text: /* 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/>.
  ***********************************************************************/
  
  #ifdef __clang__
  #pragma clang diagnostic ignored "-Wlogical-op-parentheses"
  #pragma clang diagnostic ignored "-Wsign-conversion"
  #endif
  
  #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);
        mpz_mul(q, &x->q, &y->p);
        mpz_add(p, p, q);
        mpz_mul(q, &x->q, &y->q);
        mpz_set(&z->p, p);
        mpz_set(&z->q, q);
        mpz_clear(p);
        mpz_clear(q);
        mpq_canonicalize(z);
        return;
  }
  
  void mpq_sub(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);
        mpz_mul(q, &x->q, &y->p);
        mpz_sub(p, p, q);
        mpz_mul(q, &x->q, &y->q);
        mpz_set(&z->p, p);
        mpz_set(&z->q, q);
        mpz_clear(p);
        mpz_clear(q);
        mpq_canonicalize(z);
        return;
  }
  
  void mpq_mul(mpq_t z, mpq_t x, mpq_t y)
  {     /* set z to x * y */
        mpz_mul(&z->p, &x->p, &y->p);
        mpz_mul(&z->q, &x->q, &y->q);
        mpq_canonicalize(z);
        return;
  }
  
  void mpq_div(mpq_t z, mpq_t x, mpq_t y)
  {     /* set z to x / y */
        mpz_t p, q;
        if (mpq_sgn(y) == 0)
           xfault("mpq_div: zero divisor not allowed\n");
        mpz_init(p);
        mpz_init(q);
        mpz_mul(p, &x->p, &y->q);
        mpz_mul(q, &x->q, &y->p);
        mpz_set(&z->p, p);
        mpz_set(&z->q, q);
        mpz_clear(p);
        mpz_clear(q);
        mpq_canonicalize(z);
        return;
  }
  
  void mpq_neg(mpq_t z, mpq_t x)
  {     /* set z to 0 - x */
        mpq_set(z, x);
        mpz_neg(&z->p, &z->p);
        return;
  }
  
  void mpq_abs(mpq_t z, mpq_t x)
  {     /* set z to the absolute value of x */
        mpq_set(z, x);
        mpz_abs(&z->p, &z->p);
        xassert(mpz_sgn(&x->q) > 0);
        return;
  }
  
  int mpq_cmp(mpq_t x, mpq_t y)
  {     /* compare x and y; return a positive value if x > y, zero if
           x = y, or a nefative value if x < y */
        mpq_t temp;
        int s;
        mpq_init(temp);
        mpq_sub(temp, x, y);
        s = mpq_sgn(temp);
        mpq_clear(temp);
        return s;
  }
  
  int mpq_sgn(mpq_t x)
  {     /* return +1 if x > 0, 0 if x = 0, and -1 if x < 0 */
        int s;
        s = mpz_sgn(&x->p);
        xassert(mpz_sgn(&x->q) > 0);
        return s;
  }
  
  int mpq_out_str(void *_fp, int base, mpq_t x)
  {     /* output x on stream fp, as a string in given base; the base
           may vary from 2 to 36; output is in the form 'num/den' or if
           the denominator is 1 then just 'num';
           if the parameter fp is a null pointer, stdout is assumed;
           return the number of bytes written, or if an error occurred,
           return 0 */
        FILE *fp = _fp;
        int nwr;
        if (!(2 <= base && base <= 36))
           xfault("mpq_out_str: base = %d; invalid base\n", base);
        /* if (fp == NULL) fp = stdout; */
        nwr = mpz_out_str(fp, base, &x->p);
        if (x->q.val == 1 && x->q.ptr == NULL)
           ;
        else
        {  fputc('/', fp), nwr++;
           nwr += mpz_out_str(fp, base, &x->q);
        }
        if (ferror(fp)) nwr = 0;
        return nwr;
  }
  
  #endif
  
  /* eof */
  