/src/hermes/external/dtoa/dtoa.inc

Source (jump to first uncovered line)
/* 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. 112-126].
 *
 * 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 *
g_dtoa
#ifdef KR_headers
  (dalloc, dd, mode, ndigits, decpt, sign, rve)
  dtoa_alloc *dalloc; double dd; int mode, ndigits, *decpt, *sign; char **rve;
#else
  (dtoa_alloc *dalloc, double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
#endif
{
 /* 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.
    4,5 ==> similar to 2 and 3, respectively, but (in
      round-nearest mode) with the tests of mode 0 to
      possibly return a shorter string that rounds to d.
      With IEEE arithmetic and compilation with
      -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
      as modes 2 and 3 when FLT_ROUNDS != 1.
    6-9 ==> Debugging modes similar to mode - 4:  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 = 0, k, k0, k_check, leftright, m2, m5, s2, s5,
    spec_case, try_quick;
  Long L;
#ifndef Sudden_Underflow
  int denorm;
  ULong x;
#endif
  Bigint *b, *b1, *delta, *mlo, *mhi, *S;
  U d2, eps, u;
  double ds;
  char *s, *s0;
#ifndef No_leftright
#ifdef IEEE_Arith
  U eps1;
#endif
#endif
#ifdef SET_INEXACT
  int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS /*{*/
  int Rounding;
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
  Rounding = Flt_Rounds;
#else /*}{*/
  Rounding = 1;
  switch(fegetround()) {
    case FE_TOWARDZERO: Rounding = 0; break;
    case FE_UPWARD: Rounding = 2; break;
    case FE_DOWNWARD: Rounding = 3;
    }
#endif /*}}*/
#endif /*}*/

#ifndef MULTIPLE_THREADS
  if (dtoa_result) {
    g_freedtoa(dtoa_result);
    dtoa_result = 0;
    }
#endif

  u.d = dd;
  if (word0(&u) & Sign_bit) {
    /* set sign for everything, including 0's and NaNs */
    *sign = 1;
    word0(&u) &= ~Sign_bit; /* clear sign bit */
    }
  else
    *sign = 0;

#if defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
  if ((word0(&u) & Exp_mask) == Exp_mask)
#else
  if (word0(&u)  == 0x8000)
#endif
    {
    /* Infinity or NaN */
    *decpt = 9999;
#ifdef IEEE_Arith
    if (!word1(&u) && !(word0(&u) & 0xfffff))
      return nrv_alloc(dalloc, "Infinity", rve, 8);
#endif
    return nrv_alloc(dalloc, "NaN", rve, 3);
    }
#endif
#ifdef IBM
  dval(&u) += 0; /* normalize */
#endif
  if (!dval(&u)) {
    *decpt = 1;
    return nrv_alloc(dalloc, "0", rve, 1);
    }

#ifdef SET_INEXACT
  try_quick = oldinexact = get_inexact();
  inexact = 1;
#endif
#ifdef Honor_FLT_ROUNDS
  if (Rounding >= 2) {
    if (*sign)
      Rounding = Rounding == 2 ? 0 : 2;
    else
      if (Rounding != 2)
        Rounding = 0;
    }
#endif

  b = d2b(dalloc, &u, &be, &bbits);
#ifdef Sudden_Underflow
  i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
  if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
#endif
    dval(&d2) = dval(&u);
    word0(&d2) &= Frac_mask1;
    word0(&d2) |= Exp_11;
#ifdef IBM
    if (j = 11 - hi0bits(word0(&d2) & Frac_mask))
      dval(&d2) /= 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(&u) << (64 - i) | word1(&u) >> (i - 32)
          : word1(&u) << (32 - i);
    dval(&d2) = x;
    word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
    i -= (Bias + (P-1) - 1) + 1;
    denorm = 1;
    }
#endif
  ds = (dval(&d2)-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 (dval(&u) < 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;

#ifndef SET_INEXACT
#ifdef Check_FLT_ROUNDS
  try_quick = Rounding == 1;
#else
  try_quick = 1;
#endif
#endif /*SET_INEXACT*/

  if (mode > 5) {
    mode -= 4;
    try_quick = 0;
    }
  leftright = 1;
  ilim = ilim1 = -1;  /* Values for cases 0 and 1; done here to */
        /* silence erroneous "gcc -Wall" warning. */
  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;
    }
  s = s0 = rv_alloc(dalloc, i);

#ifdef Honor_FLT_ROUNDS
  if (mode > 1 && Rounding != 1)
    leftright = 0;
#endif

  if (ilim >= 0 && ilim <= Quick_max && try_quick) {

    /* Try to get by with floating-point arithmetic. */

    i = 0;
    dval(&d2) = dval(&u);
    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;
        dval(&u) /= bigtens[n_bigtens-1];
        ieps++;
        }
      for(; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          ds *= bigtens[i];
          }
      dval(&u) /= ds;
      }
    else if ((j1 = -k)) {
      dval(&u) *= tens[j1 & 0xf];
      for(j = j1 >> 4; j; j >>= 1, i++)
        if (j & 1) {
          ieps++;
          dval(&u) *= bigtens[i];
          }
      }
    if (k_check && dval(&u) < 1. && ilim > 0) {
      if (ilim1 <= 0)
        goto fast_failed;
      ilim = ilim1;
      k--;
      dval(&u) *= 10.;
      ieps++;
      }
    dval(&eps) = ieps*dval(&u) + 7.;
    word0(&eps) -= (P-1)*Exp_msk1;
    if (ilim == 0) {
      S = mhi = 0;
      dval(&u) -= 5.;
      if (dval(&u) > dval(&eps))
        goto one_digit;
      if (dval(&u) < -dval(&eps))
        goto no_digits;
      goto fast_failed;
      }
#ifndef No_leftright
    if (leftright) {
      /* Use Steele & White method of only
       * generating digits needed.
       */
      dval(&eps) = 0.5/tens[ilim-1] - dval(&eps);
#ifdef IEEE_Arith
      if (k0 < 0 && j1 >= 307) {
        eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */
        word0(&eps1) -= Exp_msk1 * (Bias+P-1);
        dval(&eps1) *= tens[j1 & 0xf];
        for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++)
          if (j & 1)
            dval(&eps1) *= bigtens[i];
        if (eps.d < eps1.d)
          eps.d = eps1.d;
        }
#endif
      for(i = 0;;) {
        L = dval(&u);
        dval(&u) -= L;
        *s++ = '0' + (int)L;
        if (1. - dval(&u) < dval(&eps))
          goto bump_up;
        if (dval(&u) < dval(&eps))
          goto ret1;
        if (++i >= ilim)
          break;
        dval(&eps) *= 10.;
        dval(&u) *= 10.;
        }
      }
    else {
#endif
      /* Generate ilim digits, then fix them up. */
      dval(&eps) *= tens[ilim-1];
      for(i = 1;; i++, dval(&u) *= 10.) {
        L = (Long)(dval(&u));
        if (!(dval(&u) -= L))
          ilim = i;
        *s++ = '0' + (int)L;
        if (i == ilim) {
          if (dval(&u) > 0.5 + dval(&eps))
            goto bump_up;
          else if (dval(&u) < 0.5 - dval(&eps)) {
            while(*--s == '0');
            s++;
            goto ret1;
            }
          break;
          }
        }
#ifndef No_leftright
      }
#endif
 fast_failed:
    s = s0;
    dval(&u) = dval(&d2);
    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 || dval(&u) <= 5*ds)
        goto no_digits;
      goto one_digit;
      }
    for(i = 1;; i++, dval(&u) *= 10.) {
      L = (Long)(dval(&u) / ds);
      dval(&u) -= L*ds;
#ifdef Check_FLT_ROUNDS
      /* If FLT_ROUNDS == 2, L will usually be high by 1 */
      if (dval(&u) < 0) {
        L--;
        dval(&u) += ds;
        }
#endif
      *s++ = '0' + (int)L;
      if (!dval(&u)) {
#ifdef SET_INEXACT
        inexact = 0;
#endif
        break;
        }
      if (i == ilim) {
#ifdef Honor_FLT_ROUNDS
        if (mode > 1)
        switch(Rounding) {
          case 0: goto ret1;
          case 2: goto bump_up;
          }
#endif
        dval(&u) += dval(&u);
#ifdef ROUND_BIASED
        if (dval(&u) >= ds)
#else
        if (dval(&u) > ds || (dval(&u) == ds && L & 1))
#endif
          {
 bump_up:
          while(*--s == '9')
            if (s == s0) {
              k++;
              *s = '0';
              break;
              }
          ++*s++;
          }
        break;
        }
      }
    goto ret1;
    }

  m2 = b2;
  m5 = b5;
  mhi = mlo = 0;
  if (leftright) {
    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
    b2 += i;
    s2 += i;
    mhi = i2b(dalloc, 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(dalloc, mhi, m5);
        b1 = mult(dalloc, mhi, b);
        Bfree(dalloc, b);
        b = b1;
        }
      if ((j = b5 - m5))
        b = pow5mult(dalloc, b, j);
      }
    else
      b = pow5mult(dalloc, b, b5);
    }
  S = i2b(dalloc, 1);
  if (s5 > 0)
    S = pow5mult(dalloc, S, s5);

  /* Check for special case that d is a normalized power of 2. */

  spec_case = 0;
  if ((mode < 2 || leftright)
#ifdef Honor_FLT_ROUNDS
      && Rounding == 1
#endif
        ) {
    if (!word1(&u) && !(word0(&u) & Bndry_mask)
#ifndef Sudden_Underflow
     && word0(&u) & (Exp_mask & ~Exp_msk1)
#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.
   */
  i = dshift(S, s2);
  b2 += i;
  m2 += i;
  s2 += i;
  if (b2 > 0)
    b = lshift(dalloc, b, b2);
  if (s2 > 0)
    S = lshift(dalloc, S, s2);
  if (k_check) {
    if (cmp(b,S) < 0) {
      k--;
      b = multadd(dalloc, b, 10, 0);  /* we botched the k estimate */
      if (leftright)
        mhi = multadd(dalloc, mhi, 10, 0);
      ilim = ilim1;
      }
    }
  if (ilim <= 0 && (mode == 3 || mode == 5)) {
#ifndef HERMES_FIXEDPOINT_HACK
    if (ilim < 0 || cmp(b,S = multadd(dalloc, S,5,0)) <= 0) {
#else
                /// NOTE: The original line here checks that the cmp result is <= 0.
                /// This only works for IEEE-754 unbiased rounding, which would
                /// make 0.5 round to 0. However, for fixed-point rounding in
                /// ES5.1, we need 0.5 to round to 1. JSC modifies the check the same way.
    if (ilim < 0 || cmp(b,S = multadd(dalloc, S,5,0)) < 0) {
#endif
      /* 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(dalloc, mhi, m2);

    /* Compute mlo -- check for special case
     * that d is a normalized power of 2.
     */

    mlo = mhi;
    if (spec_case) {
      mhi = Balloc(dalloc, mhi->k);
      Bcopy(mhi, mlo);
      mhi = lshift(dalloc, 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(dalloc, S, mhi);
      j1 = delta->sign ? 1 : cmp(b, delta);
      Bfree(dalloc, delta);
#ifndef ROUND_BIASED
      if (j1 == 0 && mode != 1 && !(word1(&u) & 1)
#ifdef Honor_FLT_ROUNDS
        && Rounding >= 1
#endif
                   ) {
        if (dig == '9')
          goto round_9_up;
        if (j > 0)
          dig++;
#ifdef SET_INEXACT
        else if (!b->x[0] && b->wds <= 1)
          inexact = 0;
#endif
        *s++ = dig;
        goto ret;
        }
#endif
      if (j < 0 || (j == 0 && mode != 1
#ifndef ROUND_BIASED
              && !(word1(&u) & 1)
#endif
          )) {
        if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
          inexact = 0;
#endif
          goto accept_dig;
          }
#ifdef Honor_FLT_ROUNDS
        if (mode > 1)
         switch(Rounding) {
          case 0: goto accept_dig;
          case 2: goto keep_dig;
          }
#endif /*Honor_FLT_ROUNDS*/
        if (j1 > 0) {
          b = lshift(dalloc, b, 1);
          j1 = cmp(b, S);
#ifdef ROUND_BIASED
          if (j1 >= 0 /*)*/
#else
          if ((j1 > 0 || (j1 == 0 && dig & 1))
#endif
          && dig++ == '9')
            goto round_9_up;
          }
 accept_dig:
        *s++ = dig;
        goto ret;
        }
      if (j1 > 0) {
#ifdef Honor_FLT_ROUNDS
        if (!Rounding)
          goto accept_dig;
#endif
        if (dig == '9') { /* possible if i == 1 */
 round_9_up:
          *s++ = '9';
          goto roundoff;
          }
        *s++ = dig + 1;
        goto ret;
        }
#ifdef Honor_FLT_ROUNDS
 keep_dig:
#endif
      *s++ = dig;
      if (i == ilim)
        break;
      b = multadd(dalloc, b, 10, 0);
      if (mlo == mhi)
        mlo = mhi = multadd(dalloc, mhi, 10, 0);
      else {
        mlo = multadd(dalloc, mlo, 10, 0);
        mhi = multadd(dalloc, mhi, 10, 0);
        }
      }
    }
  else
    for(i = 1;; i++) {
      *s++ = dig = quorem(b,S) + '0';
      if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
        inexact = 0;
#endif
        goto ret;
        }
      if (i >= ilim)
        break;
      b = multadd(dalloc, b, 10, 0);
      }

  /* Round off last digit */

#ifdef Honor_FLT_ROUNDS
  switch(Rounding) {
    case 0: goto trimzeros;
    case 2: goto roundoff;
    }
#endif
  b = lshift(dalloc, b, 1);
  j = cmp(b, S);
#ifdef ROUND_BIASED
  if (j >= 0)
#else
  if (j > 0 || (j == 0 && dig & 1))
#endif
    {
 roundoff:
    while(*--s == '9')
      if (s == s0) {
        k++;
        *s++ = '1';
        goto ret;
        }
    ++*s++;
    }
  else {
#ifdef Honor_FLT_ROUNDS
 trimzeros:
#endif
    while(*--s == '0');
    s++;
    }
 ret:
  Bfree(dalloc, S);
  if (mhi) {
    if (mlo && mlo != mhi)
      Bfree(dalloc, mlo);
    Bfree(dalloc, mhi);
    }
 ret1:
#ifdef SET_INEXACT
  if (inexact) {
    if (!oldinexact) {
      word0(&u) = Exp_1 + (70 << Exp_shift);
      word1(&u) = 0;
      dval(&u) += 1.;
      }
    }
  else if (!oldinexact)
    clear_inexact();
#endif
  Bfree(dalloc, b);
  *s = 0;
  *decpt = k + 1;
  if (rve)
    *rve = s;
  return s0;
  }

Coverage Report

Created: 2023-02-22 06:51