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

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