X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/a86e33af1ea11503350b37dbf64a7518c27b583e..f654f4218ac36981a1174b1f09823997239b0358:/mpx-kmul.c

diff --git a/mpx-kmul.c b/mpx-kmul.c
index d97700f..dd492ad 100644
--- a/mpx-kmul.c
+++ b/mpx-kmul.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpx-kmul.c,v 1.1 1999/12/10 23:23:51 mdw Exp $
+ * $Id: mpx-kmul.c,v 1.4 2000/06/17 11:42:11 mdw Exp $
  *
  * Karatsuba's multiplication algorithm
  *
@@ -30,6 +30,16 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpx-kmul.c,v $
+ * Revision 1.4  2000/06/17 11:42:11  mdw
+ * Moved the Karatsuba macros into a separate file for better sharing.
+ * Fixed some comments.
+ *
+ * Revision 1.3  1999/12/13 15:35:01  mdw
+ * Simplify and improve.
+ *
+ * Revision 1.2  1999/12/11 10:58:02  mdw
+ * Remove tweakable comments.
+ *
  * Revision 1.1  1999/12/10 23:23:51  mdw
  * Karatsuba-Ofman multiplication algorithm.
  *
@@ -37,94 +47,19 @@
 
 /*----- Header files ------------------------------------------------------*/
 
+#include <assert.h>
 #include <stdio.h>
 
 #include "mpx.h"
+#include "mpx-kmac.h"
 
 /*----- Tweakables --------------------------------------------------------*/
 
-/* --- @KARATSUBA_CUTOFF@ --- *
- *
- * If either of the arguments to @mpx_kmul@ contains this number of words or
- * fewer, the job is dumped out to @mpx_umul@ instead.  Reduce the size when
- * testing, to ensure better coverage.
- */
-
 #ifdef TEST_RIG
 #  undef KARATSUBA_CUTOFF
 #  define KARATSUBA_CUTOFF 2
 #endif
 
-/*----- Addition macros ---------------------------------------------------*/
-
-#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)
-
-#define UADD2(dv, dvl, av, avl, bv, bvl) do {				\
-  mpw *_dv = (dv), *_dvl = (dvl);					\
-  const mpw *_av = (av), *_avl = (avl);					\
-  const mpw *_bv = (bv), *_bvl = (bvl);					\
-  mpw _c = 0;								\
-									\
-  while (_av < _avl || _bv < _bvl) {					\
-    mpw _a, _b;								\
-    mpd _x;								\
-    _a = (_av < _avl) ? *_av++ : 0;					\
-    _b = (_bv < _bvl) ? *_bv++ : 0;					\
-    _x = (mpd)_a + (mpd)_b + _c;					\
-    *_dv++ = MPW(_x);							\
-    _c = _x >> MPW_BITS;						\
-  }									\
-  *_dv++ = _c;								\
-  while (_dv < _dvl)							\
-    *_dv++ = 0;								\
-} while (0)
-
-#define USUB(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)_b - (mpd)_a - _c;					\
-    *_dv++ = MPW(_x);							\
-    if (_x >> MPW_BITS)							\
-      _c = 1;								\
-    else								\
-      _c = 0;								\
-  }									\
-  while (_c) {								\
-    mpd _x = (mpd)*_dv - (mpd)_c;					\
-    *_dv++ = MPW(_x);							\
-    if (_x >> MPW_BITS)							\
-      _c = 1;								\
-    else								\
-      _c = 0;								\
-  }									\
-} while (0)
-
 /*----- Main code ---------------------------------------------------------*/
 
 /* --- @mpx_kmul@ --- *
@@ -144,10 +79,6 @@
  *		The destination must be twice as large as the larger
  *		argument.  The scratch space must be twice as large as the
  *		larger argument, plus the magic number @KARATSUBA_SLOP@.
- *		(Actually, a number of words proportional to the depth of
- *		recursion, but since recusion is strongly bounded by memory,
- *		I can replace it with a constant as long as it's `big
- *		enough'.)
  */
 
 void mpx_kmul(mpw *dv, mpw *dvl,
@@ -176,11 +107,11 @@ void mpx_kmul(mpw *dv, mpw *dvl,
 
   /* --- How the algorithm works --- *
    *
-   * Let %$A = xb + y$% and %$B = ub + v$%.  Then, simply by expanding, %$AB
-   * = x u b^2 + b(x v + y u) + y v$%.  That's not helped any, because I've
-   * got four multiplications, each four times easier than the one I started
-   * with.  However, note that I can rewrite the coefficient of %$b$% as
-   * %$xv + yu = (x + y)(u + v) - xu - yv$%.  The terms %$xu$% and %$yv$%
+   * Let %$A = xb + y$% and %$B = ub + v$%.  Then, simply by expanding,
+   * %$AB = x u b^2 + b(x v + y u) + y v$%.  That's not helped any, because
+   * I've got four multiplications, each four times easier than the one I
+   * started with.  However, note that I can rewrite the coefficient of %$b$%
+   * as %$xv + yu = (x + y)(u + v) - xu - yv$%.  The terms %$xu$% and %$yv$%
    * I've already calculated, and that leaves only one more multiplication to
    * do.  So now I have three multiplications, each four times easier, and
    * that's a win.
@@ -209,64 +140,51 @@ void mpx_kmul(mpw *dv, mpw *dvl,
       avm = avl;
   }
 
-  /* --- Sort out the middle term --- *
-   *
-   * I'm going to keep track of the carry by hand rather than pass it down to
-   * the next level, because it means multiplication by one or zero, which I
-   * can do easily myself.
-   */
+  assert(((void)"Destination too small for Karatsuba multiply",
+	  dvl - dv >= 4 * m));
+  assert(((void)"Not enough workspace for Karatsuba multiply",
+	  svl - sv >= 4 * m));
+
+  /* --- Sort out the middle term --- */
 
   {
-    unsigned f = 0;
-    enum {
-      carry_a = 1,
-      carry_b = 2
-    };
-
-    mpw *bsv = sv + m, *ssv = bsv + m;
-    mpw *rdv = dv + m, *rdvl = rdv + 2 * m;
-
-    UADD2(sv, bsv + 1, av, avm, avm, avl);
-    if (*bsv)
-      f |= carry_a;
-    UADD2(bsv, ssv + 1, bv, bvm, bvm, bvl);
-    if (*ssv)
-      f |= carry_b;
-    MPX_ZERO(dv, rdv);
+    mpw *bsv = sv + m + 1, *ssv = bsv + m + 1;
+    mpw *rdv = dv + m, *rdvl = rdv + 2 * (m + 2);
+
+    UADD2(sv, bsv, av, avm, avm, avl);
+    UADD2(bsv, ssv, bv, bvm, bvm, bvl);
     if (m > KARATSUBA_CUTOFF)
       mpx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
     else
       mpx_umul(rdv, rdvl, sv, bsv, bsv, ssv);
-    MPX_ZERO(rdvl, dvl);
-    rdv += m; rdvl += m;
-    if (f & carry_b)
-      UADD(rdv, sv, bsv);
-    if (f & carry_a)
-      UADD(rdv, bsv, ssv);
-    if (!(~f & (carry_a | carry_b)))
-      MPX_UADDN(rdv + m, rdvl, 1);
   }
 
   /* --- Sort out the other two terms --- */
 
   {
-    mpw *ssv = sv + 2 * m;
+    mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
     mpw *tdv = dv + m;
     mpw *rdv = tdv + m;
 
-    if (m > KARATSUBA_CUTOFF)
-      mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
-    else
-      mpx_umul(sv, ssv, avm, avl, bvm, bvl);
-    UADD(rdv, sv, ssv);
-    USUB(tdv, sv, ssv);
-    
+    if (avl == avm || bvl == bvm)
+      MPX_ZERO(rdv + m + 1, dvl);
+    else {
+      if (m > KARATSUBA_CUTOFF)
+	mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
+      else
+	mpx_umul(sv, ssv, avm, avl, bvm, bvl);
+      MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
+      UADD(rdv, sv, svm + 1);
+      USUB(tdv, sv, svn);
+    }
+
     if (m > KARATSUBA_CUTOFF)
       mpx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
     else
       mpx_umul(sv, ssv, av, avm, bv, bvm);
-    USUB(tdv, sv, ssv);
-    UADD(dv, sv, ssv);
+    MPX_COPY(dv, tdv, sv, svm);
+    USUB(tdv, sv, svn);
+    UADD(tdv, svm, svn);
   }
 }