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Diff for /OpenXM_contrib/gmp/mpfr/Attic/div.c between version 1.1 and 1.1.1.2

version 1.1, 2000/09/09 14:12:19 version 1.1.1.2, 2003/08/25 16:06:06
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 /* mpfr_div -- divide two floating-point numbers  /* mpfr_div -- divide two floating-point numbers
   
 Copyright (C) 1999 PolKA project, Inria Lorraine and Loria  Copyright 1999, 2001 Free Software Foundation.
   
 This file is part of the MPFR Library.  This file is part of the MPFR Library.
   
 The MPFR Library is free software; you can redistribute it and/or modify  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  it under the terms of the GNU Lesser General Public License as published by
 the Free Software Foundation; either version 2 of the License, or (at your  the Free Software Foundation; either version 2.1 of the License, or (at your
 option) any later version.  option) any later version.
   
 The MPFR Library is distributed in the hope that it will be useful, but  The MPFR Library is distributed in the hope that it will be useful, but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 License for more details.  License for more details.
   
 You should have received a copy of the GNU Library General Public License  You should have received a copy of the GNU Lesser General Public License
 along with the MPFR Library; see the file COPYING.LIB.  If not, write to  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,  the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 MA 02111-1307, USA. */  MA 02111-1307, USA. */
   
 #include <math.h>  
 #include <stdio.h>  
 #include <stdlib.h>  
 #include "gmp.h"  #include "gmp.h"
 #include "gmp-impl.h"  #include "gmp-impl.h"
 #include "mpfr.h"  
 #include "longlong.h"  #include "longlong.h"
   #include "mpfr.h"
   #include "mpfr-impl.h"
   
 /* #define DEBUG */  int
   mpfr_div (mpfr_ptr q, mpfr_srcptr u, mpfr_srcptr v, mp_rnd_t rnd_mode)
 void  
 mpfr_div (mpfr_ptr r, mpfr_srcptr u, mpfr_srcptr v, unsigned char rnd_mode)  
 {  {
   mp_srcptr up, vp;    mp_srcptr up, vp, bp;
   mp_ptr rp, tp, tp0, tmp;    mp_size_t usize, vsize;
   mp_size_t usize, vsize, rrsize;  
   mp_size_t rsize;    mp_ptr ap, qp, rp;
   mp_size_t sign_quotient;    mp_size_t asize, bsize, qsize, rsize;
   mp_size_t prec, err;    mp_exp_t qexp;
   mp_limb_t q_limb;  
   mp_exp_t rexp;    mp_rnd_t rnd_mode1, rnd_mode2;
   long k, mult, vn;  
   unsigned long cc = 0, rw, nw;    mp_size_t err, k;
   char can_round = 0;    mp_limb_t near;
     int inex, sh, can_round, can_round2, sign_quotient;
     unsigned int cc = 0, rw;
   
   TMP_DECL (marker);    TMP_DECL (marker);
   
   if (FLAG_NAN(u) || FLAG_NAN(v)) { SET_NAN(r); return; }  
   
   usize = (PREC(u) - 1)/BITS_PER_MP_LIMB + 1;  
   vsize = (PREC(v) - 1)/BITS_PER_MP_LIMB + 1;  
   sign_quotient = (SIGN(u) == SIGN(v) ? 1 : -1);  
   prec = PREC(r);  
   
   if (!NOTZERO(u)) { SET_ZERO(r); return; }    /**************************************************************************
      *                                                                        *
      *              This part of the code deals with special cases            *
      *                                                                        *
      **************************************************************************/
   
   if (!NOTZERO(v))    if (MPFR_IS_NAN(u) || MPFR_IS_NAN(v))
     vsize = 1 / v->_mp_d[vsize - 1];    /* Gestion des infinis ? */  
   
   if (!NOTZERO(v))  
     {      {
       r->_mp_exp = 0;        MPFR_SET_NAN(q);
       MPN_ZERO(r->_mp_d, r->_mp_size);        MPFR_RET_NAN;
       return;  
     }      }
   
   up = u->_mp_d;    MPFR_CLEAR_NAN(q);
   vp = v->_mp_d;  
   
 #ifdef DEBUG    sign_quotient = MPFR_SIGN(u) * MPFR_SIGN(v);
       printf("Entering division : ");    if (MPFR_SIGN(q) != sign_quotient)
       for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); }      MPFR_CHANGE_SIGN(q);
       printf(" by ");  
       for(k = vsize - 1; k >= 0; k--) { printf("%lu ", vp[k]); }  
       printf(".\n");  
 #endif  
   
   /* Compare the mantissas */    if (MPFR_IS_INF(u))
   mult = mpn_cmp(up, vp, (usize > vsize ? vsize : usize));  
   if (mult == 0 && vsize > usize)  
     {      {
       vn = vsize - usize;        if (MPFR_IS_INF(v))
       while (vn >= 0) if (vp[vn--]) { mult = 1; break; }          {
       /* On peut diagnostiquer ici pour pas cher le cas u = v */            MPFR_SET_NAN(q);
             MPFR_RET_NAN;
           }
         else
           {
             MPFR_SET_INF(q);
             MPFR_RET(0);
           }
     }      }
   else { mult = (mult < 0 ? 1 : 0); }    else
       if (MPFR_IS_INF(v))
         {
           MPFR_CLEAR_INF(q);
           MPFR_SET_ZERO(q);
           MPFR_RET(0);
         }
   
   rsize = (PREC(r) + 3)/BITS_PER_MP_LIMB + 1;    MPFR_CLEAR_INF(q); /* clear Inf flag */
   rrsize = 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, USIZE DOIT RESTER > A VSIZE !!!!!!!! */    if (MPFR_IS_ZERO(v))
       {
         if (MPFR_IS_ZERO(u))
           {
             MPFR_SET_NAN(q);
             MPFR_RET_NAN;
           }
         else
           {
             MPFR_SET_INF(q);
             MPFR_RET(0);
           }
       }
   
   do    if (MPFR_IS_ZERO(u))
     {      {
       TMP_MARK (marker);        MPFR_SET_ZERO(q);
         MPFR_RET(0);
       }
   
       rexp = u->_mp_exp - v->_mp_exp;    /**************************************************************************
      *                                                                        *
       err = rsize*BITS_PER_MP_LIMB;     *              End of the part concerning special values.                *
       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;  
       tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);  
       rp = (mp_ptr) TMP_ALLOC (rrsize * BYTES_PER_MP_LIMB);  
   
       if (vsize >= rsize) {  
         MPN_COPY (tmp, vp + vsize - rsize, rsize);  
       }  
       else {  
         MPN_COPY (tmp + rsize - vsize, vp, vsize);  
         MPN_ZERO (tmp, rsize - vsize);  
       }  
   
       if (usize >= rsize) {    up = MPFR_MANT(u);
         MPN_COPY (tp, up + usize - rsize, rsize);    vp = MPFR_MANT(v);
       }  
       else {  
         MPN_COPY (tp + rsize - usize, up, usize);  
         MPN_ZERO (tp, rsize - usize);  
       }  
   
       /* Do the real job */    TMP_MARK (marker);
     usize = MPFR_ESIZE(u);
 #ifdef DEBUG    vsize = MPFR_ESIZE(v);
       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  
   
       q_limb = (rsize==rrsize) /* use Burnikel-Ziegler algorithm */    /**************************************************************************
         ? mpn_divrem_n (rp, tp0, tmp, rsize)     *                                                                        *
         : mpn_divrem (rp, 0, tp0, rsize+rrsize, tmp, rsize);     *   First try to use only part of u, v. If this is not sufficient,       *
       tp = tp0; /* location of remainder */     *   use the full u and v, to avoid long computations eg. in the case     *
      *   u = v.                                                               *
      *                                                                        *
      **************************************************************************/
   
 #ifdef DEBUG    /* The dividend is a, length asize. The divisor is b, length bsize. */
       printf("The result is : \n");  
       printf("Quotient : ");    qsize = (MPFR_PREC(q) + 3)/BITS_PER_MP_LIMB + 1;
       for(k = rrsize - 1; k >= 0; k--) { printf("%lu ", rp[k]); }    if (vsize < qsize)
       printf("Remainder : ");      {
       for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tp[k]); }        bsize = vsize;
       printf("(q_limb = %lu)\n", q_limb);        bp = vp;
 #endif      }
     else
       {
         bsize = qsize;
         bp = (mp_srcptr)vp + vsize - qsize;
       }
   
     asize = bsize + qsize;
     ap = (mp_ptr) TMP_ALLOC(asize * BYTES_PER_MP_LIMB);
     if (asize > usize)
       {
         MPN_COPY(ap + asize - usize, up, usize);
         MPN_ZERO(ap, asize - usize);
       }
     else
       MPN_COPY(ap, up + usize - asize, asize);
   
     /* Allocate limbs for quotient and remainder. */
     qp = (mp_ptr) TMP_ALLOC ((qsize + 1) * BYTES_PER_MP_LIMB);
     rp = (mp_ptr) TMP_ALLOC (bsize * BYTES_PER_MP_LIMB);
     rsize = bsize;
   
     mpn_tdiv_qr(qp, rp, 0, ap, asize, bp, bsize);
   
     /* Estimate number of correct bits. */
   
     err = qsize * BITS_PER_MP_LIMB;
     if (bsize < vsize) err -= 2; else if (asize < usize) err --;
   
     /* We want to check if rounding is possible, but without normalizing
        because we might have to divide again if rounding is impossible, or
        if the result might be exact. We have however to mimic normalization */
   
     if (qp[qsize] != 0) { sh = -1; }
     else { count_leading_zeros(sh, qp[qsize - 1]); }
   
     /*
        To detect asap if the result is inexact, so as to avoid doing the
        division completely, we perform the following check :
   
        - if rnd_mode == GMP_RNDN, and the result is exact, we are unable
        to round simultaneously to zero and to infinity ;
   
        - if rnd_mode == GMP_RNDN, and if we can round to zero with one extra
        bit of precision, we can decide rounding. Hence in that case, check
        as in the case of GMP_RNDN, with one extra bit. Note that in the case
        of close to even rounding we shall do the division completely, but
        this is necessary anyway : we need to know whether this is really
        even rounding or not.
     */
   
     if (rnd_mode == GMP_RNDN)
       {
         rnd_mode1 = GMP_RNDZ;
         near = 1;
       }
     else
       {
         rnd_mode1 = rnd_mode;
         near = 0;
       }
   
     sh += near;
     can_round = mpfr_can_round_raw(qp, qsize + 1, sign_quotient, err + sh +
                                    BITS_PER_MP_LIMB, GMP_RNDN, rnd_mode1,
                                    MPFR_PREC(q) + sh + BITS_PER_MP_LIMB);
   
     switch (rnd_mode1)
       {
       case GMP_RNDU : rnd_mode2 = GMP_RNDD; break;
       case GMP_RNDD : rnd_mode2 = GMP_RNDU; break;
       case GMP_RNDZ : rnd_mode2 = sign_quotient == 1 ? GMP_RNDU : GMP_RNDD;
         break;
       default : rnd_mode2 = GMP_RNDZ;
       }
   
     can_round2 = mpfr_can_round_raw(qp, qsize + 1, sign_quotient, err + sh +
                                     BITS_PER_MP_LIMB, GMP_RNDN, rnd_mode2,
                                     MPFR_PREC(q) + sh + BITS_PER_MP_LIMB);
   
     sh -= near;
   
     /* If either can_round or can_round2 is 0, either we cannot round or
        the result might be exact. If asize >= usize and bsize >= vsize, we
        can just check this by looking at the remainder. Otherwise, we
        have to correct our first approximation. */
   
     if ((!can_round || !can_round2) && (asize < usize || bsize < vsize))
       {
         int b = 0;
         mp_ptr rem, rem2;
   
     /**************************************************************************
      *                                                                        *
      *   The attempt to use only part of u and v failed. We first compute a   *
      *   correcting term, then perform the full division.                     *
      *   Put u = uhi + ulo, v = vhi + vlo. We have uhi = vhi * qp + rp,       *
      *   thus u - qp * v = rp + ulo - qp * vlo, that we shall divide by v.    *
      *                                                                        *
      **************************************************************************/
   
         rsize = qsize + 1 +
                 (usize - asize > vsize - bsize
                  ? usize - asize
                  : vsize - bsize);
   
         /*
           TODO : One operand is probably enough, but then we have to
           perform one further comparison (compute first vlo * q,
           try to substract r, try to substract ulo. Which is best ?
           NB : ulo and r do not overlap. Draw advantage of this
           [eg. HI(vlo*q) = r => compare LO(vlo*q) with b.]
         */
   
         rem = TMP_ALLOC(rsize * BYTES_PER_MP_LIMB);
         rem2 = TMP_ALLOC(rsize * BYTES_PER_MP_LIMB);
   
         rem[rsize - 1] = rem2 [rsize - 1] = 0;
   
         if (bsize < vsize)
           {
             /* Compute vlo * q */
             if (qsize + 1 > vsize - bsize)
               mpn_mul(rem + rsize - vsize - qsize - 1 + bsize,
                       qp, qsize + 1, vp, vsize - bsize);
             else
               mpn_mul(rem + rsize - vsize - qsize - 1 + bsize,
                       vp, vsize - bsize, qp, qsize + 1);
   
             MPN_ZERO(rem, rsize - vsize - qsize - 1 + bsize);
           }
         else MPN_ZERO(rem, rsize);
   
         /* Compute ulo + r. The two of them do not overlap. */
         MPN_COPY(rem2 + rsize - 1 - qsize, rp, bsize);
   
       /* msb-normalize the result */        if (qsize + 1 > bsize)
           MPN_ZERO(rem2 + rsize - 1 - qsize + bsize, qsize + 1 - bsize);
       if (q_limb)  
         if (asize < usize)
         {          {
           count_leading_zeros(k, q_limb);            MPN_COPY(rem2 + rsize - 1 - qsize - usize + asize,
           mpn_rshift(rp, rp, rrsize, BITS_PER_MP_LIMB - k);                     up, usize - asize);
           rp[rrsize - 1] |= (q_limb << k);            MPN_ZERO(rem2, rsize - 1 - qsize - usize + asize);
           rexp += BITS_PER_MP_LIMB - k;  
         }          }
       else        else
           MPN_ZERO(rem2, rsize - 1 - qsize);
   
         b = 0;
         if (mpn_cmp(rem2, rem, rsize) >= 0)
           {
             /* Positive correction is at most 1. */
   
             mpn_sub_n(rem, rem2, rem, rsize);
             if (rem[rsize - 1] != 0 ||
                 mpn_cmp(rem + rsize - vsize - 1, vp, vsize) >= 0)
               {
                 rem[rsize - 1] -=
                   mpn_sub_n(rem + rsize - vsize - 1,
                             rem + rsize - vsize - 1,
                             vp, vsize);
                 qp[qsize] -= mpn_add_1(qp, qp, qsize, 1);
               }
           }
         else
         {          {
           count_leading_zeros(k, rp[rrsize - 1]);            /* Negative correction is at most 3 */
           if (k) { mpn_lshift(rp, rp, rrsize, k); }            do
           rexp -= k;              {
                 b++;
                 rem2[rsize - 1] +=
                   mpn_add_n(rem2 + rsize - vsize - 1,
                             rem2 + rsize - vsize - 1, vp, vsize);
               }
             while (mpn_cmp(rem2, rem, rsize) < 0);
   
             qp[qsize] -= mpn_sub_1(qp, qp, qsize, b);
             mpn_sub_n(rem, rem2, rem, rsize);
         }          }
   
         if (qp[qsize] != 0)
           sh = -1;
         else
           count_leading_zeros(sh, qp[qsize - 1]);
   
       can_round = (mpfr_can_round_raw(rp, rrsize, sign_quotient, err,        err = BITS_PER_MP_LIMB * qsize;
                                      GMP_RNDN, rnd_mode, PREC(r))        rp = rem;
         || (usize == rsize && vsize == rsize &&      }
             mpfr_can_round_raw(rp, rrsize, sign_quotient, err,  
                                GMP_RNDZ, rnd_mode, PREC(r))));    /**************************************************************************
      *                                                                        *
      *                       Final stuff (rounding and so.)                   *
      *  From now on : qp is the quotient [size qsize], rp the remainder       *
      *  [size rsize].                                                         *
      **************************************************************************/
   
       /* If we used all the limbs of both the dividend and the divisor,    qexp = MPFR_EXP(u) - MPFR_EXP(v);
          then we have the correct RNDZ rounding */  
   
       if (!can_round && (rsize < usize || rsize < vsize))    if (qp[qsize] != 0)
       /* Hack : qp[qsize] is 0, 1 or 2, hence if not 0, = 2^(qp[qsize] - 1). */
       {
         near = mpn_rshift(qp, qp, qsize, qp[qsize]);
         qp[qsize - 1] |= GMP_LIMB_HIGHBIT; qexp += qp[qsize];
       }
     else
       {
         near = 0;
         if (sh != 0)
         {          {
 #ifdef DEBUG            mpn_lshift(qp, qp, qsize, sh);
           printf("Increasing the precision.\n");            qexp -= sh;
 #endif  
           printf("#");  
           TMP_FREE(marker);  
         }          }
     }      }
   while (!can_round && (rsize < usize || rsize < vsize)  
          && (rsize++) && (rrsize++));    cc = mpfr_round_raw_generic(qp, qp, err, (sign_quotient == -1 ? 1 : 0),
                                 MPFR_PREC(q), rnd_mode, &inex, 1);
   
   /* ON PEUT PROBABLEMENT SE DEBROUILLER DES QUE rsize >= vsize */    qp += qsize - MPFR_ESIZE(q); /* 0 or 1 */
   /* MAIS IL FAUT AJOUTER LE BOUT QUI MANQUE DE usize A rsize */    qsize = MPFR_ESIZE(q);
   
   if (can_round)    /*
        At that point, either we were able to round from the beginning,
        and know thus that the result is inexact.
   
        Or we have performed a full division. In that case, we might still
        be wrong if both
        - the remainder is nonzero ;
        - we are rounding to infinity or to nearest (the nasty case of even
        rounding).
        - inex = 0, meaning that the non-significant bits of the quotients are 0,
        except when rounding to nearest (the nasty case of even rounding again).
     */
   
     if (!can_round || !can_round2) /* Lazy case. */
     {      {
       cc = mpfr_round_raw(rp, rp, err, (sign_quotient == -1 ? 1 : 0),        if (inex == 0)
                           PREC(r), rnd_mode);          {
       rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;            k = rsize - 1;
     }  
   else            /* If a bit has been shifted out during normalization, hence
     /* Use the remainder to find out the correct rounding */               the remainder is nonzero. */
     /* Note that at this point the division has been done */            if (near == 0)
     /* EXACTLY. */              while (k >= 0) { if (rp[k]) break; k--; }
     if ((rnd_mode == GMP_RNDD && sign_quotient == -1)  
         || (rnd_mode == GMP_RNDU && sign_quotient == 1)            if (k >= 0) /* Remainder is nonzero. */
         || (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)  
           cc = mpn_add_1(rp, rp, rrsize, (mp_limb_t)1 << (BITS_PER_MP_LIMB -  
                                                (PREC(r) &  
                                                 (BITS_PER_MP_LIMB - 1))));  
         else  
           if (rnd_mode == GMP_RNDN) /* even rounding */  
             {              {
               rw = (PREC(r) + 1) & (BITS_PER_MP_LIMB - 1);                if ((rnd_mode == GMP_RNDD && sign_quotient == -1)
               if (rw) { rw = BITS_PER_MP_LIMB - rw; nw = 0; } else nw = 1;                    || (rnd_mode == GMP_RNDU && sign_quotient == 1))
               if ((rw ? (rp[nw] >> (rw + 1)) & 1 :                  /* Rounding to infinity. */
                    (rp[nw] >> (BITS_PER_MP_LIMB - 1)) & 1))  
                 {                  {
                   cc = mpn_add_1(rp + nw, rp + nw, rrsize,                    inex = sign_quotient;
                                  ((mp_limb_t)1) << rw);                    cc = 1;
                 }                  }
                 /* rounding to zero. */
                 else inex = -sign_quotient;
             }              }
         /* cas 0111111 */          }
       }        else /* We might have to correct an even rounding if remainder
                 is nonzero and if even rounding was towards 0. */
           if (rnd_mode == GMP_RNDN && (inex == MPFR_EVEN_INEX
                                        || inex == -MPFR_EVEN_INEX))
             {
               k = rsize - 1;
   
   if (sign_quotient != SIGN(r)) { CHANGE_SIGN(r); }            /* If a bit has been shifted out during normalization, hence
   r->_mp_exp = rexp;               the remainder is nonzero. */
               if (near == 0)
                 while (k >= 0)
                   {
                     if (rp[k])
                       break;
                     k--;
                   }
   
               if (k >= 0) /* In fact the quotient is larger than expected */
                 {
                   inex = sign_quotient; /* To infinity, finally. */
                   cc = 1;
                 }
             }
       }
   
     /* Final modification due to rounding */
     if (cc)
       {
         sh = MPFR_PREC(q) & (BITS_PER_MP_LIMB - 1);
         if (sh)
           cc = mpn_add_1 (qp, qp, qsize,
                           MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - sh));
         else
           cc = mpn_add_1 (qp, qp, qsize, MP_LIMB_T_ONE);
   
   if (cc) {        if (cc)
     mpn_rshift(rp, rp, rrsize, 1);          {
     rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1);            mpn_rshift (qp, qp, qsize, 1);
     r->_mp_exp++;            qp[qsize-1] |= GMP_LIMB_HIGHBIT;
   }            qexp++;
           }
   rsize = rrsize;      }
   rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;  
   MPN_COPY(r->_mp_d, rp + rsize - rrsize, rrsize);  
   MANT(r) [0] &= ~(((mp_limb_t)1 << (BITS_PER_MP_LIMB -  
                     (PREC(r) & (BITS_PER_MP_LIMB - 1)))) - 1) ;  
   
     rw = qsize * BITS_PER_MP_LIMB - MPFR_PREC(q);
     MPN_COPY(MPFR_MANT(q), qp, qsize);
   TMP_FREE (marker);    TMP_FREE (marker);
   
     MPFR_MANT(q)[0] &= ~((MP_LIMB_T_ONE << rw) - MP_LIMB_T_ONE);
     MPFR_EXP(q) = qexp;
   
     MPFR_RET(inex);
 }  }
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  Added in v.1.1.1.2
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