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
206
207
208
209
|
/* mpfr_get_ld, mpfr_get_ld_2exp -- convert a multiple precision floating-point
number to a machine long double
Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 GNU 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 GNU MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include <float.h>
#include "mpfr-impl.h"
#ifndef HAVE_LDOUBLE_IEEE_EXT_LITTLE
long double
mpfr_get_ld (mpfr_srcptr x, mp_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return (long double) mpfr_get_d (x, rnd_mode);
else /* now x is a normal non-zero number */
{
long double r; /* result */
long double m;
double s; /* part of result */
mp_exp_t sh; /* exponent shift, so that x/2^sh is in the double range */
mpfr_t y, z;
int sign;
/* first round x to the target long double precision, so that
all subsequent operations are exact (this avoids double rounding
problems) */
mpfr_init2 (y, MPFR_LDBL_MANT_DIG);
mpfr_init2 (z, IEEE_DBL_MANT_DIG);
mpfr_set (y, x, rnd_mode);
sh = MPFR_GET_EXP (y);
sign = MPFR_SIGN (y);
MPFR_SET_EXP (y, 0);
MPFR_SET_POS (y);
r = 0.0;
do {
s = mpfr_get_d (y, GMP_RNDN); /* high part of y */
r += (long double) s;
mpfr_set_d (z, s, GMP_RNDN); /* exact */
mpfr_sub (y, y, z, GMP_RNDN); /* exact */
} while (!MPFR_IS_ZERO (y));
mpfr_clear (z);
mpfr_clear (y);
/* we now have to multiply back by 2^sh */
MPFR_ASSERTD (r > 0);
if (sh != 0)
{
/* An overflow may occurs (example: 0.5*2^1024) */
while (r < 1.0)
{
r += r;
sh--;
}
if (sh > 0)
m = 2.0;
else
{
m = 0.5;
sh = -sh;
}
for (;;)
{
if (sh % 2)
r = r * m;
sh >>= 1;
if (sh == 0)
break;
m = m * m;
}
}
if (sign < 0)
r = -r;
return r;
}
}
#else
long double
mpfr_get_ld (mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_long_double_t ld;
mpfr_t tmp;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_SAVE_EXPO_MARK (expo);
mpfr_set_emin (-16382-63);
mpfr_set_emax (16383);
mpfr_init2 (tmp, MPFR_LDBL_MANT_DIG);
mpfr_subnormalize(tmp, mpfr_set (tmp, x, rnd_mode), rnd_mode);
mpfr_prec_round (tmp, 64, GMP_RNDZ); /* exact */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (tmp)))
ld.ld = (long double) mpfr_get_d (tmp, rnd_mode);
else
{
mp_limb_t *tmpmant;
mp_exp_t e, denorm;
tmpmant = MPFR_MANT (tmp);
e = MPFR_GET_EXP (tmp);
denorm = MPFR_UNLIKELY (e < -16382) ? - e - 16382 + 1 : 0;
#if BITS_PER_MP_LIMB >= 64
ld.s.manl = (tmpmant[0] >> denorm);
ld.s.manh = (tmpmant[0] >> denorm) >> 32;
#elif BITS_PER_MP_LIMB == 32
if (MPFR_LIKELY (denorm == 0))
{
ld.s.manl = tmpmant[0];
ld.s.manh = tmpmant[1];
}
else if (denorm < 32)
{
ld.s.manl = (tmpmant[0] >> denorm) | (tmpmant[1] << (32 - denorm));
ld.s.manh = tmpmant[1] >> denorm;
}
else /* 32 <= denorm <= 64 */
{
ld.s.manl = tmpmant[1] >> (denorm - 32);
ld.s.manh = 0;
}
#else
# error "BITS_PER_MP_LIMB must be 32 or >= 64"
/* Other values have never been supported anyway. */
#endif
if (MPFR_LIKELY (denorm == 0))
{
ld.s.exph = (e + 0x3FFE) >> 8;
ld.s.expl = (e + 0x3FFE);
}
else
ld.s.exph = ld.s.expl = 0;
ld.s.sign = MPFR_IS_NEG (x);
}
mpfr_clear (tmp);
MPFR_SAVE_EXPO_FREE (expo);
return ld.ld;
}
#endif
/* contributed by Damien Stehle */
long double
mpfr_get_ld_2exp (long *expptr, mpfr_srcptr src, mp_rnd_t rnd_mode)
{
long double ret;
mp_exp_t exp;
mpfr_t tmp;
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
return (long double) mpfr_get_d_2exp (expptr, src, rnd_mode);
tmp[0] = *src; /* Hack copy mpfr_t */
MPFR_SET_EXP (tmp, 0);
ret = mpfr_get_ld (tmp, rnd_mode);
if (MPFR_IS_PURE_FP(src))
{
exp = MPFR_GET_EXP (src);
/* rounding can give 1.0, adjust back to 0.5 <= abs(ret) < 1.0 */
if (ret == 1.0)
{
ret = 0.5;
exp ++;
}
else if (ret == -1.0)
{
ret = -0.5;
exp ++;
}
MPFR_ASSERTN ((ret >= 0.5 && ret < 1.0)
|| (ret <= -0.5 && ret > -1.0));
MPFR_ASSERTN (exp >= LONG_MIN && exp <= LONG_MAX);
}
else
exp = 0;
*expptr = exp;
return ret;
}
|
