4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync/* $NetBSD: dtoa.c,v 1.3.4.1.4.1 2008/04/08 21:10:55 jdc Exp $ */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync/****************************************************************
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncThe author of this software is David M. Gay.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncCopyright (C) 1998, 1999 by Lucent Technologies
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncAll Rights Reserved
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncPermission to use, copy, modify, and distribute this software and
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncits documentation for any purpose and without fee is hereby
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncgranted, provided that the above copyright notice appear in all
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsynccopies and that both that the copyright notice and this
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncpermission notice and warranty disclaimer appear in supporting
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncdocumentation, and that the name of Lucent or any of its entities
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncnot be used in advertising or publicity pertaining to
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncdistribution of the software without specific, written prior
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncLUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncINCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncIN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncSPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncWHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncIN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsyncTHIS SOFTWARE.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync****************************************************************/
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync/* Please send bug reports to David M. Gay (dmg at acm dot org,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * with " at " changed at "@" and " dot " changed to "."). */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * Inspired by "How to Print Floating-Point Numbers Accurately" by
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * Modifications:
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * 1. Rather than iterating, we use a simple numeric overestimate
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * to determine k = floor(log10(d)). We scale relevant
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * quantities using O(log2(k)) rather than O(k) multiplications.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * try to generate digits strictly left to right. Instead, we
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * compute with fewer bits and propagate the carry if necessary
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * when rounding the final digit up. This is often faster.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * 3. Under the assumption that input will be rounded nearest,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * That is, we allow equality in stopping tests when the
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * round-nearest rule will give the same floating-point value
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * as would satisfaction of the stopping test with strict
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * inequality.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * 4. We remove common factors of powers of 2 from relevant
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * quantities.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * 5. When converting floating-point integers less than 1e16,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * we use floating-point arithmetic rather than resorting
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * to multiple-precision integers.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * 6. When asked to produce fewer than 15 digits, we first try
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * to get by with floating-point arithmetic; we resort to
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * multiple-precision integer arithmetic only if we cannot
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * guarantee that the floating-point calculation has given
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * the correctly rounded result. For k requested digits and
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * "uniformly" distributed input, the probability is
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * something like 10^(k-15) that we must resort to the Long
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * calculation.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync// Disable: warning C4700: uninitialized local variable 'xx' used
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync#endif /* defined(_MSC_VER) */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync double d; int mode, ndigits, *decpt, *sign; char **rve;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Arguments ndigits, decpt, sign are similar to those
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync of ecvt and fcvt; trailing zeros are suppressed from
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync the returned string. If not null, *rve is set to point
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync to the end of the return value. If d is +-Infinity or NaN,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync then *decpt is set to 9999.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 0 ==> shortest string that yields d when read in
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync and rounded to nearest.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 1 ==> like 0, but with Steele & White stopping rule;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync e.g. with IEEE P754 arithmetic , mode 0 gives
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 1e23 whereas mode 1 gives 9.999999999999999e22.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 2 ==> max(1,ndigits) significant digits. This gives a
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync return value similar to that of ecvt, except
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync that trailing zeros are suppressed.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 3 ==> through ndigits past the decimal point. This
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync gives a return value similar to that from fcvt,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync except that trailing zeros are suppressed, and
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync ndigits can be negative.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 4,5 ==> similar to 2 and 3, respectively, but (in
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync round-nearest mode) with the tests of mode 0 to
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync possibly return a shorter string that rounds to d.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync With IEEE arithmetic and compilation with
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync as modes 2 and 3 when FLT_ROUNDS != 1.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 6-9 ==> Debugging modes similar to mode - 4: don't try
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync fast floating-point estimate (if applicable).
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync Values of mode other than 0-9 are treated as mode 0.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync Sufficient space is allocated to the return value
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync to hold the suppressed trailing zeros.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* set sign for everything, including 0's and NaNs */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Infinity or NaN */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (( i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)) )!=0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (( j = 11 - hi0bits(word0(d2) & Frac_mask) )!=0)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * log10(x) = log(x) / log(10)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * This suggests computing an approximation k to log10(d) by
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * k = (i - Bias)*0.301029995663981
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * We want k to be too large rather than too small.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * The error in the first-order Taylor series approximation
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * is in our favor, so we just round up the constant enough
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * to compensate for any error in the multiplication of
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * adding 1e-13 to the constant term more than suffices.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * Hence we adjust the constant term to 0.1760912590558.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * (We could get a more accurate k by invoking log10,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * but this is probably not worthwhile.)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* d is denormalized */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync k--; /* want k = floor(ds) */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (k >= 0 && k <= Ten_pmax) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (j >= 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (k >= 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync#endif /*SET_INEXACT*/
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* FALLTHROUGH */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* FALLTHROUGH */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (i <= 0)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Try to get by with floating-point arithmetic. */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (k > 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync j = (unsigned int)k >> 4;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* prevent overflows */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync for(; j; j = (unsigned int)j >> 1, i++)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (j & 1) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync else if (( jj1 = -k )!=0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (j & 1) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (ilim == 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Use Steele & White method of only
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * generating digits needed.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync for(i = 0;;) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = (char)('0' + (int)L);
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (++i >= ilim)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Generate ilim digits, then fix them up. */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (!(dval(d) -= L))
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = (char)('0' + (int)L);
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (i == ilim) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(*--s == '0');
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Do we have a "small" integer? */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* If FLT_ROUNDS == 2, L will usually be high by 1 */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (dval(d) < 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = (char)('0' + (int)L);
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (i == ilim) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync case 0: goto ret1;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(*--s == '9')
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (s == s0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Check for special case that d is a normalized power of 2. */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* The special case */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Arrange for convenient computation of quotients:
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * shift left if necessary so divisor has 4 leading 0 bits.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * Perhaps we should just compute leading 28 bits of S once
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * and for all and pass them and a shift to quorem, so it
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * can do shifts and ors to compute the numerator for q.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f )!=0)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync i = 32 - i;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf )!=0)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync i = 16 - i;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (i > 4) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync else if (i < 4) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (cmp(b,S) < 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync b = multadd(b, 10, 0); /* we botched the k estimate */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* no digits, fcvt style */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = '1';
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Compute mlo -- check for special case
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * that d is a normalized power of 2.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync for(i = 1;;i++) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Do we yet have the shortest decimal string
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync * that will round to d?
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = (char)dig;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync case 0: goto accept_dig;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync#endif /*Honor_FLT_ROUNDS*/
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = (char)dig;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = '9';
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = (char)dig;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync for(i = 1;; i++) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Round off last digit */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync case 0: goto trimzeros;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(*--s == '9')
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (s == s0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = '1';
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(*--s == '0');
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = '0';