1 /* mpz_powm_ui(res,base,exp,mod) -- Set RES to (base**exp) mod MOD.
2
3 Copyright 1991, 1993, 1994, 1996, 1997, 2000, 2001, 2002, 2005 Free Software
4 Foundation, Inc.
5
6 This file is part of the GNU MP Library.
7
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of the GNU Lesser General Public License as published by
10 the Free Software Foundation; either version 3 of the License, or (at your
11 option) any later version.
12
13 The GNU MP Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
17
18 You should have received a copy of the GNU Lesser General Public License
19 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
20
21
22 #include "gmp.h"
23 #include "gmp-impl.h"
24 #include "longlong.h"
25
26 /* Compute t = a mod m, a is defined by (ap,an), m is defined by (mp,mn), and
27 t is defined by (tp,mn). */
28 static void
reduce(mp_ptr tp,mp_srcptr ap,mp_size_t an,mp_srcptr mp,mp_size_t mn)29 reduce (mp_ptr tp, mp_srcptr ap, mp_size_t an, mp_srcptr mp, mp_size_t mn)
30 {
31 mp_ptr qp;
32 TMP_DECL;
33
34 TMP_MARK;
35 qp = TMP_ALLOC_LIMBS (an - mn + 1);
36
37 mpn_tdiv_qr (qp, tp, 0L, ap, an, mp, mn);
38
39 TMP_FREE;
40 }
41
42 void
mpz_powm_ui(mpz_ptr r,mpz_srcptr b,unsigned long int el,mpz_srcptr m)43 mpz_powm_ui (mpz_ptr r, mpz_srcptr b, unsigned long int el, mpz_srcptr m)
44 {
45 mp_ptr xp, tp, qp, mp, bp;
46 mp_size_t xn, tn, mn, bn;
47 int m_zero_cnt;
48 int c;
49 mp_limb_t e;
50 TMP_DECL;
51
52 mp = PTR(m);
53 mn = ABSIZ(m);
54 if (mn == 0)
55 DIVIDE_BY_ZERO;
56
57 if (el == 0)
58 {
59 /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
60 depending on if MOD equals 1. */
61 SIZ(r) = (mn == 1 && mp[0] == 1) ? 0 : 1;
62 PTR(r)[0] = 1;
63 return;
64 }
65
66 TMP_MARK;
67
68 /* Normalize m (i.e. make its most significant bit set) as required by
69 division functions below. */
70 count_leading_zeros (m_zero_cnt, mp[mn - 1]);
71 m_zero_cnt -= GMP_NAIL_BITS;
72 if (m_zero_cnt != 0)
73 {
74 mp_ptr new_mp = TMP_ALLOC_LIMBS (mn);
75 mpn_lshift (new_mp, mp, mn, m_zero_cnt);
76 mp = new_mp;
77 }
78
79 bn = ABSIZ(b);
80 bp = PTR(b);
81 if (bn > mn)
82 {
83 /* Reduce possibly huge base. Use a function call to reduce, since we
84 don't want the quotient allocation to live until function return. */
85 mp_ptr new_bp = TMP_ALLOC_LIMBS (mn);
86 reduce (new_bp, bp, bn, mp, mn);
87 bp = new_bp;
88 bn = mn;
89 /* Canonicalize the base, since we are potentially going to multiply with
90 it quite a few times. */
91 MPN_NORMALIZE (bp, bn);
92 }
93
94 if (bn == 0)
95 {
96 SIZ(r) = 0;
97 TMP_FREE;
98 return;
99 }
100
101 tp = TMP_ALLOC_LIMBS (2 * mn + 1);
102 xp = TMP_ALLOC_LIMBS (mn);
103
104 qp = TMP_ALLOC_LIMBS (mn + 1);
105
106 MPN_COPY (xp, bp, bn);
107 xn = bn;
108
109 e = el;
110 count_leading_zeros (c, e);
111 e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
112 c = GMP_LIMB_BITS - 1 - c;
113
114 /* Main loop. */
115
116 /* If m is already normalized (high bit of high limb set), and b is the
117 same size, but a bigger value, and e==1, then there's no modular
118 reductions done and we can end up with a result out of range at the
119 end. */
120 if (c == 0)
121 {
122 if (xn == mn && mpn_cmp (xp, mp, mn) >= 0)
123 mpn_sub_n (xp, xp, mp, mn);
124 goto finishup;
125 }
126
127 while (c != 0)
128 {
129 mpn_sqr (tp, xp, xn);
130 tn = 2 * xn; tn -= tp[tn - 1] == 0;
131 if (tn < mn)
132 {
133 MPN_COPY (xp, tp, tn);
134 xn = tn;
135 }
136 else
137 {
138 mpn_tdiv_qr (qp, xp, 0L, tp, tn, mp, mn);
139 xn = mn;
140 }
141
142 if ((mp_limb_signed_t) e < 0)
143 {
144 mpn_mul (tp, xp, xn, bp, bn);
145 tn = xn + bn; tn -= tp[tn - 1] == 0;
146 if (tn < mn)
147 {
148 MPN_COPY (xp, tp, tn);
149 xn = tn;
150 }
151 else
152 {
153 mpn_tdiv_qr (qp, xp, 0L, tp, tn, mp, mn);
154 xn = mn;
155 }
156 }
157 e <<= 1;
158 c--;
159 }
160
161 finishup:
162 /* We shifted m left m_zero_cnt steps. Adjust the result by reducing
163 it with the original MOD. */
164 if (m_zero_cnt != 0)
165 {
166 mp_limb_t cy;
167 cy = mpn_lshift (tp, xp, xn, m_zero_cnt);
168 tp[xn] = cy; xn += cy != 0;
169
170 if (xn < mn)
171 {
172 MPN_COPY (xp, tp, xn);
173 }
174 else
175 {
176 mpn_tdiv_qr (qp, xp, 0L, tp, xn, mp, mn);
177 xn = mn;
178 }
179 mpn_rshift (xp, xp, xn, m_zero_cnt);
180 }
181 MPN_NORMALIZE (xp, xn);
182
183 if ((el & 1) != 0 && SIZ(b) < 0 && xn != 0)
184 {
185 mp = PTR(m); /* want original, unnormalized m */
186 mpn_sub (xp, mp, mn, xp, xn);
187 xn = mn;
188 MPN_NORMALIZE (xp, xn);
189 }
190 MPZ_REALLOC (r, xn);
191 SIZ (r) = xn;
192 MPN_COPY (PTR(r), xp, xn);
193
194 TMP_FREE;
195 }
196