1 /* mpn_powlo -- Compute R = U^E mod B^n, where B is the limb base. 2 3 Copyright 2007, 2008, 2009 Free Software Foundation, Inc. 4 5 This file is part of the GNU MP Library. 6 7 The GNU MP Library is free software; you can redistribute it and/or modify 8 it under the terms of the GNU Lesser General Public License as published by 9 the Free Software Foundation; either version 3 of the License, or (at your 10 option) any later version. 11 12 The GNU MP Library is distributed in the hope that it will be useful, but 13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 15 License for more details. 16 17 You should have received a copy of the GNU Lesser General Public License 18 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 19 20 21 #include "gmp.h" 22 #include "gmp-impl.h" 23 #include "longlong.h" 24 25 26 #define getbit(p,bi) \ 27 ((p[(bi - 1) / GMP_LIMB_BITS] >> (bi - 1) % GMP_LIMB_BITS) & 1) 28 29 static inline mp_limb_t 30 getbits (const mp_limb_t *p, mp_bitcnt_t bi, int nbits) 31 { 32 int nbits_in_r; 33 mp_limb_t r; 34 mp_size_t i; 35 36 if (bi < nbits) 37 { 38 return p[0] & (((mp_limb_t) 1 << bi) - 1); 39 } 40 else 41 { 42 bi -= nbits; /* bit index of low bit to extract */ 43 i = bi / GMP_NUMB_BITS; /* word index of low bit to extract */ 44 bi %= GMP_NUMB_BITS; /* bit index in low word */ 45 r = p[i] >> bi; /* extract (low) bits */ 46 nbits_in_r = GMP_NUMB_BITS - bi; /* number of bits now in r */ 47 if (nbits_in_r < nbits) /* did we get enough bits? */ 48 r += p[i + 1] << nbits_in_r; /* prepend bits from higher word */ 49 return r & (((mp_limb_t ) 1 << nbits) - 1); 50 } 51 } 52 53 static inline int 54 win_size (mp_bitcnt_t eb) 55 { 56 int k; 57 static mp_bitcnt_t x[] = {1,7,25,81,241,673,1793,4609,11521,28161,~(mp_bitcnt_t)0}; 58 for (k = 0; eb > x[k]; k++) 59 ; 60 return k; 61 } 62 63 /* rp[n-1..0] = bp[n-1..0] ^ ep[en-1..0] mod B^n, B is the limb base. 64 Requires that ep[en-1] is non-zero. 65 Uses scratch space tp[3n-1..0], i.e., 3n words. */ 66 void 67 mpn_powlo (mp_ptr rp, mp_srcptr bp, 68 mp_srcptr ep, mp_size_t en, 69 mp_size_t n, mp_ptr tp) 70 { 71 int cnt; 72 mp_bitcnt_t ebi; 73 int windowsize, this_windowsize; 74 mp_limb_t expbits; 75 mp_limb_t *pp, *this_pp, *last_pp; 76 mp_limb_t *b2p; 77 long i; 78 TMP_DECL; 79 80 ASSERT (en > 1 || (en == 1 && ep[0] > 1)); 81 82 TMP_MARK; 83 84 count_leading_zeros (cnt, ep[en - 1]); 85 ebi = (mp_bitcnt_t) en * GMP_LIMB_BITS - cnt; 86 87 windowsize = win_size (ebi); 88 89 pp = TMP_ALLOC_LIMBS ((n << (windowsize - 1)) + n); /* + n is for mullo ign part */ 90 91 this_pp = pp; 92 93 MPN_COPY (this_pp, bp, n); 94 95 b2p = tp + 2*n; 96 97 /* Store b^2 in b2. */ 98 mpn_sqr (tp, bp, n); /* FIXME: Use "mpn_sqrlo" */ 99 MPN_COPY (b2p, tp, n); 100 101 /* Precompute odd powers of b and put them in the temporary area at pp. */ 102 for (i = (1 << (windowsize - 1)) - 1; i > 0; i--) 103 { 104 last_pp = this_pp; 105 this_pp += n; 106 mpn_mullo_n (this_pp, last_pp, b2p, n); 107 } 108 109 expbits = getbits (ep, ebi, windowsize); 110 if (ebi < windowsize) 111 ebi = 0; 112 else 113 ebi -= windowsize; 114 115 count_trailing_zeros (cnt, expbits); 116 ebi += cnt; 117 expbits >>= cnt; 118 119 MPN_COPY (rp, pp + n * (expbits >> 1), n); 120 121 while (ebi != 0) 122 { 123 while (getbit (ep, ebi) == 0) 124 { 125 mpn_sqr (tp, rp, n); /* FIXME: Use "mpn_sqrlo" */ 126 MPN_COPY (rp, tp, n); 127 ebi--; 128 if (ebi == 0) 129 goto done; 130 } 131 132 /* The next bit of the exponent is 1. Now extract the largest block of 133 bits <= windowsize, and such that the least significant bit is 1. */ 134 135 expbits = getbits (ep, ebi, windowsize); 136 this_windowsize = windowsize; 137 if (ebi < windowsize) 138 { 139 this_windowsize -= windowsize - ebi; 140 ebi = 0; 141 } 142 else 143 ebi -= windowsize; 144 145 count_trailing_zeros (cnt, expbits); 146 this_windowsize -= cnt; 147 ebi += cnt; 148 expbits >>= cnt; 149 150 do 151 { 152 mpn_sqr (tp, rp, n); 153 MPN_COPY (rp, tp, n); 154 this_windowsize--; 155 } 156 while (this_windowsize != 0); 157 158 mpn_mullo_n (tp, rp, pp + n * (expbits >> 1), n); 159 MPN_COPY (rp, tp, n); 160 } 161 162 done: 163 TMP_FREE; 164 } 165