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-/****************************************************************
-
-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;
- }
generated by cgit v1.2.3 (git 2.39.1) at 2025-01-11 04:54:58 +0000