/* glpgmp.c */

/***********************************************************************

*  This code is part of GLPK (GNU Linear Programming Kit).

*

*  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

*  2009, 2010 Andrew Makhorin, Department for Applied Informatics,

*  Moscow Aviation Institute, Moscow, Russia. All rights reserved.

*  E-mail: <mao@gnu.org>.

*

*  GLPK 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 3 of the License, or

*  (at your option) any later version.

*

*  GLPK 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 GLPK. If not, see <http://www.gnu.org/licenses/>.

***********************************************************************/

#define _GLPSTD_STDIO

#include "glpdmp.h"

#include "glpgmp.h"

#define xfault xerror

#ifdef HAVE_GMP               /* use GNU MP bignum library */

int gmp_pool_count(void) { return 0; }

void gmp_free_mem(void) { return; }

#else                         /* use GLPK bignum module */

static DMP *gmp_pool = NULL;

static int gmp_size = 0;

static unsigned short *gmp_work = NULL;

void *gmp_get_atom(int size)

{     if (gmp_pool == NULL)

         gmp_pool = dmp_create_pool();

      return dmp_get_atom(gmp_pool, size);

}

void gmp_free_atom(void *ptr, int size)

{     xassert(gmp_pool != NULL);

      dmp_free_atom(gmp_pool, ptr, size);

      return;

}

int gmp_pool_count(void)

{     if (gmp_pool == NULL)

         return 0;

      else

         return dmp_in_use(gmp_pool).lo;

}

unsigned short *gmp_get_work(int size)

{     xassert(size > 0);

      if (gmp_size < size)

      {  if (gmp_size == 0)

         {  xassert(gmp_work == NULL);

            gmp_size = 100;

         }

         else

         {  xassert(gmp_work != NULL);

            xfree(gmp_work);

         }

         while (gmp_size < size) gmp_size += gmp_size;

         gmp_work = xcalloc(gmp_size, sizeof(unsigned short));

      }

      return gmp_work;

}

void gmp_free_mem(void)

{     if (gmp_pool != NULL) dmp_delete_pool(gmp_pool);

      if (gmp_work != NULL) xfree(gmp_work);

      gmp_pool = NULL;

      gmp_size = 0;

      gmp_work = NULL;

      return;

}

/*====================================================================*/

mpz_t _mpz_init(void)

{     /* initialize x, and set its value to 0 */

      mpz_t x;

      x = gmp_get_atom(sizeof(struct mpz));

      x->val = 0;

      x->ptr = NULL;

      return x;

}

void mpz_clear(mpz_t x)

{     /* free the space occupied by x */

      mpz_set_si(x, 0);

      xassert(x->ptr == NULL);

      /* free the number descriptor */

      gmp_free_atom(x, sizeof(struct mpz));

      return;

}

void mpz_set(mpz_t z, mpz_t x)

{     /* set the value of z from x */

      struct mpz_seg *e, *ee, *es;

      if (z != x)

      {  mpz_set_si(z, 0);

         z->val = x->val;

         xassert(z->ptr == NULL);

         for (e = x->ptr, es = NULL; e != NULL; e = e->next)

         {  ee = gmp_get_atom(sizeof(struct mpz_seg));

            memcpy(ee->d, e->d, 12);

            ee->next = NULL;

            if (z->ptr == NULL)

               z->ptr = ee;

            else

               es->next = ee;

            es = ee;

         }

      }

      return;

}

void mpz_set_si(mpz_t x, int val)

{     /* set the value of x to val */

      struct mpz_seg *e;

      /* free existing segments, if any */

      while (x->ptr != NULL)

      {  e = x->ptr;

         x->ptr = e->next;

         gmp_free_atom(e, sizeof(struct mpz_seg));

      }

      /* assign new value */

      if (val == 0x80000000)

      {  /* long format is needed */

         x->val = -1;

         x->ptr = e = gmp_get_atom(sizeof(struct mpz_seg));

         memset(e->d, 0, 12);

         e->d[1] = 0x8000;

         e->next = NULL;

      }

      else

      {  /* short format is enough */

         x->val = val;

      }

      return;

}

double mpz_get_d(mpz_t x)

{     /* convert x to a double, truncating if necessary */

      struct mpz_seg *e;

      int j;

      double val, deg;

      if (x->ptr == NULL)

         val = (double)x->val;

      else

      {  xassert(x->val != 0);

         val = 0.0;

         deg = 1.0;

         for (e = x->ptr; e != NULL; e = e->next)

         {  for (j = 0; j <= 5; j++)

            {  val += deg * (double)((int)e->d[j]);

               deg *= 65536.0;

            }

         }

         if (x->val < 0) val = - val;

      }

      return val;

}

double mpz_get_d_2exp(int *exp, mpz_t x)

{     /* convert x to a double, truncating if necessary (i.e. rounding

         towards zero), and returning the exponent separately;

         the return value is in the range 0.5 <= |d| < 1 and the

         exponent is stored to *exp; d*2^exp is the (truncated) x value;

         if x is zero, the return is 0.0 and 0 is stored to *exp;

         this is similar to the standard C frexp function */

      struct mpz_seg *e;

      int j, n, n1;

      double val;

      if (x->ptr == NULL)

         val = (double)x->val, n = 0;

      else

      {  xassert(x->val != 0);

         val = 0.0, n = 0;

         for (e = x->ptr; e != NULL; e = e->next)

         {  for (j = 0; j <= 5; j++)

            {  val += (double)((int)e->d[j]);

               val /= 65536.0, n += 16;

            }

         }

         if (x->val < 0) val = - val;

      }

      val = frexp(val, &n1);

      *exp = n + n1;

      return val;

}

void mpz_swap(mpz_t x, mpz_t y)

{     /* swap the values x and y efficiently */

      int val;

      void *ptr;

      val = x->val, ptr = x->ptr;

      x->val = y->val, x->ptr = y->ptr;

      y->val = val, y->ptr = ptr;

      return;

}

static void normalize(mpz_t x)

{     /* normalize integer x that includes removing non-significant

         (leading) zeros and converting to short format, if possible */

      struct mpz_seg *es, *e;

      /* if the integer is in short format, it remains unchanged */

      if (x->ptr == NULL)

      {  xassert(x->val != 0x80000000);

         goto done;

      }

      xassert(x->val == +1 || x->val == -1);

      /* find the last (most significant) non-zero segment */

      es = NULL;

      for (e = x->ptr; e != NULL; e = e->next)

      {  if (e->d[0] || e->d[1] || e->d[2] ||

             e->d[3] || e->d[4] || e->d[5]) es = e;

      }

      /* if all segments contain zeros, the integer is zero */

      if (es == NULL)

      {  mpz_set_si(x, 0);

         goto done;

      }

      /* remove non-significant (leading) zero segments */

      while (es->next != NULL)

      {  e = es->next;

         es->next = e->next;

         gmp_free_atom(e, sizeof(struct mpz_seg));

      }

      /* convert the integer to short format, if possible */

      e = x->ptr;

      if (e->next == NULL && e->d[1] <= 0x7FFF &&

         !e->d[2] && !e->d[3] && !e->d[4] && !e->d[5])

      {  int val;

         val = (int)e->d[0] + ((int)e->d[1] << 16);

         if (x->val < 0) val = - val;

         mpz_set_si(x, val);

      }

done: return;

}

void mpz_add(mpz_t z, mpz_t x, mpz_t y)

{     /* set z to x + y */

      static struct mpz_seg zero = { { 0, 0, 0, 0, 0, 0 }, NULL };

      struct mpz_seg dumx, dumy, *ex, *ey, *ez, *es, *ee;

      int k, sx, sy, sz;

      unsigned int t;

      /* if [x] = 0 then [z] = [y] */

      if (x->val == 0)

      {  xassert(x->ptr == NULL);

         mpz_set(z, y);

         goto done;

      }

      /* if [y] = 0 then [z] = [x] */

      if (y->val == 0)

      {  xassert(y->ptr == NULL);

         mpz_set(z, x);

         goto done;

      }

      /* special case when both [x] and [y] are in short format */

      if (x->ptr == NULL && y->ptr == NULL)

      {  int xval = x->val, yval = y->val, zval = x->val + y->val;

         xassert(xval != 0x80000000 && yval != 0x80000000);

         if (!(xval > 0 && yval > 0 && zval <= 0 ||

               xval < 0 && yval < 0 && zval >= 0))

         {  mpz_set_si(z, zval);

            goto done;

         }

      }

      /* convert [x] to long format, if necessary */

      if (x->ptr == NULL)

      {  xassert(x->val != 0x80000000);

         if (x->val >= 0)

         {  sx = +1;

            t = (unsigned int)(+ x->val);

         }

         else

         {  sx = -1;

            t = (unsigned int)(- x->val);

         }

         ex = &dumx;

         ex->d[0] = (unsigned short)t;

         ex->d[1] = (unsigned short)(t >> 16);

         ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;

         ex->next = NULL;

      }

      else

      {  sx = x->val;

         xassert(sx == +1 || sx == -1);

         ex = x->ptr;

      }

      /* convert [y] to long format, if necessary */

      if (y->ptr == NULL)

      {  xassert(y->val != 0x80000000);

         if (y->val >= 0)

         {  sy = +1;

            t = (unsigned int)(+ y->val);

         }

         else

         {  sy = -1;

            t = (unsigned int)(- y->val);

         }

         ey = &dumy;

         ey->d[0] = (unsigned short)t;

         ey->d[1] = (unsigned short)(t >> 16);

         ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;

         ey->next = NULL;

      }

      else

      {  sy = y->val;

         xassert(sy == +1 || sy == -1);

         ey = y->ptr;

      }

      /* main fragment */

      sz = sx;

      ez = es = NULL;

      if (sx > 0 && sy > 0 || sx < 0 && sy < 0)

      {  /* [x] and [y] have identical signs -- addition */

         t = 0;

         for (; ex || ey; ex = ex->next, ey = ey->next)

         {  if (ex == NULL) ex = &zero;

            if (ey == NULL) ey = &zero;

            ee = gmp_get_atom(sizeof(struct mpz_seg));

            for (k = 0; k <= 5; k++)

            {  t += (unsigned int)ex->d[k];

               t += (unsigned int)ey->d[k];

               ee->d[k] = (unsigned short)t;

               t >>= 16;

            }

            ee->next = NULL;

            if (ez == NULL)

               ez = ee;

            else

               es->next = ee;

            es = ee;

         }

         if (t)

         {  /* overflow -- one extra digit is needed */

            ee = gmp_get_atom(sizeof(struct mpz_seg));

            ee->d[0] = 1;

            ee->d[1] = ee->d[2] = ee->d[3] = ee->d[4] = ee->d[5] = 0;

            ee->next = NULL;

            xassert(es != NULL);

            es->next = ee;

         }

      }

      else

      {  /* [x] and [y] have different signs -- subtraction */

         t = 1;

         for (; ex || ey; ex = ex->next, ey = ey->next)

         {  if (ex == NULL) ex = &zero;

            if (ey == NULL) ey = &zero;

            ee = gmp_get_atom(sizeof(struct mpz_seg));

            for (k = 0; k <= 5; k++)

            {  t += (unsigned int)ex->d[k];

               t += (0xFFFF - (unsigned int)ey->d[k]);

               ee->d[k] = (unsigned short)t;

               t >>= 16;

            }

            ee->next = NULL;

            if (ez == NULL)

               ez = ee;

            else

               es->next = ee;

            es = ee;

         }

         if (!t)

         {  /* |[x]| < |[y]| -- result in complement coding */

            sz = - sz;

            t = 1;

            for (ee = ez; ee != NULL; ee = ee->next)

            for (k = 0; k <= 5; k++)

            {  t += (0xFFFF - (unsigned int)ee->d[k]);

               ee->d[k] = (unsigned short)t;

               t >>= 16;

            }

         }

      }

      /* contruct and normalize result */

      mpz_set_si(z, 0);

      z->val = sz;

      z->ptr = ez;

      normalize(z);

done: return;

}

void mpz_sub(mpz_t z, mpz_t x, mpz_t y)

{     /* set z to x - y */

      if (x == y)

         mpz_set_si(z, 0);

      else

      {  y->val = - y->val;

         mpz_add(z, x, y);

         if (y != z) y->val = - y->val;

      }

      return;

}

void mpz_mul(mpz_t z, mpz_t x, mpz_t y)

{     /* set z to x * y */

      struct mpz_seg dumx, dumy, *ex, *ey, *es, *e;

      int sx, sy, k, nx, ny, n;

      unsigned int t;

      unsigned short *work, *wx, *wy;

      /* if [x] = 0 then [z] = 0 */

      if (x->val == 0)

      {  xassert(x->ptr == NULL);

         mpz_set_si(z, 0);

         goto done;

      }

      /* if [y] = 0 then [z] = 0 */

      if (y->val == 0)

      {  xassert(y->ptr == NULL);

         mpz_set_si(z, 0);

         goto done;

      }

      /* special case when both [x] and [y] are in short format */

      if (x->ptr == NULL && y->ptr == NULL)

      {  int xval = x->val, yval = y->val, sz = +1;

         xassert(xval != 0x80000000 && yval != 0x80000000);

         if (xval < 0) xval = - xval, sz = - sz;

         if (yval < 0) yval = - yval, sz = - sz;

         if (xval <= 0x7FFFFFFF / yval)

         {  mpz_set_si(z, sz * (xval * yval));

            goto done;

         }

      }

      /* convert [x] to long format, if necessary */

      if (x->ptr == NULL)

      {  xassert(x->val != 0x80000000);

         if (x->val >= 0)

         {  sx = +1;

            t = (unsigned int)(+ x->val);

         }

         else

         {  sx = -1;

            t = (unsigned int)(- x->val);

         }

         ex = &dumx;

         ex->d[0] = (unsigned short)t;

         ex->d[1] = (unsigned short)(t >> 16);

         ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;

         ex->next = NULL;

      }

      else

      {  sx = x->val;

         xassert(sx == +1 || sx == -1);

         ex = x->ptr;

      }

      /* convert [y] to long format, if necessary */

      if (y->ptr == NULL)

      {  xassert(y->val != 0x80000000);

         if (y->val >= 0)

         {  sy = +1;

            t = (unsigned int)(+ y->val);

         }

         else

         {  sy = -1;

            t = (unsigned int)(- y->val);

         }

         ey = &dumy;

         ey->d[0] = (unsigned short)t;

         ey->d[1] = (unsigned short)(t >> 16);

         ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;

         ey->next = NULL;

      }

      else

      {  sy = y->val;

         xassert(sy == +1 || sy == -1);

         ey = y->ptr;

      }

      /* determine the number of digits of [x] */

      nx = n = 0;

      for (e = ex; e != NULL; e = e->next)

      for (k = 0; k <= 5; k++)

      {  n++;

         if (e->d[k]) nx = n;

      }

      xassert(nx > 0);

      /* determine the number of digits of [y] */

      ny = n = 0;

      for (e = ey; e != NULL; e = e->next)

      for (k = 0; k <= 5; k++)

      {  n++;

         if (e->d[k]) ny = n;

      }

      xassert(ny > 0);

      /* we need working array containing at least nx+ny+ny places */

      work = gmp_get_work(nx+ny+ny);

      /* load digits of [x] */

      wx = &work[0];

      for (n = 0; n < nx; n++) wx[ny+n] = 0;

      for (n = 0, e = ex; e != NULL; e = e->next)

         for (k = 0; k <= 5; k++, n++)

            if (e->d[k]) wx[ny+n] = e->d[k];

      /* load digits of [y] */

      wy = &work[nx+ny];

      for (n = 0; n < ny; n++) wy[n] = 0;

      for (n = 0, e = ey; e != NULL; e = e->next)

         for (k = 0; k <= 5; k++, n++)

            if (e->d[k]) wy[n] = e->d[k];

      /* compute [x] * [y] */

      bigmul(nx, ny, wx, wy);

      /* construct and normalize result */

      mpz_set_si(z, 0);

      z->val = sx * sy;

      es = NULL;

      k = 6;

      for (n = 0; n < nx+ny; n++)

      {  if (k > 5)

         {  e = gmp_get_atom(sizeof(struct mpz_seg));

            e->d[0] = e->d[1] = e->d[2] = 0;

            e->d[3] = e->d[4] = e->d[5] = 0;

            e->next = NULL;

            if (z->ptr == NULL)

               z->ptr = e;

            else

               es->next = e;

            es = e;

            k = 0;

         }

         es->d[k++] = wx[n];

      }

      normalize(z);

done: return;

}

void mpz_neg(mpz_t z, mpz_t x)

{     /* set z to 0 - x */

      mpz_set(z, x);

      z->val = - z->val;

      return;

}

void mpz_abs(mpz_t z, mpz_t x)

{     /* set z to the absolute value of x */

      mpz_set(z, x);

      if (z->val < 0) z->val = - z->val;

      return;

}

void mpz_div(mpz_t q, mpz_t r, mpz_t x, mpz_t y)

{     /* divide x by y, forming quotient q and/or remainder r

         if q = NULL then quotient is not stored; if r = NULL then

         remainder is not stored

         the sign of quotient is determined as in algebra while the

         sign of remainder is the same as the sign of dividend:

         +26 : +7 = +3, remainder is +5

         -26 : +7 = -3, remainder is -5

         +26 : -7 = -3, remainder is +5

         -26 : -7 = +3, remainder is -5 */

      struct mpz_seg dumx, dumy, *ex, *ey, *es, *e;

      int sx, sy, k, nx, ny, n;

      unsigned int t;

      unsigned short *work, *wx, *wy;

      /* divide by zero is not allowed */

      if (y->val == 0)

      {  xassert(y->ptr == NULL);

         xfault("mpz_div: divide by zero not allowed\n");

      }

      /* if [x] = 0 then [q] = [r] = 0 */

      if (x->val == 0)

      {  xassert(x->ptr == NULL);

         if (q != NULL) mpz_set_si(q, 0);

         if (r != NULL) mpz_set_si(r, 0);

         goto done;

      }

      /* special case when both [x] and [y] are in short format */

      if (x->ptr == NULL && y->ptr == NULL)

      {  int xval = x->val, yval = y->val;

         xassert(xval != 0x80000000 && yval != 0x80000000);

         if (q != NULL) mpz_set_si(q, xval / yval);

         if (r != NULL) mpz_set_si(r, xval % yval);

         goto done;

      }

      /* convert [x] to long format, if necessary */

      if (x->ptr == NULL)

      {  xassert(x->val != 0x80000000);

         if (x->val >= 0)

         {  sx = +1;

            t = (unsigned int)(+ x->val);

         }

         else

         {  sx = -1;

            t = (unsigned int)(- x->val);

         }

         ex = &dumx;

         ex->d[0] = (unsigned short)t;

         ex->d[1] = (unsigned short)(t >> 16);

         ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;

         ex->next = NULL;

      }

      else

      {  sx = x->val;

         xassert(sx == +1 || sx == -1);

         ex = x->ptr;

      }

      /* convert [y] to long format, if necessary */

      if (y->ptr == NULL)

      {  xassert(y->val != 0x80000000);

         if (y->val >= 0)

         {  sy = +1;

            t = (unsigned int)(+ y->val);

         }

         else

         {  sy = -1;

            t = (unsigned int)(- y->val);

         }

         ey = &dumy;

         ey->d[0] = (unsigned short)t;

         ey->d[1] = (unsigned short)(t >> 16);

         ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;

         ey->next = NULL;

      }

      else

      {  sy = y->val;

         xassert(sy == +1 || sy == -1);

         ey = y->ptr;

      }

      /* determine the number of digits of [x] */

      nx = n = 0;

      for (e = ex; e != NULL; e = e->next)

      for (k = 0; k <= 5; k++)

      {  n++;

         if (e->d[k]) nx = n;

      }

      xassert(nx > 0);

      /* determine the number of digits of [y] */

      ny = n = 0;

      for (e = ey; e != NULL; e = e->next)

      for (k = 0; k <= 5; k++)

      {  n++;

         if (e->d[k]) ny = n;

      }

      xassert(ny > 0);

      /* if nx < ny then [q] = 0 and [r] = [x] */

      if (nx < ny)

      {  if (r != NULL) mpz_set(r, x);

         if (q != NULL) mpz_set_si(q, 0);

         goto done;

      }

      /* we need working array containing at least nx+ny+1 places */

      work = gmp_get_work(nx+ny+1);

      /* load digits of [x] */

      wx = &work[0];

      for (n = 0; n < nx; n++) wx[n] = 0;

      for (n = 0, e = ex; e != NULL; e = e->next)

         for (k = 0; k <= 5; k++, n++)

            if (e->d[k]) wx[n] = e->d[k];

      /* load digits of [y] */

      wy = &work[nx+1];

      for (n = 0; n < ny; n++) wy[n] = 0;

      for (n = 0, e = ey; e != NULL; e = e->next)

         for (k = 0; k <= 5; k++, n++)

            if (e->d[k]) wy[n] = e->d[k];

      /* compute quotient and remainder */

      xassert(wy[ny-1] != 0);

      bigdiv(nx-ny, ny, wx, wy);

      /* construct and normalize quotient */

      if (q != NULL)

      {  mpz_set_si(q, 0);

         q->val = sx * sy;

         es = NULL;

         k = 6;

         for (n = ny; n <= nx; n++)

         {  if (k > 5)

            {  e = gmp_get_atom(sizeof(struct mpz_seg));

               e->d[0] = e->d[1] = e->d[2] = 0;

               e->d[3] = e->d[4] = e->d[5] = 0;

               e->next = NULL;

               if (q->ptr == NULL)

                  q->ptr = e;

               else

                  es->next = e;

               es = e;

               k = 0;

            }

            es->d[k++] = wx[n];

         }

         normalize(q);

      }

      /* construct and normalize remainder */

      if (r != NULL)

      {  mpz_set_si(r, 0);

         r->val = sx;

         es = NULL;

         k = 6;

         for (n = 0; n < ny; n++)

         {  if (k > 5)

            {  e = gmp_get_atom(sizeof(struct mpz_seg));

               e->d[0] = e->d[1] = e->d[2] = 0;

               e->d[3] = e->d[4] = e->d[5] = 0;

               e->next = NULL;

               if (r->ptr == NULL)

                  r->ptr = e;

               else

                  es->next = e;

               es = e;

               k = 0;

            }

            es->d[k++] = wx[n];

         }

         normalize(r);

      }

done: return;

}

void mpz_gcd(mpz_t z, mpz_t x, mpz_t y)

{     /* set z to the greatest common divisor of x and y */

      /* in case of arbitrary integers GCD(x, y) = GCD(|x|, |y|), and,

         in particular, GCD(0, 0) = 0 */

      mpz_t u, v, r;

      mpz_init(u);

      mpz_init(v);

      mpz_init(r);

      mpz_abs(u, x);

      mpz_abs(v, y);

      while (mpz_sgn(v))

      {  mpz_div(NULL, r, u, v);

         mpz_set(u, v);

         mpz_set(v, r);

      }

      mpz_set(z, u);

      mpz_clear(u);

      mpz_clear(v);

      mpz_clear(r);

      return;

}

int mpz_cmp(mpz_t x, mpz_t y)

{     /* compare x and y; return a positive value if x > y, zero if

         x = y, or a nefative value if x < y */

      static struct mpz_seg zero = { { 0, 0, 0, 0, 0, 0 }, NULL };

      struct mpz_seg dumx, dumy, *ex, *ey;

      int cc, sx, sy, k;

      unsigned int t;

      if (x == y)

      {  cc = 0;

         goto done;

      }

      /* special case when both [x] and [y] are in short format */

      if (x->ptr == NULL && y->ptr == NULL)

      {  int xval = x->val, yval = y->val;

         xassert(xval != 0x80000000 && yval != 0x80000000);

         cc = (xval > yval ? +1 : xval < yval ? -1 : 0);

         goto done;

      }

      /* special case when [x] and [y] have different signs */

      if (x->val > 0 && y->val <= 0 || x->val == 0 && y->val < 0)

      {  cc = +1;

         goto done;

      }

      if (x->val < 0 && y->val >= 0 || x->val == 0 && y->val > 0)

      {  cc = -1;

         goto done;

      }

      /* convert [x] to long format, if necessary */

      if (x->ptr == NULL)

      {  xassert(x->val != 0x80000000);

         if (x->val >= 0)

         {  sx = +1;

            t = (unsigned int)(+ x->val);

         }

         else

         {  sx = -1;

            t = (unsigned int)(- x->val);

         }

         ex = &dumx;

         ex->d[0] = (unsigned short)t;

         ex->d[1] = (unsigned short)(t >> 16);

         ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;

         ex->next = NULL;

      }

      else

      {  sx = x->val;

         xassert(sx == +1 || sx == -1);

         ex = x->ptr;

      }

      /* convert [y] to long format, if necessary */

      if (y->ptr == NULL)

      {  xassert(y->val != 0x80000000);

         if (y->val >= 0)

         {  sy = +1;

            t = (unsigned int)(+ y->val);

         }

         else

         {  sy = -1;

            t = (unsigned int)(- y->val);

         }

         ey = &dumy;

         ey->d[0] = (unsigned short)t;

         ey->d[1] = (unsigned short)(t >> 16);

         ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;

         ey->next = NULL;

      }

      else

      {  sy = y->val;

         xassert(sy == +1 || sy == -1);

         ey = y->ptr;

      }

      /* main fragment */

      xassert(sx > 0 && sy > 0 || sx < 0 && sy < 0);

      cc = 0;

      for (; ex || ey; ex = ex->next, ey = ey->next)

      {  if (ex == NULL) ex = &zero;

         if (ey == NULL) ey = &zero;

         for (k = 0; k <= 5; k++)

         {  if (ex->d[k] > ey->d[k]) cc = +1;

            if (ex->d[k] < ey->d[k]) cc = -1;

         }

      }

      if (sx < 0) cc = - cc;

done: return cc;

}

int mpz_sgn(mpz_t x)

{     /* return +1 if x > 0, 0 if x = 0, and -1 if x < 0 */

      int s;

      s = (x->val > 0 ? +1 : x->val < 0 ? -1 : 0);

      return s;

}

int mpz_out_str(void *_fp, int base, mpz_t x)

{     /* output x on stream fp, as a string in given base; the base

         may vary from 2 to 36;

         return the number of bytes written, or if an error occurred,

         return 0 */

      FILE *fp = _fp;

      mpz_t b, y, r;

      int n, j, nwr = 0;

      unsigned char *d;

      static char *set = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";

      if (!(2 <= base && base <= 36))

         xfault("mpz_out_str: base = %d; invalid base\n", base);

      mpz_init(b);

      mpz_set_si(b, base);

      mpz_init(y);

      mpz_init(r);

      /* determine the number of digits */

      mpz_abs(y, x);

      for (n = 0; mpz_sgn(y) != 0; n++)

         mpz_div(y, NULL, y, b);

      if (n == 0) n = 1;

      /* compute the digits */

      d = xmalloc(n);

      mpz_abs(y, x);

      for (j = 0; j < n; j++)

      {  mpz_div(y, r, y, b);

         xassert(0 <= r->val && r->val < base && r->ptr == NULL);

         d[j] = (unsigned char)r->val;

      }

      /* output the integer to the stream */

      if (fp == NULL) fp = stdout;

      if (mpz_sgn(x) < 0)

         fputc('-', fp), nwr++;

      for (j = n-1; j >= 0; j--)

         fputc(set[d[j]], fp), nwr++;

      if (ferror(fp)) nwr = 0;

      mpz_clear(b);

      mpz_clear(y);

      mpz_clear(r);

      xfree(d);

      return nwr;

}

/*====================================================================*/

mpq_t _mpq_init(void)

{     /* initialize x, and set its value to 0/1 */

      mpq_t x;

      x = gmp_get_atom(sizeof(struct mpq));

      x->p.val = 0;

      x->p.ptr = NULL;

      x->q.val = 1;

      x->q.ptr = NULL;

      return x;

}

void mpq_clear(mpq_t x)

{     /* free the space occupied by x */

      mpz_set_si(&x->p, 0);

      xassert(x->p.ptr == NULL);

      mpz_set_si(&x->q, 0);

      xassert(x->q.ptr == NULL);

      /* free the number descriptor */

      gmp_free_atom(x, sizeof(struct mpq));

      return;

}

void mpq_canonicalize(mpq_t x)

{     /* remove any factors that are common to the numerator and

         denominator of x, and make the denominator positive */

      mpz_t f;

      xassert(x->q.val != 0);

      if (x->q.val < 0)

      {  mpz_neg(&x->p, &x->p);

         mpz_neg(&x->q, &x->q);

      }

      mpz_init(f);

      mpz_gcd(f, &x->p, &x->q);

      if (!(f->val == 1 && f->ptr == NULL))

      {  mpz_div(&x->p, NULL, &x->p, f);

         mpz_div(&x->q, NULL, &x->q, f);

      }

      mpz_clear(f);

      return;

}

void mpq_set(mpq_t z, mpq_t x)

{     /* set the value of z from x */

      if (z != x)

      {  mpz_set(&z->p, &x->p);

         mpz_set(&z->q, &x->q);

      }

      return;

}

void mpq_set_si(mpq_t x, int p, unsigned int q)

{     /* set the value of x to p/q */

      if (q == 0)

         xfault("mpq_set_si: zero denominator not allowed\n");

      mpz_set_si(&x->p, p);

      xassert(q <= 0x7FFFFFFF);

      mpz_set_si(&x->q, q);

      return;

}

double mpq_get_d(mpq_t x)

{     /* convert x to a double, truncating if necessary */

      int np, nq;

      double p, q;

      p = mpz_get_d_2exp(&np, &x->p);

      q = mpz_get_d_2exp(&nq, &x->q);

      return ldexp(p / q, np - nq);

}

void mpq_set_d(mpq_t x, double val)

{     /* set x to val; there is no rounding, the conversion is exact */

      int s, n, d, j;

      double f;

      mpz_t temp;

      xassert(-DBL_MAX <= val && val <= +DBL_MAX);

      mpq_set_si(x, 0, 1);

      if (val > 0.0)

         s = +1;

      else if (val < 0.0)

         s = -1;

      else

         goto done;

      f = frexp(fabs(val), &n);

      /* |val| = f * 2^n, where 0.5 <= f < 1.0 */

      mpz_init(temp);

      while (f != 0.0)

      {  f *= 16.0, n -= 4;

         d = (int)f;

         xassert(0 <= d && d <= 15);

         f -= (double)d;

         /* x := 16 * x + d */

         mpz_set_si(temp, 16);

         mpz_mul(&x->p, &x->p, temp);

         mpz_set_si(temp, d);

         mpz_add(&x->p, &x->p, temp);

      }

      mpz_clear(temp);

      /* x := x * 2^n */

      if (n > 0)

      {  for (j = 1; j <= n; j++)

            mpz_add(&x->p, &x->p, &x->p);

      }

      else if (n < 0)

      {  for (j = 1; j <= -n; j++)

            mpz_add(&x->q, &x->q, &x->q);

         mpq_canonicalize(x);

      }

      if (s < 0) mpq_neg(x, x);

done: return;

}

void mpq_add(mpq_t z, mpq_t x, mpq_t y)

{     /* set z to x + y */

      mpz_t p, q;

      mpz_init(p);

      mpz_init(q);

      mpz_mul(p, &x->p, &y->q);