/* -*-c-*-
*
- * $Id: mpx-ksqr.c,v 1.1 1999/12/11 10:57:43 mdw Exp $
+ * $Id: mpx-ksqr.c,v 1.5 2000/10/08 12:11:01 mdw Exp $
*
* Karatsuba-based squaring algorithm
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpx-ksqr.c,v $
+ * Revision 1.5 2000/10/08 12:11:01 mdw
+ * Use @mpx_ueq@ instead of @MPX_UCMP@.
+ *
+ * Revision 1.4 2000/07/29 17:04:02 mdw
+ * Remove useless header `mpscan.h'.
+ *
+ * Revision 1.3 2000/06/17 11:42:54 mdw
+ * Moved the Karatsuba macros into a separate file for better sharing.
+ * Fixed some comments. Use an improved technique so that all the
+ * operations are squarings.
+ *
+ * Revision 1.2 1999/12/13 15:35:01 mdw
+ * Simplify and improve.
+ *
* Revision 1.1 1999/12/11 10:57:43 mdw
* Karatsuba squaring algorithm.
*
/*----- Header files ------------------------------------------------------*/
+#include <assert.h>
#include <stdio.h>
#include "mpx.h"
+#include "mpx-kmac.h"
/*----- Tweakables --------------------------------------------------------*/
# define KARATSUBA_CUTOFF 2
#endif
-/*----- Addition macros ---------------------------------------------------*/
-
-#define ULSL1(dv, av, avl) do { \
- mpw *_dv = (dv); \
- const mpw *_av = (av), *_avl = (avl); \
- mpw _c = 0; \
- \
- while (_av < _avl) { \
- mpw _x = *_av++; \
- *_dv++ = MPW(_c | (_x << 1)); \
- _c = MPW(_x >> (MPW_BITS - 1)); \
- } \
- *_dv++ = _c; \
-} while (0)
-
-#define UADD(dv, av, avl) do { \
- mpw *_dv = (dv); \
- const mpw *_av = (av), *_avl = (avl); \
- mpw _c = 0; \
- \
- while (_av < _avl) { \
- mpw _a, _b; \
- mpd _x; \
- _a = *_av++; \
- _b = *_dv; \
- _x = (mpd)_a + (mpd)_b + _c; \
- *_dv++ = MPW(_x); \
- _c = _x >> MPW_BITS; \
- } \
- while (_c) { \
- mpd _x = (mpd)*_dv + (mpd)_c; \
- *_dv++ = MPW(_x); \
- _c = _x >> MPW_BITS; \
- } \
-} while (0)
-
/*----- Main code ---------------------------------------------------------*/
/* --- @mpx_ksqr@ --- *
/* --- How the algorithm works --- *
*
- * Unlike Karatsuba's identity for multiplication which isn't particularly
- * obvious, the identity for multiplication is known to all schoolchildren.
- * Let %$A = xb + y$%. Then %$A^2 = x^2 b^x + 2 x y b + y^2$%. So now I
- * have three multiplications, each four times easier, and that's a win.
+ * The identity for squaring is known to all schoolchildren.
+ * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now,
+ * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
+ * squarings.
*/
/* --- First things --- *
m = (avl - av + 1) >> 1;
avm = av + m;
+ assert(((void)"Destination too small for Karatsuba square",
+ dvl - dv >= 4 * m));
+ assert(((void)"Not enough workspace for Karatsuba square",
+ svl - sv >= 4 * m));
+
/* --- Sort out everything --- */
{
- mpw *ssv = sv + 2 * m;
+ mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
mpw *tdv = dv + m;
mpw *rdv = tdv + m;
- /* --- The cross term in the middle needs a multiply --- *
- *
- * This isn't actually true, since %$x y = ((x + y)^2 - (x - y)^2)/4%.
- * But that's two squarings, versus one multiplication.
- */
-
+ UADD2(sv, svm, av, avm, avm, avl);
if (m > KARATSUBA_CUTOFF)
- mpx_kmul(sv, ssv, av, avm, avm, avl, ssv, svl);
+ mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
else
- mpx_umul(sv, ssv, av, avm, avm, avl);
- ULSL1(tdv, sv, ssv);
- MPX_ZERO(dv, tdv);
- MPX_ZERO(rdv + m + 1, dvl);
+ mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
if (m > KARATSUBA_CUTOFF)
mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
else
mpx_usqr(sv, ssv, avm, avl);
- UADD(rdv, sv, ssv);
+ MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
+ UADD(rdv, sv, svm + 1);
+ USUB(tdv, sv, svn);
if (m > KARATSUBA_CUTOFF)
mpx_ksqr(sv, ssv, av, avm, ssv, svl);
else
mpx_usqr(sv, ssv, av, avm);
- UADD(dv, sv, ssv);
+ MPX_COPY(dv, tdv, sv, svm);
+ UADD(tdv, svm, svn);
+ USUB(tdv, sv, svn);
}
}
#include <mLib/alloc.h>
#include <mLib/testrig.h>
-#include "mpscan.h"
-
#define ALLOC(v, vl, sz) do { \
size_t _sz = (sz); \
mpw *_vv = xmalloc(MPWS(_sz)); \
ALLOC(s, sl, 2 * m + 32);
mpx_ksqr(d, dl, a, al, s, sl);
- if (MPX_UCMP(d, dl, !=, c, cl)) {
+ if (!mpx_ueq(d, dl, c, cl)) {
fprintf(stderr, "\n*** usqr failed\n");
dumpmp(" a", a, al);
dumpmp("expected", c, cl);