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
|
/* mpfr_mul -- multiply two floating-point numbers
Copyright 1999, 2000, 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. 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"
int
mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
{
int sign_product, cc, inexact, ec, em = 0;
mp_exp_t bx, cx;
mp_limb_t *ap, *bp, *cp, *tmp;
mp_limb_t b1;
mp_prec_t aq, bq, cq;
mp_size_t an, bn, cn, tn, k;
TMP_DECL(marker);
/* deal with NaN and zero */
if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(a);
sign_product = MPFR_SIGN(b) * MPFR_SIGN(c);
if (MPFR_IS_INF(b))
{
if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
{
if (MPFR_SIGN(a) != sign_product)
MPFR_CHANGE_SIGN(a);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF(c))
{
if (MPFR_NOTZERO(b))
{
if (MPFR_SIGN(a) != sign_product)
MPFR_CHANGE_SIGN(a);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
MPFR_ASSERTN(MPFR_IS_FP(b) && MPFR_IS_FP(c));
MPFR_CLEAR_INF(a); /* clear Inf flag */
if (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c))
{
if (MPFR_SIGN(a) != sign_product)
MPFR_CHANGE_SIGN(a);
MPFR_SET_ZERO(a);
MPFR_RET(0); /* 0 * 0 is exact */
}
bx = MPFR_EXP(b);
cx = MPFR_EXP(c);
/* Note: exponent of the result will be bx + cx + ec with ec in {-1,0,1} */
if (bx >= 0 && cx > 0)
{ /* bx + cx > 0 */
if (__mpfr_emax < 0 ||
(mp_exp_unsigned_t) bx + cx > (mp_exp_unsigned_t) __mpfr_emax + 1)
return mpfr_set_overflow(a, rnd_mode, sign_product);
if ((mp_exp_unsigned_t) bx + cx == (mp_exp_unsigned_t) __mpfr_emax + 1)
em = 1;
}
else if (bx <= 0 && cx < 0)
{ /* bx + cx < 0 */
if (__mpfr_emin > 0 ||
(mp_exp_unsigned_t) bx + cx < (mp_exp_unsigned_t) __mpfr_emin - 1)
return mpfr_set_underflow(a, rnd_mode, sign_product);
if ((mp_exp_unsigned_t) bx + cx == (mp_exp_unsigned_t) __mpfr_emin - 1)
em = -1;
}
else
{ /* bx != 0 and cx doesn't have the same sign */
if ((bx + cx) - 1 > __mpfr_emax)
return mpfr_set_overflow(a, rnd_mode, sign_product);
if ((bx + cx) - 1 == __mpfr_emax)
em = 1;
if ((bx + cx) + 1 < __mpfr_emin)
return mpfr_set_underflow(a, rnd_mode, sign_product);
if ((bx + cx) + 1 == __mpfr_emin)
em = -1;
}
ap = MPFR_MANT(a);
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
aq = MPFR_PREC(a);
bq = MPFR_PREC(b);
cq = MPFR_PREC(c);
an = (aq-1)/BITS_PER_MP_LIMB + 1; /* number of significant limbs of a */
bn = (bq-1)/BITS_PER_MP_LIMB + 1; /* number of significant limbs of b */
cn = (cq-1)/BITS_PER_MP_LIMB + 1; /* number of significant limbs of c */
MPFR_ASSERTN((mp_size_unsigned_t) bn + cn <= MP_SIZE_T_MAX);
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
MPFR_ASSERTN(bq + cq >= bq); /* no integer overflow */
tn = (bq + cq - 1) / BITS_PER_MP_LIMB + 1; /* <= k, thus no int overflow */
MPFR_ASSERTN(k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
TMP_MARK(marker);
tmp = (mp_limb_t *) TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);
/* multiplies two mantissa in temporary allocated space */
b1 = (bn >= cn) ? mpn_mul (tmp, bp, bn, cp, cn)
: mpn_mul (tmp, cp, cn, bp, bn);
/* now tmp[0]..tmp[k-1] contains the product of both mantissa,
with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
b1 >>= BITS_PER_MP_LIMB - 1; /* msb from the product */
tmp += k - tn;
if (b1 == 0)
mpn_lshift (tmp, tmp, tn, 1);
cc = mpfr_round_raw (ap, tmp, bq + cq, sign_product < 0, aq,
rnd_mode, &inexact);
if (cc) /* cc = 1 ==> result is a power of two */
ap[an-1] = MP_LIMB_T_HIGHBIT;
TMP_FREE(marker);
ec = b1 - 1 + cc;
if (em == 0)
{
mp_exp_t ax = bx + cx;
if (ax == __mpfr_emax && ec > 0)
return mpfr_set_overflow(a, rnd_mode, sign_product);
if (ax == __mpfr_emin && ec < 0)
return mpfr_set_underflow(a, rnd_mode, sign_product);
MPFR_EXP(a) = ax + ec;
}
else if (em > 0)
{
if (ec >= 0)
return mpfr_set_overflow(a, rnd_mode, sign_product);
MPFR_EXP(a) = __mpfr_emax;
}
else
{
if (ec <= 0)
return mpfr_set_underflow(a, rnd_mode, sign_product);
MPFR_EXP(a) = __mpfr_emin;
}
if (MPFR_SIGN(a) != sign_product)
MPFR_CHANGE_SIGN(a);
return inexact;
}
|
