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
|
/* double mpq_get_d (mpq_t src) -- Return the double approximation to SRC.
Copyright (C) 1995, 1996 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.
The GNU MP 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 Library General Public
License for more details.
You should have received a copy of the GNU Library General Public License
along with the GNU MP 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 "longlong.h"
/* Algorithm:
1. Develop >= n bits of src.num / src.den, where n is the number of bits
in a double. This (partial) division will use all bits from the
denominator.
2. Use the remainder to determine how to round the result.
3. Assign the integral result to a temporary double.
4. Scale the temporary double, and return the result.
An alternative algorithm, that would be faster:
0. Let n be somewhat larger than the number of significant bits in a double.
1. Extract the most significant n bits of the denominator, and an equal
number of bits from the numerator.
2. Interpret the extracted numbers as integers, call them a and b
respectively, and develop n bits of the fractions ((a + 1) / b) and
(a / (b + 1)) using mpn_divrem.
3. If the computed values are identical UP TO THE POSITION WE CARE ABOUT,
we are done. If they are different, repeat the algorithm from step 1,
but first let n = n * 2.
4. If we end up using all bits from the numerator and denominator, fall
back to the first algorithm above.
5. Just to make life harder, The computation of a + 1 and b + 1 above
might give carry-out... Needs special handling. It might work to
subtract 1 in both cases instead.
*/
double
#if __STDC__
mpq_get_d (const MP_RAT *src)
#else
mpq_get_d (src)
const MP_RAT *src;
#endif
{
mp_ptr np, dp;
mp_ptr rp;
mp_size_t nsize = src->_mp_num._mp_size;
mp_size_t dsize = src->_mp_den._mp_size;
mp_size_t qsize, rsize;
mp_size_t sign_quotient = nsize ^ dsize;
unsigned normalization_steps;
mp_limb_t qlimb;
#define N_QLIMBS (1 + (sizeof (double) + BYTES_PER_MP_LIMB-1) / BYTES_PER_MP_LIMB)
mp_limb_t qp[N_QLIMBS + 1];
TMP_DECL (marker);
if (nsize == 0)
return 0.0;
TMP_MARK (marker);
nsize = ABS (nsize);
dsize = ABS (dsize);
np = src->_mp_num._mp_d;
dp = src->_mp_den._mp_d;
rsize = dsize + N_QLIMBS;
rp = (mp_ptr) TMP_ALLOC ((rsize + 1) * BYTES_PER_MP_LIMB);
count_leading_zeros (normalization_steps, dp[dsize - 1]);
/* Normalize the denominator, i.e. make its most significant bit set by
shifting it NORMALIZATION_STEPS bits to the left. Also shift the
numerator the same number of steps (to keep the quotient the same!). */
if (normalization_steps != 0)
{
mp_ptr tp;
mp_limb_t nlimb;
/* Shift up the denominator setting the most significant bit of
the most significant limb. Use temporary storage not to clobber
the original contents of the denominator. */
tp = (mp_ptr) TMP_ALLOC (dsize * BYTES_PER_MP_LIMB);
mpn_lshift (tp, dp, dsize, normalization_steps);
dp = tp;
if (rsize > nsize)
{
MPN_ZERO (rp, rsize - nsize);
nlimb = mpn_lshift (rp + (rsize - nsize),
np, nsize, normalization_steps);
}
else
{
nlimb = mpn_lshift (rp, np + (nsize - rsize),
rsize, normalization_steps);
}
if (nlimb != 0)
{
rp[rsize] = nlimb;
rsize++;
}
}
else
{
if (rsize > nsize)
{
MPN_ZERO (rp, rsize - nsize);
MPN_COPY (rp + (rsize - nsize), np, nsize);
}
else
{
MPN_COPY (rp, np + (nsize - rsize), rsize);
}
}
qlimb = mpn_divmod (qp, rp, rsize, dp, dsize);
qsize = rsize - dsize;
if (qlimb)
{
qp[qsize] = qlimb;
qsize++;
}
{
double res;
mp_size_t i;
res = qp[qsize - 1];
for (i = qsize - 2; i >= 0; i--)
res = res * MP_BASE_AS_DOUBLE + qp[i];
res = __gmp_scale2 (res, BITS_PER_MP_LIMB * (nsize - dsize - N_QLIMBS));
TMP_FREE (marker);
return sign_quotient >= 0 ? res : -res;
}
}
|
