From: mdw Date: Tue, 15 Oct 2002 22:58:29 +0000 (+0000) Subject: Fast estimation of number representation lengths. X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/commitdiff_plain/0cbfe12eb239d2fbfe95a3f798308f861bc6a819 Fast estimation of number representation lengths. --- diff --git a/Makefile.m4 b/Makefile.m4 index 19c6eba..0f2e3c3 100644 --- a/Makefile.m4 +++ b/Makefile.m4 @@ -1,6 +1,6 @@ ## -*-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 ## @@ -29,6 +29,9 @@ ##----- 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. ## @@ -317,6 +320,7 @@ define(`MP_SOURCES', 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 \ diff --git a/mptext-len.c b/mptext-len.c new file mode 100644 index 0000000..e9aee49 --- /dev/null +++ b/mptext-len.c @@ -0,0 +1,106 @@ +/* -*-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 -------------------------------------------------*/ diff --git a/mptext.h b/mptext.h index db4e591..57c4dc2 100644 --- a/mptext.h +++ b/mptext.h @@ -1,6 +1,6 @@ /* -*-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 * @@ -30,6 +30,9 @@ /*----- 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. * @@ -107,6 +110,20 @@ extern mp *mp_read(mp */*m*/, int /*radix*/, 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