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/* lrsmp.h (lrs extended precision arithmetic library) */
/* Copyright: David Avis 2000, avis@cs.mcgill.ca */
/* Version 4.0, February 17, 2000 */
/* This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
/******************************************************************************/
/* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for lrs usage instructions */
/******************************************************************************/
/* This package contains the extended precision routines used by lrs
and some other miscellaneous routines. The maximum precision depends on
the parameter MAX_DIGITS defined below, with usual default of 255L. This
gives a maximum of 1020 decimal digits on 32 bit machines. The procedure
lrs_mp_init(dec_digits) may set a smaller number of dec_digits, and this
is useful if arrays or matrices will be used.
*/
/***********/
/* defines */
/***********/
/*
this is number of longwords. Increasing this won't cost you that much
since only variables other than the A matrix are allocated this size.
Changing affects running time in small but not very predictable ways.
*/
#define MAX_DIGITS 255L
/*
this is in decimal digits, you pay in memory if you increase this,
unless you override by a line with
digits n
before the begin line of your file.
*/
#define DEFAULT_DIGITS 100L
/**********MACHINE DEPENDENT CONSTANTS***********/
/* MAXD is 2^(k-1)-1 where k=16,32,64 word size */
/* MAXD must be at least 2*BASE^2 */
/* If BASE is 10^k, use "%k.ku" for FORMAT */
/* INTSIZE is number of bytes for integer */
/* 32/64 bit machines */
/***********************************************/
#ifndef B64
/*32 bit machines */
#define FORMAT "%4.4lu"
#define MAXD 2147483647L
#define BASE 10000L
#define BASE_DIG 4
#define INTSIZE 8L
#define BIT "32bit"
#else
/* 64 bit machines */
#define MAXD 9223372036854775807L
#define BASE 1000000000L
#define FORMAT "%9.9lu"
#define BASE_DIG 9
#define INTSIZE 16L
#define BIT "64bit"
#endif
#define MAXINPUT 1000 /*max length of any input rational */
#define POS 1L
#define NEG -1L
#ifndef TRUE
#define TRUE 1L
#endif
#ifndef FALSE
#define FALSE 0L
#endif
#define ONE 1L
#define TWO 2L
#define ZERO 0L
/**********************************/
/* MACROS */
/* dependent on mp implementation */
/**********************************/
#define exactdivint(a,b,c) divint((a),(b),(c)) /*should use special code here */
#define positive(a) (((a)[0] < 2 || ((a)[0]==2 && (a)[1]==0))?FALSE:TRUE)
#define negative(a) (((a)[0] > -2 || ((a)[0]==-2 && (a)[1]==0))?FALSE:TRUE)
#define zero(a) ((((a)[0]==2 || (a)[0]==-2) && (a)[1]==0)?TRUE:FALSE)
#define one(a) (((a)[0]==2 && (a)[1]==1)?TRUE:FALSE)
#define length(a) (((a)[0] > 0) ? (a)[0] : -(a)[0])
#define sign(a) (((a)[0] < 0) ? NEG : POS)
#define storesign(a,sa) a[0]=((a)[0] > 0) ? (sa)*((a)[0]) : -(sa)*((a)[0])
#define changesign(a) a[0]= -(a)[0]
#define storelength(a,la) a[0]=((a)[0] > 0) ? (la) : -(la)
/*
* convert between decimal and machine (longword digits). Notice lovely
* implementation of ceiling function :-)
*/
#define DEC2DIG(d) ( (d) % BASE_DIG ? (d)/BASE_DIG+1 : (d)/BASE_DIG)
#define DIG2DEC(d) ((d)*BASE_DIG)
#include <stdlib.h>
#ifdef SIGNALS
#include <signal.h>
#include <unistd.h>
#define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);}
#endif
#define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__)
/*************/
/* typedefs */
/*************/
typedef long lrs_mp[MAX_DIGITS + 1]; /* type lrs_mp holds one multi-precision integer */
typedef long *lrs_mp_t;
typedef long **lrs_mp_vector;
typedef long ***lrs_mp_matrix;
/*********************/
/*global variables */
/*********************/
long lrs_digits; /* max permitted no. of digits */
long lrs_record_digits; /* this is the biggest acheived so far. */
FILE *lrs_ifp; /* input file pointer */
FILE *lrs_ofp; /* output file pointer */
/*********************************************************/
/* Initialization and allocation procedures - must use! */
/******************************************************* */
/* next two functions are not used by lrsmp, but are for lrsgmp compatability */
#define lrs_alloc_mp(a)
#define lrs_clear_mp(a)
lrs_mp_t lrs_alloc_mp_t(); /* dynamic allocation of lrs_mp */
lrs_mp_vector lrs_alloc_mp_vector (long n); /* allocate lrs_mp_vector for n+1 lrs_mp numbers */
lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n); /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp */
void lrs_clear_mp_vector (lrs_mp_vector a, long n);
void lrs_clear_mp_matrix (lrs_mp_matrix a, long m, long n);
long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */
/*********************************************************/
/* Core library functions - depend on mp implementation */
/******************************************************* */
void atomp (char s[], lrs_mp a); /* convert string to lrs_mp integer */
long compare (lrs_mp a, lrs_mp b); /* a ? b and returns -1,0,1 for <,=,> */
void copy (lrs_mp a, lrs_mp b); /* assigns a=b */
void divint (lrs_mp a, lrs_mp b, lrs_mp c); /* c=a/b, a contains remainder on return */
void gcd (lrs_mp u, lrs_mp v); /* returns u=gcd(u,v) destroying v */
long greater (lrs_mp a, lrs_mp b); /* tests if a > b and returns (TRUE=POS) */
void itomp (long in, lrs_mp a); /* convert integer i to lrs_mp */
void linint (lrs_mp a, long ka, lrs_mp b, long kb); /* compute a*ka+b*kb --> a */
void mptodouble (lrs_mp a, double *x); /* convert lrs_mp to double */
long mptoi (lrs_mp a); /* convert lrs_mp to long integer */
void mulint (lrs_mp a, lrs_mp b, lrs_mp c); /* multiply two integers a*b --> c */
void normalize (lrs_mp a); /* normalize lrs_mp after computation */
void pmp (char name[], lrs_mp a); /* print the long precision integer a */
void prat (char name[], lrs_mp Nt, lrs_mp Dt); /* reduce and print Nt/Dt */
void readmp (lrs_mp a); /* read an integer and convert to lrs_mp */
long readrat (lrs_mp Na, lrs_mp Da); /* read a rational or int and convert to lrs_mp */
void reduce (lrs_mp Na, lrs_mp Da); /* reduces Na Da by gcd(Na,Da) */
/*********************************************************/
/* Standard arithmetic & misc. functions */
/* should be independent of mp implementation */
/******************************************************* */
void atoaa (char in[], char num[], char den[]); /* convert rational string in to num/den strings */
void addint (lrs_mp a, lrs_mp b, lrs_mp c); /* compute c=a+b */
long atos (char s[]); /* convert s to integer */
long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd); /* +1 if Na*Nb > Nc*Nd,-1 if Na*Nb > Nc*Nd else 0 */
void decint (lrs_mp a, lrs_mp b); /* compute a=a-b */
void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc);
/* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */
void getfactorial (lrs_mp factorial, long k); /* compute k factorial in lrs_mp */
void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc);
void lcm (lrs_mp a, lrs_mp b); /* a = least common multiple of a, b; b is saved */
void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc);
/* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */
long myrandom (long num, long nrange); /* return a random number in range 0..nrange-1 */
void notimpl (char s[]); /* bail out - help! */
void rattodouble (lrs_mp a, lrs_mp b, double *x); /* convert lrs_mp rational to double */
void reduceint (lrs_mp Na, lrs_mp Da); /* divide Na by Da and return it */
void reducearray (lrs_mp_vector p, long n); /* find gcd of p[0]..p[n-1] and divide through by */
void scalerat (lrs_mp Na, lrs_mp Da, long ka); /* scales rational by ka */
void subint (lrs_mp a, lrs_mp b, lrs_mp c); /* compute c=a-b */
/**********************************/
/* Miscellaneous functions */
/******************************** */
void free (void *);
void lrs_getdigits (long *a, long *b); /* send digit information to user */
void stringcpy (char *s, char *t); /* copy t to s pointer version */
void *calloc ();
void *malloc ();
void *xcalloc (long n, long s, long l, char *f);
void lrs_default_digits_overflow ();
void digits_overflow ();
/* end of lrsmp.h (vertex enumeration using lexicographic reverse search) */
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