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/****************************************************************
 *
 * The author of this software is David M. Gay.
 *
 * Copyright (c) 1991 by AT&T.
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose without fee is hereby granted, provided that this entire notice
 * is included in all copies of any software which is or includes a copy
 * or modification of this software and in all copies of the supporting
 * documentation for such software.
 *
 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
 *
 ***************************************************************/
 
/* Please send bug reports to
        David M. Gay
        AT&T Bell Laboratories, Room 2C-463
        600 Mountain Avenue
        Murray Hill, NJ 07974-2070
        U.S.A.
        dmg@research.att.com or research!dmg
 */
 
#include <_ansi.h>
#include <stdlib.h>
#include <reent.h>
#include <string.h>
#include "mprec.h"
 
static int
_DEFUN (quorem,
        (b, S),
        _Bigint * b _AND _Bigint * S)
{
  int n;
  __Long borrow, y;
  __ULong carry, q, ys;
  __ULong *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
  __Long z;
  __ULong si, zs;
#endif
 
  n = S->_wds;
#ifdef DEBUG
  /*debug*/ if (b->_wds > n)
    /*debug*/ Bug ("oversize b in quorem");
#endif
  if (b->_wds < n)
    return 0;
  sx = S->_x;
  sxe = sx + --n;
  bx = b->_x;
  bxe = bx + n;
  q = *bxe / (*sxe + 1);        /* ensure q <= true quotient */
#ifdef DEBUG
  /*debug*/ if (q > 9)
    /*debug*/ Bug ("oversized quotient in quorem");
#endif
  if (q)
    {
      borrow = 0;
      carry = 0;
      do
        {
#ifdef Pack_32
          si = *sx++;
          ys = (si & 0xffff) * q + carry;
          zs = (si >> 16) * q + (ys >> 16);
          carry = zs >> 16;
          y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
          borrow = y >> 16;
          Sign_Extend (borrow, y);
          z = (*bx >> 16) - (zs & 0xffff) + borrow;
          borrow = z >> 16;
          Sign_Extend (borrow, z);
          Storeinc (bx, z, y);
#else
          ys = *sx++ * q + carry;
          carry = ys >> 16;
          y = *bx - (ys & 0xffff) + borrow;
          borrow = y >> 16;
          Sign_Extend (borrow, y);
          *bx++ = y & 0xffff;
#endif
        }
      while (sx <= sxe);
      if (!*bxe)
        {
          bx = b->_x;
          while (--bxe > bx && !*bxe)
            --n;
          b->_wds = n;
        }
    }
  if (cmp (b, S) >= 0)
    {
      q++;
      borrow = 0;
      carry = 0;
      bx = b->_x;
      sx = S->_x;
      do
        {
#ifdef Pack_32
          si = *sx++;
          ys = (si & 0xffff) + carry;
          zs = (si >> 16) + (ys >> 16);
          carry = zs >> 16;
          y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
          borrow = y >> 16;
          Sign_Extend (borrow, y);
          z = (*bx >> 16) - (zs & 0xffff) + borrow;
          borrow = z >> 16;
          Sign_Extend (borrow, z);
          Storeinc (bx, z, y);
#else
          ys = *sx++ + carry;
          carry = ys >> 16;
          y = *bx - (ys & 0xffff) + borrow;
          borrow = y >> 16;
          Sign_Extend (borrow, y);
          *bx++ = y & 0xffff;
#endif
        }
      while (sx <= sxe);
      bx = b->_x;
      bxe = bx + n;
      if (!*bxe)
        {
          while (--bxe > bx && !*bxe)
            --n;
          b->_wds = n;
        }
    }
  return q;
}
 
/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
 *
 * Inspired by "How to Print Floating-Point Numbers Accurately" by
 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
 *
 * Modifications:
 *      1. Rather than iterating, we use a simple numeric overestimate
 *         to determine k = floor(log10(d)).  We scale relevant
 *         quantities using O(log2(k)) rather than O(k) multiplications.
 *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
 *         try to generate digits strictly left to right.  Instead, we
 *         compute with fewer bits and propagate the carry if necessary
 *         when rounding the final digit up.  This is often faster.
 *      3. Under the assumption that input will be rounded nearest,
 *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
 *         That is, we allow equality in stopping tests when the
 *         round-nearest rule will give the same floating-point value
 *         as would satisfaction of the stopping test with strict
 *         inequality.
 *      4. We remove common factors of powers of 2 from relevant
 *         quantities.
 *      5. When converting floating-point integers less than 1e16,
 *         we use floating-point arithmetic rather than resorting
 *         to multiple-precision integers.
 *      6. When asked to produce fewer than 15 digits, we first try
 *         to get by with floating-point arithmetic; we resort to
 *         multiple-precision integer arithmetic only if we cannot
 *         guarantee that the floating-point calculation has given
 *         the correctly rounded result.  For k requested digits and
 *         "uniformly" distributed input, the probability is
 *         something like 10^(k-15) that we must resort to the long
 *         calculation.
 */
 
 
char *
_DEFUN (_dtoa_r,
        (ptr, _d, mode, ndigits, decpt, sign, rve),
        struct _reent *ptr _AND
        double _d _AND
        int mode _AND
        int ndigits _AND
        int *decpt _AND
        int *sign _AND
        char **rve)
{
  /*    Arguments ndigits, decpt, sign are similar to those
        of ecvt and fcvt; trailing zeros are suppressed from
        the returned string.  If not null, *rve is set to point
        to the end of the return value.  If d is +-Infinity or NaN,
        then *decpt is set to 9999.
 
        mode:
 
                        and rounded to nearest.
                1 ==> like 0, but with Steele & White stopping rule;
                        e.g. with IEEE P754 arithmetic , mode 0 gives
                        1e23 whereas mode 1 gives 9.999999999999999e22.
                2 ==> max(1,ndigits) significant digits.  This gives a
                        return value similar to that of ecvt, except
                        that trailing zeros are suppressed.
                3 ==> through ndigits past the decimal point.  This
                        gives a return value similar to that from fcvt,
                        except that trailing zeros are suppressed, and
                        ndigits can be negative.
                4-9 should give the same return values as 2-3, i.e.,
                        4 <= mode <= 9 ==> same return as mode
                        2 + (mode & 1).  These modes are mainly for
                        debugging; often they run slower but sometimes
                        faster than modes 2-3.
                4,5,8,9 ==> left-to-right digit generation.
                6-9 ==> don't try fast floating-point estimate
                        (if applicable).
 
                Values of mode other than 0-9 are treated as mode 0.
 
                Sufficient space is allocated to the return value
                to hold the suppressed trailing zeros.
        */
 
  int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0,
    k_check, leftright, m2, m5, s2, s5, spec_case, try_quick;
  union double_union d, d2, eps;
  __Long L;
#ifndef Sudden_Underflow
  int denorm;
  __ULong x;
#endif
  _Bigint *b, *b1, *delta, *mlo, *mhi, *S;
  double ds;
  char *s, *s0;
 
  d.d = _d;
 
  if (ptr->_result)
    {
      ptr->_result->_k = ptr->_result_k;
      ptr->_result->_maxwds = 1 << ptr->_result_k;
      Bfree (ptr, ptr->_result);
      ptr->_result = 0;
    }
 
  if (word0 (d) & Sign_bit)
    {
      /* set sign for everything, including 0's and NaNs */
      *sign = 1;
      word0 (d) &= ~Sign_bit;   /* clear sign bit */
    }
  else
    *sign = 0;
 
#if defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
  if ((word0 (d) & Exp_mask) == Exp_mask)
#else
  if (word0 (d) == 0x8000)
#endif
    {
      /* Infinity or NaN */
      *decpt = 9999;
      s =
#ifdef IEEE_Arith
        !word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" :
#endif
        "NaN";
      if (rve)
        *rve =
#ifdef IEEE_Arith
          s[3] ? s + 8 :
#endif
          s + 3;
      return s;
    }
#endif
#ifdef IBM
  d.d += 0;                      /* normalize */
#endif
  if (!d.d)
    {
      *decpt = 1;
      s = "0";
      if (rve)
        *rve = s + 1;
      return s;
    }
 
  b = d2b (ptr, d.d, &be, &bbits);
#ifdef Sudden_Underflow
  i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
#else
  if (i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))
    {
#endif
      d2.d = d.d;
      word0 (d2) &= Frac_mask1;
      word0 (d2) |= Exp_11;
#ifdef IBM
      if (j = 11 - hi0bits (word0 (d2) & Frac_mask))
        d2.d /= 1 << j;
#endif
 
      /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
                 * log10(x)      =  log(x) / log(10)
                 *              ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
                 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
                 *
                 * This suggests computing an approximation k to log10(d) by
                 *
                 * k = (i - Bias)*0.301029995663981
                 *      + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
                 *
                 * We want k to be too large rather than too small.
                 * The error in the first-order Taylor series approximation
                 * is in our favor, so we just round up the constant enough
                 * to compensate for any error in the multiplication of
                 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
                 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
                 * adding 1e-13 to the constant term more than suffices.
                 * Hence we adjust the constant term to 0.1760912590558.
                 * (We could get a more accurate k by invoking log10,
                 *  but this is probably not worthwhile.)
                 */
 
      i -= Bias;
#ifdef IBM
      i <<= 2;
      i += j;
#endif
#ifndef Sudden_Underflow
      denorm = 0;
    }
  else
    {
      /* d is denormalized */
 
      i = bbits + be + (Bias + (P - 1) - 1);
      x = i > 32 ? word0 (d) << 64 - i | word1 (d) >> i - 32
        : word1 (d) << 32 - i;
      d2.d = x;
      word0 (d2) -= 31 * Exp_msk1;      /* adjust exponent */
      i -= (Bias + (P - 1) - 1) + 1;
      denorm = 1;
    }
#endif
  ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
  k = (int) ds;
  if (ds < 0. && ds != k)
    k--;                        /* want k = floor(ds) */
  k_check = 1;
  if (k >= 0 && k <= Ten_pmax)
    {
      if (d.d < tens[k])
        k--;
      k_check = 0;
    }
  j = bbits - i - 1;
  if (j >= 0)
    {
      b2 = 0;
      s2 = j;
    }
  else
    {
      b2 = -j;
      s2 = 0;
    }
  if (k >= 0)
    {
      b5 = 0;
      s5 = k;
      s2 += k;
    }
  else
    {
      b2 -= k;
      b5 = -k;
      s5 = 0;
    }
  if (mode < 0 || mode > 9)
    mode = 0;
  try_quick = 1;
  if (mode > 5)
    {
      mode -= 4;
      try_quick = 0;
    }
  leftright = 1;
  switch (mode)
    {
    case 0:
    case 1:
      ilim = ilim1 = -1;
      i = 18;
      ndigits = 0;
      break;
    case 2:
      leftright = 0;
      /* no break */
    case 4:
      if (ndigits <= 0)
        ndigits = 1;
      ilim = ilim1 = i = ndigits;
      break;
    case 3:
      leftright = 0;
      /* no break */
    case 5:
      i = ndigits + k + 1;
      ilim = i;
      ilim1 = i - 1;
      if (i <= 0)
        i = 1;
    }
  j = sizeof (__ULong);
  for (ptr->_result_k = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i;
       j <<= 1)
    ptr->_result_k++;
  ptr->_result = Balloc (ptr, ptr->_result_k);
  s = s0 = (char *) ptr->_result;
 
  if (ilim >= 0 && ilim <= Quick_max && try_quick)
    {
      /* Try to get by with floating-point arithmetic. */
 
      i = 0;
      d2.d = d.d;
      k0 = k;
      ilim0 = ilim;
      ieps = 2;                 /* conservative */
      if (k > 0)
        {
          ds = tens[k & 0xf];
          j = k >> 4;
          if (j & Bletch)
            {
              /* prevent overflows */
              j &= Bletch - 1;
              d.d /= bigtens[n_bigtens - 1];
              ieps++;
            }
          for (; j; j >>= 1, i++)
            if (j & 1)
              {
                ieps++;
                ds *= bigtens[i];
              }
          d.d /= ds;
        }
      else if (j1 = -k)
        {
          d.d *= tens[j1 & 0xf];
          for (j = j1 >> 4; j; j >>= 1, i++)
            if (j & 1)
              {
                ieps++;
                d.d *= bigtens[i];
              }
        }
      if (k_check && d.d < 1. && ilim > 0)
        {
          if (ilim1 <= 0)
            goto fast_failed;
          ilim = ilim1;
          k--;
          d.d *= 10.;
          ieps++;
        }
      eps.d = ieps * d.d + 7.;
      word0 (eps) -= (P - 1) * Exp_msk1;
      if (ilim == 0)
        {
          S = mhi = 0;
          d.d -= 5.;
          if (d.d > eps.d)
            goto one_digit;
          if (d.d < -eps.d)
            goto no_digits;
          goto fast_failed;
        }
#ifndef No_leftright
      if (leftright)
        {
          /* Use Steele & White method of only
           * generating digits needed.
           */
          eps.d = 0.5 / tens[ilim - 1] - eps.d;
          for (i = 0;;)
            {
              L = d.d;
              d.d -= L;
              *s++ = '0' + (int) L;
              if (d.d < eps.d)
                goto ret1;
              if (1. - d.d < eps.d)
                goto bump_up;
              if (++i >= ilim)
                break;
              eps.d *= 10.;
              d.d *= 10.;
            }
        }
      else
        {
#endif
          /* Generate ilim digits, then fix them up. */
          eps.d *= tens[ilim - 1];
          for (i = 1;; i++, d.d *= 10.)
            {
              L = d.d;
              d.d -= L;
              *s++ = '0' + (int) L;
              if (i == ilim)
                {
                  if (d.d > 0.5 + eps.d)
                    goto bump_up;
                  else if (d.d < 0.5 - eps.d)
                    {
                      while (*--s == '0');
                      s++;
                      goto ret1;
                    }
                  break;
                }
            }
#ifndef No_leftright
        }
#endif
    fast_failed:
      s = s0;
      d.d = d2.d;
      k = k0;
      ilim = ilim0;
    }
 
  /* Do we have a "small" integer? */
 
  if (be >= 0 && k <= Int_max)
    {
      /* Yes. */
      ds = tens[k];
      if (ndigits < 0 && ilim <= 0)
        {
          S = mhi = 0;
          if (ilim < 0 || d.d <= 5 * ds)
            goto no_digits;
          goto one_digit;
        }
      for (i = 1;; i++)
        {
          L = d.d / ds;
          d.d -= L * ds;
#ifdef Check_FLT_ROUNDS
          /* If FLT_ROUNDS == 2, L will usually be high by 1 */
          if (d.d < 0)
            {
              L--;
              d.d += ds;
            }
#endif
          *s++ = '0' + (int) L;
          if (i == ilim)
            {
              d.d += d.d;
              if (d.d > ds || d.d == ds && L & 1)
                {
                bump_up:
                  while (*--s == '9')
                    if (s == s0)
                      {
                        k++;
                        *s = '0';
                        break;
                      }
                  ++*s++;
                }
              break;
            }
          if (!(d.d *= 10.))
            break;
        }
      goto ret1;
    }
 
  m2 = b2;
  m5 = b5;
  mhi = mlo = 0;
  if (leftright)
    {
      if (mode < 2)
        {
          i =
#ifndef Sudden_Underflow
            denorm ? be + (Bias + (P - 1) - 1 + 1) :
#endif
#ifdef IBM
            1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3);
#else
            1 + P - bbits;
#endif
        }
      else
        {
          j = ilim - 1;
          if (m5 >= j)
            m5 -= j;
          else
            {
              s5 += j -= m5;
              b5 += j;
              m5 = 0;
            }
          if ((i = ilim) < 0)
            {
              m2 -= i;
              i = 0;
            }
        }
      b2 += i;
      s2 += i;
      mhi = i2b (ptr, 1);
    }
  if (m2 > 0 && s2 > 0)
    {
      i = m2 < s2 ? m2 : s2;
      b2 -= i;
      m2 -= i;
      s2 -= i;
    }
  if (b5 > 0)
    {
      if (leftright)
        {
          if (m5 > 0)
            {
              mhi = pow5mult (ptr, mhi, m5);
              b1 = mult (ptr, mhi, b);
              Bfree (ptr, b);
              b = b1;
            }
          if (j = b5 - m5)
            b = pow5mult (ptr, b, j);
        }
      else
        b = pow5mult (ptr, b, b5);
    }
  S = i2b (ptr, 1);
  if (s5 > 0)
    S = pow5mult (ptr, S, s5);
 
  /* Check for special case that d is a normalized power of 2. */
 
  if (mode < 2)
    {
      if (!word1 (d) && !(word0 (d) & Bndry_mask)
#ifndef Sudden_Underflow
          && word0 (d) & Exp_mask
#endif
        )
        {
          /* The special case */
          b2 += Log2P;
          s2 += Log2P;
          spec_case = 1;
        }
      else
        spec_case = 0;
    }
 
  /* Arrange for convenient computation of quotients:
   * shift left if necessary so divisor has 4 leading 0 bits.
   *
   * Perhaps we should just compute leading 28 bits of S once
   * and for all and pass them and a shift to quorem, so it
   * can do shifts and ors to compute the numerator for q.
   */
 
#ifdef Pack_32
  if (i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0x1f)
    i = 32 - i;
#else
  if (i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf)
    i = 16 - i;
#endif
  if (i > 4)
    {
      i -= 4;
      b2 += i;
      m2 += i;
      s2 += i;
    }
  else if (i < 4)
    {
      i += 28;
      b2 += i;
      m2 += i;
      s2 += i;
    }
  if (b2 > 0)
    b = lshift (ptr, b, b2);
  if (s2 > 0)
    S = lshift (ptr, S, s2);
  if (k_check)
    {
      if (cmp (b, S) < 0)
        {
          k--;
          b = multadd (ptr, b, 10, 0);   /* we botched the k estimate */
          if (leftright)
            mhi = multadd (ptr, mhi, 10, 0);
          ilim = ilim1;
        }
    }
  if (ilim <= 0 && mode > 2)
    {
      if (ilim < 0 || cmp (b, S = multadd (ptr, S, 5, 0)) <= 0)
        {
          /* no digits, fcvt style */
        no_digits:
          k = -1 - ndigits;
          goto ret;
        }
    one_digit:
      *s++ = '1';
      k++;
      goto ret;
    }
  if (leftright)
    {
      if (m2 > 0)
        mhi = lshift (ptr, mhi, m2);
 
      /* Compute mlo -- check for special case
       * that d is a normalized power of 2.
       */
 
      mlo = mhi;
      if (spec_case)
        {
          mhi = Balloc (ptr, mhi->_k);
          Bcopy (mhi, mlo);
          mhi = lshift (ptr, mhi, Log2P);
        }
 
      for (i = 1;; i++)
        {
          dig = quorem (b, S) + '0';
          /* Do we yet have the shortest decimal string
           * that will round to d?
           */
          j = cmp (b, mlo);
          delta = diff (ptr, S, mhi);
          j1 = delta->_sign ? 1 : cmp (b, delta);
          Bfree (ptr, delta);
#ifndef ROUND_BIASED
          if (j1 == 0 && !mode && !(word1 (d) & 1))
            {
              if (dig == '9')
                goto round_9_up;
              if (j > 0)
                dig++;
              *s++ = dig;
              goto ret;
            }
#endif
          if (j < 0 || j == 0 && !mode
#ifndef ROUND_BIASED
              && !(word1 (d) & 1)
#endif
            )
            {
              if (j1 > 0)
                {
                  b = lshift (ptr, b, 1);
                  j1 = cmp (b, S);
                  if ((j1 > 0 || j1 == 0 && dig & 1)
                      && dig++ == '9')
                    goto round_9_up;
                }
              *s++ = dig;
              goto ret;
            }
          if (j1 > 0)
            {
              if (dig == '9')
                {               /* possible if i == 1 */
                round_9_up:
                  *s++ = '9';
                  goto roundoff;
                }
              *s++ = dig + 1;
              goto ret;
            }
          *s++ = dig;
          if (i == ilim)
            break;
          b = multadd (ptr, b, 10, 0);
          if (mlo == mhi)
            mlo = mhi = multadd (ptr, mhi, 10, 0);
          else
            {
              mlo = multadd (ptr, mlo, 10, 0);
              mhi = multadd (ptr, mhi, 10, 0);
            }
        }
    }
  else
    for (i = 1;; i++)
      {
        *s++ = dig = quorem (b, S) + '0';
        if (i >= ilim)
          break;
        b = multadd (ptr, b, 10, 0);
      }
 
  /* Round off last digit */
 
  b = lshift (ptr, b, 1);
  j = cmp (b, S);
  if (j > 0 || j == 0 && dig & 1)
    {
    roundoff:
      while (*--s == '9')
        if (s == s0)
          {
            k++;
            *s++ = '1';
            goto ret;
          }
      ++*s++;
    }
  else
    {
      while (*--s == '0');
      s++;
    }
ret:
  Bfree (ptr, S);
  if (mhi)
    {
      if (mlo && mlo != mhi)
        Bfree (ptr, mlo);
      Bfree (ptr, mhi);
    }
ret1:
  Bfree (ptr, b);
  *s = 0;
  *decpt = k + 1;
  if (rve)
    *rve = s;
  return s0;
}

Line No.	Rev	Author	Line
1	39	lampret	`/****************************************************************`
2			`*`
3			`* The author of this software is David M. Gay.`
4			`*`
5			`* Copyright (c) 1991 by AT&T.`
6			`*`
7			`* Permission to use, copy, modify, and distribute this software for any`
8			`* purpose without fee is hereby granted, provided that this entire notice`
9			`* is included in all copies of any software which is or includes a copy`
10			`* or modification of this software and in all copies of the supporting`
11			`* documentation for such software.`
12			`*`
13			`* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED`
14			`* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY`
15			`* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY`
16			`* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.`
17			`*`
18			`***************************************************************/`
19
20			`/* Please send bug reports to`
21			`David M. Gay`
22			`AT&T Bell Laboratories, Room 2C-463`
23			`600 Mountain Avenue`
24			`Murray Hill, NJ 07974-2070`
25			`U.S.A.`
26			`dmg@research.att.com or research!dmg`
27			`*/`
28
29			`#include <_ansi.h>`
30			`#include <stdlib.h>`
31			`#include <reent.h>`
32			`#include <string.h>`
33			`#include "mprec.h"`
34
35			`static int`
36			`_DEFUN (quorem,`
37			`(b, S),`
38			`_Bigint * b _AND _Bigint * S)`
39			`{`
40			`int n;`
41	56	joel	`__Long borrow, y;`
42			`__ULong carry, q, ys;`
43			`__ULong bx, bxe, sx, sxe;`
44	39	lampret	`#ifdef Pack_32`
45	56	joel	`__Long z;`
46			`__ULong si, zs;`
47	39	lampret	`#endif`
48
49			`n = S->_wds;`
50			`#ifdef DEBUG`
51			`/debug/ if (b->_wds > n)`
52			`/debug/ Bug ("oversize b in quorem");`
53			`#endif`
54			`if (b->_wds < n)`
55			`return 0;`
56			`sx = S->_x;`
57			`sxe = sx + --n;`
58			`bx = b->_x;`
59			`bxe = bx + n;`
60			`q = bxe / (sxe + 1); /* ensure q <= true quotient */`
61			`#ifdef DEBUG`
62			`/debug/ if (q > 9)`
63			`/debug/ Bug ("oversized quotient in quorem");`
64			`#endif`
65			`if (q)`
66			`{`
67			`borrow = 0;`
68			`carry = 0;`
69			`do`
70			`{`
71			`#ifdef Pack_32`
72			`si = *sx++;`
73			`ys = (si & 0xffff) * q + carry;`
74			`zs = (si >> 16) * q + (ys >> 16);`
75			`carry = zs >> 16;`
76			`y = (*bx & 0xffff) - (ys & 0xffff) + borrow;`
77			`borrow = y >> 16;`
78			`Sign_Extend (borrow, y);`
79			`z = (*bx >> 16) - (zs & 0xffff) + borrow;`
80			`borrow = z >> 16;`
81			`Sign_Extend (borrow, z);`
82			`Storeinc (bx, z, y);`
83			`#else`
84			`ys = sx++ q + carry;`
85			`carry = ys >> 16;`
86			`y = *bx - (ys & 0xffff) + borrow;`
87			`borrow = y >> 16;`
88			`Sign_Extend (borrow, y);`
89			`*bx++ = y & 0xffff;`
90			`#endif`
91			`}`
92			`while (sx <= sxe);`
93			`if (!*bxe)`
94			`{`
95			`bx = b->_x;`
96			`while (--bxe > bx && !*bxe)`
97			`--n;`
98			`b->_wds = n;`
99			`}`
100			`}`
101			`if (cmp (b, S) >= 0)`
102			`{`
103			`q++;`
104			`borrow = 0;`
105			`carry = 0;`
106			`bx = b->_x;`
107			`sx = S->_x;`
108			`do`
109			`{`
110			`#ifdef Pack_32`
111			`si = *sx++;`
112			`ys = (si & 0xffff) + carry;`
113			`zs = (si >> 16) + (ys >> 16);`
114			`carry = zs >> 16;`
115			`y = (*bx & 0xffff) - (ys & 0xffff) + borrow;`
116			`borrow = y >> 16;`
117			`Sign_Extend (borrow, y);`
118			`z = (*bx >> 16) - (zs & 0xffff) + borrow;`
119			`borrow = z >> 16;`
120			`Sign_Extend (borrow, z);`
121			`Storeinc (bx, z, y);`
122			`#else`
123			`ys = *sx++ + carry;`
124			`carry = ys >> 16;`
125			`y = *bx - (ys & 0xffff) + borrow;`
126			`borrow = y >> 16;`
127			`Sign_Extend (borrow, y);`
128			`*bx++ = y & 0xffff;`
129			`#endif`
130			`}`
131			`while (sx <= sxe);`
132			`bx = b->_x;`
133			`bxe = bx + n;`
134			`if (!*bxe)`
135			`{`
136			`while (--bxe > bx && !*bxe)`
137			`--n;`
138			`b->_wds = n;`
139			`}`
140			`}`
141			`return q;`
142			`}`
143
144			`/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.`
145			`*`
146			`* Inspired by "How to Print Floating-Point Numbers Accurately" by`
147			`* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].`
148			`*`
149			`* Modifications:`
150			`* 1. Rather than iterating, we use a simple numeric overestimate`
151			`* to determine k = floor(log10(d)). We scale relevant`
152			`* quantities using O(log2(k)) rather than O(k) multiplications.`
153			`* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't`
154			`* try to generate digits strictly left to right. Instead, we`
155			`* compute with fewer bits and propagate the carry if necessary`
156			`* when rounding the final digit up. This is often faster.`
157			`* 3. Under the assumption that input will be rounded nearest,`
158			`* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.`
159			`* That is, we allow equality in stopping tests when the`
160			`* round-nearest rule will give the same floating-point value`
161			`* as would satisfaction of the stopping test with strict`
162			`* inequality.`
163			`* 4. We remove common factors of powers of 2 from relevant`
164			`* quantities.`
165			`* 5. When converting floating-point integers less than 1e16,`
166			`* we use floating-point arithmetic rather than resorting`
167			`* to multiple-precision integers.`
168			`* 6. When asked to produce fewer than 15 digits, we first try`
169			`* to get by with floating-point arithmetic; we resort to`
170			`* multiple-precision integer arithmetic only if we cannot`
171			`* guarantee that the floating-point calculation has given`
172			`* the correctly rounded result. For k requested digits and`
173			`* "uniformly" distributed input, the probability is`
174			`* something like 10^(k-15) that we must resort to the long`
175			`* calculation.`
176			`*/`
177
178
179			`char *`
180			`_DEFUN (_dtoa_r,`
181			`(ptr, _d, mode, ndigits, decpt, sign, rve),`
182			`struct _reent *ptr _AND`
183			`double _d _AND`
184			`int mode _AND`
185			`int ndigits _AND`
186			`int *decpt _AND`
187			`int *sign _AND`
188			`char **rve)`
189			`{`
190			`/* Arguments ndigits, decpt, sign are similar to those`
191			`of ecvt and fcvt; trailing zeros are suppressed from`
192			`the returned string. If not null, *rve is set to point`
193			`to the end of the return value. If d is +-Infinity or NaN,`
194			`then *decpt is set to 9999.`
195
196			`mode:`
197
198			`and rounded to nearest.`
199			`1 ==> like 0, but with Steele & White stopping rule;`
200			`e.g. with IEEE P754 arithmetic , mode 0 gives`
201			`1e23 whereas mode 1 gives 9.999999999999999e22.`
202			`2 ==> max(1,ndigits) significant digits. This gives a`
203			`return value similar to that of ecvt, except`
204			`that trailing zeros are suppressed.`
205			`3 ==> through ndigits past the decimal point. This`
206			`gives a return value similar to that from fcvt,`
207			`except that trailing zeros are suppressed, and`
208			`ndigits can be negative.`
209			`4-9 should give the same return values as 2-3, i.e.,`
210			`4 <= mode <= 9 ==> same return as mode`
211			`2 + (mode & 1). These modes are mainly for`
212			`debugging; often they run slower but sometimes`
213			`faster than modes 2-3.`
214			`4,5,8,9 ==> left-to-right digit generation.`
215			`6-9 ==> don't try fast floating-point estimate`
216			`(if applicable).`
217
218			`Values of mode other than 0-9 are treated as mode 0.`
219
220			`Sufficient space is allocated to the return value`
221			`to hold the suppressed trailing zeros.`
222			`*/`
223
224			`int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0,`
225			`k_check, leftright, m2, m5, s2, s5, spec_case, try_quick;`
226			`union double_union d, d2, eps;`
227	56	joel	`__Long L;`
228	39	lampret	`#ifndef Sudden_Underflow`
229			`int denorm;`
230	56	joel	`__ULong x;`
231	39	lampret	`#endif`
232			`_Bigint b, b1, delta, mlo, mhi, S;`
233			`double ds;`
234			`char s, s0;`
235
236			`d.d = _d;`
237
238			`if (ptr->_result)`
239			`{`
240			`ptr->_result->_k = ptr->_result_k;`
241			`ptr->_result->_maxwds = 1 << ptr->_result_k;`
242			`Bfree (ptr, ptr->_result);`
243			`ptr->_result = 0;`
244			`}`
245
246			`if (word0 (d) & Sign_bit)`
247			`{`
248			`/* set sign for everything, including 0's and NaNs */`
249			`*sign = 1;`
250			`word0 (d) &= ~Sign_bit; /* clear sign bit */`
251			`}`
252			`else`
253			`*sign = 0;`
254
255			`#if defined(IEEE_Arith) + defined(VAX)`
256			`#ifdef IEEE_Arith`
257			`if ((word0 (d) & Exp_mask) == Exp_mask)`
258			`#else`
259			`if (word0 (d) == 0x8000)`
260			`#endif`
261			`{`
262			`/* Infinity or NaN */`
263			`*decpt = 9999;`
264			`s =`
265			`#ifdef IEEE_Arith`
266			`!word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" :`
267			`#endif`
268			`"NaN";`
269			`if (rve)`
270			`*rve =`
271			`#ifdef IEEE_Arith`
272			`s[3] ? s + 8 :`
273			`#endif`
274			`s + 3;`
275			`return s;`
276			`}`
277			`#endif`
278			`#ifdef IBM`
279			`d.d += 0; /* normalize */`
280			`#endif`
281			`if (!d.d)`
282			`{`
283			`*decpt = 1;`
284			`s = "0";`
285			`if (rve)`
286			`*rve = s + 1;`
287			`return s;`
288			`}`
289
290			`b = d2b (ptr, d.d, &be, &bbits);`
291			`#ifdef Sudden_Underflow`
292			`i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));`
293			`#else`
294			`if (i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))`
295			`{`
296			`#endif`
297			`d2.d = d.d;`
298			`word0 (d2) &= Frac_mask1;`
299			`word0 (d2) \|= Exp_11;`
300			`#ifdef IBM`
301			`if (j = 11 - hi0bits (word0 (d2) & Frac_mask))`
302			`d2.d /= 1 << j;`
303			`#endif`
304
305			`/* log(x) ~=~ log(1.5) + (x-1.5)/1.5`
306			`* log10(x) = log(x) / log(10)`
307			`* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))`
308			`* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)`
309			`*`
310			`* This suggests computing an approximation k to log10(d) by`
311			`*`
312			`* k = (i - Bias)*0.301029995663981`
313			`* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );`
314			`*`
315			`* We want k to be too large rather than too small.`
316			`* The error in the first-order Taylor series approximation`
317			`* is in our favor, so we just round up the constant enough`
318			`* to compensate for any error in the multiplication of`
319			`* (i - Bias) by 0.301029995663981; since \|i - Bias\| <= 1077,`
320			`* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,`
321			`* adding 1e-13 to the constant term more than suffices.`
322			`* Hence we adjust the constant term to 0.1760912590558.`
323			`* (We could get a more accurate k by invoking log10,`
324			`* but this is probably not worthwhile.)`
325			`*/`
326
327			`i -= Bias;`
328			`#ifdef IBM`
329			`i <<= 2;`
330			`i += j;`
331			`#endif`
332			`#ifndef Sudden_Underflow`
333			`denorm = 0;`
334			`}`
335			`else`
336			`{`
337			`/* d is denormalized */`
338
339			`i = bbits + be + (Bias + (P - 1) - 1);`
340			`x = i > 32 ? word0 (d) << 64 - i \| word1 (d) >> i - 32`
341			`: word1 (d) << 32 - i;`
342			`d2.d = x;`
343			`word0 (d2) -= 31 * Exp_msk1; /* adjust exponent */`
344			`i -= (Bias + (P - 1) - 1) + 1;`
345			`denorm = 1;`
346			`}`
347			`#endif`
348			`ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;`
349			`k = (int) ds;`
350			`if (ds < 0. && ds != k)`
351			`k--; /* want k = floor(ds) */`
352			`k_check = 1;`
353			`if (k >= 0 && k <= Ten_pmax)`
354			`{`
355			`if (d.d < tens[k])`
356			`k--;`
357			`k_check = 0;`
358			`}`
359			`j = bbits - i - 1;`
360			`if (j >= 0)`
361			`{`
362			`b2 = 0;`
363			`s2 = j;`
364			`}`
365			`else`
366			`{`
367			`b2 = -j;`
368			`s2 = 0;`
369			`}`
370			`if (k >= 0)`
371			`{`
372			`b5 = 0;`
373			`s5 = k;`
374			`s2 += k;`
375			`}`
376			`else`
377			`{`
378			`b2 -= k;`
379			`b5 = -k;`
380			`s5 = 0;`
381			`}`
382			`if (mode < 0 \|\| mode > 9)`
383			`mode = 0;`
384			`try_quick = 1;`
385			`if (mode > 5)`
386			`{`
387			`mode -= 4;`
388			`try_quick = 0;`
389			`}`
390			`leftright = 1;`
391			`switch (mode)`
392			`{`
393			`case 0:`
394			`case 1:`
395			`ilim = ilim1 = -1;`
396			`i = 18;`
397			`ndigits = 0;`
398			`break;`
399			`case 2:`
400			`leftright = 0;`
401			`/* no break */`
402			`case 4:`
403			`if (ndigits <= 0)`
404			`ndigits = 1;`
405			`ilim = ilim1 = i = ndigits;`
406			`break;`
407			`case 3:`
408			`leftright = 0;`
409			`/* no break */`
410			`case 5:`
411			`i = ndigits + k + 1;`
412			`ilim = i;`
413			`ilim1 = i - 1;`
414			`if (i <= 0)`
415			`i = 1;`
416			`}`
417	56	joel	`j = sizeof (__ULong);`
418			`for (ptr->_result_k = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i;`
419	39	lampret	`j <<= 1)`
420			`ptr->_result_k++;`
421			`ptr->_result = Balloc (ptr, ptr->_result_k);`
422			`s = s0 = (char *) ptr->_result;`
423
424			`if (ilim >= 0 && ilim <= Quick_max && try_quick)`
425			`{`
426			`/* Try to get by with floating-point arithmetic. */`
427
428			`i = 0;`
429			`d2.d = d.d;`
430			`k0 = k;`
431			`ilim0 = ilim;`
432			`ieps = 2; /* conservative */`
433			`if (k > 0)`
434			`{`
435			`ds = tens[k & 0xf];`
436			`j = k >> 4;`
437			`if (j & Bletch)`
438			`{`
439			`/* prevent overflows */`
440			`j &= Bletch - 1;`
441			`d.d /= bigtens[n_bigtens - 1];`
442			`ieps++;`
443			`}`
444			`for (; j; j >>= 1, i++)`
445			`if (j & 1)`
446			`{`
447			`ieps++;`
448			`ds *= bigtens[i];`
449			`}`
450			`d.d /= ds;`
451			`}`
452			`else if (j1 = -k)`
453			`{`
454			`d.d *= tens[j1 & 0xf];`
455			`for (j = j1 >> 4; j; j >>= 1, i++)`
456			`if (j & 1)`
457			`{`
458			`ieps++;`
459			`d.d *= bigtens[i];`
460			`}`
461			`}`
462			`if (k_check && d.d < 1. && ilim > 0)`
463			`{`
464			`if (ilim1 <= 0)`
465			`goto fast_failed;`
466			`ilim = ilim1;`
467			`k--;`
468			`d.d *= 10.;`
469			`ieps++;`
470			`}`
471			`eps.d = ieps * d.d + 7.;`
472			`word0 (eps) -= (P - 1) * Exp_msk1;`
473			`if (ilim == 0)`
474			`{`
475			`S = mhi = 0;`
476			`d.d -= 5.;`
477			`if (d.d > eps.d)`
478			`goto one_digit;`
479			`if (d.d < -eps.d)`
480			`goto no_digits;`
481			`goto fast_failed;`
482			`}`
483			`#ifndef No_leftright`
484			`if (leftright)`
485			`{`
486			`/* Use Steele & White method of only`
487			`* generating digits needed.`
488			`*/`
489			`eps.d = 0.5 / tens[ilim - 1] - eps.d;`
490			`for (i = 0;;)`
491			`{`
492			`L = d.d;`
493			`d.d -= L;`
494			`*s++ = '0' + (int) L;`
495			`if (d.d < eps.d)`
496			`goto ret1;`
497			`if (1. - d.d < eps.d)`
498			`goto bump_up;`
499			`if (++i >= ilim)`
500			`break;`

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