Added a reference to gdtoa, for doing expected conversion of double to amount.

1 files changed, 753 insertions, 0 deletions

diff --git a/gdtoa/dtoa.c b/gdtoa/dtoa.c
new file mode 100644
index 00000000..e808cc1f
--- /dev/null
+++ b/gdtoa/dtoa.c
@@ -0,0 +1,753 @@
+/****************************************************************
+
+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
+#define Rounding rounding
+#undef Check_FLT_ROUNDS
+#define Check_FLT_ROUNDS
+#else
+#define Rounding Flt_Rounds
+#endif
+
+ char *
+dtoa
+#ifdef KR_headers
+	(d, mode, ndigits, decpt, sign, rve)
+	double d; int mode, ndigits, *decpt, *sign; char **rve;
+#else
+	(double d, 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, 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;
+	double d2, ds, eps;
+	char *s, *s0;
+#ifdef Honor_FLT_ROUNDS
+	int rounding;
+#endif
+#ifdef SET_INEXACT
+	int inexact, oldinexact;
+#endif
+
+#ifndef MULTIPLE_THREADS
+	if (dtoa_result) {
+		freedtoa(dtoa_result);
+		dtoa_result = 0;
+		}
+#endif
+
+	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;
+#ifdef IEEE_Arith
+		if (!word1(d) && !(word0(d) & 0xfffff))
+			return nrv_alloc("Infinity", rve, 8);
+#endif
+		return nrv_alloc("NaN", rve, 3);
+		}
+#endif
+#ifdef IBM
+	dval(d) += 0; /* normalize */
+#endif
+	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 = Flt_Rounds) >= 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;
+#ifdef IBM
+		if (( j = 11 - hi0bits(word0(d2) & Frac_mask) )!=0)
+			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(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;
+	switch(mode) {
+		case 0:
+		case 1:
+			ilim = ilim1 = -1;
+			i = 18;
+			ndigits = 0;
+			break;
+		case 2:
+			leftright = 0;
+			/* no break */
+		case 4:
+			if (ndigits <= 0)
+				ndigits = 1;
+			ilim = ilim1 = i = ndigits;
+			break;
+		case 3:
+			leftright = 0;
+			/* no break */
+		case 5:
+			i = ndigits + k + 1;
+			ilim = i;
+			ilim1 = i - 1;
+			if (i <= 0)
+				i = 1;
+		}
+	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 (( j1 = -k )!=0) {
+			dval(d) *= tens[j1 & 0xf];
+			for(j = j1 >> 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);
+				if (dval(d) > ds || dval(d) == ds && L & 1) {
+ 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(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);
+			j1 = delta->sign ? 1 : cmp(b, delta);
+			Bfree(delta);
+#ifndef ROUND_BIASED
+			if (j1 == 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 (j1 > 0) {
+					b = lshift(b, 1);
+					j1 = cmp(b, S);
+					if ((j1 > 0 || j1 == 0 && dig & 1)
+					&& 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(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);
+	if (j > 0 || j == 0 && dig & 1) {
+ roundoff:
+		while(*--s == '9')
+			if (s == s0) {
+				k++;
+				*s++ = '1';
+				goto ret;
+				}
+		++*s++;
+		}
+	else {
+ trimzeros:
+		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;
+	}