* just one bit */
Nt += 1 + _mpfr_ceil_log2(Nt) + 20;
/* initialise the intermediary variables */
mpfr_init(u);
mpfr_init(t);
/* First computation of fma */
do
{
if (accu++ > 2)
{
mpfr_clear(t);
mpfr_clear(u);
/* General case */
/* Detail of the compute */
/* u <- x*y exact */
/* s <- z+u */
/* if we take prec(u) >= prec(x) + prec(y), the product
u <- x*y is always exact */
mpfr_init2 (u, MPFR_PREC(x) + MPFR_PREC(y));
mpfr_mul (u, x, y, GMP_RNDN); /* always exact */
inexact = mpfr_add (s, z, u, rnd_mode);
mpfr_clear(u);
return inexact;
}
/* reactualisation of the precision */
mpfr_set_prec(u, Nt);
mpfr_set_prec(t, Nt);
/* computations */
not_exact = mpfr_mul (u, x, y, GMP_RNDN);
not_exact |= mpfr_add (t, z, u, GMP_RNDN);
/* Nt = Nt + (d+1) + _mpfr_ceil_log2(Nt); */
d = MPFR_EXP(u) - MPFR_EXP(t);
/* estimate of the error */
err = Nt - (d+1);
/* actualisation of the precision */
Nt += (1-first_pass) * d + first_pass * 10;
if (Nt < 0)
Nt = 0;
first_pass = 1;
}
while (not_exact &&
((err < 0) || !mpfr_can_round (t, err, GMP_RNDN, rnd_mode, Ns)));
inexact = mpfr_set (s, t, rnd_mode);
mpfr_clear(t);
mpfr_clear(u);
}
if (not_exact == 0 && inexact == 0)
return 0;
if (not_exact != 0 && inexact == 0)
return 1;
return inexact;
}
|
