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, *t, *spare = 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     t = a; a = b; b = t;
  78     f |= f_swap;
  79   }
  80
  81   /* --- Check for zeroness --- */
  82
  83   if (MP_ZEROP(b)) {
  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 **tt = xx; xx = yy; yy = tt;
 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_div(&q, &u, u, v);
 136     if (f & f_ext) {
 137       t = mp_mul(spare, X, q);
 138       t = mp_sub(t, x, t);
 139       spare = x; x = X; X = t;
 140       t = mp_mul(spare, Y, q);
 141       t = mp_sub(t, y, t);
 142       spare = y; y = Y; Y = t;
 143     }
 144     t = u; u = v; v = t;
 145   }
 146
 147   MP_DROP(q); if (spare) MP_DROP(spare);
 148   if (!gcd)
 149     MP_DROP(u);
 150   else {
 151     if (*gcd) MP_DROP(*gcd);
 152     u->f &= ~MP_NEG;
 153     *gcd = u;
 154   }
 155
 156   /* --- Perform a little normalization --- *
 157    *
 158    * Ensure that the coefficient returned is positive, if there is only one.
 159    * If there are two, favour @y@.  Of course, if the original arguments were
 160    * negative then I'll need to twiddle their signs as well.
 161    */
 162
 163   if (f & f_ext) {
 164
 165     /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
 166
 167     if (f & f_swap) {
 168       t = x; x = y; y = t;
 169       t = a; a = b; b = t;
 170     }
 171
 172     /* --- Sort out the signs --- *
 173      *
 174      * Note that %$ax + by = a(x - b) + b(y + a)$%.
 175      *
 176      * This is currently bodgy.  It needs sorting out at some time.
 177      */
 178
 179     if (yy) {
 180       if (MP_NEGP(y)) {
 181         do {
 182           y = mp_add(y, y, a);
 183           x = mp_sub(x, x, b);
 184         } while (MP_NEGP(y));
 185       } else {
 186         while (MP_CMP(y, >=, a)) {
 187           y = mp_sub(y, y, a);
 188           x = mp_add(x, x, b);
 189         }
 190       }
 191     } else {
 192       if (MP_NEGP(x)) {
 193         do
 194           x = mp_add(x, x, b);
 195         while (MP_NEGP(x));
 196       } else {
 197         while (MP_CMP(x, >=, b))
 198           x = mp_sub(x, x, b);
 199       }
 200     }
 201
 202     /* --- Twiddle the signs --- */
 203
 204     if (f & f_aneg)
 205       x->f ^= MP_NEG;
 206     if (f & f_bneg)
 207       y->f ^= MP_NEG;
 208
 209     /* --- Store the results --- */
 210
 211     if (!xx)
 212       MP_DROP(x);
 213     else {
 214       if (*xx) MP_DROP(*xx);
 215       *xx = x;
 216     }
 217
 218     if (!yy)
 219       MP_DROP(y);
 220     else {
 221       if (*yy) MP_DROP(*yy);
 222       *yy = y;
 223     }
 224   }
 225
 226   MP_DROP(v);
 227   MP_DROP(X); MP_DROP(Y);
 228   MP_DROP(a); MP_DROP(b);
 229 }
 230
 231 /* -- @mp_modinv@ --- *
 232  *
 233  * Arguments:   @mp *d@ = destination
 234  *              @mp *x@ = argument
 235  *              @mp *p@ = modulus
 236  *
 237  * Returns:     The inverse %$x^{-1} \bmod p$%.
 238  *
 239  * Use:         Computes a modular inverse.    An assertion fails if %$p$%
 240  *              has no inverse.
 241  */
 242
 243 mp *mp_modinv(mp *d, mp *x, mp *p)
 244 {
 245   mp *g = MP_NEW;
 246   mp_gcd(&g, 0, &d, p, x);
 247   assert(MP_EQ(g, MP_ONE));
 248   mp_drop(g);
 249   return (d);
 250 }
 251
 252 /*----- Test rig ----------------------------------------------------------*/
 253
 254 #ifdef TEST_RIG
 255
 256 static int modinv(dstr *v)
 257 {
 258   int ok = 1;
 259   mp *x = *(mp **)v[0].buf;
 260   mp *m = *(mp **)v[1].buf;
 261   mp *r = *(mp **)v[2].buf;
 262
 263   mp *y = mp_modinv(MP_NEW, x, m);
 264   if (!MP_EQ(y, r)) {
 265     fputs("\n*** mp_modinv failed", stderr);
 266     fputs("\nx      = ", stderr); mp_writefile(x, stderr, 10);
 267     fputs("\nm      = ", stderr); mp_writefile(m, stderr, 10);
 268     fputs("\nexpect = ", stderr); mp_writefile(r, stderr, 10);
 269     fputs("\nresult = ", stderr); mp_writefile(y, stderr, 10);
 270     ok = 0;
 271   }
 272   MP_DROP(x); MP_DROP(m); MP_DROP(r); MP_DROP(y);
 273   assert(mparena_count(MPARENA_GLOBAL) == 0);
 274   return (ok);
 275 }
 276
 277 static int gcd(dstr *v)
 278 {
 279   int ok = 1;
 280   mp *a = *(mp **)v[0].buf;
 281   mp *b = *(mp **)v[1].buf;
 282   mp *g = *(mp **)v[2].buf;
 283   mp *x = *(mp **)v[3].buf;
 284   mp *y = *(mp **)v[4].buf;
 285
 286   mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
 287   mp_gcd(&gg, &xx, &yy, a, b);
 288   if (!MP_EQ(x, xx)) {
 289     fputs("\n*** mp_gcd(x) failed", stderr);
 290     fputs("\na      = ", stderr); mp_writefile(a, stderr, 10);
 291     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 10);
 292     fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10);
 293     fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10);
 294     fputc('\n', stderr);
 295     ok = 0;
 296   }
 297   if (!MP_EQ(y, yy)) {
 298     fputs("\n*** mp_gcd(y) failed", stderr);
 299     fputs("\na      = ", stderr); mp_writefile(a, stderr, 10);
 300     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 10);
 301     fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10);
 302     fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10);
 303     fputc('\n', stderr);
 304     ok = 0;
 305   }
 306
 307   if (!ok) {
 308     mp *ax = mp_mul(MP_NEW, a, xx);
 309     mp *by = mp_mul(MP_NEW, b, yy);
 310     ax = mp_add(ax, ax, by);
 311     if (MP_EQ(ax, gg))
 312       fputs("\n*** (Alternative result found.)\n", stderr);
 313     MP_DROP(ax);
 314     MP_DROP(by);
 315   }
 316
 317   if (!MP_EQ(g, gg)) {
 318     fputs("\n*** mp_gcd(gcd) failed", stderr);
 319     fputs("\na      = ", stderr); mp_writefile(a, stderr, 10);
 320     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 10);
 321     fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10);
 322     fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10);
 323     fputc('\n', stderr);
 324     ok = 0;
 325   }
 326   MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
 327   MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
 328   assert(mparena_count(MPARENA_GLOBAL) == 0);
 329   return (ok);
 330 }
 331
 332 static test_chunk tests[] = {
 333   { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 334   { "modinv", modinv, { &type_mp, &type_mp, &type_mp, 0 } },
 335   { 0, 0, { 0 } }
 336 };
 337
 338 int main(int argc, char *argv[])
 339 {
 340   sub_init();
 341   test_run(argc, argv, tests, SRCDIR "/tests/mp");
 342   return (0);
 343 }
 344
 345 #endif
 346
 347 /*----- That's all, folks -------------------------------------------------*/