3 * $Id: mpx-ksqr.c,v 1.4 2000/07/29 17:04:02 mdw Exp $
5 * Karatsuba-based squaring algorithm
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
32 * $Log: mpx-ksqr.c,v $
33 * Revision 1.4 2000/07/29 17:04:02 mdw
34 * Remove useless header `mpscan.h'.
36 * Revision 1.3 2000/06/17 11:42:54 mdw
37 * Moved the Karatsuba macros into a separate file for better sharing.
38 * Fixed some comments. Use an improved technique so that all the
39 * operations are squarings.
41 * Revision 1.2 1999/12/13 15:35:01 mdw
42 * Simplify and improve.
44 * Revision 1.1 1999/12/11 10:57:43 mdw
45 * Karatsuba squaring algorithm.
49 /*----- Header files ------------------------------------------------------*/
57 /*----- Tweakables --------------------------------------------------------*/
60 # undef KARATSUBA_CUTOFF
61 # define KARATSUBA_CUTOFF 2
64 /*----- Main code ---------------------------------------------------------*/
66 /* --- @mpx_ksqr@ --- *
68 * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
69 * @const mpw *av, *avl@ = pointer to first argument
70 * @mpw *sv, *svl@ = pointer to scratch workspace
74 * Use: Squares a multiprecision integers using something similar to
75 * Karatsuba's multiplication algorithm. This is rather faster
76 * than traditional long multiplication (e.g., @mpx_umul@) on
77 * large numbers, although more expensive on small ones, and
78 * rather simpler than full-blown Karatsuba multiplication.
80 * The destination must be twice as large as the argument. The
81 * scratch space must be twice as large as the argument, plus
82 * the magic number @KARATSUBA_SLOP@.
85 void mpx_ksqr(mpw *dv, mpw *dvl,
86 const mpw *av, const mpw *avl,
92 /* --- Dispose of easy cases to @mpx_usqr@ --- *
94 * Karatsuba is only a win on large numbers, because of all the
95 * recursiveness and bookkeeping. The recursive calls make a quick check
96 * to see whether to bottom out to @mpx_usqr@ which should help quite a
97 * lot, but sometimes the only way to know is to make sure...
102 if (avl - av <= KARATSUBA_CUTOFF) {
103 mpx_usqr(dv, dvl, av, avl);
107 /* --- How the algorithm works --- *
109 * The identity for squaring is known to all schoolchildren.
110 * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now,
111 * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
115 /* --- First things --- *
117 * Sort out where to break the factor in half.
120 m = (avl - av + 1) >> 1;
123 assert(((void)"Destination too small for Karatsuba square",
125 assert(((void)"Not enough workspace for Karatsuba square",
128 /* --- Sort out everything --- */
131 mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
135 UADD2(sv, svm, av, avm, avm, avl);
136 if (m > KARATSUBA_CUTOFF)
137 mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
139 mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
141 if (m > KARATSUBA_CUTOFF)
142 mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
144 mpx_usqr(sv, ssv, avm, avl);
145 MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
146 UADD(rdv, sv, svm + 1);
149 if (m > KARATSUBA_CUTOFF)
150 mpx_ksqr(sv, ssv, av, avm, ssv, svl);
152 mpx_usqr(sv, ssv, av, avm);
153 MPX_COPY(dv, tdv, sv, svm);
159 /*----- Test rig ----------------------------------------------------------*/
163 #include <mLib/alloc.h>
164 #include <mLib/testrig.h>
166 #define ALLOC(v, vl, sz) do { \
168 mpw *_vv = xmalloc(MPWS(_sz)); \
169 mpw *_vvl = _vv + _sz; \
174 #define LOAD(v, vl, d) do { \
175 const dstr *_d = (d); \
177 ALLOC(_v, _vl, MPW_RQ(_d->len)); \
178 mpx_loadb(_v, _vl, _d->buf, _d->len); \
183 #define MAX(x, y) ((x) > (y) ? (x) : (y))
185 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
190 fprintf(stderr, " %08lx", (unsigned long)*--vl);
194 static int usqr(dstr *v)
207 ALLOC(s, sl, 2 * m + 32);
209 mpx_ksqr(d, dl, a, al, s, sl);
210 if (MPX_UCMP(d, dl, !=, c, cl)) {
211 fprintf(stderr, "\n*** usqr failed\n");
213 dumpmp("expected", c, cl);
214 dumpmp(" result", d, dl);
218 free(a); free(c); free(d); free(s);
222 static test_chunk defs[] = {
223 { "usqr", usqr, { &type_hex, &type_hex, 0 } },
227 int main(int argc, char *argv[])
229 test_run(argc, argv, defs, SRCDIR"/tests/mpx");
235 /*----- That's all, folks -------------------------------------------------*/