## -*-makefile-*-
##
-## $Id: Makefile.m4,v 1.56 2001/06/16 13:01:10 mdw Exp $
+## $Id: Makefile.m4,v 1.57 2002/10/15 22:58:29 mdw Exp $
##
## Makefile for Catacomb
##
##----- Revision history ----------------------------------------------------
##
## $Log: Makefile.m4,v $
+## Revision 1.57 2002/10/15 22:58:29 mdw
+## Fast estimation of number representation lengths.
+##
## Revision 1.56 2001/06/16 13:01:10 mdw
## New source files and tests.
##
mp-misc.c mp-mem.c mp-const.c mp-io.c mp-arith.c mp-test.c \
mp-sqrt.c mp-gcd.c mp-jacobi.c mp-modsqrt.c \
mpint.c mptext.c mptext-file.c mptext-string.c mptext-dstr.c \
+ mptext-len.c \
exp.c mpcrt.c mpmul.c mprand.c \
mpbarrett.c mpbarrett-mexp.c mpbarrett-exp.h \
mpmont.c mpmont-mexp.c mpmont-exp.h \
--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: mptext-len.c,v 1.1 2002/10/15 22:58:29 mdw Exp $
+ *
+ * Work out length of a number's string representation
+ *
+ * (c) 2002 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: mptext-len.c,v $
+ * Revision 1.1 2002/10/15 22:58:29 mdw
+ * Fast estimation of number representation lengths.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "mp.h"
+#include "mptext.h"
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @mptext_len@ --- *
+ *
+ * Arguments: @mp *x@ = number to work on
+ * @int r@ = radix the number will be expressed in
+ *
+ * Returns: The number of digits needed to represent the number in the
+ * given base. This will not include space for a leading sign
+ * (use @MP_ISNEG@ to check that, or just add one on for luck);
+ * neither will it add space for a terminating null. In general
+ * the answer will be an overestimate.
+ */
+
+size_t mptext_len(mp *x, int r)
+{
+ unsigned long b = mp_bits(x);
+ int s, ss = 2;
+ size_t n;
+ unsigned d = 0;
+
+ /* --- Huh? --- *
+ *
+ * The number of digits is at most %$\lceil b \log 2/\log r \rceil$%. We
+ * produce an underestimate of %$\log_2 r = \log r/\log 2$% and divide by
+ * that. How? By linear interpolation between known points on the curve.
+ * The known points are precisely the powers of 2, so we can find a pair
+ * efficiently by doubling up. The log curve is convex, so linear
+ * interpolation between points on the curve is always an underestimate.
+ *
+ * The integer maths here is a bit weird, so here's how it works. If
+ * %$s = 2^d$% is the power of 2 below %$r$% then we want to compute
+ * %$\lceil b/(d + (r - s)/s) \rceil = \lceil (b s)/(s(d - 1) + r \rceil$%
+ * which is %$\lfloor (r + s (b + d - 1) - 1)/(r + s(d - 1)) \rfloor$%.
+ * Gluing the whole computation together like this makes the code hard to
+ * read, but means that there are fewer possibilities for rounding errors
+ * and thus we get a tighter bound.
+ */
+
+ /* --- Find the right pair of points --- */
+
+ do {
+ s = ss;
+ d++;
+ if (r == s) {
+ n = (b + (d - 1))/d;
+ goto done;
+ }
+ ss = s << 1;
+ } while (ss <= r);
+
+ /* --- Do the interpolation --- */
+
+ n = (r + s*(b + d - 1) - 1)/(r + s*(d - 1));
+
+ /* --- Fixups --- */
+
+done:
+ if (!n)
+ n = 1;
+ return (n);
+}
+
+/*----- That's all, folks -------------------------------------------------*/
/* -*-c-*-
*
- * $Id: mptext.h,v 1.5 2000/10/08 12:04:58 mdw Exp $
+ * $Id: mptext.h,v 1.6 2002/10/15 22:58:29 mdw Exp $
*
* Textual representation of multiprecision numbers
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mptext.h,v $
+ * Revision 1.6 2002/10/15 22:58:29 mdw
+ * Fast estimation of number representation lengths.
+ *
* Revision 1.5 2000/10/08 12:04:58 mdw
* (MP_DOFPRINTFR): cope with null pointers.
*
extern int mp_write(mp */*m*/, int /*radix*/,
const mptext_ops */*ops*/, void */*p*/);
+/* --- @mptext_len@ --- *
+ *
+ * Arguments: @mp *x@ = number to work on
+ * @int r@ = radix the number will be expressed in
+ *
+ * Returns: The number of digits needed to represent the number in the
+ * given base. This will not include space for a leading sign
+ * (use @MP_ISNEG@ to check that, or just add one on for luck);
+ * neither will it add space for a terminating null. In general
+ * the answer will be an overestimate.
+ */
+
+extern size_t mptext_len(mp */*x*/, int /*r*/);
+
/*----- File I/O ----------------------------------------------------------*/
#include <stdio.h>
projects / u / mdw / catacomb / commitdiff