mirror of
https://github.com/ZDoom/gzdoom.git
synced 2024-11-16 01:11:50 +00:00
755 lines
16 KiB
C
755 lines
16 KiB
C
|
/****************************************************************
|
||
|
|
|
||
|
|
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"
|
||
|
|
#include <limits.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 INT_MAX.
|
||
|
|
|
||
|
|
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 = INT_MAX;
|
||
|
|
#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 = (Long)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;
|
||
|
|
}
|