/* lrslong.c library code for lrs extended precision arithmetic */
/* Version 4.0, April 13, 2000 */
/* Copyright: David Avis 1999, avis@cs.mcgill.ca */
/* Derived from prs_single.c ( rational arithmetic for lrs and prs) */
/* authored by Ambros Marzetta Revision 1.2 1998/05/27 */
#include <stdio.h>
#include <stdlib.h>
#include "lrslong.h"
long digits;
long record_digits;
#define MAXINPUT 1000 /*max length of any input rational */
void
gcd (lrs_mp u, lrs_mp v)
/* Returns u=gcd(u,v) using classic Euclid's algorithm.
v is destroyed. Knuth, II, p.320 */
{
unsigned long ul, vl, r;
ul = labs (*u);
vl = labs (*v);
if (ul == 0)
{
*u = vl;
return;
}
while (vl != 0)
{
r = ul % vl;
ul = vl;
vl = r;
}
*u = ul;
} /* gcd */
void
lcm (a, b) /* a = least common multiple of a, b; b is preserved */
lrs_mp a, b;
{
lrs_mp u, v;
copy (u, a);
copy (v, b);
gcd (u, v);
exactdivint (a, u, v); /* v=a/u a contains remainder = 0 */
mulint (v, b, a);
} /* end of lcm */
/***************************************************************/
/* */
/* Package of routines for rational arithmetic */
/* (Built on top of package for multiprecision arithmetic */
/* */
/***************************************************************/
void
reduce (lrs_mp Na, lrs_mp Da) /* reduces Na/Da by gcd(Na,Da) */
{
lrs_mp Nb, Db, Nc, Dc;
copy (Nb, Na);
copy (Db, Da);
storesign (Nb, POS);
storesign (Db, POS);
copy (Nc, Na);
copy (Dc, Da);
gcd (Nb, Db); /* Nb is the gcd(Na,Da) */
exactdivint (Nc, Nb, Na);
exactdivint (Dc, Nb, Da);
}
void
reduceint (lrs_mp Na, lrs_mp Da) /* divide Na by Da and return */
{
lrs_mp Temp;
copy (Temp, Na);
exactdivint (Temp, Da, Na);
}
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 */
/* 0 if Na*Nb = Nc*Nd */
{
long mc;
mc = *Na * *Nb - *Nc * *Nd;
if (mc > 0)
return 1;
if (mc < 0)
return -1;
return 0;
}
void
linrat (Na, Da, ka, Nb, Db, kb, Nc, Dc) /* computes Nc/Dc = ka*Na/Da +kb* Nb/Db
and reduces answer by gcd(Nc,Dc) */
lrs_mp Na, Da, Nb, Db, Nc, Dc;
long ka, kb;
{
lrs_mp c;
mulint (Na, Db, Nc);
mulint (Da, Nb, c);
linint (Nc, ka, c, kb); /* Nc = (ka*Na*Db)+(kb*Da*Nb) */
mulint (Da, Db, Dc); /* Dc = Da*Db */
reduce (Nc, Dc);
}
void
divrat (Na, Da, Nb, Db, Nc, Dc) /* computes Nc/Dc = (Na/Da) / ( Nb/Db )
and reduces answer by gcd(Nc,Dc) */
lrs_mp Na, Da, Nb, Db, Nc, Dc;
{
mulint (Na, Db, Nc);
mulint (Da, Nb, Dc);
reduce (Nc, Dc);
}
void
mulrat (Na, Da, Nb, Db, Nc, Dc) /* computes Nc/Dc = Na/Da * Nb/Db
and reduces answer by gcd(Nc,Dc) */
lrs_mp Na, Da, Nb, Db, Nc, Dc;
{
mulint (Na, Nb, Nc);
mulint (Da, Db, Dc);
reduce (Nc, Dc);
}
/***************************************************************/
/* */
/* Conversion and I/O functions */
/* */
/***************************************************************/
void
atomp (const char *s, lrs_mp a) /*convert string to lrs_mp integer */
/* based on atoi KR p.58 */
{
long diff, ten, i, sig;
lrs_mp mpone;
itomp (ONE, mpone);
ten = 10L;
for (i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++);
/*skip white space */
sig = POS;
if (s[i] == '+' || s[i] == '-') /* sign */
sig = (s[i++] == '+') ? POS : NEG;
itomp (0L, a);
while (s[i] >= '0' && s[i] <= '9')
{
diff = s[i] - '0';
linint (a, ten, mpone, diff);
i++;
}
storesign (a, sig);
if (s[i])
{
fprintf (stderr, "\nIllegal character in number: '%s'\n", s + i);
exit (1);
}
} /* end of atomp */
void
atoaa (const char *in, char *num, char *den)
/* convert rational string in to num/den strings */
{
long i, j;
for (i = 0; in[i] != '\0' && in[i] != '/'; i++)
num[i] = in[i];
num[i] = '\0';
den[0] = '\0';
if (in[i] == '/')
{
for (j = 0; in[j + i + 1] != '\0'; j++)
den[j] = in[i + j + 1];
den[j] = '\0';
}
} /* end of atoaa */
void
mptodouble (lrs_mp a, double *x) /* convert lrs_mp to double */
{
(*x) = (*a);
}
long
mptoi (lrs_mp a) /* convert lrs_mp to long */
{
return (*a);
}
void
rattodouble (lrs_mp a, lrs_mp b, double *x) /* convert lrs_mp rati
onal to double */
{
double y;
mptodouble (a, &y);
mptodouble (b, x);
*x = y / (*x);
}
long
readrat (lrs_mp Na, lrs_mp Da) /* read a rational or integer and convert to lrs_mp */
/* returns true if denominator is not one */
{
char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT];
fscanf (lrs_ifp, "%s", in);
atoaa (in, num, den); /*convert rational to num/dem strings */
atomp (num, Na);
if (den[0] == '\0')
{
itomp (1L, Da);
return (FALSE);
}
atomp (den, Da);
return (TRUE);
}
void
readmp (lrs_mp a) /* read an integer and convert to lrs_mp */
{
long in;
fscanf (lrs_ifp, "%ld", &in);
itomp (in, a);
}
void
pmp (char name[], lrs_mp Nt)
{
fprintf (lrs_ofp, "%s", name);
if (sign (Nt) != NEG)
fprintf (lrs_ofp, " ");
fprintf (lrs_ofp, "%ld", *Nt);
fprintf (lrs_ofp, " ");
}
void
prat (const char *name, lrs_mp Nin, lrs_mp Din)
/*print the long precision rational Nt/Dt */
{
lrs_mp Nt, Dt;
copy (Nt, Nin);
copy (Dt, Din);
reduce (Nt, Dt);
if (sign (Nt) != NEG)
fprintf (lrs_ofp, " ");
fprintf (lrs_ofp, "%s%ld", name, *Nt);
if (*Dt != 1)
fprintf (lrs_ofp, "/%ld", *Dt);
fprintf (lrs_ofp, " ");
} /* prat */
/***************************************************************/
/* */
/* Memory allocation functions */
/* */
/***************************************************************/
lrs_mp_t
lrs_alloc_mp_t ()
/* dynamic allocation of lrs_mp number */
{
lrs_mp_t p;
p=(long *)calloc (1, sizeof (long));
return p;
}
lrs_mp_vector
lrs_alloc_mp_vector (long n)
/* allocate lrs_mp_vector for n+1 lrs_mp numbers */
{
lrs_mp_vector p;
long i;
p = CALLOC ((n + 1), sizeof (lrs_mp *));
for (i = 0; i <= n; i++)
p[i] = CALLOC (1, sizeof (lrs_mp));
return p;
}
void
lrs_clear_mp_vector (lrs_mp_vector p, long n)
/* free space allocated to p */
{
long i;
for (i = 0; i <= n; i++)
free (p[i]);
free (p);
}
lrs_mp_matrix
lrs_alloc_mp_matrix (long m, long n)
/* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp numbers */
{
lrs_mp_matrix a;
long *araw;
int mp_width, row_width;
int i, j;
mp_width = lrs_digits + 1;
row_width = (n + 1) * mp_width;
araw = calloc ((m + 1) * row_width, sizeof (long));
a = calloc ((m + 1), sizeof (lrs_mp_vector));
for (i = 0; i < m + 1; i++)
{
a[i] = calloc ((n + 1), sizeof (lrs_mp *));
for (j = 0; j < n + 1; j++)
a[i][j] = (araw + i * row_width + j * mp_width);
}
return a;
}
void
lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n)
/* free space allocated to lrs_mp_matrix p */
{
long i;
/* p[0][0] is araw, the actual matrix storage address */
free(p[0][0]);
for (i = 0; i < m + 1; i++)
free (p[i]);
}
void
lrs_getdigits (long *a, long *b)
{
/* send digit information to user */
*a = DIG2DEC (ZERO);
*b = DIG2DEC (ZERO);
return;
}
void *
xcalloc (long n, long s, long l, char *f)
{
void *tmp;
tmp = calloc (n, s);
if (tmp == 0)
{
char buf[200];
sprintf (buf, "\n\nFatal error on line %ld of %s", l, f);
perror (buf);
exit (1);
}
return tmp;
}
long
lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout)
/* max number of decimal digits for the computation */
/* long int version */
{
lrs_ifp = fpin;
lrs_ofp = fpout;
lrs_record_digits = 0;
lrs_digits = 0; /* max permitted no. of digits */
return TRUE;
}
void
notimpl (char s[])
{
fflush (stdout);
fprintf (stderr, "\nAbnormal Termination %s\n", s);
exit (1);
}
/***************************************************************/
/* */
/* Misc. functions */
/* */
/***************************************************************/
void
reducearray (lrs_mp_vector p, long n)
/* find largest gcd of p[0]..p[n-1] and divide through */
{
lrs_mp divisor;
lrs_mp Temp;
long i = 0L;
while ((i < n) && zero (p[i]))
i++;
if (i == n)
return;
copy (divisor, p[i]);
storesign (divisor, POS);
i++;
while (i < n)
{
if (!zero (p[i]))
{
copy (Temp, p[i]);
storesign (Temp, POS);
gcd (divisor, Temp);
}
i++;
}
/* reduce by divisor */
for (i = 0; i < n; i++)
if (!zero (p[i]))
reduceint (p[i], divisor);
} /* end of reducearray */
long
myrandom (long num, long nrange)
/* return a random number in range 0..nrange-1 */
{
long i;
i = (num * 401 + 673) % nrange;
return (i);
}
void
getfactorial (lrs_mp factorial, long k) /* compute k factorial
in lrs_mp */
{
lrs_mp temp;
long i;
itomp (ONE, factorial);
for (i = 2; i <= k; i++)
{
itomp (i, temp);
mulint (temp, factorial, factorial);
}
} /* end of getfactorial */
void
stringcpy (char *s, char *t) /*copy t to s pointer version */
{
while (((*s++) = (*t++)) != '\0');
}
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