/* -*-c-*-
*
- * $Id: mpx.h,v 1.7 1999/12/11 01:51:28 mdw Exp $
+ * $Id: mpx.h,v 1.8 1999/12/11 10:57:43 mdw Exp $
*
* Low level multiprecision arithmetic
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpx.h,v $
+ * Revision 1.8 1999/12/11 10:57:43 mdw
+ * Karatsuba squaring algorithm.
+ *
* Revision 1.7 1999/12/11 01:51:28 mdw
* Change Karatsuba parameters slightly.
*
mpw _cc = 0; \
mpd _m = (m); \
\
- while (_av < _avl) { \
+ while (_dv < _dvl && _av < _avl) { \
mpd _x; \
- if (_dv >= _dvl) \
- break; \
_x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \
*_dv++ = MPW(_x); \
_cc = _x >> MPW_BITS; \
extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/,
const mpw */*av*/, const mpw */*avl*/);
+/* --- @mpx_udiv@ --- *
+ *
+ * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit
+ * @mpw *rv, *rvl@ = dividend/remainder vector base and limit
+ * @const mpw *dv, *dvl@ = divisor vector base and limit
+ * @mpw *sv, *svl@ = scratch workspace
+ *
+ * Returns: ---
+ *
+ * Use: Performs unsigned integer division. If the result overflows
+ * the quotient vector, high-order bits are discarded. (Clearly
+ * the remainder vector can't overflow.) The various vectors
+ * may not overlap in any way. Yes, I know it's a bit odd
+ * requiring the dividend to be in the result position but it
+ * does make some sense really. The remainder must have
+ * headroom for at least two extra words. The scratch space
+ * must be at least one word larger than the divisor.
+ */
+
+extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/,
+ const mpw */*dv*/, const mpw */*dvl*/,
+ mpw */*sv*/, mpw */*svl*/);
+
+/*----- Karatsuba multiplication algorithms -------------------------------*/
+
+/* --- @KARATSUBA_CUTOFF@ --- *
+ *
+ * This is the limiting length for using Karatsuba algorithms. It's best to
+ * use the simpler classical multiplication method on numbers smaller than
+ * this.
+ */
+
+#define KARATSUBA_CUTOFF 16
+
+/* --- @KARATSUBA_SLOP@ --- *
+ *
+ * The extra number of words required as scratch space by the Karatsuba
+ * routines. This is a (generous) guess, since the actual amount of space
+ * required is proportional to the recursion depth.
+ */
+
+#define KARATSUBA_SLOP 32
+
/* --- @mpx_kmul@ --- *
*
* Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
* more expensive on small ones.
*
* The destination and scratch buffers must be twice as large as
- * the larger argument.
+ * the larger argument. The scratch space must be twice as
+ * large as the larger argument, plus the magic number
+ * @KARATSUBA_SLOP@.
*/
-#define KARATSUBA_CUTOFF 20
-#define KARATSUBA_SLOP 32
-
extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/,
const mpw */*av*/, const mpw */*avl*/,
const mpw */*bv*/, const mpw */*bvl*/,
mpw */*sv*/, mpw */*svl*/);
-/* --- @mpx_udiv@ --- *
+/* --- @mpx_ksqr@ --- *
*
- * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit
- * @mpw *rv, *rvl@ = dividend/remainder vector base and limit
- * @const mpw *dv, *dvl@ = divisor vector base and limit
- * @mpw *sv, *svl@ = scratch workspace
+ * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
+ * @const mpw *av, *avl@ = pointer to first argument
+ * @mpw *sv, *svl@ = pointer to scratch workspace
*
* Returns: ---
*
- * Use: Performs unsigned integer division. If the result overflows
- * the quotient vector, high-order bits are discarded. (Clearly
- * the remainder vector can't overflow.) The various vectors
- * may not overlap in any way. Yes, I know it's a bit odd
- * requiring the dividend to be in the result position but it
- * does make some sense really. The remainder must have
- * headroom for at least two extra words. The scratch space
- * must be at least one word larger than the divisor.
+ * Use: Squares a multiprecision integers using something similar to
+ * Karatsuba's multiplication algorithm. This is rather faster
+ * than traditional long multiplication (e.g., @mpx_umul@) on
+ * large numbers, although more expensive on small ones, and
+ * rather simpler than full-blown Karatsuba multiplication.
+ *
+ * The destination must be twice as large as the argument. The
+ * scratch space must be twice as large as the argument, plus
+ * the magic number @KARATSUBA_SLOP@.
*/
-extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/,
- const mpw */*dv*/, const mpw */*dvl*/,
+extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/,
+ const mpw */*av*/, const mpw */*avl*/,
mpw */*sv*/, mpw */*svl*/);
/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff