4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync/* $NetBSD: gdtoa.c,v 1.1.1.1.4.1.4.1 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 /* Disable warnings about conversions to narrower data types. */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync // Squelch bogus warnings about uninitialized variable use.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(i < nbits) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync x = x0 = b->x;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(!x0[--i])
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 (FPI *fpi, int be, ULong *bits, int *kindp, int mode, int ndigits, int *decpt, char **rve)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Arguments ndigits and decpt are similar to the second and third
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync arguments 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 4-9 should give the same return values as 2-3, i.e.,
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 4 <= mode <= 9 ==> same return as mode
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 2 + (mode & 1). These modes are mainly for
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync debugging; often they run slower but sometimes
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync faster than modes 2-3.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 4,5,8,9 ==> left-to-right digit generation.
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 6-9 ==> don't try fast floating-point estimate
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync (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 int bbits, b2, b5, be0, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, inex;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync int j, jj1, k, k0, k_check, kind, leftright, m2, m5, nbits;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if ( (i = trailz(b)) !=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 ds = (dval(d)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* correct assumption about exponent range */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if ((j = i) < 0)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if ((j -= 1077) > 0)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync k--; /* want k = floor(ds) */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (k >= 0 && k <= Ten_pmax) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (j >= 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (k >= 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /*FALLTHROUGH*/
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /*FALLTHROUGH*/
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (i <= 0)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Now rdir = 0 ==> round near, 1 ==> round up, 2 ==> round down. */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (ilim >= 0 && ilim <= Quick_max && try_quick && !rdir
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 /= 2, i++)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (j & 1) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync 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++ = '0' + (int)L;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (++i >= ilim)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Generate ilim digits, then fix them up. */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = '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++ = '0' + (int)L;
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (dval(d) == 0.)
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (i == ilim) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(*--s == '9')
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (s == s0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* denormal */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if ((i = ilim) < 0) {
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 if (jj1 == 0 && !mode && !(bits[0] & 1) && !rdir) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (j <= 0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (j < 0 || (j == 0 && !mode
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = '9';
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync for(i = 1;; i++) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync /* Round off last digit */
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(*--s == '9')
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync if (s == s0) {
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync *s++ = '1';
4fd606d1f5abe38e1f42c38de1d2e895166bd0f4vboxsync while(*--s == '0'){}