path: root/div.c

/* mpfr_div -- divide two floating-point numbers

Copyright (C) 1999 Free Software Foundation.

This file is part of the MPFR Library.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.

The MPFR Library 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 Library General Public
License for more details.

You should have received a copy of the GNU Library General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "mpfr.h"
#include "gmp-impl.h"
#include "longlong.h"

/* #define DEBUG */

void
#if __STDC__
mpfr_div (mpfr_ptr r, mpfr_srcptr u, mpfr_srcptr v, mp_rnd_t rnd_mode)
#else
mpfr_div (r, u, v, rnd_mode)
     mpfr_ptr r;
     mpfr_srcptr u;
     mpfr_srcptr v;
     mp_rnd_t rnd_mode;
#endif
{
  mp_srcptr up, vp;
  mp_ptr rp, tp, tp0, tmp, tmp2;
  mp_size_t usize, vsize, rrsize, oldrrsize;
  mp_size_t rsize;
  mp_size_t sign_quotient;
  mp_size_t prec, err;
  mp_limb_t q_limb;
  mp_exp_t rexp;
  long k, mult, vn, t; 
  unsigned long cc = 0, rw, nw; 
  char can_round = 0; 
  TMP_DECL (marker);

  if (MPFR_IS_NAN(u) || MPFR_IS_NAN(v)) { MPFR_SET_NAN(r); return; }
  if (MPFR_IS_INF(u)) 
    { 
      if (MPFR_IS_INF(v)) 
	{
	  MPFR_SET_NAN(r); return; 
	}
      else
	{ 
	  MPFR_SET_INF(r); 
	  if (MPFR_SIGN(r) != MPFR_SIGN(u) * MPFR_SIGN(v)) 
	    { MPFR_CHANGE_SIGN(r); }
	  return; 
	}
    }
  else
    { 
      if (MPFR_IS_INF(v)) 
	{
	  MPFR_SET_ZERO(r); 
	  if (MPFR_SIGN(r) != MPFR_SIGN(u) * MPFR_SIGN(v)) 
	    { MPFR_CHANGE_SIGN(r); }
	  return; 
	}
    }

  usize = (MPFR_PREC(u) - 1)/BITS_PER_MP_LIMB + 1; 
  vsize = (MPFR_PREC(v) - 1)/BITS_PER_MP_LIMB + 1; 
  sign_quotient = ((MPFR_SIGN(u) * MPFR_SIGN(v) > 0) ? 1 : -1); 
  prec = MPFR_PREC(r);


  if (!MPFR_NOTZERO(v))
    {
      if (!MPFR_NOTZERO(u)) 
	{ MPFR_SET_NAN(r); return; }
      else
	{
	  MPFR_SET_INF(r); 
	  if (MPFR_SIGN(r) != MPFR_SIGN(v) * MPFR_SIGN(u)) 
	    MPFR_CHANGE_SIGN(r); 
	  return;
	}
    }
  
  if (!MPFR_NOTZERO(u)) { MPFR_SET_ZERO(r); return; }

  up = MPFR_MANT(u);
  vp = MPFR_MANT(v);

#ifdef DEBUG
      printf("Entering division : "); 
      for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); }
      printf(" by "); 
      for(k = vsize - 1; k >= 0; k--) { printf("%lu ", vp[k]); }
      printf(".\n"); 
#endif

  /* Compare the mantissas */
  mult = mpn_cmp(up, vp, (usize > vsize ? vsize : usize)); 
  if (mult == 0 && vsize > usize)
    {
      vn = vsize - usize; 
      while (vn >= 0) if (vp[vn--]) { mult = 1; break; }
      /* On peut diagnostiquer ici pour pas cher le cas u = v */
    }
  else { mult = (mult < 0 ? 1 : 0); }

  rsize = (MPFR_PREC(r) + 3)/BITS_PER_MP_LIMB + 1; 
  rrsize = MPFR_PREC(r)/BITS_PER_MP_LIMB + 1;
  /* Three extra bits are needed in order to get the quotient with enough
     precision ; take one extra bit for rrsize in order to solve more 
     easily the problem of rounding to nearest. */

  /* ATTENTION, UMPFR_SIZE DOIT RESTER > A VMPFR_SIZE !!!!!!!! */

  do
    {
      TMP_MARK (marker);

      rexp = u->_mp_exp - v->_mp_exp;
      
      err = rsize*BITS_PER_MP_LIMB; 
      if (rsize < vsize) { err-=2; } 
      if (rsize < usize) { err--; }
      if (err > rrsize * BITS_PER_MP_LIMB) 
	{ err = rrsize * BITS_PER_MP_LIMB; }
      
      tp0 = (mp_ptr) TMP_ALLOC ((rsize+rrsize) * BYTES_PER_MP_LIMB);
      /* fill by zero rrsize low limbs of t */
      MPN_ZERO(tp0, rrsize); tp = tp0 + rrsize; 
      rp = (mp_ptr) TMP_ALLOC ((rrsize+1) * BYTES_PER_MP_LIMB); 

      if (vsize >= rsize) { 
	tmp = (mp_ptr) vp + vsize - rsize;
      }
      else { 
	tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
	MPN_COPY (tmp + rsize - vsize, vp, vsize);
	MPN_ZERO (tmp, rsize - vsize); 
      }

      if (usize >= rsize) { 
	MPN_COPY (tp, up + usize - rsize, rsize);
      }
      else {
	MPN_COPY (tp + rsize - usize, up, usize); 
	MPN_ZERO (tp, rsize - usize); 
      }

      /* Do the real job */
 
#ifdef DEBUG
      printf("Dividing : "); 
      for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tp[k]); }
      printf(" by "); 
      for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tmp[k]); }
      printf(".\n"); 
#endif

#if (__GNU_MP_VERSION < 3)
      q_limb = mpn_divrem (rp, 0, tp0, rsize+rrsize, tmp, rsize);
      tp = tp0; /* location of remainder */
#else /* mpn_tdiv_qr is the preferred division interface in GMP 3 */
      tmp2 = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
      mpn_tdiv_qr(rp, tmp2, 0, tp0, rsize+rrsize, tmp, rsize);
      q_limb = rp[rrsize];
      tp = tmp2; /* location of remainder */
#endif

#ifdef DEBUG
      printf("The result is : \n"); 
      printf("Quotient : "); 
      for(k = rrsize - 1; k >= 0; k--) { printf("%lu ", rp[k]); }
      printf("Remainder : "); 
      for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tp[k]); }
      printf("(q_limb = %lu)\n", q_limb); 
#endif
      
      /* msb-normalize the result */
      
      if (q_limb)
	{
	  count_leading_zeros(k, q_limb); 
	  mpn_rshift(rp, rp, rrsize, BITS_PER_MP_LIMB - k);
	  rp[rrsize - 1] |= (q_limb << k);
	  rexp += BITS_PER_MP_LIMB - k; 
	}
      else
	{ 
	  count_leading_zeros(k, rp[rrsize - 1]); 
	  if (k) { mpn_lshift(rp, rp, rrsize, k); }
	  rexp -= k; 
	}

      can_round = (mpfr_can_round_raw(rp, rrsize, sign_quotient, err, 
				     GMP_RNDN, rnd_mode, MPFR_PREC(r))
	|| (usize == rsize && vsize == rsize && 
	    mpfr_can_round_raw(rp, rrsize, sign_quotient, err, 
			       GMP_RNDZ, rnd_mode, MPFR_PREC(r))));

      /* If we used all the limbs of both the dividend and the divisor, 
	 then we have the correct RNDZ rounding */

      if (!can_round && (rsize < usize || rsize < vsize)) 
	{
#ifdef DEBUG
	  printf("Increasing the precision.\n");
#endif
	  TMP_FREE(marker);
	  /* in case we can't round at the first iteration,
	     jump right away to the maximum precision of both
	     operands, to avoid multiple iterations when for 
	     example the divisor is 1.0.
	  */
	  if (rsize < usize) rsize = usize - 1;
	  if (rsize < vsize) rsize = vsize - 1;
	}
    }
  while (!can_round && (rsize < usize || rsize < vsize) 
	 && (rsize++) && (rrsize++));

  /* ON PEUT PROBABLEMENT SE DEBROUILLER DES QUE rsize >= vsize */
  /* MAIS IL FAUT AJOUTER LE BOUT QUI MANQUE DE usize A rsize */
    
  oldrrsize = rrsize;
  rrsize = (MPFR_PREC(r) - 1)/BITS_PER_MP_LIMB + 1;

  if (can_round) 
    {
      cc = mpfr_round_raw(rp, rp, err, (sign_quotient == -1 ? 1 : 0),
			  MPFR_PREC(r), rnd_mode);
    }
  else {
    /* Use the remainder to find out the correct rounding */
    /* Note that at this point the division has been done */
    /* EXACTLY. */
    if ((rnd_mode == GMP_RNDD && sign_quotient == -1) 
	|| (rnd_mode == GMP_RNDU && sign_quotient == 1)
	|| (rnd_mode == GMP_RNDN))
      {
	/* We cannot round, so that the last bits of the quotient
	   have to be zero; just look if the remainder is nonzero */
	k = rsize - 1; 
	while (k >= 0) { if (tp[k]) break; k--; }
	if (k >= 0) 
	  {
	    t = MPFR_PREC(r) & (BITS_PER_MP_LIMB - 1); 
	    if (t)
	      {
		cc = mpn_add_1(rp, rp, rrsize, 
			       (mp_limb_t)1 << (BITS_PER_MP_LIMB - t)); 
	      }
	    else
	      {
		cc = mpn_add_1(rp, rp, rrsize, 1); 
	      }
	  }
	else
	  if (rnd_mode == GMP_RNDN) /* even rounding */
	    {
	      rw = (MPFR_PREC(r) + 1) & (BITS_PER_MP_LIMB - 1);
	      if (rw) { rw = BITS_PER_MP_LIMB - rw; nw = 0; } else nw = 1; 
	      if ((rw ? (rp[nw] >> (rw + 1)) & 1 : 
		   (rp[nw] >> (BITS_PER_MP_LIMB - 1)) & 1))
		{
		  cc = mpn_add_1(rp + nw, rp + nw, rrsize, 
				 ((mp_limb_t)1) << rw); 
		}
	    }
	/* cas 0111111 */
      }
    /* Warning: we computed the result on oldrrsize limbs, but we want it
       on rrsize limbs only. Both can differ, especially when the target
       precision is a multiple of the number of bits per limb, since we've
       taken an extra bit to make rounding to nearest easier. */
    rp += oldrrsize-rrsize;
  }


  if (sign_quotient * MPFR_SIGN(r) < 0) { MPFR_CHANGE_SIGN(r); } 
  r->_mp_exp = rexp;

  if (cc) {
    mpn_rshift(rp, rp, rrsize, 1);
    rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1);
    r->_mp_exp++; 
  }
    
  rw = rrsize * BITS_PER_MP_LIMB - MPFR_PREC(r);
  MPN_COPY(MPFR_MANT(r), rp, rrsize); 
  MPFR_MANT(r)[0] &= ~(((mp_limb_t)1 << rw) - 1);

  TMP_FREE (marker);
}