New interface for computing products of many (small) integers.

diff --git a/mpmul.c b/mpmul.c
new file mode 100644 (file)
index 0000000..46f7b72
--- /dev/null
+++ b/mpmul.c
@@ -0,0 +1,149 @@
+/* -*-c-*-
+ *
+ * $Id: mpmul.c,v 1.1 2000/07/01 11:21:39 mdw Exp $
+ *
+ * Multiply many small numbers together
+ *
+ * (c) 2000 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------* 
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ * 
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU Library General Public License for more details.
+ * 
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: mpmul.c,v $
+ * Revision 1.1  2000/07/01 11:21:39  mdw
+ * New interface for computing products of many (small) integers.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mpint.h"
+#include "mpmul.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @mpmul_init@ --- *
+ *
+ * Arguments:  @mpmul *b@ = pointer to multiplier context to initialize
+ *
+ * Returns:    ---
+ *
+ * Use:                Initializes a big multiplier context for use.
+ */
+
+void mpmul_init(mpmul *b)
+{
+  b->i = 0;
+}
+
+/* --- @mpmul_add@ --- *
+ *
+ * Arguments:  @mpmul *b@ = pointer to multiplier context
+ *             @mp *x@ = the next factor to multiply in
+ *
+ * Returns:    ---
+ *
+ * Use:                Contributes another factor to the mix.  It's important that
+ *             the integer lasts at least as long as the multiplication
+ *             context; this sort of rules out @mp_build@ integers.
+ */
+
+void mpmul_add(mpmul *b, mp *x)
+{
+  size_t i = b->i;
+
+  /* --- Now do the reduction step --- */
+
+  x = MP_COPY(x);
+
+  while (i > 0) {
+    if (MP_LEN(b->v[i - 1]) > MP_LEN(x))
+      break;
+    i--;
+    x = mp_mul(x, x, b->v[i]);
+    MP_DROP(b->v[i]);
+  }
+
+  if (i > HWM) {
+    while (i > LWM) {
+      i--;
+      x = mp_mul(x, x, b->v[i]);
+      MP_DROP(b->v[i]);
+    }
+  }
+
+  b->v[i] = x;
+  b->i = i;
+}
+
+/* --- @mpmul_done@ --- *
+ *
+ * Arguments:  @mpmul *b@ = pointer to big multiplication context
+ *
+ * Returns:    The product of all the numbers contributed.
+ *
+ * Use:                Returns a (large) product of numbers.  The context is
+ *             deallocated.
+ */
+
+mp *mpmul_done(mpmul *b)
+{
+  size_t i = b->i;
+  mp *x;
+
+  if (!i)
+    return (MP_ONE);
+  i--;
+  x = b->v[i];
+  while (i > 0) {
+    i--;
+    x = mp_mul(x, x, b->v[i]);
+    MP_DROP(b->v[i]);
+  }
+  return (x);
+}
+
+/* --- @mp_factorial@ --- *
+ *
+ * Arguments:  @unsigned long i@ = number whose factorial should be
+ *                     computed.
+ *
+ * Returns:    The requested factorial.
+ */
+
+mp *mp_factorial(unsigned long i)
+{
+  unsigned long j;
+  mp *x = MP_NEW;
+  mpmul b = MPMUL_INIT;
+
+  for (j = 1; j <= i; j++) {
+    x = mp_fromulong(x, j);
+    mpmul_add(&b, x);
+  }
+  mp_drop(x);
+  return (mpmul_done(&b));
+}
+
+/*----- That's all, folks -------------------------------------------------*/

diff --git a/mpmul.h b/mpmul.h
new file mode 100644 (file)
index 0000000..76c9559
--- /dev/null
+++ b/mpmul.h
@@ -0,0 +1,152 @@
+/* -*-c-*-
+ *
+ * $Id: mpmul.h,v 1.1 2000/07/01 11:21:39 mdw Exp $
+ *
+ * Multiply many small numbers together
+ *
+ * (c) 2000 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------* 
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ * 
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU Library General Public License for more details.
+ * 
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: mpmul.h,v $
+ * Revision 1.1  2000/07/01 11:21:39  mdw
+ * New interface for computing products of many (small) integers.
+ *
+ */
+
+#ifndef CATACOMB_MPMUL_H
+#define CATACOMB_MPMUL_H
+
+#ifdef __cplusplus
+  extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#ifndef CATACOMB_MP_H
+#  include "mp.h"
+#endif
+
+/*----- Magic numbers -----------------------------------------------------*/
+
+/* --- How the algorithm works --- *
+ *
+ * Multiplication on large integers is least wasteful when the numbers
+ * multiplied are approximately the same size.  When a new multiplier is
+ * added to the system, we push it onto a stack.  Then we `reduce' the stack:
+ * while the value on the top of the stack is not shorter than the value
+ * below it, replace the top two elements by their product.
+ *
+ * Let %$b$% be the radix of our multiprecision integers, and let %$Z$% be
+ * the maximum number of digits.  Then the largest integer we can represent
+ * is %$M - 1 = b^Z - 1$%.  We could assume that all of the integers we're
+ * given are about the same size.  This would give us the same upper bound as
+ * that derived in `mptext.c'.
+ *
+ * However, we're in less control over our inputs.  In particular, if a
+ * sequence of integers with strictly decreasing lengths is input then we're
+ * sunk.  Suppose that the stack contains, from top to bottom, %$b^i$%,
+ * %$b^{i+1}$%, ..., %$b^n$%.  The final product will therefore be
+ * %$p = b^{(n+i)(n-i+1)/2}$%.  We must now find the maximum stack depth
+ * %$d = n - i$% such that %$p > M$%.
+ *
+ * Taking logs of both sides gives that %$(d + 2 i)(d + 1) > 2 Z$%.  We can
+ * maximize %$d$% by taking %$i = 0$%, which gives that %$d^2 + d > 2 Z$%, so
+ * %$d$% must be approximately %$(\sqrt{8 Z + 1} - 1)/2$%, which is
+ * uncomfortably large.
+ *
+ * We compromise by choosing double the `mptext' bound and imposing high- and
+ * low-water marks for forced reduction.
+ */
+
+#define MPMUL_DEPTH (2 * (CHAR_BIT * sizeof(size_t) + 10))
+
+#define HWM (MPMUL_DEPTH - 20)
+#define LWM (MPMUL_DEPTH / 2)
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef struct mpmul {
+  size_t i;
+  mp *v[MPMUL_DEPTH];
+} mpmul;
+
+#define MPMUL_INIT { 0 }
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @mpmul_init@ --- *
+ *
+ * Arguments:  @mpmul *b@ = pointer to multiplier context to initialize
+ *
+ * Returns:    ---
+ *
+ * Use:                Initializes a big multiplier context for use.
+ */
+
+extern void mpmul_init(mpmul */*b*/);
+
+/* --- @mpmul_add@ --- *
+ *
+ * Arguments:  @mpmul *b@ = pointer to multiplier context
+ *             @mp *x@ = the next factor to multiply in
+ *
+ * Returns:    ---
+ *
+ * Use:                Contributes another factor to the mix.  It's important that
+ *             the integer lasts at least as long as the multiplication
+ *             context; this sort of rules out @mp_build@ integers.
+ */
+
+extern void mpmul_add(mpmul */*b*/, mp */*x*/);
+
+/* --- @mpmul_done@ --- *
+ *
+ * Arguments:  @mpmul *b@ = pointer to big multiplication context
+ *
+ * Returns:    The product of all the numbers contributed.
+ *
+ * Use:                Returns a (large) product of numbers.  The context is
+ *             deallocated.
+ */
+
+extern mp *mpmul_done(mpmul */*b*/);
+
+/* --- @mp_factorial@ --- *
+ *
+ * Arguments:  @unsigned long i@ = number whose factorial should be
+ *                     computed.
+ *
+ * Returns:    The requested factorial.
+ */
+
+extern mp *mp_factorial(unsigned long /*i*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+  }
+#endif
+
+#endif