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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"
+
+ static Bigint *
+#ifdef KR_headers
+bitstob(bits, nbits, bbits) ULong *bits; int nbits; int *bbits;
+#else
+bitstob(ULong *bits, int nbits, int *bbits)
+#endif
+{
+ int i, k;
+ Bigint *b;
+ ULong *be, *x, *x0;
+
+ i = ULbits;
+ k = 0;
+ while(i < nbits) {
+ i <<= 1;
+ k++;
+ }
+#ifndef Pack_32
+ if (!k)
+ k = 1;
+#endif
+ b = Balloc(k);
+ be = bits + ((nbits - 1) >> kshift);
+ x = x0 = b->x;
+ do {
+ *x++ = *bits & ALL_ON;
+#ifdef Pack_16
+ *x++ = (*bits >> 16) & ALL_ON;
+#endif
+ } while(++bits <= be);
+ i = x - x0;
+ while(!x0[--i])
+ if (!i) {
+ b->wds = 0;
+ *bbits = 0;
+ goto ret;
+ }
+ b->wds = i + 1;
+ *bbits = i*ULbits + 32 - hi0bits(b->x[i]);
+ ret:
+ return b;
+ }
+
+/* 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 *
+gdtoa
+#ifdef KR_headers
+ (fpi, be, bits, kindp, mode, ndigits, decpt, rve)
+ FPI *fpi; int be; ULong *bits;
+ int *kindp, mode, ndigits, *decpt; char **rve;
+#else
+ (FPI *fpi, int be, ULong *bits, int *kindp, int mode, int ndigits, int *decpt, char **rve)
+#endif
+{
+ /* Arguments ndigits and decpt are similar to the second and third
+ arguments 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.
+ 4-9 should give the same return values as 2-3, i.e.,
+ 4 <= mode <= 9 ==> same return as mode
+ 2 + (mode & 1). These modes are mainly for
+ debugging; often they run slower but sometimes
+ faster than modes 2-3.
+ 4,5,8,9 ==> left-to-right digit generation.
+ 6-9 ==> 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, be0, dig, i, ieps, ilim, ilim0, ilim1, inex;
+ int j, j1, k, k0, k_check, kind, leftright, m2, m5, nbits;
+ int rdir, s2, s5, spec_case, try_quick;
+ Long L;
+ Bigint *b, *b1, *delta, *mlo, *mhi, *mhi1, *S;
+ double d, d2, ds, eps;
+ char *s, *s0;
+
+#ifndef MULTIPLE_THREADS
+ if (dtoa_result) {
+ freedtoa(dtoa_result);
+ dtoa_result = 0;
+ }
+#endif
+ inex = 0;
+ kind = *kindp &= ~STRTOG_Inexact;
+ switch(kind & STRTOG_Retmask) {
+ case STRTOG_Zero:
+ goto ret_zero;
+ case STRTOG_Normal:
+ case STRTOG_Denormal:
+ break;
+ case STRTOG_Infinite:
+ *decpt = -32768;
+ return nrv_alloc("Infinity", rve, 8);
+ case STRTOG_NaN:
+ *decpt = -32768;
+ return nrv_alloc("NaN", rve, 3);
+ default:
+ return 0;
+ }
+ b = bitstob(bits, nbits = fpi->nbits, &bbits);
+ be0 = be;
+ if ( (i = trailz(b)) !=0) {
+ rshift(b, i);
+ be += i;
+ bbits -= i;
+ }
+ if (!b->wds) {
+ Bfree(b);
+ ret_zero:
+ *decpt = 1;
+ return nrv_alloc("0", rve, 1);
+ }
+
+ dval(d) = b2d(b, &i);
+ i = be + bbits - 1;
+ word0(d) &= Frac_mask1;
+ word0(d) |= Exp_11;
+#ifdef IBM
+ if ( (j = 11 - hi0bits(word0(d) & Frac_mask)) !=0)
+ dval(d) /= 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.)
+ */
+#ifdef IBM
+ i <<= 2;
+ i += j;
+#endif
+ ds = (dval(d)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
+
+ /* correct assumption about exponent range */
+ if ((j = i) < 0)
+ j = -j;
+ if ((j -= 1077) > 0)
+ ds += j * 7e-17;
+
+ k = (int)ds;
+ if (ds < 0. && ds != k)
+ k--; /* want k = floor(ds) */
+ k_check = 1;
+#ifdef IBM
+ j = be + bbits - 1;
+ if ( (j1 = j & 3) !=0)
+ dval(d) *= 1 << j1;
+ word0(d) += j << Exp_shift - 2 & Exp_mask;
+#else
+ word0(d) += (be + bbits - 1) << Exp_shift;
+#endif
+ 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;
+ try_quick = 1;
+ if (mode > 5) {
+ mode -= 4;
+ try_quick = 0;
+ }
+ leftright = 1;
+ switch(mode) {
+ case 0:
+ case 1:
+ ilim = ilim1 = -1;
+ i = (int)(nbits * .30103) + 3;
+ 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);
+
+ if ( (rdir = fpi->rounding - 1) !=0) {
+ if (rdir < 0)
+ rdir = 2;
+ if (kind & STRTOG_Neg)
+ rdir = 3 - rdir;
+ }
+
+ /* Now rdir = 0 ==> round near, 1 ==> round up, 2 ==> round down. */
+
+ if (ilim >= 0 && ilim <= Quick_max && try_quick && !rdir
+#ifndef IMPRECISE_INEXACT
+ && k == 0
+#endif
+ ) {
+
+ /* Try to get by with floating-point arithmetic. */
+
+ i = 0;
+ d2 = dval(d);
+#ifdef IBM
+ if ( (j = 11 - hi0bits(word0(d) & Frac_mask)) !=0)
+ dval(d) /= 1 << j;
+#endif
+ 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];
+ }
+ }
+ else {
+ ds = 1.;
+ 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) = ds*0.5/tens[ilim-1] - dval(eps);
+ for(i = 0;;) {
+ L = (Long)(dval(d)/ds);
+ dval(d) -= L*ds;
+ *s++ = '0' + (int)L;
+ if (dval(d) < dval(eps)) {
+ if (dval(d))
+ inex = STRTOG_Inexlo;
+ goto ret1;
+ }
+ if (ds - 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.) {
+ if ( (L = (Long)(dval(d)/ds)) !=0)
+ dval(d) -= L*ds;
+ *s++ = '0' + (int)L;
+ if (i == ilim) {
+ ds *= 0.5;
+ if (dval(d) > ds + dval(eps))
+ goto bump_up;
+ else if (dval(d) < ds - dval(eps)) {
+ while(*--s == '0'){}
+ s++;
+ if (dval(d))
+ inex = STRTOG_Inexlo;
+ goto ret1;
+ }
+ break;
+ }
+ }
+#ifndef No_leftright
+ }
+#endif
+ fast_failed:
+ s = s0;
+ dval(d) = 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 = 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) == 0.)
+ break;
+ if (i == ilim) {
+ if (rdir) {
+ if (rdir == 1)
+ goto bump_up;
+ inex = STRTOG_Inexlo;
+ goto ret1;
+ }
+ dval(d) += dval(d);
+ if (dval(d) > ds || dval(d) == ds && L & 1) {
+ bump_up:
+ inex = STRTOG_Inexhi;
+ while(*--s == '9')
+ if (s == s0) {
+ k++;
+ *s = '0';
+ break;
+ }
+ ++*s++;
+ }
+ else
+ inex = STRTOG_Inexlo;
+ break;
+ }
+ }
+ goto ret1;
+ }
+
+ m2 = b2;
+ m5 = b5;
+ mhi = mlo = 0;
+ if (leftright) {
+ if (mode < 2) {
+ i = nbits - bbits;
+ if (be - i++ < fpi->emin)
+ /* denormal */
+ i = be - fpi->emin + 1;
+ }
+ else {
+ j = ilim - 1;
+ if (m5 >= j)
+ m5 -= j;
+ else {
+ s5 += j -= m5;
+ b5 += j;
+ m5 = 0;
+ }
+ if ((i = ilim) < 0) {
+ m2 -= i;
+ i = 0;
+ }
+ }
+ 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) {
+ if (bbits == 1 && be0 > fpi->emin + 1) {
+ /* The special case */
+ b2++;
+ s2++;
+ 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 > 2) {
+ if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
+ /* no digits, fcvt style */
+ no_digits:
+ k = -1 - ndigits;
+ inex = STRTOG_Inexlo;
+ goto ret;
+ }
+ one_digit:
+ inex = STRTOG_Inexhi;
+ *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, 1);
+ }
+
+ 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 && !(bits[0] & 1) && !rdir) {
+ if (dig == '9')
+ goto round_9_up;
+ if (j <= 0) {
+ if (b->wds > 1 || b->x[0])
+ inex = STRTOG_Inexlo;
+ }
+ else {
+ dig++;
+ inex = STRTOG_Inexhi;
+ }
+ *s++ = dig;
+ goto ret;
+ }
+#endif
+ if (j < 0 || j == 0 && !mode
+#ifndef ROUND_BIASED
+ && !(bits[0] & 1)
+#endif
+ ) {
+ if (rdir && (b->wds > 1 || b->x[0])) {
+ if (rdir == 2) {
+ inex = STRTOG_Inexlo;
+ goto accept;
+ }
+ while (cmp(S,mhi) > 0) {
+ *s++ = dig;
+ mhi1 = multadd(mhi, 10, 0);
+ if (mlo == mhi)
+ mlo = mhi1;
+ mhi = mhi1;
+ b = multadd(b, 10, 0);
+ dig = quorem(b,S) + '0';
+ }
+ if (dig++ == '9')
+ goto round_9_up;
+ inex = STRTOG_Inexhi;
+ goto accept;
+ }
+ if (j1 > 0) {
+ b = lshift(b, 1);
+ j1 = cmp(b, S);
+ if ((j1 > 0 || j1 == 0 && dig & 1)
+ && dig++ == '9')
+ goto round_9_up;
+ inex = STRTOG_Inexhi;
+ }
+ if (b->wds > 1 || b->x[0])
+ inex = STRTOG_Inexlo;
+ accept:
+ *s++ = dig;
+ goto ret;
+ }
+ if (j1 > 0 && rdir != 2) {
+ if (dig == '9') { /* possible if i == 1 */
+ round_9_up:
+ *s++ = '9';
+ inex = STRTOG_Inexhi;
+ goto roundoff;
+ }
+ inex = STRTOG_Inexhi;
+ *s++ = dig + 1;
+ goto ret;
+ }
+ *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 (i >= ilim)
+ break;
+ b = multadd(b, 10, 0);
+ }
+
+ /* Round off last digit */
+
+ if (rdir) {
+ if (rdir == 2 || b->wds <= 1 && !b->x[0])
+ goto chopzeros;
+ goto roundoff;
+ }
+ b = lshift(b, 1);
+ j = cmp(b, S);
+ if (j > 0 || j == 0 && dig & 1) {
+ roundoff:
+ inex = STRTOG_Inexhi;
+ while(*--s == '9')
+ if (s == s0) {
+ k++;
+ *s++ = '1';
+ goto ret;
+ }
+ ++*s++;
+ }
+ else {
+ chopzeros:
+ if (b->wds > 1 || b->x[0])
+ inex = STRTOG_Inexlo;
+ while(*--s == '0'){}
+ s++;
+ }
+ ret:
+ Bfree(S);
+ if (mhi) {
+ if (mlo && mlo != mhi)
+ Bfree(mlo);
+ Bfree(mhi);
+ }
+ ret1:
+ Bfree(b);
+ *s = 0;
+ *decpt = k + 1;
+ if (rve)
+ *rve = s;
+ *kindp |= inex;
+ return s0;
+ }
generated by cgit v1.2.3 (git 2.39.1) at 2025-01-10 12:34:00 +0000