/* lrsmp.c     library code for lrs extended precision arithmetic */
/* Version 4.0b, Feb. 8, 2000                             */
/* Copyright: David Avis 1999, avis@cs.mcgill.ca          */

/* 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.
 */

/******************************************************************/
/* digit overflow is caught by digits_overflow at the end of this */
/* file, make sure it is either user supplied or uncomment        */
/*  the define below                                              */
/******************************************************************/

#define digits_overflow() lrs_default_digits_overflow()

#include <stdio.h>
#include <string.h>
#include "lrsmp.h"

/*********************************************************/
/* Initialization and allocation procedures - must use!  */
/******************************************************* */

long 
lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout)
/* max number of decimal digits for the computation */
{
/* global variables lrs_ifp and lrs_ofp are file pointers for input and output   */

  lrs_ifp = fpin;
  lrs_ofp = fpout;
  lrs_record_digits = 0;

  if (dec_digits <= 0)
    dec_digits = DEFAULT_DIGITS;

  lrs_digits = DEC2DIG (dec_digits);	/* max permitted no. of digits   */

  if (lrs_digits > MAX_DIGITS)
    {
      fprintf (lrs_ofp, "\nDigits must be at most %ld\nChange MAX_DIGITS and recompile\n",
	       DIG2DEC (MAX_DIGITS));
      lrs_digits = MAX_DIGITS;
      return FALSE;
    }

  return TRUE;
}

lrs_mp_t
lrs_alloc_mp_t ()
 /* dynamic allocation of lrs_mp number */
{
  lrs_mp_t p;
  p=(long *)calloc (lrs_digits+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]);
 free(p);
}

/*********************************************************/
/* Core library functions - depend on mp implementation  */
/******************************************************* */

void 
copy (lrs_mp a, lrs_mp b)	/* assigns a=b  */
{
  long i;
  for (i = 0; i <= length (b); i++)
    a[i] = b[i];
}

/********************************************************/
/* Divide two multiple precision integers (c=a/b).      */
/* a is destroyed and contains the remainder on return. */
/* From Knuth Vol.2 SemiNumerical Algorithms            */
/* coded by J. Quinn                                    */
/********************************************************/
void 
divint (lrs_mp a, lrs_mp b, lrs_mp c)	/* c=a/b, a contains remainder on return */
{
  long cy, la, lb, lc, d1, s, t, sig;
  long i, j, qh;

/*  figure out and save sign, do everything with positive numbers */
  sig = sign (a) * sign (b);

  la = length (a);
  lb = length (b);
  lc = la - lb + 2;
  if (la < lb)
    {
      storelength (c, TWO);
      storesign (c, POS);
      c[1] = 0;
      normalize (c);
      return;
    }
  for (i = 1; i < lc; i++)
    c[i] = 0;
  storelength (c, lc);
  storesign (c, (sign (a) == sign (b)) ? POS : NEG);

/******************************/
  /* division by a single word: */
  /*  do it directly            */
/******************************/

  if (lb == 2)
    {
      cy = 0;
      t = b[1];
      for (i = la - 1; i > 0; i--)
	{
	  cy = cy * BASE + a[i];
	  a[i] = 0;
	  cy -= (c[i] = cy / t) * t;
	}
      a[1] = cy;
      storesign (a, (cy == 0) ? POS : sign (a));
      storelength (a, TWO);
      /*      set sign of c to sig  (**mod**)            */
      storesign (c, sig);
      normalize (c);
      return;
    }
  else
    {
      /* mp's are actually DIGITS+1 in length, so if length of a or b = */
      /* DIGITS, there will still be room after normalization. */
/****************************************************/
      /* Step D1 - normalize numbers so b > floor(BASE/2) */
      d1 = BASE / (b[lb - 1] + 1);
      if (d1 > 1)
	{
	  cy = 0;
	  for (i = 1; i < la; i++)
	    {
	      cy = (a[i] = a[i] * d1 + cy) / BASE;
	      a[i] %= BASE;
	    }
	  a[i] = cy;
	  cy = 0;
	  for (i = 1; i < lb; i++)
	    {
	      cy = (b[i] = b[i] * d1 + cy) / BASE;
	      b[i] %= BASE;
	    }
	  b[i] = cy;
	}
      else
	{
	  a[la] = 0;		/* if la or lb = DIGITS this won't work */
	  b[lb] = 0;
	}
/*********************************************/
      /* Steps D2 & D7 - start and end of the loop */
      for (j = 0; j <= la - lb; j++)
	{
/*************************************/
	  /* Step D3 - determine trial divisor */
	  if (a[la - j] == b[lb - 1])
	    qh = BASE - 1;
	  else
	    {
	      s = (a[la - j] * BASE + a[la - j - 1]);
	      qh = s / b[lb - 1];
	      while (qh * b[lb - 2] > (s - qh * b[lb - 1]) * BASE + a[la - j - 2])
		qh--;
	    }
/*******************************************************/
	  /* Step D4 - divide through using qh as quotient digit */
	  cy = 0;
	  for (i = 1; i <= lb; i++)
	    {
	      s = qh * b[i] + cy;
	      a[la - j - lb + i] -= s % BASE;
	      cy = s / BASE;
	      if (a[la - j - lb + i] < 0)
		{
		  a[la - j - lb + i] += BASE;
		  cy++;
		}
	    }
/*****************************************************/
	  /* Step D6 - adjust previous step if qh is 1 too big */
	  if (cy)
	    {
	      qh--;
	      cy = 0;
	      for (i = 1; i <= lb; i++)		/* add a back in */
		{
		  a[la - j - lb + i] += b[i] + cy;
		  cy = a[la - j - lb + i] / BASE;
		  a[la - j - lb + i] %= BASE;
		}
	    }
/***********************************************************************/
	  /* Step D5 - write final value of qh.  Saves calculating array indices */
	  /* to do it here instead of before D6 */

	  c[la - lb - j + 1] = qh;

	}
/**********************************************************************/
      /* Step D8 - unnormalize a and b to get correct remainder and divisor */

      for (i = lc; c[i - 1] == 0 && i > 2; i--);	/* strip excess 0's from quotient */
      storelength (c, i);
      if (i == 2 && c[1] == 0)
	storesign (c, POS);
      cy = 0;
      for (i = lb - 1; i >= 1; i--)
	{
	  cy = (a[i] += cy * BASE) % d1;
	  a[i] /= d1;
	}
      for (i = la; a[i - 1] == 0 && i > 2; i--);	/* strip excess 0's from quotient */
      storelength (a, i);
      if (i == 2 && a[1] == 0)
	storesign (a, POS);
      if (cy)
	fprintf (lrs_ofp, "divide error");
      for (i = lb - 1; i >= 1; i--)
	{
	  cy = (b[i] += cy * BASE) % d1;
	  b[i] /= d1;
	}
    }
}
/* end of divint */

void 
gcd (lrs_mp u, lrs_mp v)	/*returns u=gcd(u,v) destroying v */
	     /*Euclid's algorithm.  Knuth, II, p.320  
	        modified to avoid copies r=u,u=v,v=r
	        Switches to single precision when possible for greater speed */
{
  lrs_mp r;
  unsigned long ul, vl;
  long i;
  static unsigned long maxspval = MAXD;		/* Max value for the last digit to guarantee */
  /* fitting into a single long integer. */

  static long maxsplen;		/* Maximum digits for a number that will fit */
  /* into a single long integer. */

  static long firstime = TRUE;

  if (firstime)			/* initialize constants */
    {
      for (maxsplen = 2; maxspval >= BASE; maxsplen++)
	maxspval /= BASE;
      firstime = FALSE;
    }
  if (greater (v, u))
    goto bigv;
bigu:
  if (zero (v))
    return;
  if ((i = length (u)) < maxsplen || (i == maxsplen && u[maxsplen - 1] < maxspval))
    goto quickfinish;
  divint (u, v, r);
  normalize (u);

bigv:
  if (zero (u))
    {
      copy (u, v);
      return;
    }
  if ((i = length (v)) < maxsplen || (i == maxsplen && v[maxsplen - 1] < maxspval))
    goto quickfinish;
  divint (v, u, r);
  normalize (v);
  goto bigu;
  /* Base 10000 only at the moment */
  /* when u and v are small enough, transfer to single precision integers */
  /* and finish with euclid's algorithm, then transfer back to lrs_mp */
quickfinish:
  ul = vl = 0;
  for (i = length (u) - 1; i > 0; i--)
    ul = BASE * ul + u[i];
  for (i = length (v) - 1; i > 0; i--)
    vl = BASE * vl + v[i];
  if (ul > vl)
    goto qv;
qu:
  if (!vl)
    {
      for (i = 1; ul; i++)
	{
	  u[i] = ul % BASE;
	  ul = ul / BASE;
	}
      storelength (u, i);
      return;
    }
  ul %= vl;
qv:
  if (!ul)
    {
      for (i = 1; vl; i++)
	{
	  u[i] = vl % BASE;
	  vl = vl / BASE;
	}
      storelength (u, i);
      return;
    }
  vl %= ul;
  goto qu;
}

long 
compare (lrs_mp a, lrs_mp b)	/* a ? b and returns -1,0,1 for <,=,> */
{
  long i;

  if (a[0] > b[0])
    return 1L;
  if (a[0] < b[0])
    return -1L;

  for (i = length (a) - 1; i >= 1; i--)
    {
      if (a[i] < b[i])
	{
	  if (sign (a) == POS)
	    return -1L;
	  else
	    return 1L;
	}
      if (a[i] > b[i])
	{
	  if (sign (a) == NEG)
	    return -1L;
	  else
	    return 1L;
	}
    }
  return 0L;
}


long 
greater (lrs_mp a, lrs_mp b)	/* tests if a > b and returns (TRUE=POS) */
{
  long i;

  if (a[0] > b[0])
    return (TRUE);
  if (a[0] < b[0])
    return (FALSE);

  for (i = length (a) - 1; i >= 1; i--)
    {
      if (a[i] < b[i])
	{
	  if (sign (a) == POS)
	    return (0);
	  else
	    return (1);
	}
      if (a[i] > b[i])
	{
	  if (sign (a) == NEG)
	    return (0);
	  else
	    return (1);
	}
    }
  return (0);
}
void 
itomp (long in, lrs_mp a)
    /* convert integer i to multiple precision with base BASE */
{
  long i;
  a[0] = 2;			/* initialize to zero */
  for (i = 1; i < lrs_digits; i++)
    a[i] = 0;
  if (in < 0)
    {
      storesign (a, NEG);
      in = in * (-1);
    }
  i = 0;
  while (in != 0)
    {
      i++;
      a[i] = in - BASE * (in / BASE);
      in = in / BASE;
      storelength (a, i + 1);
    }
}				/* end of itomp */


void 
linint (lrs_mp a, long ka, lrs_mp b, long kb)	/*compute a*ka+b*kb --> a */
/***Handbook of Algorithms and Data Structures P.239 ***/
{
  long i, la, lb;
  la = length (a);
  lb = length (b);
  for (i = 1; i < la; i++)
    a[i] *= ka;
  if (sign (a) != sign (b))
    kb = (-kb);
  if (lb > la)
    {
      storelength (a, lb);
      for (i = la; i < lb; i++)
	a[i] = 0;
    }
  for (i = 1; i < lb; i++)
    a[i] += kb * b[i];
  normalize (a);
}
/***end of linint***/


void 
mptodouble (lrs_mp a, double *x)	/* convert lrs_mp to double */
{
  long i, la;
  double y = 1.0;

  (*x) = 0;
  la = length (a);
  for (i = 1; i < la; i++)
    {
      (*x) = (*x) + y * a[i];
      y = y * BASE;
    }
  if (negative (a))
    (*x)= -(*x);
}

void 
mulint (lrs_mp a, lrs_mp b, lrs_mp c)	/* multiply two integers a*b --> c */

/***Handbook of Algorithms and Data Structures, p239  ***/
{
  long nlength, i, j, la, lb;
/*** b and c may coincide ***/
  la = length (a);
  lb = length (b);
  nlength = la + lb - 2;
  if (nlength > lrs_digits)
    digits_overflow ();

  for (i = 0; i < la - 2; i++)
    c[lb + i] = 0;
  for (i = lb - 1; i > 0; i--)
    {
      for (j = 2; j < la; j++)
	if ((c[i + j - 1] += b[i] * a[j]) >
	    MAXD - (BASE - 1) * (BASE - 1) - MAXD / BASE)
	  {
	    c[i + j - 1] -= (MAXD / BASE) * BASE;
	    c[i + j] += MAXD / BASE;
	  }
      c[i] = b[i] * a[1];
    }
  storelength (c, nlength);
  storesign (c, sign (a) == sign (b) ? POS : NEG);
  normalize (c);
}
/***end of mulint ***/

void 
normalize (lrs_mp a)
{
  long cy, i, la;
  la = length (a);
start:
  cy = 0;
  for (i = 1; i < la; i++)
    {
      cy = (a[i] += cy) / BASE;
      a[i] -= cy * BASE;
      if (a[i] < 0)
	{
	  a[i] += BASE;
	  cy--;
	}
    }
  while (cy > 0)
    {
      a[i++] = cy % BASE;
      cy /= BASE;
    }
  if (cy < 0)
    {
      a[la - 1] += cy * BASE;
      for (i = 1; i < la; i++)
	a[i] = (-a[i]);
      storesign (a, sign (a) == POS ? NEG : POS);
      goto start;
    }
  while (a[i - 1] == 0 && i > 2)
    i--;
  if (i > lrs_record_digits)
    {
      if ((lrs_record_digits = i) > lrs_digits)
	digits_overflow ();
    };
  storelength (a, i);
  if (i == 2 && a[1] == 0)
    storesign (a, POS);
}				/* end of normalize */


long 
mptoi (lrs_mp a)		/* convert lrs_mp to long integer */
{
  long len = length (a);
  if (len == 2)
    return sign (a) * a[1];
  if (len == 3)
    return sign (a) * (a[1] + BASE * a[2]);
  notimpl ("mp to large for conversion to long");
  return 0;			/* never executed */
}

void 
pmp (char name[], lrs_mp a)	/*print the long precision integer a */
{
  long i;
  fprintf (lrs_ofp, "%s", name);
  if (sign (a) == NEG)
    fprintf (lrs_ofp, "-");
  else
    fprintf (lrs_ofp, " ");
  fprintf (lrs_ofp, "%lu", a[length (a) - 1]);
  for (i = length (a) - 2; i >= 1; i--)
    fprintf (lrs_ofp, FORMAT, a[i]);
  fprintf (lrs_ofp, " ");
}


void 
prat (char name[], lrs_mp Nin, lrs_mp Din)	/*reduce and print Nin/Din  */
{
  lrs_mp Nt, Dt;
  long i;
  fprintf (lrs_ofp, "%s", name);
/* reduce fraction */
  copy (Nt, Nin);
  copy (Dt, Din);
  reduce (Nt, Dt);
/* print out       */
  if (sign (Nin) * sign (Din) == NEG)
    fprintf (lrs_ofp, "-");
  else
    fprintf (lrs_ofp, " ");
  fprintf (lrs_ofp, "%lu", Nt[length (Nt) - 1]);
  for (i = length (Nt) - 2; i >= 1; i--)
    fprintf (lrs_ofp, FORMAT, Nt[i]);
  if (!(Dt[0] == 2 && Dt[1] == 1))	/* rational */
    {
      fprintf (lrs_ofp, "/");
      fprintf (lrs_ofp, "%lu", Dt[length (Dt) - 1]);
      for (i = length (Dt) - 2; i >= 1; i--)
	fprintf (lrs_ofp, FORMAT, Dt[i]);
    }
  fprintf (lrs_ofp, " ");
}

void 
readmp (lrs_mp a)
      /* read an integer and convert to lrs_mp with base BASE */
{
  char in[MAXINPUT];
  fscanf (lrs_ifp, "%s", in);
  atomp (in, a);
}

long 
readrat (lrs_mp Na, lrs_mp Da)
 /* read a rational or integer and convert to lrs_mp with base BASE */
 /* 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 
addint (lrs_mp a, lrs_mp b, lrs_mp c)	/* compute c=a+b */
{
  copy (c, a);
  linint (c, 1, b, 1);
}

void 
atomp (char s[], lrs_mp a)	/*convert string to lrs_mp integer */
{
  lrs_mp mpone;
  long diff, ten, i, sig;
  itomp (1L, 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 
subint (lrs_mp a, lrs_mp b, lrs_mp c)	/* compute c=a-b */

{
  copy (c, a);
  linint (a, 1, b, -1);
}

void 
decint (lrs_mp a, lrs_mp b)	/* compute a=a-b */

{
  linint (a, 1, b, -1);
}


long 
myrandom (long num, long nrange)
/* return a random number in range 0..nrange-1 */

{
  long i;
  i = (num * 401 + 673) % nrange;
  return (i);
}


long 
atos (char s[])			/* convert s to integer */
{
  long i, j;
  j = 0;
  for (i = 0; s[i] >= '0' && s[i] <= '9'; ++i)
    j = 10 * j + s[i] - '0';
  return (j);
}

void 
stringcpy (char *s, char *t)	/*copy t to s pointer version */
{
  while (((*s++) = (*t++)) != '\0');
}


void 
rattodouble (lrs_mp a, lrs_mp b, double *x)	/* convert lrs_mp rational to double */

{
  double y;
  mptodouble (a, &y);
  mptodouble (b, x);
  *x = y / (*x);
}


void 
atoaa (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 
lcm (lrs_mp a, lrs_mp b)
/* a = least common multiple of a, b; b is preserved */
{
  lrs_mp u, v;
  copy (u, a);
  copy (v, b);
  gcd (u, v);
  exactdivint (a, u, v);		/* v=a/u   no remainder*/
  mulint (v, b, a);
}				/* end of lcm */

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 */


void 
reduceint (lrs_mp Na, lrs_mp Da)	/* divide Na by Da and return */
{
  lrs_mp Temp;
  copy (Temp, Na);
  exactdivint (Temp, Da, Na);
}

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);
}


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  */
{
  lrs_mp mc, md;
  mulint (Na, Nb, mc);
  mulint (Nc, Nd, md);
  linint (mc, ONE, md, -ONE);
  if (positive (mc))
    return (1);
  if (negative (mc))
    return (-1);
  return (0);
}


void 
notimpl (char s[])
{
  fflush (stdout);
  fprintf (stderr, "\nAbnormal Termination  %s\n", s);
  exit (1);
}

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 */
/***************************************************************/
/*     Package of routines for rational arithmetic             */
/***************************************************************/

void 
scalerat (lrs_mp Na, lrs_mp Da, long ka)	/* scales rational by ka */
{
  lrs_mp Nt;
  copy (Nt, Na);
  itomp (ZERO, Na);
  linint (Na, ZERO, Nt, ka);
  reduce (Na, Da);
}

void 
linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc)
/* computes Nc/Dc = ka*Na/Da  +kb* Nb/Db
   and reduces answer by gcd(Nc,Dc) */
{
  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 (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 reduces answer by gcd(Nc,Dc) */
{
  mulint (Na, Db, Nc);
  mulint (Da, Nb, Dc);
  reduce (Nc, Dc);
}

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 reduces by gcd(Nc,Dc) */
{
  mulint (Na, Nb, Nc);
  mulint (Da, Db, Dc);
  reduce (Nc, Dc);
}

/*     End package of routines for rational arithmetic         */

/***************************************************************/
/*                                                             */
/*  End of package for multiple precision arithmetic           */
/*                                                             */
/***************************************************************/


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;
}

void 
lrs_getdigits (long *a, long *b)
{
/* send digit information to user */
  *a = DIG2DEC (lrs_digits);
  *b = DIG2DEC (lrs_record_digits);
  return;
}

void 
lrs_default_digits_overflow ()
{
  fprintf (lrs_ofp, "\nOverflow at digits=%ld", DIG2DEC (lrs_digits));
  fprintf (lrs_ofp, "\nInitialize lrs_mp_init with  n > %ldL\n", DIG2DEC (lrs_digits));

  exit (1);
}

/* end of lrsmp.c */