mpi-genesis~ 1
mpi-genesis~ 2 * Copyright (C) 1994, 1996 Free Software Foundation, Inc.
mpi-genesis~ 3 * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
mpi-genesis~ 4 *
mpi-genesis~ 5 * This file is part of GnuPG.
mpi-genesis~ 6 *
mpi-genesis~ 7 * GnuPG is free software; you can redistribute it and/or modify
mpi-genesis~ 8 * it under the terms of the GNU General Public License as published by
mpi-genesis~ 9 * the Free Software Foundation; either version 3 of the License, or
mpi-genesis~ 10 * (at your option) any later version.
mpi-genesis~ 11 *
mpi-genesis~ 12 * GnuPG is distributed in the hope that it will be useful,
mpi-genesis~ 13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
mpi-genesis~ 14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
mpi-genesis~ 15 * GNU General Public License for more details.
mpi-genesis~ 16 *
mpi-genesis~ 17 * You should have received a copy of the GNU General Public License
mpi-genesis~ 18 * along with this program; if not, see <http:
mpi-genesis~ 19 *
mpi-genesis~ 20 * Note: This code is heavily based on the GNU MP Library.
mpi-genesis~ 21 * Actually it's the same code with only minor changes in the
mpi-genesis~ 22 * way the data is stored; this is to support the abstraction
mpi-genesis~ 23 * of an optional secure memory allocation which may be used
mpi-genesis~ 24 * to avoid revealing of sensitive data due to paging etc.
mpi-genesis~ 25 * The GNU MP Library itself is published under the LGPL;
mpi-genesis~ 26 * however I decided to publish this code under the plain GPL.
mpi-genesis~ 27 */
mpi-genesis~ 28
mpi-genesis~ 29 #include <config.h>
mpi-genesis~ 30 #include <stdio.h>
mpi-genesis~ 31 #include <stdlib.h>
mpi-genesis~ 32 #include "mpi-internal.h"
mpi-genesis~ 33 #include "longlong.h"
mpi-genesis~ 34
mpi-genesis~ 35
mpi-genesis~ 36
mpi-genesis~ 37 void
mpi-genesis~ 38 mpi_fdiv_r( MPI rem, MPI dividend, MPI divisor )
mpi-genesis~ 39 {
mpi-genesis~ 40 int divisor_sign = divisor->sign;
mpi-genesis~ 41 MPI temp_divisor = NULL;
mpi-genesis~ 42
mpi-genesis~ 43
mpi-genesis~ 44 * preliminary calculated. We have to copy it to temporary space if it's
mpi-genesis~ 45 * the same variable as REM. */
mpi-genesis~ 46 if( rem == divisor ) {
mpi-genesis~ 47 temp_divisor = mpi_copy( divisor );
mpi-genesis~ 48 divisor = temp_divisor;
mpi-genesis~ 49 }
mpi-genesis~ 50
mpi-genesis~ 51 mpi_tdiv_r( rem, dividend, divisor );
mpi-genesis~ 52
mpi-genesis~ 53 if( ((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs )
mpi-genesis~ 54 mpi_add( rem, rem, divisor);
mpi-genesis~ 55
mpi-genesis~ 56 if( temp_divisor )
mpi-genesis~ 57 mpi_free(temp_divisor);
mpi-genesis~ 58 }
mpi-genesis~ 59
mpi-genesis~ 60
mpi-genesis~ 61
mpi-genesis~ 62
mpi-genesis~ 63 * Division rounding the quotient towards -infinity.
mpi-genesis~ 64 * The remainder gets the same sign as the denominator.
mpi-genesis~ 65 * rem is optional
mpi-genesis~ 66 */
mpi-genesis~ 67
mpi-genesis~ 68 ulong
mpi-genesis~ 69 mpi_fdiv_r_ui( MPI rem, MPI dividend, ulong divisor )
mpi-genesis~ 70 {
mpi-genesis~ 71 mpi_limb_t rlimb;
mpi-genesis~ 72
mpi-genesis~ 73 rlimb = mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );
mpi-genesis~ 74 if( rlimb && dividend->sign )
mpi-genesis~ 75 rlimb = divisor - rlimb;
mpi-genesis~ 76
mpi-genesis~ 77 if( rem ) {
mpi-genesis~ 78 rem->d[0] = rlimb;
mpi-genesis~ 79 rem->nlimbs = rlimb? 1:0;
mpi-genesis~ 80 }
mpi-genesis~ 81 return rlimb;
mpi-genesis~ 82 }
mpi-genesis~ 83
mpi-genesis~ 84
mpi-genesis~ 85 void
mpi-genesis~ 86 mpi_fdiv_q( MPI quot, MPI dividend, MPI divisor )
mpi-genesis~ 87 {
mpi-genesis~ 88 MPI tmp = mpi_alloc( mpi_get_nlimbs(quot) );
mpi-genesis~ 89 mpi_fdiv_qr( quot, tmp, dividend, divisor);
mpi-genesis~ 90 mpi_free(tmp);
mpi-genesis~ 91 }
mpi-genesis~ 92
mpi-genesis~ 93 void
mpi-genesis~ 94 mpi_fdiv_qr( MPI quot, MPI rem, MPI dividend, MPI divisor )
mpi-genesis~ 95 {
mpi-genesis~ 96 int divisor_sign = divisor->sign;
mpi-genesis~ 97 MPI temp_divisor = NULL;
mpi-genesis~ 98
mpi-genesis~ 99 if( quot == divisor || rem == divisor ) {
mpi-genesis~ 100 temp_divisor = mpi_copy( divisor );
mpi-genesis~ 101 divisor = temp_divisor;
mpi-genesis~ 102 }
mpi-genesis~ 103
mpi-genesis~ 104 mpi_tdiv_qr( quot, rem, dividend, divisor );
mpi-genesis~ 105
mpi-genesis~ 106 if( (divisor_sign ^ dividend->sign) && rem->nlimbs ) {
mpi-genesis~ 107 mpi_sub_ui( quot, quot, 1 );
mpi-genesis~ 108 mpi_add( rem, rem, divisor);
mpi-genesis~ 109 }
mpi-genesis~ 110
mpi-genesis~ 111 if( temp_divisor )
mpi-genesis~ 112 mpi_free(temp_divisor);
mpi-genesis~ 113 }
mpi-genesis~ 114
mpi-genesis~ 115
mpi-genesis~ 116
mpi-genesis~ 117 * If den == rem, den needs temporary storage.
mpi-genesis~ 118 * If num == quot, num needs temporary storage.
mpi-genesis~ 119 * If den has temporary storage, it can be normalized while being copied,
mpi-genesis~ 120 * i.e no extra storage should be allocated.
mpi-genesis~ 121 */
mpi-genesis~ 122
mpi-genesis~ 123 void
mpi-genesis~ 124 mpi_tdiv_r( MPI rem, MPI num, MPI den)
mpi-genesis~ 125 {
mpi-genesis~ 126 mpi_tdiv_qr(NULL, rem, num, den );
mpi-genesis~ 127 }
mpi-genesis~ 128
mpi-genesis~ 129 void
mpi-genesis~ 130 mpi_tdiv_qr( MPI quot, MPI rem, MPI num, MPI den)
mpi-genesis~ 131 {
mpi-genesis~ 132 mpi_ptr_t np, dp;
mpi-genesis~ 133 mpi_ptr_t qp, rp;
mpi-genesis~ 134 mpi_size_t nsize = num->nlimbs;
mpi-genesis~ 135 mpi_size_t dsize = den->nlimbs;
mpi-genesis~ 136 mpi_size_t qsize, rsize;
mpi-genesis~ 137 mpi_size_t sign_remainder = num->sign;
mpi-genesis~ 138 mpi_size_t sign_quotient = num->sign ^ den->sign;
mpi-genesis~ 139 unsigned normalization_steps;
mpi-genesis~ 140 mpi_limb_t q_limb;
mpi-genesis~ 141 mpi_ptr_t marker[5];
mpi-genesis~ 142 int markidx=0;
mpi-genesis~ 143
mpi-genesis~ 144
mpi-genesis~ 145 * We need space for an extra limb in the remainder, because it's
mpi-genesis~ 146 * up-shifted (normalized) below. */
mpi-genesis~ 147 rsize = nsize + 1;
mpi-genesis~ 148 mpi_resize( rem, rsize);
mpi-genesis~ 149
mpi-genesis~ 150 qsize = rsize - dsize;
mpi-genesis~ 151 if( qsize <= 0 ) {
mpi-genesis~ 152 if( num != rem ) {
mpi-genesis~ 153 rem->nlimbs = num->nlimbs;
mpi-genesis~ 154 rem->sign = num->sign;
mpi-genesis~ 155 MPN_COPY(rem->d, num->d, nsize);
mpi-genesis~ 156 }
mpi-genesis~ 157 if( quot ) {
mpi-genesis~ 158
mpi-genesis~ 159 * numerator and quotient are the same. */
mpi-genesis~ 160 quot->nlimbs = 0;
mpi-genesis~ 161 quot->sign = 0;
mpi-genesis~ 162 }
mpi-genesis~ 163 return;
mpi-genesis~ 164 }
mpi-genesis~ 165
mpi-genesis~ 166 if( quot )
mpi-genesis~ 167 mpi_resize( quot, qsize);
mpi-genesis~ 168
mpi-genesis~ 169
mpi-genesis~ 170 np = num->d;
mpi-genesis~ 171 dp = den->d;
mpi-genesis~ 172 rp = rem->d;
mpi-genesis~ 173
mpi-genesis~ 174
mpi-genesis~ 175 if( dsize == 1 ) {
mpi-genesis~ 176 mpi_limb_t rlimb;
mpi-genesis~ 177 if( quot ) {
mpi-genesis~ 178 qp = quot->d;
mpi-genesis~ 179 rlimb = mpihelp_divmod_1( qp, np, nsize, dp[0] );
mpi-genesis~ 180 qsize -= qp[qsize - 1] == 0;
mpi-genesis~ 181 quot->nlimbs = qsize;
mpi-genesis~ 182 quot->sign = sign_quotient;
mpi-genesis~ 183 }
mpi-genesis~ 184 else
mpi-genesis~ 185 rlimb = mpihelp_mod_1( np, nsize, dp[0] );
mpi-genesis~ 186 rp[0] = rlimb;
mpi-genesis~ 187 rsize = rlimb != 0?1:0;
mpi-genesis~ 188 rem->nlimbs = rsize;
mpi-genesis~ 189 rem->sign = sign_remainder;
mpi-genesis~ 190 return;
mpi-genesis~ 191 }
mpi-genesis~ 192
mpi-genesis~ 193
mpi-genesis~ 194 if( quot ) {
mpi-genesis~ 195 qp = quot->d;
mpi-genesis~ 196
mpi-genesis~ 197 * numerator would be gradually overwritten by the quotient limbs. */
mpi-genesis~ 198 if(qp == np) {
mpi-genesis~ 199 np = marker[markidx++] = mpi_alloc_limb_space(nsize,
mpi-genesis~ 200 mpi_is_secure(quot));
mpi-genesis~ 201 MPN_COPY(np, qp, nsize);
mpi-genesis~ 202 }
mpi-genesis~ 203 }
mpi-genesis~ 204 else
mpi-genesis~ 205 qp = rp + dsize;
mpi-genesis~ 206
mpi-genesis~ 207 count_leading_zeros( normalization_steps, dp[dsize - 1] );
mpi-genesis~ 208
mpi-genesis~ 209
mpi-genesis~ 210 * shifting it NORMALIZATION_STEPS bits to the left. Also shift the
mpi-genesis~ 211 * numerator the same number of steps (to keep the quotient the same!).
mpi-genesis~ 212 */
mpi-genesis~ 213 if( normalization_steps ) {
mpi-genesis~ 214 mpi_ptr_t tp;
mpi-genesis~ 215 mpi_limb_t nlimb;
mpi-genesis~ 216
mpi-genesis~ 217
mpi-genesis~ 218 * the most significant word. Use temporary storage not to clobber
mpi-genesis~ 219 * the original contents of the denominator. */
mpi-genesis~ 220 tp = marker[markidx++] = mpi_alloc_limb_space(dsize,mpi_is_secure(den));
mpi-genesis~ 221 mpihelp_lshift( tp, dp, dsize, normalization_steps );
mpi-genesis~ 222 dp = tp;
mpi-genesis~ 223
mpi-genesis~ 224
mpi-genesis~ 225 * significant word. Move the shifted numerator in the remainder
mpi-genesis~ 226 * meanwhile. */
mpi-genesis~ 227 nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
mpi-genesis~ 228 if( nlimb ) {
mpi-genesis~ 229 rp[nsize] = nlimb;
mpi-genesis~ 230 rsize = nsize + 1;
mpi-genesis~ 231 }
mpi-genesis~ 232 else
mpi-genesis~ 233 rsize = nsize;
mpi-genesis~ 234 }
mpi-genesis~ 235 else {
mpi-genesis~ 236
mpi-genesis~ 237 * temporary space if it overlaps with the quotient or remainder. */
mpi-genesis~ 238 if( dp == rp || (quot && (dp == qp))) {
mpi-genesis~ 239 mpi_ptr_t tp;
mpi-genesis~ 240
mpi-genesis~ 241 tp = marker[markidx++] = mpi_alloc_limb_space(dsize, mpi_is_secure(den));
mpi-genesis~ 242 MPN_COPY( tp, dp, dsize );
mpi-genesis~ 243 dp = tp;
mpi-genesis~ 244 }
mpi-genesis~ 245
mpi-genesis~ 246
mpi-genesis~ 247 if( rp != np )
mpi-genesis~ 248 MPN_COPY(rp, np, nsize);
mpi-genesis~ 249
mpi-genesis~ 250 rsize = nsize;
mpi-genesis~ 251 }
mpi-genesis~ 252
mpi-genesis~ 253 q_limb = mpihelp_divrem( qp, 0, rp, rsize, dp, dsize );
mpi-genesis~ 254
mpi-genesis~ 255 if( quot ) {
mpi-genesis~ 256 qsize = rsize - dsize;
mpi-genesis~ 257 if(q_limb) {
mpi-genesis~ 258 qp[qsize] = q_limb;
mpi-genesis~ 259 qsize += 1;
mpi-genesis~ 260 }
mpi-genesis~ 261
mpi-genesis~ 262 quot->nlimbs = qsize;
mpi-genesis~ 263 quot->sign = sign_quotient;
mpi-genesis~ 264 }
mpi-genesis~ 265
mpi-genesis~ 266 rsize = dsize;
mpi-genesis~ 267 MPN_NORMALIZE (rp, rsize);
mpi-genesis~ 268
mpi-genesis~ 269 if( normalization_steps && rsize ) {
mpi-genesis~ 270 mpihelp_rshift(rp, rp, rsize, normalization_steps);
mpi-genesis~ 271 rsize -= rp[rsize - 1] == 0?1:0;
mpi-genesis~ 272 }
mpi-genesis~ 273
mpi-genesis~ 274 rem->nlimbs = rsize;
mpi-genesis~ 275 rem->sign = sign_remainder;
mpi-genesis~ 276 while( markidx )
mpi-genesis~ 277 mpi_free_limb_space(marker[--markidx]);
mpi-genesis~ 278 }
mpi-genesis~ 279
mpi-genesis~ 280 void
mpi-genesis~ 281 mpi_tdiv_q_2exp( MPI w, MPI u, unsigned count )
mpi-genesis~ 282 {
mpi-genesis~ 283 mpi_size_t usize, wsize;
mpi-genesis~ 284 mpi_size_t limb_cnt;
mpi-genesis~ 285
mpi-genesis~ 286 usize = u->nlimbs;
mpi-genesis~ 287 limb_cnt = count / BITS_PER_MPI_LIMB;
mpi-genesis~ 288 wsize = usize - limb_cnt;
mpi-genesis~ 289 if( limb_cnt >= usize )
mpi-genesis~ 290 w->nlimbs = 0;
mpi-genesis~ 291 else {
mpi-genesis~ 292 mpi_ptr_t wp;
mpi-genesis~ 293 mpi_ptr_t up;
mpi-genesis~ 294
mpi-genesis~ 295 RESIZE_IF_NEEDED( w, wsize );
mpi-genesis~ 296 wp = w->d;
mpi-genesis~ 297 up = u->d;
mpi-genesis~ 298
mpi-genesis~ 299 count %= BITS_PER_MPI_LIMB;
mpi-genesis~ 300 if( count ) {
mpi-genesis~ 301 mpihelp_rshift( wp, up + limb_cnt, wsize, count );
mpi-genesis~ 302 wsize -= !wp[wsize - 1];
mpi-genesis~ 303 }
mpi-genesis~ 304 else {
mpi-genesis~ 305 MPN_COPY_INCR( wp, up + limb_cnt, wsize);
mpi-genesis~ 306 }
mpi-genesis~ 307
mpi-genesis~ 308 w->nlimbs = wsize;
mpi-genesis~ 309 }
mpi-genesis~ 310 }
mpi-genesis~ 311
mpi-genesis~ 312
mpi-genesis~ 313 * Check whether dividend is divisible by divisor
mpi-genesis~ 314 * (note: divisor must fit into a limb)
mpi-genesis~ 315 */
mpi-genesis~ 316 int
mpi-genesis~ 317 mpi_divisible_ui(MPI dividend, ulong divisor )
mpi-genesis~ 318 {
mpi-genesis~ 319 return !mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );
mpi-genesis~ 320 }
mpi-genesis~ 321