text: /* double mpq_get_d (mpq_t src) -- Return the double approximation to SRC.
  
  Copyright (C) 1995, 1996 Free Software Foundation, Inc.
  
  This file is part of the GNU MP Library.
  
  The GNU MP Library is free software; you can redistribute it and/or modify
  it under the terms of the GNU Lesser General Public License as published by
  the Free Software Foundation; either version 2.1 of the License, or (at your
  option) any later version.
  
  The GNU MP 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 Lesser General Public
  License for more details.
  
  You should have received a copy of the GNU Lesser General Public License
  along with the GNU MP 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 "gmp.h"
  #include "gmp-impl.h"
  #include "longlong.h"
  
  /* Algorithm:
     1. Develop >= n bits of src.num / src.den, where n is the number of bits
        in a double.  This (partial) division will use all bits from the
        denominator.
     2. Use the remainder to determine how to round the result.
     3. Assign the integral result to a temporary double.
     4. Scale the temporary double, and return the result.
  
     An alternative algorithm, that would be faster:
     0. Let n be somewhat larger than the number of significant bits in a double.
     1. Extract the most significant n bits of the denominator, and an equal
        number of bits from the numerator.
     2. Interpret the extracted numbers as integers, call them a and b
        respectively, and develop n bits of the fractions ((a + 1) / b) and
        (a / (b + 1)) using mpn_divrem.
     3. If the computed values are identical UP TO THE POSITION WE CARE ABOUT,
        we are done.  If they are different, repeat the algorithm from step 1,
        but first let n = n * 2.
     4. If we end up using all bits from the numerator and denominator, fall
        back to the first algorithm above.
     5. Just to make life harder, The computation of a + 1 and b + 1 above
        might give carry-out...  Needs special handling.  It might work to
        subtract 1 in both cases instead.
  */
  
  double
  #if __STDC__
  mpq_get_d (const MP_RAT *src)
  #else
  mpq_get_d (src)
       const MP_RAT *src;
  #endif
  {
    mp_ptr np, dp;
    mp_ptr rp;
    mp_size_t nsize = src->_mp_num._mp_size;
    mp_size_t dsize = src->_mp_den._mp_size;
    mp_size_t qsize, rsize;
    mp_size_t sign_quotient = nsize ^ dsize;
    unsigned normalization_steps;
    mp_limb_t qlimb;
  #define N_QLIMBS (1 + (sizeof (double) + BYTES_PER_MP_LIMB-1) / BYTES_PER_MP_LIMB)
    mp_limb_t qarr[N_QLIMBS + 1];
    mp_ptr qp = qarr;
    TMP_DECL (marker);
  
    if (nsize == 0)
      return 0.0;
  
    TMP_MARK (marker);
    nsize = ABS (nsize);
    dsize = ABS (dsize);
    np = src->_mp_num._mp_d;
    dp = src->_mp_den._mp_d;
  
    rsize = dsize + N_QLIMBS;
    rp = (mp_ptr) TMP_ALLOC ((rsize + 1) * BYTES_PER_MP_LIMB);
  
    count_leading_zeros (normalization_steps, dp[dsize - 1]);
  
    /* Normalize the denominator, i.e. make its most significant bit set by
       shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
       numerator the same number of steps (to keep the quotient the same!).  */
    if (normalization_steps != 0)
      {
        mp_ptr tp;
        mp_limb_t nlimb;
  
        /* Shift up the denominator setting the most significant bit of
  	 the most significant limb.  Use temporary storage not to clobber
  	 the original contents of the denominator.  */
        tp = (mp_ptr) TMP_ALLOC (dsize * BYTES_PER_MP_LIMB);
        mpn_lshift (tp, dp, dsize, normalization_steps);
        dp = tp;
  
        if (rsize > nsize)
  	{
  	  MPN_ZERO (rp, rsize - nsize);
  	  nlimb = mpn_lshift (rp + (rsize - nsize),
  			      np, nsize, normalization_steps);
  	}
        else
  	{
  	  nlimb = mpn_lshift (rp, np + (nsize - rsize),
  			      rsize, normalization_steps);
  	}
        if (nlimb != 0)
  	{
  	  rp[rsize] = nlimb;
  	  rsize++;
  	}
      }
    else
      {
        if (rsize > nsize)
  	{
  	  MPN_ZERO (rp, rsize - nsize);
  	  MPN_COPY (rp + (rsize - nsize), np, nsize);
  	}
        else
  	{
  	  MPN_COPY (rp, np + (nsize - rsize), rsize);
  	}
      }
  
    qlimb = mpn_divmod (qp, rp, rsize, dp, dsize);
    qsize = rsize - dsize;
    if (qlimb)
      {
        qp[qsize] = qlimb;
        qsize++;
      }
  
    {
      double res;
      mp_size_t i;
      int scale = nsize - dsize - N_QLIMBS;
  
  #if defined (__vax__)
      /* Ignore excess quotient limbs.  This is necessary on a vax
         with its small double exponent, since we'd otherwise get
         exponent overflow while forming RES.  */
      if (qsize > N_QLIMBS)
        {
  	qp += qsize - N_QLIMBS;
  	scale += qsize - N_QLIMBS;
  	qsize = N_QLIMBS;
        }
  #endif
  
      res = qp[qsize - 1];
      for (i = qsize - 2; i >= 0; i--)
        res = res * MP_BASE_AS_DOUBLE + qp[i];
  
      res = __gmp_scale2 (res, BITS_PER_MP_LIMB * scale);
  
      TMP_FREE (marker);
      return sign_quotient >= 0 ? res : -res;
    }
  }
  