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
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
|
/* mpn_divrem -- Divide natural numbers, producing both remainder and
quotient.
Copyright (C) 1993-2017 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 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 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library; see the file COPYING.LIB. If not, see
<http://www.gnu.org/licenses/>. */
#include <gmp.h>
#include "gmp-impl.h"
#include "longlong.h"
/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
the NSIZE-DSIZE least significant quotient limbs at QP
and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
non-zero, generate that many fraction bits and append them after the
other quotient limbs.
Return the most significant limb of the quotient, this is always 0 or 1.
Preconditions:
0. NSIZE >= DSIZE.
1. The most significant bit of the divisor must be set.
2. QP must either not overlap with the input operands at all, or
QP + DSIZE >= NP must hold true. (This means that it's
possible to put the quotient in the high part of NUM, right after the
remainder in NUM.
3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */
mp_limb_t
mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs,
mp_ptr np, mp_size_t nsize,
mp_srcptr dp, mp_size_t dsize)
{
mp_limb_t most_significant_q_limb = 0;
switch (dsize)
{
case 0:
/* We are asked to divide by zero, so go ahead and do it! (To make
the compiler not remove this statement, return the value.) */
return 1 / dsize;
case 1:
{
mp_size_t i;
mp_limb_t n1;
mp_limb_t d;
d = dp[0];
n1 = np[nsize - 1];
if (n1 >= d)
{
n1 -= d;
most_significant_q_limb = 1;
}
qp += qextra_limbs;
for (i = nsize - 2; i >= 0; i--)
udiv_qrnnd (qp[i], n1, n1, np[i], d);
qp -= qextra_limbs;
for (i = qextra_limbs - 1; i >= 0; i--)
udiv_qrnnd (qp[i], n1, n1, 0, d);
np[0] = n1;
}
break;
case 2:
{
mp_size_t i;
mp_limb_t n1, n0, n2;
mp_limb_t d1, d0;
np += nsize - 2;
d1 = dp[1];
d0 = dp[0];
n1 = np[1];
n0 = np[0];
if (n1 >= d1 && (n1 > d1 || n0 >= d0))
{
sub_ddmmss (n1, n0, n1, n0, d1, d0);
most_significant_q_limb = 1;
}
for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--)
{
mp_limb_t q;
mp_limb_t r;
if (i >= qextra_limbs)
np--;
else
np[0] = 0;
if (n1 == d1)
{
/* Q should be either 111..111 or 111..110. Need special
treatment of this rare case as normal division would
give overflow. */
q = ~(mp_limb_t) 0;
r = n0 + d1;
if (r < d1) /* Carry in the addition? */
{
add_ssaaaa (n1, n0, r - d0, np[0], 0, d0);
qp[i] = q;
continue;
}
n1 = d0 - (d0 != 0);
n0 = -d0;
}
else
{
udiv_qrnnd (q, r, n1, n0, d1);
umul_ppmm (n1, n0, d0, q);
}
n2 = np[0];
q_test:
if (n1 > r || (n1 == r && n0 > n2))
{
/* The estimated Q was too large. */
q--;
sub_ddmmss (n1, n0, n1, n0, 0, d0);
r += d1;
if (r >= d1) /* If not carry, test Q again. */
goto q_test;
}
qp[i] = q;
sub_ddmmss (n1, n0, r, n2, n1, n0);
}
np[1] = n1;
np[0] = n0;
}
break;
default:
{
mp_size_t i;
mp_limb_t dX, d1, n0;
np += nsize - dsize;
dX = dp[dsize - 1];
d1 = dp[dsize - 2];
n0 = np[dsize - 1];
if (n0 >= dX)
{
if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0)
{
mpn_sub_n (np, np, dp, dsize);
n0 = np[dsize - 1];
most_significant_q_limb = 1;
}
}
for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--)
{
mp_limb_t q;
mp_limb_t n1, n2;
mp_limb_t cy_limb;
if (i >= qextra_limbs)
{
np--;
n2 = np[dsize];
}
else
{
n2 = np[dsize - 1];
MPN_COPY_DECR (np + 1, np, dsize);
np[0] = 0;
}
if (n0 == dX)
/* This might over-estimate q, but it's probably not worth
the extra code here to find out. */
q = ~(mp_limb_t) 0;
else
{
mp_limb_t r;
udiv_qrnnd (q, r, n0, np[dsize - 1], dX);
umul_ppmm (n1, n0, d1, q);
while (n1 > r || (n1 == r && n0 > np[dsize - 2]))
{
q--;
r += dX;
if (r < dX) /* I.e. "carry in previous addition?" */
break;
n1 -= n0 < d1;
n0 -= d1;
}
}
/* Possible optimization: We already have (q * n0) and (1 * n1)
after the calculation of q. Taking advantage of that, we
could make this loop make two iterations less. */
cy_limb = mpn_submul_1 (np, dp, dsize, q);
if (n2 != cy_limb)
{
mpn_add_n (np, np, dp, dsize);
q--;
}
qp[i] = q;
n0 = np[dsize - 1];
}
}
}
return most_significant_q_limb;
}
|
