mingw-w64-crt/gdtoa/dtoa.c - mingw-w64 - Git at Google

 /****************************************************************

 The author of this software is David M. Gay.

 Copyright (C) 1998, 1999 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 ".").	*/

 #include "gdtoaimp.h"

 /* 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.
  */

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

 char *__dtoa (double d0, 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.
 		4,5 ==> 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, j2, 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;
 	union _dbl_union d, d2, eps;
 	double ds;
 	char *s, *s0;
 #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) {
 		__freedtoa(dtoa_result);
 		dtoa_result = 0;
 	}
 #endif
 	d.d = d0;
 	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 ((word0(&d) & Exp_mask) == Exp_mask)
 	{
 		/* Infinity or NaN */
 		*decpt = 9999;
 		if (!word1(&d) && !(word0(&d) & 0xfffff))
 			return nrv_alloc("Infinity", rve, 8);
 		return nrv_alloc("NaN", rve, 3);
 	}
 	if (!dval(&d)) {
 		*decpt = 1;
 		return nrv_alloc("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(dval(&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
 		dval(&d2) = dval(&d);
 		word0(&d2) &= Frac_mask1;
 		word0(&d2) |= Exp_11;

 		/* 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;
 #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);
 		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(&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;

 #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(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(&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;
 				dval(&d) /= bigtens[n_bigtens-1];
 				ieps++;
 			}
 			for(; j; j >>= 1, i++)
 				if (j & 1) {
 					ieps++;
 					ds *= bigtens[i];
 				}
 			dval(&d) /= ds;
 		}
 		else if (( j2 = -k )!=0) {
 			dval(&d) *= tens[j2 & 0xf];
 			for(j = j2 >> 4; j; j >>= 1, i++)
 				if (j & 1) {
 					ieps++;
 					dval(&d) *= bigtens[i];
 				}
 		}
 		if (k_check && dval(&d) < 1. && ilim > 0) {
 			if (ilim1 <= 0)
 				goto fast_failed;
 			ilim = ilim1;
 			k--;
 			dval(&d) *= 10.;
 			ieps++;
 		}
 		dval(&eps) = ieps*dval(&d) + 7.;
 		word0(&eps) -= (P-1)*Exp_msk1;
 		if (ilim == 0) {
 			S = mhi = 0;
 			dval(&d) -= 5.;
 			if (dval(&d) > dval(&eps))
 				goto one_digit;
 			if (dval(&d) < -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);
 			for(i = 0;;) {
 				L = dval(&d);
 				dval(&d) -= L;
 				*s++ = '0' + (int)L;
 				if (dval(&d) < dval(&eps))
 					goto ret1;
 				if (1. - dval(&d) < dval(&eps))
 					goto bump_up;
 				if (++i >= ilim)
 					break;
 				dval(&eps) *= 10.;
 				dval(&d) *= 10.;
 			}
 		}
 		else {
 #endif
 			/* Generate ilim digits, then fix them up. */
 			dval(&eps) *= tens[ilim-1];
 			for(i = 1;; i++, dval(&d) *= 10.) {
 				L = (Long)(dval(&d));
 				if (!(dval(&d) -= L))
 					ilim = i;
 				*s++ = '0' + (int)L;
 				if (i == ilim) {
 					if (dval(&d) > 0.5 + dval(&eps))
 						goto bump_up;
 					else if (dval(&d) < 0.5 - dval(&eps)) {
 						while(*--s == '0');
 						s++;
 						goto ret1;
 					}
 					break;
 				}
 			}
 #ifndef No_leftright
 		}
 #endif
  fast_failed:
 		s = s0;
 		dval(&d) = 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(&d) <= 5*ds)
 				goto no_digits;
 			goto one_digit;
 		}
 		for(i = 1;; i++, dval(&d) *= 10.) {
 			L = (Long)(dval(&d) / ds);
 			dval(&d) -= L*ds;
 #ifdef Check_FLT_ROUNDS
 			/* If FLT_ROUNDS == 2, L will usually be high by 1 */
 			if (dval(&d) < 0) {
 				L--;
 				dval(&d) += ds;
 			}
 #endif
 			*s++ = '0' + (int)L;
 			if (!dval(&d)) {
 #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(&d) += dval(&d);
 #ifdef ROUND_BIASED
 				if (dval(&d) >= ds)
 #else
 				if (dval(&d) > ds || (dval(&d) == 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
 			1 + P - bbits;
 		b2 += i;
 		s2 += i;
 		mhi = i2b(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(mhi, m5);
 				b1 = mult(mhi, b);
 				Bfree(b);
 				b = b1;
 			}
 			if (( j = b5 - m5 )!=0)
 				b = pow5mult(b, j);
 		}
 		else
 			b = pow5mult(b, b5);
 	}
 	S = i2b(1);
 	if (s5 > 0)
 		S = pow5mult(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(&d) && !(word0(&d) & Bndry_mask)
 #ifndef Sudden_Underflow
 		 && word0(&d) & (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.
 	 */
 #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(b, b2);
 	if (s2 > 0)
 		S = lshift(S, s2);
 	if (k_check) {
 		if (cmp(b,S) < 0) {
 			k--;
 			b = multadd(b, 10, 0);	/* we botched the k estimate */
 			if (leftright)
 				mhi = multadd(mhi, 10, 0);
 			ilim = ilim1;
 		}
 	}
 	if (ilim <= 0 && (mode == 3 || mode == 5)) {
 		if (ilim < 0 || cmp(b,S = multadd(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(mhi, m2);

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

 		mlo = mhi;
 		if (spec_case) {
 			mhi = Balloc(mhi->k);
 			Bcopy(mhi, mlo);
 			mhi = lshift(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(S, mhi);
 			j2 = delta->sign ? 1 : cmp(b, delta);
 			Bfree(delta);
 #ifndef ROUND_BIASED
 			if (j2 == 0 && mode != 1 && !(word1(&d) & 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(&d) & 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 (j2 > 0) {
 					b = lshift(b, 1);
 					j2 = cmp(b, S);
 #ifdef ROUND_BIASED
 					if (j2 >= 0 /*)*/
 #else
 					if ((j2 > 0 || (j2 == 0 && dig & 1))
 #endif
 					&& dig++ == '9')
 						goto round_9_up;
 				}
  accept_dig:
 				*s++ = dig;
 				goto ret;
 			}
 			if (j2 > 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(b, 10, 0);
 			if (mlo == mhi)
 				mlo = mhi = multadd(mhi, 10, 0);
 			else {
 				mlo = multadd(mlo, 10, 0);
 				mhi = multadd(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(b, 10, 0);
 		}

 	/* Round off last digit */

 #ifdef Honor_FLT_ROUNDS
 	switch(Rounding) {
 	  case 0: goto trimzeros;
 	  case 2: goto roundoff;
 	}
 #endif
 	b = lshift(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(S);
 	if (mhi) {
 		if (mlo && mlo != mhi)
 			Bfree(mlo);
 		Bfree(mhi);
 	}
  ret1:
 #ifdef SET_INEXACT
 	if (inexact) {
 		if (!oldinexact) {
 			word0(&d) = Exp_1 + (70 << Exp_shift);
 			word1(&d) = 0;
 			dval(&d) += 1.;
 		}
 	}
 	else if (!oldinexact)
 		clear_inexact();
 #endif
 	Bfree(b);
 	*s = 0;
 	*decpt = k + 1;
 	if (rve)
 		*rve = s;
 	return s0;
 }
	/****************************************************************

	The author of this software is David M. Gay.

	Copyright (C) 1998, 1999 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 "."). */

	#include "gdtoaimp.h"

	/* 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.
	*/

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

	char __dtoa (double d0, 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.
	4,5 ==> 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, j2, 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;
	union _dbl_union d, d2, eps;
	double ds;
	char s, s0;
	#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) {
	__freedtoa(dtoa_result);
	dtoa_result = 0;
	}
	#endif
	d.d = d0;
	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 ((word0(&d) & Exp_mask) == Exp_mask)
	{
	/* Infinity or NaN */
	*decpt = 9999;
	if (!word1(&d) && !(word0(&d) & 0xfffff))
	return nrv_alloc("Infinity", rve, 8);
	return nrv_alloc("NaN", rve, 3);
	}
	if (!dval(&d)) {
	*decpt = 1;
	return nrv_alloc("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(dval(&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
	dval(&d2) = dval(&d);
	word0(&d2) &= Frac_mask1;
	word0(&d2) \|= Exp_11;

	/* 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;
	#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);
	dval(&d2) = x;
	word0(&d2) -= 31Exp_msk1; / adjust exponent */
	i -= (Bias + (P-1) - 1) + 1;
	denorm = 1;
	}
	#endif
	ds = (dval(&d2)-1.5)0.289529654602168 + 0.1760912590558 + i0.301029995663981;
	k = (int)ds;
	if (ds < 0. && ds != k)
	k--; /* want k = floor(ds) */
	k_check = 1;
	if (k >= 0 && k <= Ten_pmax) {
	if (dval(&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;

	#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(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(&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;
	dval(&d) /= bigtens[n_bigtens-1];
	ieps++;
	}
	for(; j; j >>= 1, i++)
	if (j & 1) {
	ieps++;
	ds *= bigtens[i];
	}
	dval(&d) /= ds;
	}
	else if (( j2 = -k )!=0) {
	dval(&d) *= tens[j2 & 0xf];
	for(j = j2 >> 4; j; j >>= 1, i++)
	if (j & 1) {
	ieps++;
	dval(&d) *= bigtens[i];
	}
	}
	if (k_check && dval(&d) < 1. && ilim > 0) {
	if (ilim1 <= 0)
	goto fast_failed;
	ilim = ilim1;
	k--;
	dval(&d) *= 10.;
	ieps++;
	}
	dval(&eps) = ieps*dval(&d) + 7.;
	word0(&eps) -= (P-1)*Exp_msk1;
	if (ilim == 0) {
	S = mhi = 0;
	dval(&d) -= 5.;
	if (dval(&d) > dval(&eps))
	goto one_digit;
	if (dval(&d) < -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);
	for(i = 0;;) {
	L = dval(&d);
	dval(&d) -= L;
	*s++ = '0' + (int)L;
	if (dval(&d) < dval(&eps))
	goto ret1;
	if (1. - dval(&d) < dval(&eps))
	goto bump_up;
	if (++i >= ilim)
	break;
	dval(&eps) *= 10.;
	dval(&d) *= 10.;
	}
	}
	else {
	#endif
	/* Generate ilim digits, then fix them up. */
	dval(&eps) *= tens[ilim-1];
	for(i = 1;; i++, dval(&d) *= 10.) {
	L = (Long)(dval(&d));
	if (!(dval(&d) -= L))
	ilim = i;
	*s++ = '0' + (int)L;
	if (i == ilim) {
	if (dval(&d) > 0.5 + dval(&eps))
	goto bump_up;
	else if (dval(&d) < 0.5 - dval(&eps)) {
	while(*--s == '0');
	s++;
	goto ret1;
	}
	break;
	}
	}
	#ifndef No_leftright
	}
	#endif
	fast_failed:
	s = s0;
	dval(&d) = 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(&d) <= 5*ds)
	goto no_digits;
	goto one_digit;
	}
	for(i = 1;; i++, dval(&d) *= 10.) {
	L = (Long)(dval(&d) / ds);
	dval(&d) -= L*ds;
	#ifdef Check_FLT_ROUNDS
	/* If FLT_ROUNDS == 2, L will usually be high by 1 */
	if (dval(&d) < 0) {
	L--;
	dval(&d) += ds;
	}
	#endif
	*s++ = '0' + (int)L;
	if (!dval(&d)) {
	#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(&d) += dval(&d);
	#ifdef ROUND_BIASED
	if (dval(&d) >= ds)
	#else
	if (dval(&d) > ds \|\| (dval(&d) == 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
	1 + P - bbits;
	b2 += i;
	s2 += i;
	mhi = i2b(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(mhi, m5);
	b1 = mult(mhi, b);
	Bfree(b);
	b = b1;
	}
	if (( j = b5 - m5 )!=0)
	b = pow5mult(b, j);
	}
	else
	b = pow5mult(b, b5);
	}
	S = i2b(1);
	if (s5 > 0)
	S = pow5mult(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(&d) && !(word0(&d) & Bndry_mask)
	#ifndef Sudden_Underflow
	&& word0(&d) & (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.
	*/
	#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(b, b2);
	if (s2 > 0)
	S = lshift(S, s2);
	if (k_check) {
	if (cmp(b,S) < 0) {
	k--;
	b = multadd(b, 10, 0); /* we botched the k estimate */
	if (leftright)
	mhi = multadd(mhi, 10, 0);
	ilim = ilim1;
	}
	}
	if (ilim <= 0 && (mode == 3 \|\| mode == 5)) {
	if (ilim < 0 \|\| cmp(b,S = multadd(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(mhi, m2);

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

	mlo = mhi;
	if (spec_case) {
	mhi = Balloc(mhi->k);
	Bcopy(mhi, mlo);
	mhi = lshift(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(S, mhi);
	j2 = delta->sign ? 1 : cmp(b, delta);
	Bfree(delta);
	#ifndef ROUND_BIASED
	if (j2 == 0 && mode != 1 && !(word1(&d) & 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(&d) & 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 (j2 > 0) {
	b = lshift(b, 1);
	j2 = cmp(b, S);
	#ifdef ROUND_BIASED
	if (j2 >= 0 /)/
	#else
	if ((j2 > 0 \|\| (j2 == 0 && dig & 1))
	#endif
	&& dig++ == '9')
	goto round_9_up;
	}
	accept_dig:
	*s++ = dig;
	goto ret;
	}
	if (j2 > 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(b, 10, 0);
	if (mlo == mhi)
	mlo = mhi = multadd(mhi, 10, 0);
	else {
	mlo = multadd(mlo, 10, 0);
	mhi = multadd(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(b, 10, 0);
	}

	/* Round off last digit */

	#ifdef Honor_FLT_ROUNDS
	switch(Rounding) {
	case 0: goto trimzeros;
	case 2: goto roundoff;
	}
	#endif
	b = lshift(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(S);
	if (mhi) {
	if (mlo && mlo != mhi)
	Bfree(mlo);
	Bfree(mhi);
	}
	ret1:
	#ifdef SET_INEXACT
	if (inexact) {
	if (!oldinexact) {
	word0(&d) = Exp_1 + (70 << Exp_shift);
	word1(&d) = 0;
	dval(&d) += 1.;
	}
	}
	else if (!oldinexact)
	clear_inexact();
	#endif
	Bfree(b);
	*s = 0;
	*decpt = k + 1;
	if (rve)
	*rve = s;
	return s0;
	}