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
|
/* mpz_powm_ui(res,base,exp,mod) -- Set RES to (base**exp) mod MOD.
Copyright 1991, 1993, 1994, 1996, 1997, 2000, 2001, 2002 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, 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"
/* Compute t = a mod m, a is defined by (ap,an), m is defined by (mp,mn), and
t is defined by (tp,mn). */
static void
reduce (mp_ptr tp, mp_srcptr ap, mp_size_t an, mp_srcptr mp, mp_size_t mn)
{
mp_ptr qp;
TMP_DECL (marker);
TMP_MARK (marker);
qp = TMP_ALLOC_LIMBS (an - mn + 1);
mpn_tdiv_qr (qp, tp, 0L, ap, an, mp, mn);
TMP_FREE (marker);
}
void
mpz_powm_ui (mpz_ptr r, mpz_srcptr b, unsigned long int el, mpz_srcptr m)
{
mp_ptr xp, tp, qp, mp, bp;
mp_size_t xn, tn, mn, bn;
int m_zero_cnt;
int c;
mp_limb_t e;
TMP_DECL (marker);
mp = PTR(m);
mn = ABSIZ(m);
if (mn == 0)
DIVIDE_BY_ZERO;
if (el == 0)
{
/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
depending on if MOD equals 1. */
SIZ(r) = (mn == 1 && mp[0] == 1) ? 0 : 1;
PTR(r)[0] = 1;
return;
}
TMP_MARK (marker);
/* Normalize m (i.e. make its most significant bit set) as required by
division functions below. */
count_leading_zeros (m_zero_cnt, mp[mn - 1]);
m_zero_cnt -= GMP_NAIL_BITS;
if (m_zero_cnt != 0)
{
mp_ptr new_mp = TMP_ALLOC_LIMBS (mn);
mpn_lshift (new_mp, mp, mn, m_zero_cnt);
mp = new_mp;
}
bn = ABSIZ(b);
bp = PTR(b);
if (bn > mn)
{
/* Reduce possibly huge base. Use a function call to reduce, since we
don't want the quotient allocation to live until function return. */
mp_ptr new_bp = TMP_ALLOC_LIMBS (mn);
reduce (new_bp, bp, bn, mp, mn);
bp = new_bp;
bn = mn;
/* Canonicalize the base, since we are potentially going to multiply with
it quite a few times. */
MPN_NORMALIZE (bp, bn);
}
if (bn == 0)
{
SIZ(r) = 0;
TMP_FREE (marker);
return;
}
tp = TMP_ALLOC_LIMBS (2 * mn + 1);
xp = TMP_ALLOC_LIMBS (mn);
qp = TMP_ALLOC_LIMBS (mn + 1);
MPN_COPY (xp, bp, bn);
xn = bn;
e = el;
count_leading_zeros (c, e);
e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
c = BITS_PER_MP_LIMB - 1 - c;
/* Main loop. */
/* If m is already normalized (high bit of high limb set), and b is the
same size, but a bigger value, and e==1, then there's no modular
reductions done and we can end up with a result out of range at the
end. */
if (c == 0)
{
if (xn == mn && mpn_cmp (xp, mp, mn) >= 0)
mpn_sub_n (xp, xp, mp, mn);
goto finishup;
}
while (c != 0)
{
mpn_sqr_n (tp, xp, xn);
tn = 2 * xn; tn -= tp[tn - 1] == 0;
if (tn < mn)
{
MPN_COPY (xp, tp, tn);
xn = tn;
}
else
{
mpn_tdiv_qr (qp, xp, 0L, tp, tn, mp, mn);
xn = mn;
}
if ((mp_limb_signed_t) e < 0)
{
mpn_mul (tp, xp, xn, bp, bn);
tn = xn + bn; tn -= tp[tn - 1] == 0;
if (tn < mn)
{
MPN_COPY (xp, tp, tn);
xn = tn;
}
else
{
mpn_tdiv_qr (qp, xp, 0L, tp, tn, mp, mn);
xn = mn;
}
}
e <<= 1;
c--;
}
finishup:
/* We shifted m left m_zero_cnt steps. Adjust the result by reducing
it with the original MOD. */
if (m_zero_cnt != 0)
{
mp_limb_t cy;
cy = mpn_lshift (tp, xp, xn, m_zero_cnt);
tp[xn] = cy; xn += cy != 0;
if (xn < mn)
{
MPN_COPY (xp, tp, xn);
}
else
{
mpn_tdiv_qr (qp, xp, 0L, tp, xn, mp, mn);
xn = mn;
}
mpn_rshift (xp, xp, xn, m_zero_cnt);
}
MPN_NORMALIZE (xp, xn);
if ((el & 1) != 0 && SIZ(b) < 0 && xn != 0)
{
mp = PTR(m); /* want original, unnormalized m */
mpn_sub (xp, mp, mn, xp, xn);
xn = mn;
MPN_NORMALIZE (xp, xn);
}
MPZ_REALLOC (r, xn);
SIZ (r) = xn;
MPN_COPY (PTR(r), xp, xn);
TMP_FREE (marker);
}
|
