StdLib/LibC/gdtoa/strtod.c

/** @file

  Copyright (c) 2012, Intel Corporation. All rights reserved.<BR>
  This program and the accompanying materials are licensed and made available under
  the terms and conditions of the BSD License that accompanies this distribution.
  The full text of the license may be found at
  http://opensource.org/licenses/bsd-license.

  THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
  WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.

  *****************************************************************

  The author of this software is David M. Gay.

  Copyright (C) 1998-2001 by Lucent Technologies
  All Rights Reserved

  Permission to use, copy, modify, and distribute this software and
  its documentation for any purpose and without fee is hereby
  granted, provided that the above copyright notice appear in all
  copies and that both that the copyright notice and this
  permission notice and warranty disclaimer appear in supporting
  documentation, and that the name of Lucent or any of its entities
  not be used in advertising or publicity pertaining to
  distribution of the software without specific, written prior
  permission.

  LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
  INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
  IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
  SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
  IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
  ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
  THIS SOFTWARE.


  Please send bug reports to David M. Gay (dmg at acm dot org,
  with " at " changed at "@" and " dot " changed to ".").

  *****************************************************************

  NetBSD: strtod.c,v 1.4.14.1 2008/04/08 21:10:55 jdc Exp
**/
#include  <LibConfig.h>

#include "gdtoaimp.h"
#ifndef NO_FENV_H
#include <fenv.h>
#endif

#ifdef USE_LOCALE
#include "locale.h"
#endif

#ifdef IEEE_Arith
#ifndef NO_IEEE_Scale
#define Avoid_Underflow
#undef tinytens
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
/* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
    9007199254740992.e-256
    };
#endif
#endif

#ifdef Honor_FLT_ROUNDS
#define Rounding rounding
#undef Check_FLT_ROUNDS
#define Check_FLT_ROUNDS
#else
#define Rounding Flt_Rounds
#endif

//#ifndef __HAVE_LONG_DOUBLE
//__strong_alias(_strtold, strtod)
//__weak_alias(strtold, _strtold)
//#endif

#if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
// Disable: warning C4700: uninitialized local variable 'xx' used
#pragma warning ( disable : 4700 )
#endif  /* defined(_MSC_VER) */

double
strtod(CONST char *s00, char **se)
{
#ifdef Avoid_Underflow
  int scale;
  #endif
  int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, dsign,
      e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
  CONST char *s, *s0, *s1;
  double aadj, aadj1, adj, rv, rv0;
  Long L;
  ULong y, z;
  Bigint *bb = NULL, *bb1, *bd0;
  Bigint *bd = NULL, *bs = NULL, *delta = NULL; /* pacify gcc */
#ifdef SET_INEXACT
  int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS
  int rounding;
#endif

  sign = nz0 = nz = decpt = 0;
  dval(rv) = 0.;
  for(s = s00;;s++) {
    switch(*s) {
      case '-':
        sign = 1;
        /* FALLTHROUGH */
      case '+':
        if (*++s)
          goto break2;
        /* FALLTHROUGH */
      case 0:
        goto ret0;
      case '\t':
      case '\n':
      case '\v':
      case '\f':
      case '\r':
      case ' ':
        continue;
      default:
        goto break2;
    }
  }
 break2:
  if (*s == '0') {
#ifndef NO_HEX_FP
    {
    static FPI fpi = { 53, 1-1023-53+1, 2046-1023-53+1, 1, SI };
    Long expt;
    ULong bits[2];
    switch(s[1]) {
      case 'x':
      case 'X':
      {
#if defined(FE_DOWNWARD) && defined(FE_TONEAREST) && defined(FE_TOWARDZERO) && defined(FE_UPWARD)
      FPI fpi1 = fpi;
      switch(fegetround()) {
        case FE_TOWARDZERO: fpi1.rounding = 0; break;
        case FE_UPWARD: fpi1.rounding = 2; break;
        case FE_DOWNWARD: fpi1.rounding = 3;
        }
#else
#endif
      switch((i = gethex(&s, &fpi, &expt, &bb, sign)) & STRTOG_Retmask) {
        case STRTOG_NoNumber:
        s = s00;
        sign = 0;
        /* FALLTHROUGH */
        case STRTOG_Zero:
        break;
        default:
        if (bb) {
          copybits(bits, fpi.nbits, bb);
          Bfree(bb);
          }
        ULtod((/* LINTED */(U*)&rv)->L, bits, expt, i);
        }}
      goto ret;
      }
    }
#endif
    nz0 = 1;
    while(*++s == '0') ;
    if (!*s)
      goto ret;
  }
  s0 = s;
  y = z = 0;
  for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
    if (nd < 9)
      y = 10*y + c - '0';
    else if (nd < 16)
      z = 10*z + c - '0';
  nd0 = nd;
#ifdef USE_LOCALE
  if (c == *localeconv()->decimal_point)
#else
  if (c == '.')
#endif
    {
    decpt = 1;
    c = *++s;
    if (!nd) {
      for(; c == '0'; c = *++s)
        nz++;
      if (c > '0' && c <= '9') {
        s0 = s;
        nf += nz;
        nz = 0;
        goto have_dig;
        }
      goto dig_done;
      }
    for(; c >= '0' && c <= '9'; c = *++s) {
 have_dig:
      nz++;
      if (c -= '0') {
        nf += nz;
        for(i = 1; i < nz; i++)
          if (nd++ < 9)
            y *= 10;
          else if (nd <= DBL_DIG + 1)
            z *= 10;
        if (nd++ < 9)
          y = 10*y + c;
        else if (nd <= DBL_DIG + 1)
          z = 10*z + c;
        nz = 0;
        }
      }
    }
 dig_done:
  e = 0;
  if (c == 'e' || c == 'E') {
    if (!nd && !nz && !nz0) {
      goto ret0;
      }
    s00 = s;
    esign = 0;
    switch(c = *++s) {
      case '-':
        esign = 1;
        /* FALLTHROUGH */
      case '+':
        c = *++s;
      }
    if (c >= '0' && c <= '9') {
      while(c == '0')
        c = *++s;
      if (c > '0' && c <= '9') {
        L = c - '0';
        s1 = s;
        while((c = *++s) >= '0' && c <= '9')
          L = 10*L + c - '0';
        if (s - s1 > 8 || L > 19999)
          /* Avoid confusion from exponents
           * so large that e might overflow.
           */
          e = 19999; /* safe for 16 bit ints */
        else
          e = (int)L;
        if (esign)
          e = -e;
        }
      else
        e = 0;
      }
    else
      s = s00;
    }
  if (!nd) {
    if (!nz && !nz0) {
#ifdef INFNAN_CHECK
      /* Check for Nan and Infinity */
#ifndef No_Hex_NaN
      ULong bits[2];
      static FPI fpinan = /* only 52 explicit bits */
        { 52, 1-1023-53+1, 2046-1023-53+1, 1, SI };
#endif  // No_Hex_NaN
      if (!decpt)
       switch(c) {
        case 'i':
        case 'I':
        if (match(&s,"nf")) {
          --s;
          if (!match(&s,"inity"))
            ++s;
          word0(rv) = 0x7ff00000;
          word1(rv) = 0;
          goto ret;
          }
        break;
        case 'n':
        case 'N':
        if (match(&s, "an")) {
#ifndef No_Hex_NaN
          if (*s == '(' /*)*/
           && hexnan(&s, &fpinan, bits)
              == STRTOG_NaNbits) {
            word0(rv) = (UINT32)(0x7ff00000U | bits[1]);
            word1(rv) = (UINT32)bits[0];
            }
          else {
#endif
            word0(rv) = NAN_WORD0;
            word1(rv) = NAN_WORD1;
#ifndef No_Hex_NaN
            }
#endif
          goto ret;
          }
        }
#endif /* INFNAN_CHECK */
 ret0:
      s = s00;
      sign = 0;
      }
    goto ret;
    }
  e1 = e -= nf;

  /* Now we have nd0 digits, starting at s0, followed by a
   * decimal point, followed by nd-nd0 digits.  The number we're
   * after is the integer represented by those digits times
   * 10**e */

  if (!nd0)
    nd0 = nd;
  k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
  dval(rv) = (double)y;
  if (k > 9) {
#ifdef SET_INEXACT
    if (k > DBL_DIG)
      oldinexact = get_inexact();
#endif
    dval(rv) = tens[k - 9] * dval(rv) + z;
    }
  bd0 = 0;
  if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
#ifndef Honor_FLT_ROUNDS
    && Flt_Rounds == 1
#endif
#endif
      ) {
    if (!e)
      goto ret;
    if (e > 0) {
      if (e <= Ten_pmax) {
#ifdef VAX
        goto vax_ovfl_check;
#else
#ifdef Honor_FLT_ROUNDS
        /* round correctly FLT_ROUNDS = 2 or 3 */
        if (sign) {
          rv = -rv;
          sign = 0;
          }
#endif
        /* rv = */ rounded_product(dval(rv), tens[e]);
        goto ret;
#endif
        }
      i = DBL_DIG - nd;
      if (e <= Ten_pmax + i) {
        /* A fancier test would sometimes let us do
         * this for larger i values.
         */
#ifdef Honor_FLT_ROUNDS
        /* round correctly FLT_ROUNDS = 2 or 3 */
        if (sign) {
          rv = -rv;
          sign = 0;
          }
#endif
        e -= i;
        dval(rv) *= tens[i];
#ifdef VAX
        /* VAX exponent range is so narrow we must
         * worry about overflow here...
         */
 vax_ovfl_check:
        word0(rv) -= P*Exp_msk1;
        /* rv = */ rounded_product(dval(rv), tens[e]);
        if ((word0(rv) & Exp_mask)
         > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
          goto ovfl;
        word0(rv) += P*Exp_msk1;
#else
        /* rv = */ rounded_product(dval(rv), tens[e]);
#endif
        goto ret;
        }
      }
#ifndef Inaccurate_Divide
    else if (e >= -Ten_pmax) {
#ifdef Honor_FLT_ROUNDS
      /* round correctly FLT_ROUNDS = 2 or 3 */
      if (sign) {
        rv = -rv;
        sign = 0;
        }
#endif
      /* rv = */ rounded_quotient(dval(rv), tens[-e]);
      goto ret;
      }
#endif
    }
  e1 += nd - k;

#ifdef IEEE_Arith
#ifdef SET_INEXACT
  inexact = 1;
  if (k <= DBL_DIG)
    oldinexact = get_inexact();
#endif
#ifdef Avoid_Underflow
  scale = 0;
#endif
#ifdef Honor_FLT_ROUNDS
  if ((rounding = Flt_Rounds) >= 2) {
    if (sign)
      rounding = rounding == 2 ? 0 : 2;
    else
      if (rounding != 2)
        rounding = 0;
    }
#endif
#endif /*IEEE_Arith*/

  /* Get starting approximation = rv * 10**e1 */

  if (e1 > 0) {
    if ( (i = e1 & 15) !=0)
      dval(rv) *= tens[i];
    if (e1 &= ~15) {
      if (e1 > DBL_MAX_10_EXP) {
 ovfl:
#ifndef NO_ERRNO
        errno = ERANGE;
#endif
        /* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
#ifdef Honor_FLT_ROUNDS
        switch(rounding) {
          case 0: /* toward 0 */
          case 3: /* toward -infinity */
          word0(rv) = Big0;
          word1(rv) = Big1;
          break;
          default:
          word0(rv) = Exp_mask;
          word1(rv) = 0;
          }
#else /*Honor_FLT_ROUNDS*/
        word0(rv) = Exp_mask;
        word1(rv) = 0;
#endif /*Honor_FLT_ROUNDS*/
#ifdef SET_INEXACT
        /* set overflow bit */
        dval(rv0) = 1e300;
        dval(rv0) *= dval(rv0);
#endif
#else /*IEEE_Arith*/
        word0(rv) = Big0;
        word1(rv) = Big1;
#endif /*IEEE_Arith*/
        if (bd0)
          goto retfree;
        goto ret;
        }
      e1 = (unsigned int)e1 >> 4;
      for(j = 0; e1 > 1; j++, e1 = (unsigned int)e1 >> 1)
        if (e1 & 1)
          dval(rv) *= bigtens[j];
    /* The last multiplication could overflow. */
      word0(rv) -= P*Exp_msk1;
      dval(rv) *= bigtens[j];
      if ((z = word0(rv) & Exp_mask)
       > Exp_msk1*(DBL_MAX_EXP+Bias-P))
        goto ovfl;
      if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
        /* set to largest number */
        /* (Can't trust DBL_MAX) */
        word0(rv) = Big0;
        word1(rv) = Big1;
        }
      else
        word0(rv) += P*Exp_msk1;
      }
    }
  else if (e1 < 0) {
    e1 = -e1;
    if ( (i = e1 & 15) !=0)
      dval(rv) /= tens[i];
    if (e1 >>= 4) {
      if (e1 >= 1 << n_bigtens)
        goto undfl;
#ifdef Avoid_Underflow
      if (e1 & Scale_Bit)
        scale = 2*P;
      for(j = 0; e1 > 0; j++, e1 = (unsigned int)e1 >> 1)
        if (e1 & 1)
          dval(rv) *= tinytens[j];
      if (scale && (j = 2*P + 1 - (unsigned int)((word0(rv) & Exp_mask)
            >> Exp_shift)) > 0) {
        /* scaled rv is denormal; zap j low bits */
        if (j >= 32) {
          word1(rv) = 0;
          if (j >= 53)
           word0(rv) = (P+2)*Exp_msk1;
          else
           word0(rv) &= 0xffffffff << (j-32);
          }
        else
          word1(rv) &= 0xffffffff << j;
        }
#else
      for(j = 0; e1 > 1; j++, e1 >>= 1)
        if (e1 & 1)
          dval(rv) *= tinytens[j];
      /* The last multiplication could underflow. */
      dval(rv0) = dval(rv);
      dval(rv) *= tinytens[j];
      if (!dval(rv)) {
        dval(rv) = 2.*dval(rv0);
        dval(rv) *= tinytens[j];
#endif
        if (!dval(rv)) {
 undfl:
          dval(rv) = 0.;
#ifndef NO_ERRNO
          errno = ERANGE;
#endif
          if (bd0)
            goto retfree;
          goto ret;
          }
#ifndef Avoid_Underflow
        word0(rv) = Tiny0;
        word1(rv) = Tiny1;
        /* The refinement below will clean
         * this approximation up.
         */
        }
#endif
      }
    }

  /* Now the hard part -- adjusting rv to the correct value.*/

  /* Put digits into bd: true value = bd * 10^e */

  bd0 = s2b(s0, nd0, nd, y);
  if (bd0 == NULL)
    goto ovfl;

  for(;;) {
    bd = Balloc(bd0->k);
    if (bd == NULL)
      goto ovfl;
    Bcopy(bd, bd0);
    bb = d2b(dval(rv), &bbe, &bbbits);  /* rv = bb * 2^bbe */
    if (bb == NULL)
      goto ovfl;
    bs = i2b(1);
    if (bs == NULL)
      goto ovfl;

    if (e >= 0) {
      bb2 = bb5 = 0;
      bd2 = bd5 = e;
      }
    else {
      bb2 = bb5 = -e;
      bd2 = bd5 = 0;
      }
    if (bbe >= 0)
      bb2 += bbe;
    else
      bd2 -= bbe;
    bs2 = bb2;
#ifdef Honor_FLT_ROUNDS
    if (rounding != 1)
      bs2++;
#endif
#ifdef Avoid_Underflow
    j = bbe - scale;
    i = j + bbbits - 1; /* logb(rv) */
    if (i < Emin) /* denormal */
      j += P - Emin;
    else
      j = P + 1 - bbbits;
#else /*Avoid_Underflow*/
#ifdef Sudden_Underflow
#ifdef IBM
    j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
    j = P + 1 - bbbits;
#endif
#else /*Sudden_Underflow*/
    j = bbe;
    i = j + bbbits - 1; /* logb(rv) */
    if (i < Emin) /* denormal */
      j += P - Emin;
    else
      j = P + 1 - bbbits;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
    bb2 += j;
    bd2 += j;
#ifdef Avoid_Underflow
    bd2 += scale;
#endif
    i = bb2 < bd2 ? bb2 : bd2;
    if (i > bs2)
      i = bs2;
    if (i > 0) {
      bb2 -= i;
      bd2 -= i;
      bs2 -= i;
      }
    if (bb5 > 0) {
      bs = pow5mult(bs, bb5);
      if (bs == NULL)
        goto ovfl;
      bb1 = mult(bs, bb);
      if (bb1 == NULL)
        goto ovfl;
      Bfree(bb);
      bb = bb1;
      }
    if (bb2 > 0) {
      bb = lshift(bb, bb2);
      if (bb == NULL)
        goto ovfl;
      }
    if (bd5 > 0) {
      bd = pow5mult(bd, bd5);
      if (bd == NULL)
        goto ovfl;
      }
    if (bd2 > 0) {
      bd = lshift(bd, bd2);
      if (bd == NULL)
        goto ovfl;
      }
    if (bs2 > 0) {
      bs = lshift(bs, bs2);
      if (bs == NULL)
        goto ovfl;
      }
    delta = diff(bb, bd);
    if (delta == NULL)
      goto ovfl;
    dsign = delta->sign;
    delta->sign = 0;
    i = cmp(delta, bs);
#ifdef Honor_FLT_ROUNDS
    if (rounding != 1) {
      if (i < 0) {
        /* Error is less than an ulp */
        if (!delta->x[0] && delta->wds <= 1) {
          /* exact */
#ifdef SET_INEXACT
          inexact = 0;
#endif
          break;
          }
        if (rounding) {
          if (dsign) {
            adj = 1.;
            goto apply_adj;
            }
          }
        else if (!dsign) {
          adj = -1.;
          if (!word1(rv)
           && !(word0(rv) & Frac_mask)) {
            y = word0(rv) & Exp_mask;
#ifdef Avoid_Underflow
            if (!scale || y > 2*P*Exp_msk1)
#else
            if (y)
#endif
              {
              delta = lshift(delta,Log2P);
              if (cmp(delta, bs) <= 0)
              adj = -0.5;
              }
            }
 apply_adj:
#ifdef Avoid_Underflow
          if (scale && (y = word0(rv) & Exp_mask)
            <= 2*P*Exp_msk1)
            word0(adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
          if ((word0(rv) & Exp_mask) <=
              P*Exp_msk1) {
            word0(rv) += P*Exp_msk1;
            dval(rv) += adj*ulp(dval(rv));
            word0(rv) -= P*Exp_msk1;
            }
          else
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
          dval(rv) += adj*ulp(dval(rv));
          }
        break;
        }
      adj = ratio(delta, bs);
      if (adj < 1.)
        adj = 1.;
      if (adj <= 0x7ffffffe) {
        /* adj = rounding ? ceil(adj) : floor(adj); */
        y = adj;
        if (y != adj) {
          if (!((rounding>>1) ^ dsign))
            y++;
          adj = y;
          }
        }
#ifdef Avoid_Underflow
      if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
        word0(adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
      if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
        word0(rv) += P*Exp_msk1;
        adj *= ulp(dval(rv));
        if (dsign)
          dval(rv) += adj;
        else
          dval(rv) -= adj;
        word0(rv) -= P*Exp_msk1;
        goto cont;
        }
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
      adj *= ulp(dval(rv));
      if (dsign)
        dval(rv) += adj;
      else
        dval(rv) -= adj;
      goto cont;
      }
#endif /*Honor_FLT_ROUNDS*/

    if (i < 0) {
      /* Error is less than half an ulp -- check for
       * special case of mantissa a power of two.
       */
      if (dsign || word1(rv) || word0(rv) & Bndry_mask
#ifdef IEEE_Arith
#ifdef Avoid_Underflow
       || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
#else
       || (word0(rv) & Exp_mask) <= Exp_msk1
#endif
#endif
        ) {
#ifdef SET_INEXACT
        if (!delta->x[0] && delta->wds <= 1)
          inexact = 0;
#endif
        break;
        }
      if (!delta->x[0] && delta->wds <= 1) {
        /* exact result */
#ifdef SET_INEXACT
        inexact = 0;
#endif
        break;
        }
      delta = lshift(delta,Log2P);
      if (cmp(delta, bs) > 0)
        goto drop_down;
      break;
      }
    if (i == 0) {
      /* exactly half-way between */
      if (dsign) {
        if ((word0(rv) & Bndry_mask1) == Bndry_mask1
         &&  word1(rv) == (
#ifdef Avoid_Underflow
      (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
    ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
#endif
               0xffffffff)) {
          /*boundary case -- increment exponent*/
          word0(rv) = (word0(rv) & Exp_mask)
            + Exp_msk1
#ifdef IBM
            | Exp_msk1 >> 4
#endif
            ;
          word1(rv) = 0;
#ifdef Avoid_Underflow
          dsign = 0;
#endif
          break;
          }
        }
      else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
 drop_down:
        /* boundary case -- decrement exponent */
#ifdef Sudden_Underflow /*{{*/
        L = word0(rv) & Exp_mask;
#ifdef IBM
        if (L <  Exp_msk1)
#else
#ifdef Avoid_Underflow
        if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
#else
        if (L <= Exp_msk1)
#endif /*Avoid_Underflow*/
#endif /*IBM*/
          goto undfl;
        L -= Exp_msk1;
#else /*Sudden_Underflow}{*/
#ifdef Avoid_Underflow
        if (scale) {
          L = word0(rv) & Exp_mask;
          if (L <= (2*P+1)*Exp_msk1) {
            if (L > (P+2)*Exp_msk1)
              /* round even ==> */
              /* accept rv */
              break;
            /* rv = smallest denormal */
            goto undfl;
            }
          }
#endif /*Avoid_Underflow*/
        L = (word0(rv) & Exp_mask) - Exp_msk1;
#endif /*Sudden_Underflow}*/
        word0(rv) = (UINT32)(L | Bndry_mask1);
        word1(rv) = 0xffffffffU;
#ifdef IBM
        goto cont;
#else
        break;
#endif
        }
#ifndef ROUND_BIASED
      if (!(word1(rv) & LSB))
        break;
#endif
      if (dsign)
        dval(rv) += ulp(dval(rv));
#ifndef ROUND_BIASED
      else {
        dval(rv) -= ulp(dval(rv));
#ifndef Sudden_Underflow
        if (!dval(rv))
          goto undfl;
#endif
        }
#ifdef Avoid_Underflow
      dsign = 1 - dsign;
#endif
#endif
      break;
      }
    if ((aadj = ratio(delta, bs)) <= 2.) {
      if (dsign)
        aadj = aadj1 = 1.;
      else if (word1(rv) || word0(rv) & Bndry_mask) {
#ifndef Sudden_Underflow
        if (word1(rv) == Tiny1 && !word0(rv))
          goto undfl;
#endif
        aadj = 1.;
        aadj1 = -1.;
        }
      else {
        /* special case -- power of FLT_RADIX to be */
        /* rounded down... */

        if (aadj < 2./FLT_RADIX)
          aadj = 1./FLT_RADIX;
        else
          aadj *= 0.5;
        aadj1 = -aadj;
        }
      }
    else {
      aadj *= 0.5;
      aadj1 = dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
      switch(Rounding) {
        case 2: /* towards +infinity */
          aadj1 -= 0.5;
          break;
        case 0: /* towards 0 */
        case 3: /* towards -infinity */
          aadj1 += 0.5;
        }
#else
      if (Flt_Rounds == 0)
        aadj1 += 0.5;
#endif /*Check_FLT_ROUNDS*/
      }
    y = word0(rv) & Exp_mask;

    /* Check for overflow */

    if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
      dval(rv0) = dval(rv);
      word0(rv) -= P*Exp_msk1;
      adj = aadj1 * ulp(dval(rv));
      dval(rv) += adj;
      if ((word0(rv) & Exp_mask) >=
          Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
        if (word0(rv0) == Big0 && word1(rv0) == Big1)
          goto ovfl;
        word0(rv) = Big0;
        word1(rv) = Big1;
        goto cont;
        }
      else
        word0(rv) += P*Exp_msk1;
      }
    else {
#ifdef Avoid_Underflow
      if (scale && y <= 2*P*Exp_msk1) {
        if (aadj <= 0x7fffffff) {
          if ((z = (uint32_t)aadj) == 0)
            z = 1;
          aadj = (double)z;
          aadj1 = dsign ? aadj : -aadj;
          }
        word0(aadj1) += (UINT32)((2*P+1)*Exp_msk1 - y);
        }
      adj = aadj1 * ulp(dval(rv));
      dval(rv) += adj;
#else
#ifdef Sudden_Underflow
      if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
        dval(rv0) = dval(rv);
        word0(rv) += P*Exp_msk1;
        adj = aadj1 * ulp(dval(rv));
        dval(rv) += adj;
#ifdef IBM
        if ((word0(rv) & Exp_mask) <  P*Exp_msk1)
#else
        if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
#endif
          {
          if (word0(rv0) == Tiny0
           && word1(rv0) == Tiny1)
            goto undfl;
          word0(rv) = Tiny0;
          word1(rv) = Tiny1;
          goto cont;
          }
        else
          word0(rv) -= P*Exp_msk1;
        }
      else {
        adj = aadj1 * ulp(dval(rv));
        dval(rv) += adj;
        }
#else /*Sudden_Underflow*/
      /* Compute adj so that the IEEE rounding rules will
       * correctly round rv + adj in some half-way cases.
       * If rv * ulp(rv) is denormalized (i.e.,
       * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
       * trouble from bits lost to denormalization;
       * example: 1.2e-307 .
       */
      if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
        aadj1 = (double)(int)(aadj + 0.5);
        if (!dsign)
          aadj1 = -aadj1;
        }
      adj = aadj1 * ulp(dval(rv));
      dval(rv) += adj;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
      }
    z = word0(rv) & Exp_mask;
#ifndef SET_INEXACT
#ifdef Avoid_Underflow
    if (!scale)
#endif
    if (y == z) {
      /* Can we stop now? */
      L = (Long)aadj;
      aadj -= L;
      /* The tolerances below are conservative. */
      if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
        if (aadj < .4999999 || aadj > .5000001)
          break;
        }
      else if (aadj < .4999999/FLT_RADIX)
        break;
      }
#endif
 cont:
    Bfree(bb);
    Bfree(bd);
    Bfree(bs);
    Bfree(delta);
    }
#ifdef SET_INEXACT
  if (inexact) {
    if (!oldinexact) {
      word0(rv0) = Exp_1 + (70 << Exp_shift);
      word1(rv0) = 0;
      dval(rv0) += 1.;
      }
    }
  else if (!oldinexact)
    clear_inexact();
#endif
#ifdef Avoid_Underflow
  if (scale) {
    word0(rv0) = Exp_1 - 2*P*Exp_msk1;
    word1(rv0) = 0;
    dval(rv) *= dval(rv0);
#ifndef NO_ERRNO
    /* try to avoid the bug of testing an 8087 register value */
    if (word0(rv) == 0 && word1(rv) == 0)
      errno = ERANGE;
#endif
    }
#endif /* Avoid_Underflow */
#ifdef SET_INEXACT
  if (inexact && !(word0(rv) & Exp_mask)) {
    /* set underflow bit */
    dval(rv0) = 1e-300;
    dval(rv0) *= dval(rv0);
    }
#endif
 retfree:
  Bfree(bb);
  Bfree(bd);
  Bfree(bs);
  Bfree(bd0);
  Bfree(delta);
 ret:
  if (se)
    *se = __UNCONST(s);
  return sign ? -dval(rv) : dval(rv);
}