git.distorted.org.uk Git - u/mdw/catacomb/blob - mp-gcd.c

   1 /* -*-c-*-
   2  *
   3  * $Id$
   4  *
   5  * Extended GCD calculation
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "mp.h"
  33
  34 /*----- Main code ---------------------------------------------------------*/
  35
  36 /* --- @mp_gcd@ --- *
  37  *
  38  * Arguments:   @mp **gcd, **xx, **yy@ = where to write the results
  39  *              @mp *a, *b@ = sources (must be nonzero)
  40  *
  41  * Returns:     ---
  42  *
  43  * Use:         Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
  44  *              @ax + by = gcd(a, b)@.  This is useful for computing modular
  45  *              inverses.
  46  */
  47
  48 void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
  49 {
  50   mp *x = MP_ONE, *X = MP_ZERO;
  51   mp *y = MP_ZERO, *Y = MP_ONE;
  52   mp *u, *v;
  53   mp *q = MP_NEW;
  54   unsigned f = 0;
  55
  56 #define f_swap 1u
  57 #define f_aneg 2u
  58 #define f_bneg 4u
  59 #define f_ext 8u
  60
  61   /* --- Sort out some initial flags --- */
  62
  63   if (xx || yy)
  64     f |= f_ext;
  65
  66   if (MP_NEGP(a))
  67     f |= f_aneg;
  68   if (MP_NEGP(b))
  69     f |= f_bneg;
  70
  71   /* --- Ensure that @a@ is larger than @b@ --- *
  72    *
  73    * Use absolute values here!
  74    */
  75
  76   if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
  77     { mp *t = a; a = b; b = t; }
  78     f |= f_swap;
  79   }
  80
  81   /* --- Check for zeroness --- */
  82
  83   if (MP_EQ(b, MP_ZERO)) {
  84
  85     /* --- Store %$|a|$% as the GCD --- */
  86
  87     if (gcd) {
  88       if (*gcd) MP_DROP(*gcd);
  89       a = MP_COPY(a);
  90       if (MP_NEGP(a)) {
  91         MP_SPLIT(a);
  92         a->f &= ~MP_NEG;
  93         f |= f_aneg;
  94       }
  95       *gcd = a;
  96     }
  97
  98     /* --- Store %$1$% and %$0$% in the appropriate bins --- */
  99
 100     if (f & f_ext) {
 101       if (f & f_swap) {
 102         mp **t = xx; xx = yy; yy = t;
 103       }
 104       if (xx) {
 105         if (*xx) MP_DROP(*xx);
 106         if (MP_EQ(a, MP_ZERO))
 107           *xx = MP_ZERO;
 108         else if (f & f_aneg)
 109           *xx = MP_MONE;
 110         else
 111           *xx = MP_ONE;
 112       }
 113       if (yy) {
 114         if (*yy) MP_DROP(*yy);
 115         *yy = MP_ZERO;
 116       }
 117     }
 118     return;
 119   }
 120
 121   /* --- Force the signs on the arguments and take copies --- */
 122
 123   a = MP_COPY(a);
 124   b = MP_COPY(b);
 125
 126   MP_SPLIT(a); a->f &= ~MP_NEG;
 127   MP_SPLIT(b); b->f &= ~MP_NEG;
 128
 129   u = MP_COPY(a);
 130   v = MP_COPY(b);
 131
 132   /* --- Main extended Euclidean algorithm --- */
 133
 134   while (!MP_ZEROP(v)) {
 135     mp *t;
 136     mp_div(&q, &u, u, v);
 137     if (f & f_ext) {
 138       t = mp_mul(MP_NEW, X, q);
 139       t = mp_sub(t, x, t);
 140       MP_DROP(x); x = X; X = t;
 141       t = mp_mul(MP_NEW, Y, q);
 142       t = mp_sub(t, y, t);
 143       MP_DROP(y); y = Y; Y = t;
 144     }
 145     t = u; u = v; v = t;
 146   }
 147
 148   MP_DROP(q);
 149   if (!gcd)
 150     MP_DROP(u);
 151   else {
 152     if (*gcd) MP_DROP(*gcd);
 153     u->f &= ~MP_NEG;
 154     *gcd = u;
 155   }
 156
 157   /* --- Perform a little normalization --- *
 158    *
 159    * Ensure that the coefficient returned is positive, if there is only one.
 160    * If there are two, favour @y@.  Of course, if the original arguments were
 161    * negative then I'll need to twiddle their signs as well.
 162    */
 163
 164   if (f & f_ext) {
 165
 166     /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
 167
 168     if (f & f_swap) {
 169       mp *t = x; x = y; y = t;
 170       t = a; a = b; b = t;
 171     }
 172
 173     /* --- Sort out the signs --- *
 174      *
 175      * Note that %$ax + by = a(x - b) + b(y + a)$%.
 176      *
 177      * This is currently bodgy.  It needs sorting out at some time.
 178      */
 179
 180     if (yy) {
 181       if (MP_NEGP(y)) {
 182         do {
 183           y = mp_add(y, y, a);
 184           x = mp_sub(x, x, b);
 185         } while (MP_NEGP(y));
 186       } else {
 187         while (MP_CMP(y, >=, a)) {
 188           y = mp_sub(y, y, a);
 189           x = mp_add(x, x, b);
 190         }
 191       }
 192     } else {
 193       if (MP_NEGP(x)) {
 194         do
 195           x = mp_add(x, x, b);
 196         while (MP_NEGP(x));
 197       } else {
 198         while (MP_CMP(x, >=, b))
 199           x = mp_sub(x, x, b);
 200       }
 201     }
 202
 203     /* --- Twiddle the signs --- */
 204
 205     if (f & f_aneg)
 206       x->f ^= MP_NEG;
 207     if (f & f_bneg)
 208       y->f ^= MP_NEG;
 209
 210     /* --- Store the results --- */
 211
 212     if (!xx)
 213       MP_DROP(x);
 214     else {
 215       if (*xx) MP_DROP(*xx);
 216       *xx = x;
 217     }
 218
 219     if (!yy)
 220       MP_DROP(y);
 221     else {
 222       if (*yy) MP_DROP(*yy);
 223       *yy = y;
 224     }
 225   }
 226
 227   MP_DROP(v);
 228   MP_DROP(X); MP_DROP(Y);
 229   MP_DROP(a); MP_DROP(b);
 230 }
 231
 232 /* -- @mp_modinv@ --- *
 233  *
 234  * Arguments:   @mp *d@ = destination
 235  *              @mp *x@ = argument
 236  *              @mp *p@ = modulus
 237  *
 238  * Returns:     The inverse %$x^{-1} \bmod p$%.
 239  *
 240  * Use:         Computes a modular inverse.    An assertion fails if %$p$%
 241  *              has no inverse.
 242  */
 243
 244 mp *mp_modinv(mp *d, mp *x, mp *p)
 245 {
 246   mp *g = MP_NEW;
 247   mp_gcd(&g, 0, &d, p, x);
 248   assert(MP_EQ(g, MP_ONE));
 249   mp_drop(g);
 250   return (d);
 251 }
 252
 253 /*----- Test rig ----------------------------------------------------------*/
 254
 255 #ifdef TEST_RIG
 256
 257 static int modinv(dstr *v)
 258 {
 259   int ok = 1;
 260   mp *x = *(mp **)v[0].buf;
 261   mp *m = *(mp **)v[1].buf;
 262   mp *r = *(mp **)v[2].buf;
 263
 264   mp *y = mp_modinv(MP_NEW, x, m);
 265   if (!MP_EQ(y, r)) {
 266     fputs("\n*** mp_modinv failed", stderr);
 267     fputs("\nx      = ", stderr); mp_writefile(x, stderr, 10);
 268     fputs("\nm      = ", stderr); mp_writefile(m, stderr, 10);
 269     fputs("\nexpect = ", stderr); mp_writefile(r, stderr, 10);
 270     fputs("\nresult = ", stderr); mp_writefile(y, stderr, 10);
 271     ok = 0;
 272   }
 273   MP_DROP(x); MP_DROP(m); MP_DROP(r); MP_DROP(y);
 274   assert(mparena_count(MPARENA_GLOBAL) == 0);
 275   return (ok);
 276 }
 277
 278 static int gcd(dstr *v)
 279 {
 280   int ok = 1;
 281   mp *a = *(mp **)v[0].buf;
 282   mp *b = *(mp **)v[1].buf;
 283   mp *g = *(mp **)v[2].buf;
 284   mp *x = *(mp **)v[3].buf;
 285   mp *y = *(mp **)v[4].buf;
 286
 287   mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
 288   mp_gcd(&gg, &xx, &yy, a, b);
 289   if (!MP_EQ(x, xx)) {
 290     fputs("\n*** mp_gcd(x) failed", stderr);
 291     fputs("\na      = ", stderr); mp_writefile(a, stderr, 10);
 292     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 10);
 293     fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10);
 294     fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10);
 295     fputc('\n', stderr);
 296     ok = 0;
 297   }
 298   if (!MP_EQ(y, yy)) {
 299     fputs("\n*** mp_gcd(y) failed", stderr);
 300     fputs("\na      = ", stderr); mp_writefile(a, stderr, 10);
 301     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 10);
 302     fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10);
 303     fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10);
 304     fputc('\n', stderr);
 305     ok = 0;
 306   }
 307
 308   if (!ok) {
 309     mp *ax = mp_mul(MP_NEW, a, xx);
 310     mp *by = mp_mul(MP_NEW, b, yy);
 311     ax = mp_add(ax, ax, by);
 312     if (MP_EQ(ax, gg))
 313       fputs("\n*** (Alternative result found.)\n", stderr);
 314     MP_DROP(ax);
 315     MP_DROP(by);
 316   }
 317
 318   if (!MP_EQ(g, gg)) {
 319     fputs("\n*** mp_gcd(gcd) failed", stderr);
 320     fputs("\na      = ", stderr); mp_writefile(a, stderr, 10);
 321     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 10);
 322     fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10);
 323     fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10);
 324     fputc('\n', stderr);
 325     ok = 0;
 326   }
 327   MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
 328   MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
 329   assert(mparena_count(MPARENA_GLOBAL) == 0);
 330   return (ok);
 331 }
 332
 333 static test_chunk tests[] = {
 334   { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 335   { "modinv", modinv, { &type_mp, &type_mp, &type_mp, 0 } },
 336   { 0, 0, { 0 } }
 337 };
 338
 339 int main(int argc, char *argv[])
 340 {
 341   sub_init();
 342   test_run(argc, argv, tests, SRCDIR "/tests/mp");
 343   return (0);
 344 }
 345
 346 #endif
 347
 348 /*----- That's all, folks -------------------------------------------------*/