3 * $Id: mpx-ksqr.c,v 1.3 2000/06/17 11:42:54 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 1.3 2000/06/17 11:42:54 mdw
34 * Moved the Karatsuba macros into a separate file for better sharing.
35 * Fixed some comments. Use an improved technique so that all the
36 * operations are squarings.
38 * Revision 1.2 1999/12/13 15:35:01 mdw
39 * Simplify and improve.
41 * Revision 1.1 1999/12/11 10:57:43 mdw
42 * Karatsuba squaring algorithm.
46 /*----- Header files ------------------------------------------------------*/
54 /*----- Tweakables --------------------------------------------------------*/
57 # undef KARATSUBA_CUTOFF
58 # define KARATSUBA_CUTOFF 2
61 /*----- Main code ---------------------------------------------------------*/
63 /* --- @mpx_ksqr@ --- *
65 * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
66 * @const mpw *av, *avl@ = pointer to first argument
67 * @mpw *sv, *svl@ = pointer to scratch workspace
71 * Use: Squares a multiprecision integers using something similar to
72 * Karatsuba's multiplication algorithm. This is rather faster
73 * than traditional long multiplication (e.g., @mpx_umul@) on
74 * large numbers, although more expensive on small ones, and
75 * rather simpler than full-blown Karatsuba multiplication.
77 * The destination must be twice as large as the argument. The
78 * scratch space must be twice as large as the argument, plus
79 * the magic number @KARATSUBA_SLOP@.
82 void mpx_ksqr(mpw
*dv
, mpw
*dvl
,
83 const mpw
*av
, const mpw
*avl
,
89 /* --- Dispose of easy cases to @mpx_usqr@ --- *
91 * Karatsuba is only a win on large numbers, because of all the
92 * recursiveness and bookkeeping. The recursive calls make a quick check
93 * to see whether to bottom out to @mpx_usqr@ which should help quite a
94 * lot, but sometimes the only way to know is to make sure...
99 if (avl
- av
<= KARATSUBA_CUTOFF
) {
100 mpx_usqr(dv
, dvl
, av
, avl
);
104 /* --- How the algorithm works --- *
106 * The identity for squaring is known to all schoolchildren.
107 * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now,
108 * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
112 /* --- First things --- *
114 * Sort out where to break the factor in half.
117 m
= (avl
- av
+ 1) >> 1;
120 assert(((void)"Destination too small for Karatsuba square",
122 assert(((void)"Not enough workspace for Karatsuba square",
125 /* --- Sort out everything --- */
128 mpw
*svm
= sv
+ m
, *svn
= svm
+ m
, *ssv
= svn
+ 4;
132 UADD2(sv
, svm
, av
, avm
, avm
, avl
);
133 if (m
> KARATSUBA_CUTOFF
)
134 mpx_ksqr(tdv
, rdv
+ m
+ 4, sv
, svm
+ 1, ssv
, svl
);
136 mpx_usqr(tdv
, rdv
+ m
+ 4, sv
, svm
+ 1);
138 if (m
> KARATSUBA_CUTOFF
)
139 mpx_ksqr(sv
, ssv
, avm
, avl
, ssv
, svl
);
141 mpx_usqr(sv
, ssv
, avm
, avl
);
142 MPX_COPY(rdv
+ m
+ 1, dvl
, svm
+ 1, svn
);
143 UADD(rdv
, sv
, svm
+ 1);
146 if (m
> KARATSUBA_CUTOFF
)
147 mpx_ksqr(sv
, ssv
, av
, avm
, ssv
, svl
);
149 mpx_usqr(sv
, ssv
, av
, avm
);
150 MPX_COPY(dv
, tdv
, sv
, svm
);
156 /*----- Test rig ----------------------------------------------------------*/
160 #include <mLib/alloc.h>
161 #include <mLib/testrig.h>
165 #define ALLOC(v, vl, sz) do { \
167 mpw *_vv = xmalloc(MPWS(_sz)); \
168 mpw *_vvl = _vv + _sz; \
173 #define LOAD(v, vl, d) do { \
174 const dstr *_d = (d); \
176 ALLOC(_v, _vl, MPW_RQ(_d->len)); \
177 mpx_loadb(_v, _vl, _d->buf, _d->len); \
182 #define MAX(x, y) ((x) > (y) ? (x) : (y))
184 static void dumpmp(const char *msg
, const mpw
*v
, const mpw
*vl
)
189 fprintf(stderr
, " %08lx", (unsigned long)*--vl
);
193 static int usqr(dstr
*v
)
206 ALLOC(s
, sl
, 2 * m
+ 32);
208 mpx_ksqr(d
, dl
, a
, al
, s
, sl
);
209 if (MPX_UCMP(d
, dl
, !=, c
, cl
)) {
210 fprintf(stderr
, "\n*** usqr failed\n");
212 dumpmp("expected", c
, cl
);
213 dumpmp(" result", d
, dl
);
217 free(a
); free(c
); free(d
); free(s
);
221 static test_chunk defs
[] = {
222 { "usqr", usqr
, { &type_hex
, &type_hex
, 0 } },
226 int main(int argc
, char *argv
[])
228 test_run(argc
, argv
, defs
, SRCDIR
"/tests/mpx");
234 /*----- That's all, folks -------------------------------------------------*/