alpar@1: /* glpgmp.c */
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  This code is part of GLPK (GNU Linear Programming Kit).
alpar@1: *
alpar@1: *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
alpar@1: *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,
alpar@1: *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.
alpar@1: *  E-mail: <mao@gnu.org>.
alpar@1: *
alpar@1: *  GLPK is free software: you can redistribute it and/or modify it
alpar@1: *  under the terms of the GNU General Public License as published by
alpar@1: *  the Free Software Foundation, either version 3 of the License, or
alpar@1: *  (at your option) any later version.
alpar@1: *
alpar@1: *  GLPK is distributed in the hope that it will be useful, but WITHOUT
alpar@1: *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
alpar@1: *  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
alpar@1: *  License for more details.
alpar@1: *
alpar@1: *  You should have received a copy of the GNU General Public License
alpar@1: *  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
alpar@1: ***********************************************************************/
alpar@1: 
alpar@1: #define _GLPSTD_STDIO
alpar@1: #include "glpdmp.h"
alpar@1: #include "glpgmp.h"
alpar@1: #define xfault xerror
alpar@1: 
alpar@1: #ifdef HAVE_GMP               /* use GNU MP bignum library */
alpar@1: 
alpar@1: int gmp_pool_count(void) { return 0; }
alpar@1: 
alpar@1: void gmp_free_mem(void) { return; }
alpar@1: 
alpar@1: #else                         /* use GLPK bignum module */
alpar@1: 
alpar@1: static DMP *gmp_pool = NULL;
alpar@1: static int gmp_size = 0;
alpar@1: static unsigned short *gmp_work = NULL;
alpar@1: 
alpar@1: void *gmp_get_atom(int size)
alpar@1: {     if (gmp_pool == NULL)
alpar@1:          gmp_pool = dmp_create_pool();
alpar@1:       return dmp_get_atom(gmp_pool, size);
alpar@1: }
alpar@1: 
alpar@1: void gmp_free_atom(void *ptr, int size)
alpar@1: {     xassert(gmp_pool != NULL);
alpar@1:       dmp_free_atom(gmp_pool, ptr, size);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: int gmp_pool_count(void)
alpar@1: {     if (gmp_pool == NULL)
alpar@1:          return 0;
alpar@1:       else
alpar@1:          return dmp_in_use(gmp_pool).lo;
alpar@1: }
alpar@1: 
alpar@1: unsigned short *gmp_get_work(int size)
alpar@1: {     xassert(size > 0);
alpar@1:       if (gmp_size < size)
alpar@1:       {  if (gmp_size == 0)
alpar@1:          {  xassert(gmp_work == NULL);
alpar@1:             gmp_size = 100;
alpar@1:          }
alpar@1:          else
alpar@1:          {  xassert(gmp_work != NULL);
alpar@1:             xfree(gmp_work);
alpar@1:          }
alpar@1:          while (gmp_size < size) gmp_size += gmp_size;
alpar@1:          gmp_work = xcalloc(gmp_size, sizeof(unsigned short));
alpar@1:       }
alpar@1:       return gmp_work;
alpar@1: }
alpar@1: 
alpar@1: void gmp_free_mem(void)
alpar@1: {     if (gmp_pool != NULL) dmp_delete_pool(gmp_pool);
alpar@1:       if (gmp_work != NULL) xfree(gmp_work);
alpar@1:       gmp_pool = NULL;
alpar@1:       gmp_size = 0;
alpar@1:       gmp_work = NULL;
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: /*====================================================================*/
alpar@1: 
alpar@1: mpz_t _mpz_init(void)
alpar@1: {     /* initialize x, and set its value to 0 */
alpar@1:       mpz_t x;
alpar@1:       x = gmp_get_atom(sizeof(struct mpz));
alpar@1:       x->val = 0;
alpar@1:       x->ptr = NULL;
alpar@1:       return x;
alpar@1: }
alpar@1: 
alpar@1: void mpz_clear(mpz_t x)
alpar@1: {     /* free the space occupied by x */
alpar@1:       mpz_set_si(x, 0);
alpar@1:       xassert(x->ptr == NULL);
alpar@1:       /* free the number descriptor */
alpar@1:       gmp_free_atom(x, sizeof(struct mpz));
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_set(mpz_t z, mpz_t x)
alpar@1: {     /* set the value of z from x */
alpar@1:       struct mpz_seg *e, *ee, *es;
alpar@1:       if (z != x)
alpar@1:       {  mpz_set_si(z, 0);
alpar@1:          z->val = x->val;
alpar@1:          xassert(z->ptr == NULL);
alpar@1:          for (e = x->ptr, es = NULL; e != NULL; e = e->next)
alpar@1:          {  ee = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:             memcpy(ee->d, e->d, 12);
alpar@1:             ee->next = NULL;
alpar@1:             if (z->ptr == NULL)
alpar@1:                z->ptr = ee;
alpar@1:             else
alpar@1:                es->next = ee;
alpar@1:             es = ee;
alpar@1:          }
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_set_si(mpz_t x, int val)
alpar@1: {     /* set the value of x to val */
alpar@1:       struct mpz_seg *e;
alpar@1:       /* free existing segments, if any */
alpar@1:       while (x->ptr != NULL)
alpar@1:       {  e = x->ptr;
alpar@1:          x->ptr = e->next;
alpar@1:          gmp_free_atom(e, sizeof(struct mpz_seg));
alpar@1:       }
alpar@1:       /* assign new value */
alpar@1:       if (val == 0x80000000)
alpar@1:       {  /* long format is needed */
alpar@1:          x->val = -1;
alpar@1:          x->ptr = e = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:          memset(e->d, 0, 12);
alpar@1:          e->d[1] = 0x8000;
alpar@1:          e->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  /* short format is enough */
alpar@1:          x->val = val;
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: double mpz_get_d(mpz_t x)
alpar@1: {     /* convert x to a double, truncating if necessary */
alpar@1:       struct mpz_seg *e;
alpar@1:       int j;
alpar@1:       double val, deg;
alpar@1:       if (x->ptr == NULL)
alpar@1:          val = (double)x->val;
alpar@1:       else
alpar@1:       {  xassert(x->val != 0);
alpar@1:          val = 0.0;
alpar@1:          deg = 1.0;
alpar@1:          for (e = x->ptr; e != NULL; e = e->next)
alpar@1:          {  for (j = 0; j <= 5; j++)
alpar@1:             {  val += deg * (double)((int)e->d[j]);
alpar@1:                deg *= 65536.0;
alpar@1:             }
alpar@1:          }
alpar@1:          if (x->val < 0) val = - val;
alpar@1:       }
alpar@1:       return val;
alpar@1: }
alpar@1: 
alpar@1: double mpz_get_d_2exp(int *exp, mpz_t x)
alpar@1: {     /* convert x to a double, truncating if necessary (i.e. rounding
alpar@1:          towards zero), and returning the exponent separately;
alpar@1:          the return value is in the range 0.5 <= |d| < 1 and the
alpar@1:          exponent is stored to *exp; d*2^exp is the (truncated) x value;
alpar@1:          if x is zero, the return is 0.0 and 0 is stored to *exp;
alpar@1:          this is similar to the standard C frexp function */
alpar@1:       struct mpz_seg *e;
alpar@1:       int j, n, n1;
alpar@1:       double val;
alpar@1:       if (x->ptr == NULL)
alpar@1:          val = (double)x->val, n = 0;
alpar@1:       else
alpar@1:       {  xassert(x->val != 0);
alpar@1:          val = 0.0, n = 0;
alpar@1:          for (e = x->ptr; e != NULL; e = e->next)
alpar@1:          {  for (j = 0; j <= 5; j++)
alpar@1:             {  val += (double)((int)e->d[j]);
alpar@1:                val /= 65536.0, n += 16;
alpar@1:             }
alpar@1:          }
alpar@1:          if (x->val < 0) val = - val;
alpar@1:       }
alpar@1:       val = frexp(val, &n1);
alpar@1:       *exp = n + n1;
alpar@1:       return val;
alpar@1: }
alpar@1: 
alpar@1: void mpz_swap(mpz_t x, mpz_t y)
alpar@1: {     /* swap the values x and y efficiently */
alpar@1:       int val;
alpar@1:       void *ptr;
alpar@1:       val = x->val, ptr = x->ptr;
alpar@1:       x->val = y->val, x->ptr = y->ptr;
alpar@1:       y->val = val, y->ptr = ptr;
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static void normalize(mpz_t x)
alpar@1: {     /* normalize integer x that includes removing non-significant
alpar@1:          (leading) zeros and converting to short format, if possible */
alpar@1:       struct mpz_seg *es, *e;
alpar@1:       /* if the integer is in short format, it remains unchanged */
alpar@1:       if (x->ptr == NULL)
alpar@1:       {  xassert(x->val != 0x80000000);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       xassert(x->val == +1 || x->val == -1);
alpar@1:       /* find the last (most significant) non-zero segment */
alpar@1:       es = NULL;
alpar@1:       for (e = x->ptr; e != NULL; e = e->next)
alpar@1:       {  if (e->d[0] || e->d[1] || e->d[2] ||
alpar@1:              e->d[3] || e->d[4] || e->d[5]) es = e;
alpar@1:       }
alpar@1:       /* if all segments contain zeros, the integer is zero */
alpar@1:       if (es == NULL)
alpar@1:       {  mpz_set_si(x, 0);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* remove non-significant (leading) zero segments */
alpar@1:       while (es->next != NULL)
alpar@1:       {  e = es->next;
alpar@1:          es->next = e->next;
alpar@1:          gmp_free_atom(e, sizeof(struct mpz_seg));
alpar@1:       }
alpar@1:       /* convert the integer to short format, if possible */
alpar@1:       e = x->ptr;
alpar@1:       if (e->next == NULL && e->d[1] <= 0x7FFF &&
alpar@1:          !e->d[2] && !e->d[3] && !e->d[4] && !e->d[5])
alpar@1:       {  int val;
alpar@1:          val = (int)e->d[0] + ((int)e->d[1] << 16);
alpar@1:          if (x->val < 0) val = - val;
alpar@1:          mpz_set_si(x, val);
alpar@1:       }
alpar@1: done: return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_add(mpz_t z, mpz_t x, mpz_t y)
alpar@1: {     /* set z to x + y */
alpar@1:       static struct mpz_seg zero = { { 0, 0, 0, 0, 0, 0 }, NULL };
alpar@1:       struct mpz_seg dumx, dumy, *ex, *ey, *ez, *es, *ee;
alpar@1:       int k, sx, sy, sz;
alpar@1:       unsigned int t;
alpar@1:       /* if [x] = 0 then [z] = [y] */
alpar@1:       if (x->val == 0)
alpar@1:       {  xassert(x->ptr == NULL);
alpar@1:          mpz_set(z, y);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* if [y] = 0 then [z] = [x] */
alpar@1:       if (y->val == 0)
alpar@1:       {  xassert(y->ptr == NULL);
alpar@1:          mpz_set(z, x);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* special case when both [x] and [y] are in short format */
alpar@1:       if (x->ptr == NULL && y->ptr == NULL)
alpar@1:       {  int xval = x->val, yval = y->val, zval = x->val + y->val;
alpar@1:          xassert(xval != 0x80000000 && yval != 0x80000000);
alpar@1:          if (!(xval > 0 && yval > 0 && zval <= 0 ||
alpar@1:                xval < 0 && yval < 0 && zval >= 0))
alpar@1:          {  mpz_set_si(z, zval);
alpar@1:             goto done;
alpar@1:          }
alpar@1:       }
alpar@1:       /* convert [x] to long format, if necessary */
alpar@1:       if (x->ptr == NULL)
alpar@1:       {  xassert(x->val != 0x80000000);
alpar@1:          if (x->val >= 0)
alpar@1:          {  sx = +1;
alpar@1:             t = (unsigned int)(+ x->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sx = -1;
alpar@1:             t = (unsigned int)(- x->val);
alpar@1:          }
alpar@1:          ex = &dumx;
alpar@1:          ex->d[0] = (unsigned short)t;
alpar@1:          ex->d[1] = (unsigned short)(t >> 16);
alpar@1:          ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;
alpar@1:          ex->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sx = x->val;
alpar@1:          xassert(sx == +1 || sx == -1);
alpar@1:          ex = x->ptr;
alpar@1:       }
alpar@1:       /* convert [y] to long format, if necessary */
alpar@1:       if (y->ptr == NULL)
alpar@1:       {  xassert(y->val != 0x80000000);
alpar@1:          if (y->val >= 0)
alpar@1:          {  sy = +1;
alpar@1:             t = (unsigned int)(+ y->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sy = -1;
alpar@1:             t = (unsigned int)(- y->val);
alpar@1:          }
alpar@1:          ey = &dumy;
alpar@1:          ey->d[0] = (unsigned short)t;
alpar@1:          ey->d[1] = (unsigned short)(t >> 16);
alpar@1:          ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;
alpar@1:          ey->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sy = y->val;
alpar@1:          xassert(sy == +1 || sy == -1);
alpar@1:          ey = y->ptr;
alpar@1:       }
alpar@1:       /* main fragment */
alpar@1:       sz = sx;
alpar@1:       ez = es = NULL;
alpar@1:       if (sx > 0 && sy > 0 || sx < 0 && sy < 0)
alpar@1:       {  /* [x] and [y] have identical signs -- addition */
alpar@1:          t = 0;
alpar@1:          for (; ex || ey; ex = ex->next, ey = ey->next)
alpar@1:          {  if (ex == NULL) ex = &zero;
alpar@1:             if (ey == NULL) ey = &zero;
alpar@1:             ee = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:             for (k = 0; k <= 5; k++)
alpar@1:             {  t += (unsigned int)ex->d[k];
alpar@1:                t += (unsigned int)ey->d[k];
alpar@1:                ee->d[k] = (unsigned short)t;
alpar@1:                t >>= 16;
alpar@1:             }
alpar@1:             ee->next = NULL;
alpar@1:             if (ez == NULL)
alpar@1:                ez = ee;
alpar@1:             else
alpar@1:                es->next = ee;
alpar@1:             es = ee;
alpar@1:          }
alpar@1:          if (t)
alpar@1:          {  /* overflow -- one extra digit is needed */
alpar@1:             ee = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:             ee->d[0] = 1;
alpar@1:             ee->d[1] = ee->d[2] = ee->d[3] = ee->d[4] = ee->d[5] = 0;
alpar@1:             ee->next = NULL;
alpar@1:             xassert(es != NULL);
alpar@1:             es->next = ee;
alpar@1:          }
alpar@1:       }
alpar@1:       else
alpar@1:       {  /* [x] and [y] have different signs -- subtraction */
alpar@1:          t = 1;
alpar@1:          for (; ex || ey; ex = ex->next, ey = ey->next)
alpar@1:          {  if (ex == NULL) ex = &zero;
alpar@1:             if (ey == NULL) ey = &zero;
alpar@1:             ee = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:             for (k = 0; k <= 5; k++)
alpar@1:             {  t += (unsigned int)ex->d[k];
alpar@1:                t += (0xFFFF - (unsigned int)ey->d[k]);
alpar@1:                ee->d[k] = (unsigned short)t;
alpar@1:                t >>= 16;
alpar@1:             }
alpar@1:             ee->next = NULL;
alpar@1:             if (ez == NULL)
alpar@1:                ez = ee;
alpar@1:             else
alpar@1:                es->next = ee;
alpar@1:             es = ee;
alpar@1:          }
alpar@1:          if (!t)
alpar@1:          {  /* |[x]| < |[y]| -- result in complement coding */
alpar@1:             sz = - sz;
alpar@1:             t = 1;
alpar@1:             for (ee = ez; ee != NULL; ee = ee->next)
alpar@1:             for (k = 0; k <= 5; k++)
alpar@1:             {  t += (0xFFFF - (unsigned int)ee->d[k]);
alpar@1:                ee->d[k] = (unsigned short)t;
alpar@1:                t >>= 16;
alpar@1:             }
alpar@1:          }
alpar@1:       }
alpar@1:       /* contruct and normalize result */
alpar@1:       mpz_set_si(z, 0);
alpar@1:       z->val = sz;
alpar@1:       z->ptr = ez;
alpar@1:       normalize(z);
alpar@1: done: return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_sub(mpz_t z, mpz_t x, mpz_t y)
alpar@1: {     /* set z to x - y */
alpar@1:       if (x == y)
alpar@1:          mpz_set_si(z, 0);
alpar@1:       else
alpar@1:       {  y->val = - y->val;
alpar@1:          mpz_add(z, x, y);
alpar@1:          if (y != z) y->val = - y->val;
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_mul(mpz_t z, mpz_t x, mpz_t y)
alpar@1: {     /* set z to x * y */
alpar@1:       struct mpz_seg dumx, dumy, *ex, *ey, *es, *e;
alpar@1:       int sx, sy, k, nx, ny, n;
alpar@1:       unsigned int t;
alpar@1:       unsigned short *work, *wx, *wy;
alpar@1:       /* if [x] = 0 then [z] = 0 */
alpar@1:       if (x->val == 0)
alpar@1:       {  xassert(x->ptr == NULL);
alpar@1:          mpz_set_si(z, 0);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* if [y] = 0 then [z] = 0 */
alpar@1:       if (y->val == 0)
alpar@1:       {  xassert(y->ptr == NULL);
alpar@1:          mpz_set_si(z, 0);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* special case when both [x] and [y] are in short format */
alpar@1:       if (x->ptr == NULL && y->ptr == NULL)
alpar@1:       {  int xval = x->val, yval = y->val, sz = +1;
alpar@1:          xassert(xval != 0x80000000 && yval != 0x80000000);
alpar@1:          if (xval < 0) xval = - xval, sz = - sz;
alpar@1:          if (yval < 0) yval = - yval, sz = - sz;
alpar@1:          if (xval <= 0x7FFFFFFF / yval)
alpar@1:          {  mpz_set_si(z, sz * (xval * yval));
alpar@1:             goto done;
alpar@1:          }
alpar@1:       }
alpar@1:       /* convert [x] to long format, if necessary */
alpar@1:       if (x->ptr == NULL)
alpar@1:       {  xassert(x->val != 0x80000000);
alpar@1:          if (x->val >= 0)
alpar@1:          {  sx = +1;
alpar@1:             t = (unsigned int)(+ x->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sx = -1;
alpar@1:             t = (unsigned int)(- x->val);
alpar@1:          }
alpar@1:          ex = &dumx;
alpar@1:          ex->d[0] = (unsigned short)t;
alpar@1:          ex->d[1] = (unsigned short)(t >> 16);
alpar@1:          ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;
alpar@1:          ex->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sx = x->val;
alpar@1:          xassert(sx == +1 || sx == -1);
alpar@1:          ex = x->ptr;
alpar@1:       }
alpar@1:       /* convert [y] to long format, if necessary */
alpar@1:       if (y->ptr == NULL)
alpar@1:       {  xassert(y->val != 0x80000000);
alpar@1:          if (y->val >= 0)
alpar@1:          {  sy = +1;
alpar@1:             t = (unsigned int)(+ y->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sy = -1;
alpar@1:             t = (unsigned int)(- y->val);
alpar@1:          }
alpar@1:          ey = &dumy;
alpar@1:          ey->d[0] = (unsigned short)t;
alpar@1:          ey->d[1] = (unsigned short)(t >> 16);
alpar@1:          ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;
alpar@1:          ey->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sy = y->val;
alpar@1:          xassert(sy == +1 || sy == -1);
alpar@1:          ey = y->ptr;
alpar@1:       }
alpar@1:       /* determine the number of digits of [x] */
alpar@1:       nx = n = 0;
alpar@1:       for (e = ex; e != NULL; e = e->next)
alpar@1:       for (k = 0; k <= 5; k++)
alpar@1:       {  n++;
alpar@1:          if (e->d[k]) nx = n;
alpar@1:       }
alpar@1:       xassert(nx > 0);
alpar@1:       /* determine the number of digits of [y] */
alpar@1:       ny = n = 0;
alpar@1:       for (e = ey; e != NULL; e = e->next)
alpar@1:       for (k = 0; k <= 5; k++)
alpar@1:       {  n++;
alpar@1:          if (e->d[k]) ny = n;
alpar@1:       }
alpar@1:       xassert(ny > 0);
alpar@1:       /* we need working array containing at least nx+ny+ny places */
alpar@1:       work = gmp_get_work(nx+ny+ny);
alpar@1:       /* load digits of [x] */
alpar@1:       wx = &work[0];
alpar@1:       for (n = 0; n < nx; n++) wx[ny+n] = 0;
alpar@1:       for (n = 0, e = ex; e != NULL; e = e->next)
alpar@1:          for (k = 0; k <= 5; k++, n++)
alpar@1:             if (e->d[k]) wx[ny+n] = e->d[k];
alpar@1:       /* load digits of [y] */
alpar@1:       wy = &work[nx+ny];
alpar@1:       for (n = 0; n < ny; n++) wy[n] = 0;
alpar@1:       for (n = 0, e = ey; e != NULL; e = e->next)
alpar@1:          for (k = 0; k <= 5; k++, n++)
alpar@1:             if (e->d[k]) wy[n] = e->d[k];
alpar@1:       /* compute [x] * [y] */
alpar@1:       bigmul(nx, ny, wx, wy);
alpar@1:       /* construct and normalize result */
alpar@1:       mpz_set_si(z, 0);
alpar@1:       z->val = sx * sy;
alpar@1:       es = NULL;
alpar@1:       k = 6;
alpar@1:       for (n = 0; n < nx+ny; n++)
alpar@1:       {  if (k > 5)
alpar@1:          {  e = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:             e->d[0] = e->d[1] = e->d[2] = 0;
alpar@1:             e->d[3] = e->d[4] = e->d[5] = 0;
alpar@1:             e->next = NULL;
alpar@1:             if (z->ptr == NULL)
alpar@1:                z->ptr = e;
alpar@1:             else
alpar@1:                es->next = e;
alpar@1:             es = e;
alpar@1:             k = 0;
alpar@1:          }
alpar@1:          es->d[k++] = wx[n];
alpar@1:       }
alpar@1:       normalize(z);
alpar@1: done: return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_neg(mpz_t z, mpz_t x)
alpar@1: {     /* set z to 0 - x */
alpar@1:       mpz_set(z, x);
alpar@1:       z->val = - z->val;
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_abs(mpz_t z, mpz_t x)
alpar@1: {     /* set z to the absolute value of x */
alpar@1:       mpz_set(z, x);
alpar@1:       if (z->val < 0) z->val = - z->val;
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_div(mpz_t q, mpz_t r, mpz_t x, mpz_t y)
alpar@1: {     /* divide x by y, forming quotient q and/or remainder r
alpar@1:          if q = NULL then quotient is not stored; if r = NULL then
alpar@1:          remainder is not stored
alpar@1:          the sign of quotient is determined as in algebra while the
alpar@1:          sign of remainder is the same as the sign of dividend:
alpar@1:          +26 : +7 = +3, remainder is +5
alpar@1:          -26 : +7 = -3, remainder is -5
alpar@1:          +26 : -7 = -3, remainder is +5
alpar@1:          -26 : -7 = +3, remainder is -5 */
alpar@1:       struct mpz_seg dumx, dumy, *ex, *ey, *es, *e;
alpar@1:       int sx, sy, k, nx, ny, n;
alpar@1:       unsigned int t;
alpar@1:       unsigned short *work, *wx, *wy;
alpar@1:       /* divide by zero is not allowed */
alpar@1:       if (y->val == 0)
alpar@1:       {  xassert(y->ptr == NULL);
alpar@1:          xfault("mpz_div: divide by zero not allowed\n");
alpar@1:       }
alpar@1:       /* if [x] = 0 then [q] = [r] = 0 */
alpar@1:       if (x->val == 0)
alpar@1:       {  xassert(x->ptr == NULL);
alpar@1:          if (q != NULL) mpz_set_si(q, 0);
alpar@1:          if (r != NULL) mpz_set_si(r, 0);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* special case when both [x] and [y] are in short format */
alpar@1:       if (x->ptr == NULL && y->ptr == NULL)
alpar@1:       {  int xval = x->val, yval = y->val;
alpar@1:          xassert(xval != 0x80000000 && yval != 0x80000000);
alpar@1:          if (q != NULL) mpz_set_si(q, xval / yval);
alpar@1:          if (r != NULL) mpz_set_si(r, xval % yval);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* convert [x] to long format, if necessary */
alpar@1:       if (x->ptr == NULL)
alpar@1:       {  xassert(x->val != 0x80000000);
alpar@1:          if (x->val >= 0)
alpar@1:          {  sx = +1;
alpar@1:             t = (unsigned int)(+ x->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sx = -1;
alpar@1:             t = (unsigned int)(- x->val);
alpar@1:          }
alpar@1:          ex = &dumx;
alpar@1:          ex->d[0] = (unsigned short)t;
alpar@1:          ex->d[1] = (unsigned short)(t >> 16);
alpar@1:          ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;
alpar@1:          ex->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sx = x->val;
alpar@1:          xassert(sx == +1 || sx == -1);
alpar@1:          ex = x->ptr;
alpar@1:       }
alpar@1:       /* convert [y] to long format, if necessary */
alpar@1:       if (y->ptr == NULL)
alpar@1:       {  xassert(y->val != 0x80000000);
alpar@1:          if (y->val >= 0)
alpar@1:          {  sy = +1;
alpar@1:             t = (unsigned int)(+ y->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sy = -1;
alpar@1:             t = (unsigned int)(- y->val);
alpar@1:          }
alpar@1:          ey = &dumy;
alpar@1:          ey->d[0] = (unsigned short)t;
alpar@1:          ey->d[1] = (unsigned short)(t >> 16);
alpar@1:          ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;
alpar@1:          ey->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sy = y->val;
alpar@1:          xassert(sy == +1 || sy == -1);
alpar@1:          ey = y->ptr;
alpar@1:       }
alpar@1:       /* determine the number of digits of [x] */
alpar@1:       nx = n = 0;
alpar@1:       for (e = ex; e != NULL; e = e->next)
alpar@1:       for (k = 0; k <= 5; k++)
alpar@1:       {  n++;
alpar@1:          if (e->d[k]) nx = n;
alpar@1:       }
alpar@1:       xassert(nx > 0);
alpar@1:       /* determine the number of digits of [y] */
alpar@1:       ny = n = 0;
alpar@1:       for (e = ey; e != NULL; e = e->next)
alpar@1:       for (k = 0; k <= 5; k++)
alpar@1:       {  n++;
alpar@1:          if (e->d[k]) ny = n;
alpar@1:       }
alpar@1:       xassert(ny > 0);
alpar@1:       /* if nx < ny then [q] = 0 and [r] = [x] */
alpar@1:       if (nx < ny)
alpar@1:       {  if (r != NULL) mpz_set(r, x);
alpar@1:          if (q != NULL) mpz_set_si(q, 0);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* we need working array containing at least nx+ny+1 places */
alpar@1:       work = gmp_get_work(nx+ny+1);
alpar@1:       /* load digits of [x] */
alpar@1:       wx = &work[0];
alpar@1:       for (n = 0; n < nx; n++) wx[n] = 0;
alpar@1:       for (n = 0, e = ex; e != NULL; e = e->next)
alpar@1:          for (k = 0; k <= 5; k++, n++)
alpar@1:             if (e->d[k]) wx[n] = e->d[k];
alpar@1:       /* load digits of [y] */
alpar@1:       wy = &work[nx+1];
alpar@1:       for (n = 0; n < ny; n++) wy[n] = 0;
alpar@1:       for (n = 0, e = ey; e != NULL; e = e->next)
alpar@1:          for (k = 0; k <= 5; k++, n++)
alpar@1:             if (e->d[k]) wy[n] = e->d[k];
alpar@1:       /* compute quotient and remainder */
alpar@1:       xassert(wy[ny-1] != 0);
alpar@1:       bigdiv(nx-ny, ny, wx, wy);
alpar@1:       /* construct and normalize quotient */
alpar@1:       if (q != NULL)
alpar@1:       {  mpz_set_si(q, 0);
alpar@1:          q->val = sx * sy;
alpar@1:          es = NULL;
alpar@1:          k = 6;
alpar@1:          for (n = ny; n <= nx; n++)
alpar@1:          {  if (k > 5)
alpar@1:             {  e = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:                e->d[0] = e->d[1] = e->d[2] = 0;
alpar@1:                e->d[3] = e->d[4] = e->d[5] = 0;
alpar@1:                e->next = NULL;
alpar@1:                if (q->ptr == NULL)
alpar@1:                   q->ptr = e;
alpar@1:                else
alpar@1:                   es->next = e;
alpar@1:                es = e;
alpar@1:                k = 0;
alpar@1:             }
alpar@1:             es->d[k++] = wx[n];
alpar@1:          }
alpar@1:          normalize(q);
alpar@1:       }
alpar@1:       /* construct and normalize remainder */
alpar@1:       if (r != NULL)
alpar@1:       {  mpz_set_si(r, 0);
alpar@1:          r->val = sx;
alpar@1:          es = NULL;
alpar@1:          k = 6;
alpar@1:          for (n = 0; n < ny; n++)
alpar@1:          {  if (k > 5)
alpar@1:             {  e = gmp_get_atom(sizeof(struct mpz_seg));
alpar@1:                e->d[0] = e->d[1] = e->d[2] = 0;
alpar@1:                e->d[3] = e->d[4] = e->d[5] = 0;
alpar@1:                e->next = NULL;
alpar@1:                if (r->ptr == NULL)
alpar@1:                   r->ptr = e;
alpar@1:                else
alpar@1:                   es->next = e;
alpar@1:                es = e;
alpar@1:                k = 0;
alpar@1:             }
alpar@1:             es->d[k++] = wx[n];
alpar@1:          }
alpar@1:          normalize(r);
alpar@1:       }
alpar@1: done: return;
alpar@1: }
alpar@1: 
alpar@1: void mpz_gcd(mpz_t z, mpz_t x, mpz_t y)
alpar@1: {     /* set z to the greatest common divisor of x and y */
alpar@1:       /* in case of arbitrary integers GCD(x, y) = GCD(|x|, |y|), and,
alpar@1:          in particular, GCD(0, 0) = 0 */
alpar@1:       mpz_t u, v, r;
alpar@1:       mpz_init(u);
alpar@1:       mpz_init(v);
alpar@1:       mpz_init(r);
alpar@1:       mpz_abs(u, x);
alpar@1:       mpz_abs(v, y);
alpar@1:       while (mpz_sgn(v))
alpar@1:       {  mpz_div(NULL, r, u, v);
alpar@1:          mpz_set(u, v);
alpar@1:          mpz_set(v, r);
alpar@1:       }
alpar@1:       mpz_set(z, u);
alpar@1:       mpz_clear(u);
alpar@1:       mpz_clear(v);
alpar@1:       mpz_clear(r);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: int mpz_cmp(mpz_t x, mpz_t y)
alpar@1: {     /* compare x and y; return a positive value if x > y, zero if
alpar@1:          x = y, or a nefative value if x < y */
alpar@1:       static struct mpz_seg zero = { { 0, 0, 0, 0, 0, 0 }, NULL };
alpar@1:       struct mpz_seg dumx, dumy, *ex, *ey;
alpar@1:       int cc, sx, sy, k;
alpar@1:       unsigned int t;
alpar@1:       if (x == y)
alpar@1:       {  cc = 0;
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* special case when both [x] and [y] are in short format */
alpar@1:       if (x->ptr == NULL && y->ptr == NULL)
alpar@1:       {  int xval = x->val, yval = y->val;
alpar@1:          xassert(xval != 0x80000000 && yval != 0x80000000);
alpar@1:          cc = (xval > yval ? +1 : xval < yval ? -1 : 0);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* special case when [x] and [y] have different signs */
alpar@1:       if (x->val > 0 && y->val <= 0 || x->val == 0 && y->val < 0)
alpar@1:       {  cc = +1;
alpar@1:          goto done;
alpar@1:       }
alpar@1:       if (x->val < 0 && y->val >= 0 || x->val == 0 && y->val > 0)
alpar@1:       {  cc = -1;
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* convert [x] to long format, if necessary */
alpar@1:       if (x->ptr == NULL)
alpar@1:       {  xassert(x->val != 0x80000000);
alpar@1:          if (x->val >= 0)
alpar@1:          {  sx = +1;
alpar@1:             t = (unsigned int)(+ x->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sx = -1;
alpar@1:             t = (unsigned int)(- x->val);
alpar@1:          }
alpar@1:          ex = &dumx;
alpar@1:          ex->d[0] = (unsigned short)t;
alpar@1:          ex->d[1] = (unsigned short)(t >> 16);
alpar@1:          ex->d[2] = ex->d[3] = ex->d[4] = ex->d[5] = 0;
alpar@1:          ex->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sx = x->val;
alpar@1:          xassert(sx == +1 || sx == -1);
alpar@1:          ex = x->ptr;
alpar@1:       }
alpar@1:       /* convert [y] to long format, if necessary */
alpar@1:       if (y->ptr == NULL)
alpar@1:       {  xassert(y->val != 0x80000000);
alpar@1:          if (y->val >= 0)
alpar@1:          {  sy = +1;
alpar@1:             t = (unsigned int)(+ y->val);
alpar@1:          }
alpar@1:          else
alpar@1:          {  sy = -1;
alpar@1:             t = (unsigned int)(- y->val);
alpar@1:          }
alpar@1:          ey = &dumy;
alpar@1:          ey->d[0] = (unsigned short)t;
alpar@1:          ey->d[1] = (unsigned short)(t >> 16);
alpar@1:          ey->d[2] = ey->d[3] = ey->d[4] = ey->d[5] = 0;
alpar@1:          ey->next = NULL;
alpar@1:       }
alpar@1:       else
alpar@1:       {  sy = y->val;
alpar@1:          xassert(sy == +1 || sy == -1);
alpar@1:          ey = y->ptr;
alpar@1:       }
alpar@1:       /* main fragment */
alpar@1:       xassert(sx > 0 && sy > 0 || sx < 0 && sy < 0);
alpar@1:       cc = 0;
alpar@1:       for (; ex || ey; ex = ex->next, ey = ey->next)
alpar@1:       {  if (ex == NULL) ex = &zero;
alpar@1:          if (ey == NULL) ey = &zero;
alpar@1:          for (k = 0; k <= 5; k++)
alpar@1:          {  if (ex->d[k] > ey->d[k]) cc = +1;
alpar@1:             if (ex->d[k] < ey->d[k]) cc = -1;
alpar@1:          }
alpar@1:       }
alpar@1:       if (sx < 0) cc = - cc;
alpar@1: done: return cc;
alpar@1: }
alpar@1: 
alpar@1: int mpz_sgn(mpz_t x)
alpar@1: {     /* return +1 if x > 0, 0 if x = 0, and -1 if x < 0 */
alpar@1:       int s;
alpar@1:       s = (x->val > 0 ? +1 : x->val < 0 ? -1 : 0);
alpar@1:       return s;
alpar@1: }
alpar@1: 
alpar@1: int mpz_out_str(void *_fp, int base, mpz_t x)
alpar@1: {     /* output x on stream fp, as a string in given base; the base
alpar@1:          may vary from 2 to 36;
alpar@1:          return the number of bytes written, or if an error occurred,
alpar@1:          return 0 */
alpar@1:       FILE *fp = _fp;
alpar@1:       mpz_t b, y, r;
alpar@1:       int n, j, nwr = 0;
alpar@1:       unsigned char *d;
alpar@1:       static char *set = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
alpar@1:       if (!(2 <= base && base <= 36))
alpar@1:          xfault("mpz_out_str: base = %d; invalid base\n", base);
alpar@1:       mpz_init(b);
alpar@1:       mpz_set_si(b, base);
alpar@1:       mpz_init(y);
alpar@1:       mpz_init(r);
alpar@1:       /* determine the number of digits */
alpar@1:       mpz_abs(y, x);
alpar@1:       for (n = 0; mpz_sgn(y) != 0; n++)
alpar@1:          mpz_div(y, NULL, y, b);
alpar@1:       if (n == 0) n = 1;
alpar@1:       /* compute the digits */
alpar@1:       d = xmalloc(n);
alpar@1:       mpz_abs(y, x);
alpar@1:       for (j = 0; j < n; j++)
alpar@1:       {  mpz_div(y, r, y, b);
alpar@1:          xassert(0 <= r->val && r->val < base && r->ptr == NULL);
alpar@1:          d[j] = (unsigned char)r->val;
alpar@1:       }
alpar@1:       /* output the integer to the stream */
alpar@1:       if (fp == NULL) fp = stdout;
alpar@1:       if (mpz_sgn(x) < 0)
alpar@1:          fputc('-', fp), nwr++;
alpar@1:       for (j = n-1; j >= 0; j--)
alpar@1:          fputc(set[d[j]], fp), nwr++;
alpar@1:       if (ferror(fp)) nwr = 0;
alpar@1:       mpz_clear(b);
alpar@1:       mpz_clear(y);
alpar@1:       mpz_clear(r);
alpar@1:       xfree(d);
alpar@1:       return nwr;
alpar@1: }
alpar@1: 
alpar@1: /*====================================================================*/
alpar@1: 
alpar@1: mpq_t _mpq_init(void)
alpar@1: {     /* initialize x, and set its value to 0/1 */
alpar@1:       mpq_t x;
alpar@1:       x = gmp_get_atom(sizeof(struct mpq));
alpar@1:       x->p.val = 0;
alpar@1:       x->p.ptr = NULL;
alpar@1:       x->q.val = 1;
alpar@1:       x->q.ptr = NULL;
alpar@1:       return x;
alpar@1: }
alpar@1: 
alpar@1: void mpq_clear(mpq_t x)
alpar@1: {     /* free the space occupied by x */
alpar@1:       mpz_set_si(&x->p, 0);
alpar@1:       xassert(x->p.ptr == NULL);
alpar@1:       mpz_set_si(&x->q, 0);
alpar@1:       xassert(x->q.ptr == NULL);
alpar@1:       /* free the number descriptor */
alpar@1:       gmp_free_atom(x, sizeof(struct mpq));
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_canonicalize(mpq_t x)
alpar@1: {     /* remove any factors that are common to the numerator and
alpar@1:          denominator of x, and make the denominator positive */
alpar@1:       mpz_t f;
alpar@1:       xassert(x->q.val != 0);
alpar@1:       if (x->q.val < 0)
alpar@1:       {  mpz_neg(&x->p, &x->p);
alpar@1:          mpz_neg(&x->q, &x->q);
alpar@1:       }
alpar@1:       mpz_init(f);
alpar@1:       mpz_gcd(f, &x->p, &x->q);
alpar@1:       if (!(f->val == 1 && f->ptr == NULL))
alpar@1:       {  mpz_div(&x->p, NULL, &x->p, f);
alpar@1:          mpz_div(&x->q, NULL, &x->q, f);
alpar@1:       }
alpar@1:       mpz_clear(f);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_set(mpq_t z, mpq_t x)
alpar@1: {     /* set the value of z from x */
alpar@1:       if (z != x)
alpar@1:       {  mpz_set(&z->p, &x->p);
alpar@1:          mpz_set(&z->q, &x->q);
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_set_si(mpq_t x, int p, unsigned int q)
alpar@1: {     /* set the value of x to p/q */
alpar@1:       if (q == 0)
alpar@1:          xfault("mpq_set_si: zero denominator not allowed\n");
alpar@1:       mpz_set_si(&x->p, p);
alpar@1:       xassert(q <= 0x7FFFFFFF);
alpar@1:       mpz_set_si(&x->q, q);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: double mpq_get_d(mpq_t x)
alpar@1: {     /* convert x to a double, truncating if necessary */
alpar@1:       int np, nq;
alpar@1:       double p, q;
alpar@1:       p = mpz_get_d_2exp(&np, &x->p);
alpar@1:       q = mpz_get_d_2exp(&nq, &x->q);
alpar@1:       return ldexp(p / q, np - nq);
alpar@1: }
alpar@1: 
alpar@1: void mpq_set_d(mpq_t x, double val)
alpar@1: {     /* set x to val; there is no rounding, the conversion is exact */
alpar@1:       int s, n, d, j;
alpar@1:       double f;
alpar@1:       mpz_t temp;
alpar@1:       xassert(-DBL_MAX <= val && val <= +DBL_MAX);
alpar@1:       mpq_set_si(x, 0, 1);
alpar@1:       if (val > 0.0)
alpar@1:          s = +1;
alpar@1:       else if (val < 0.0)
alpar@1:          s = -1;
alpar@1:       else
alpar@1:          goto done;
alpar@1:       f = frexp(fabs(val), &n);
alpar@1:       /* |val| = f * 2^n, where 0.5 <= f < 1.0 */
alpar@1:       mpz_init(temp);
alpar@1:       while (f != 0.0)
alpar@1:       {  f *= 16.0, n -= 4;
alpar@1:          d = (int)f;
alpar@1:          xassert(0 <= d && d <= 15);
alpar@1:          f -= (double)d;
alpar@1:          /* x := 16 * x + d */
alpar@1:          mpz_set_si(temp, 16);
alpar@1:          mpz_mul(&x->p, &x->p, temp);
alpar@1:          mpz_set_si(temp, d);
alpar@1:          mpz_add(&x->p, &x->p, temp);
alpar@1:       }
alpar@1:       mpz_clear(temp);
alpar@1:       /* x := x * 2^n */
alpar@1:       if (n > 0)
alpar@1:       {  for (j = 1; j <= n; j++)
alpar@1:             mpz_add(&x->p, &x->p, &x->p);
alpar@1:       }
alpar@1:       else if (n < 0)
alpar@1:       {  for (j = 1; j <= -n; j++)
alpar@1:             mpz_add(&x->q, &x->q, &x->q);
alpar@1:          mpq_canonicalize(x);
alpar@1:       }
alpar@1:       if (s < 0) mpq_neg(x, x);
alpar@1: done: return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_add(mpq_t z, mpq_t x, mpq_t y)
alpar@1: {     /* set z to x + y */
alpar@1:       mpz_t p, q;
alpar@1:       mpz_init(p);
alpar@1:       mpz_init(q);
alpar@1:       mpz_mul(p, &x->p, &y->q);
alpar@1:       mpz_mul(q, &x->q, &y->p);
alpar@1:       mpz_add(p, p, q);
alpar@1:       mpz_mul(q, &x->q, &y->q);
alpar@1:       mpz_set(&z->p, p);
alpar@1:       mpz_set(&z->q, q);
alpar@1:       mpz_clear(p);
alpar@1:       mpz_clear(q);
alpar@1:       mpq_canonicalize(z);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_sub(mpq_t z, mpq_t x, mpq_t y)
alpar@1: {     /* set z to x - y */
alpar@1:       mpz_t p, q;
alpar@1:       mpz_init(p);
alpar@1:       mpz_init(q);
alpar@1:       mpz_mul(p, &x->p, &y->q);
alpar@1:       mpz_mul(q, &x->q, &y->p);
alpar@1:       mpz_sub(p, p, q);
alpar@1:       mpz_mul(q, &x->q, &y->q);
alpar@1:       mpz_set(&z->p, p);
alpar@1:       mpz_set(&z->q, q);
alpar@1:       mpz_clear(p);
alpar@1:       mpz_clear(q);
alpar@1:       mpq_canonicalize(z);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_mul(mpq_t z, mpq_t x, mpq_t y)
alpar@1: {     /* set z to x * y */
alpar@1:       mpz_mul(&z->p, &x->p, &y->p);
alpar@1:       mpz_mul(&z->q, &x->q, &y->q);
alpar@1:       mpq_canonicalize(z);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_div(mpq_t z, mpq_t x, mpq_t y)
alpar@1: {     /* set z to x / y */
alpar@1:       mpz_t p, q;
alpar@1:       if (mpq_sgn(y) == 0)
alpar@1:          xfault("mpq_div: zero divisor not allowed\n");
alpar@1:       mpz_init(p);
alpar@1:       mpz_init(q);
alpar@1:       mpz_mul(p, &x->p, &y->q);
alpar@1:       mpz_mul(q, &x->q, &y->p);
alpar@1:       mpz_set(&z->p, p);
alpar@1:       mpz_set(&z->q, q);
alpar@1:       mpz_clear(p);
alpar@1:       mpz_clear(q);
alpar@1:       mpq_canonicalize(z);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_neg(mpq_t z, mpq_t x)
alpar@1: {     /* set z to 0 - x */
alpar@1:       mpq_set(z, x);
alpar@1:       mpz_neg(&z->p, &z->p);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void mpq_abs(mpq_t z, mpq_t x)
alpar@1: {     /* set z to the absolute value of x */
alpar@1:       mpq_set(z, x);
alpar@1:       mpz_abs(&z->p, &z->p);
alpar@1:       xassert(mpz_sgn(&x->q) > 0);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: int mpq_cmp(mpq_t x, mpq_t y)
alpar@1: {     /* compare x and y; return a positive value if x > y, zero if
alpar@1:          x = y, or a nefative value if x < y */
alpar@1:       mpq_t temp;
alpar@1:       int s;
alpar@1:       mpq_init(temp);
alpar@1:       mpq_sub(temp, x, y);
alpar@1:       s = mpq_sgn(temp);
alpar@1:       mpq_clear(temp);
alpar@1:       return s;
alpar@1: }
alpar@1: 
alpar@1: int mpq_sgn(mpq_t x)
alpar@1: {     /* return +1 if x > 0, 0 if x = 0, and -1 if x < 0 */
alpar@1:       int s;
alpar@1:       s = mpz_sgn(&x->p);
alpar@1:       xassert(mpz_sgn(&x->q) > 0);
alpar@1:       return s;
alpar@1: }
alpar@1: 
alpar@1: int mpq_out_str(void *_fp, int base, mpq_t x)
alpar@1: {     /* output x on stream fp, as a string in given base; the base
alpar@1:          may vary from 2 to 36; output is in the form 'num/den' or if
alpar@1:          the denominator is 1 then just 'num';
alpar@1:          if the parameter fp is a null pointer, stdout is assumed;
alpar@1:          return the number of bytes written, or if an error occurred,
alpar@1:          return 0 */
alpar@1:       FILE *fp = _fp;
alpar@1:       int nwr;
alpar@1:       if (!(2 <= base && base <= 36))
alpar@1:          xfault("mpq_out_str: base = %d; invalid base\n", base);
alpar@1:       if (fp == NULL) fp = stdout;
alpar@1:       nwr = mpz_out_str(fp, base, &x->p);
alpar@1:       if (x->q.val == 1 && x->q.ptr == NULL)
alpar@1:          ;
alpar@1:       else
alpar@1:       {  fputc('/', fp), nwr++;
alpar@1:          nwr += mpz_out_str(fp, base, &x->q);
alpar@1:       }
alpar@1:       if (ferror(fp)) nwr = 0;
alpar@1:       return nwr;
alpar@1: }
alpar@1: 
alpar@1: #endif
alpar@1: 
alpar@1: /* eof */