source: trunk/libs/newlib/src/newlib/libc/stdlib/dtoa.c @ 577

/****************************************************************
 *
 * 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
quorem (_Bigint * b, _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 *
_dtoa_r (struct _reent *ptr,
        double _d,
        int mode,
        int ndigits,
        int *decpt,
        int *sign,
        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:
                0 ==> shortest string that yields d when read in
                        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 = NULL, *mhi, *S;
  double ds;
  char *s, *s0;

  d.d = _d;

  _REENT_CHECK_MP(ptr);
  if (_REENT_MP_RESULT(ptr))
    {
      _REENT_MP_RESULT(ptr)->_k = _REENT_MP_RESULT_K(ptr);
      _REENT_MP_RESULT(ptr)->_maxwds = 1 << _REENT_MP_RESULT_K(ptr);
      Bfree (ptr, _REENT_MP_RESULT(ptr));
      _REENT_MP_RESULT(ptr) = 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))) != 0)
    {
#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);
#if defined (_DOUBLE_IS_32BITS)
      x = word0 (d) << (32 - i);
#else
      x = (i > 32) ? (word0 (d) << (64 - i)) | (word1 (d) >> (i - 32))
       : (word1 (d) << (32 - i));
#endif
      d2.d = x;
      word0 (d2) -= 31 * Exp_msk1;      /* adjust exponent */
      i -= (Bias + (P - 1) - 1) + 1;
      denorm = 1;
    }
#endif
#if defined (_DOUBLE_IS_32BITS)
  ds = (d2.d - 1.5) * 0.289529651 + 0.176091269 + i * 0.30103001;
#else
  ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
#endif
  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;
  ilim = ilim1 = -1;
  switch (mode)
    {
    case 0:
    case 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 (_REENT_MP_RESULT_K(ptr) = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i;
       j <<= 1)
    _REENT_MP_RESULT_K(ptr)++;
  _REENT_MP_RESULT(ptr) = Balloc (ptr, _REENT_MP_RESULT_K(ptr));
  s = s0 = (char *) _REENT_MP_RESULT(ptr);

  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) != 0)
        {
          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) != 0)
            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. */

  spec_case = 0;
  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;
        }
    }

  /* 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) != 0)
    i = 32 - i;
#else
  if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf) != 0)
    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;
}