cosmopolitan/third_party/gdtoa/gdtoa.c
Justine Tunney d5312b60f7 Make improvements to locking
This change makes pthread_mutex_lock() as fast as _spinlock() by
default. Thread instability issues on NetBSD have been resolved.
Improvements made to gdtoa thread code. Crash reporting will now
synchronize between threads in a slightly better way.
2022-06-19 01:30:12 -07:00

686 lines
19 KiB
C

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│ │
│ The author of this software is David M. Gay. │
│ Please send bug reports to David M. Gay <dmg@acm.org> │
│ or Justine Tunney <jtunney@gmail.com> │
│ │
│ 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. │
│ │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "third_party/gdtoa/gdtoa.internal.h"
/* clang-format off */
static Bigint *
bitstob(ULong *bits, int nbits, int *bbits, ThInfo **PTI)
{
int i, k;
Bigint *b;
ULong *be, *x, *x0;
i = ULbits;
k = 0;
while(i < nbits) {
i <<= 1;
k++;
}
b = __gdtoa_Balloc(k, PTI);
be = bits + ((nbits - 1) >> kshift);
x = x0 = b->x;
do {
*x++ = *bits & ALL_ON;
} 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) __gdtoa_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 as__gdtoa_sumption 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 __gdtoa_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
* __gdtoa_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(const FPI *fpi, int be, ULong *bits, int *kindp, int mode, int ndigits, int *decpt, char **rve)
{
/* 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.
be = exponent: value = (integer represented by bits) * (2 to the power of be).
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 gene__gdtoa_ration.
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.
*/
ThInfo *TI = 0;
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 d2, ds;
char *s, *s0;
U d, eps;
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 __gdtoa_nrv_alloc("Infinity", rve, 8, &TI);
case STRTOG_NaN:
*decpt = -32768;
return __gdtoa_nrv_alloc("NaN", rve, 3, &TI);
default:
return 0;
}
b = bitstob(bits, nbits = fpi->nbits, &bbits, &TI);
be0 = be;
if ( (i = __gdtoa_trailz(b)) !=0) {
__gdtoa_rshift(b, i);
be += i;
bbits -= i;
}
if (!b->wds) {
__gdtoa_Bfree(b, &TI);
ret_zero:
*decpt = 1;
return __gdtoa_nrv_alloc("0", rve, 1, &TI);
}
dval(&d) = __gdtoa_b2d(b, &i);
i = be + bbits - 1;
word0(&d) &= Frac_mask1;
word0(&d) |= Exp_11;
/* 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 __gdtoa_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.)
*/
ds = (dval(&d)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
/* correct as__gdtoa_sumption 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;
// TODO: word0(&d) += (be + bbits - 1) << Exp_shift;
// error: third_party/gdtoa/gdtoa.c:244: left shift of negative value -6 'int' 20 'int'
// 4161d8: __die at libc/log/die.c:33
// 463165: __ubsan_abort at libc/intrin/ubsan.c:270
// 4632d6: __ubsan_handle_shift_out_of_bounds at libc/intrin/ubsan.c:299
// 421d42: gdtoa at third_party/gdtoa/gdtoa.c:244
// 420449: g_dfmt_p at third_party/gdtoa/g_dfmt_p.c:105
// 413947: ConvertMatrixToStringTable at tool/viz/lib/formatmatrix-double.c:40
// 413a5f: FormatMatrixDouble at tool/viz/lib/formatmatrix-double.c:55
// 413b13: StringifyMatrixDouble at tool/viz/lib/formatmatrix-double.c:65
// 464923: GetChromaticAdaptationMatrix_testD65ToD50_soWeCanCieLab at test/dsp/core/illumination_test.c:39
// 4650c2: testlib_runtestcases at libc/testlib/testrunner.c:94
// 464676: testlib_runalltests at libc/testlib/runner.c:37
// 46455e: main at libc/testlib/testmain.c:84
// 401d30: cosmo at libc/runtime/cosmo.S:65
// 401173: _start at libc/crt/crt.S:67
word0(&d) += (unsigned)(be + bbits - 1) << Exp_shift;
if (k >= 0 && k <= Ten_pmax) {
if (dval(&d) < __gdtoa_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;
}
else if (i >= -4 - Emin || i < Emin)
try_quick = 0;
leftright = 1;
ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */
/* silence erroneous "gcc -Wall" warning. */
switch(mode) {
case 0:
case 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 = __gdtoa_rv_alloc(i, &TI);
if (mode <= 1)
rdir = 0;
else 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 && k == 0) {
/* Try to get by with floating-point arithmetic. */
i = 0;
d2 = dval(&d);
k0 = k;
ilim0 = ilim;
ieps = 2; /* conservative */
if (k > 0) {
ds = __gdtoa_tens[k&0xf];
j = k >> 4;
if (j & Bletch) {
/* prevent overflows */
j &= Bletch - 1;
dval(&d) /= __gdtoa_bigtens[n___gdtoa_bigtens-1];
ieps++;
}
for(; j; j >>= 1, i++)
if (j & 1) {
ieps++;
ds *= __gdtoa_bigtens[i];
}
}
else {
ds = 1.;
if ( (j1 = -k) !=0) {
dval(&d) *= __gdtoa_tens[j1 & 0xf];
for(j = j1 >> 4; j; j >>= 1, i++)
if (j & 1) {
ieps++;
dval(&d) *= __gdtoa_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;
}
if (leftright) {
/* Use Steele & White method of only
* generating digits needed.
*/
dval(&eps) = ds*0.5/__gdtoa_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 {
/* Generate ilim digits, then fix them up. */
dval(&eps) *= __gdtoa_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)) {
if (dval(&d))
inex = STRTOG_Inexlo;
goto ret1;
}
break;
}
}
}
fast_failed:
s = s0;
dval(&d) = d2;
k = k0;
ilim = ilim0;
}
/* Do we have a "small" integer? */
if (be >= 0 && k <= fpi->int_max) {
/* Yes. */
ds = __gdtoa_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;
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (dval(&d) < 0) {
L--;
dval(&d) += ds;
}
*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) {
i = nbits - bbits;
if (be - i++ < fpi->emin && mode != 3 && mode != 5) {
/* denormal */
i = be - fpi->emin + 1;
if (mode >= 2 && ilim > 0 && ilim < i)
goto small_ilim;
}
else if (mode >= 2) {
small_ilim:
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 = __gdtoa_i2b(1, &TI);
}
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 = __gdtoa_pow5mult(mhi, m5, &TI);
b1 = __gdtoa_mult(mhi, b, &TI);
__gdtoa_Bfree(b, &TI);
b = b1;
}
if ( (j = b5 - m5) !=0)
b = __gdtoa_pow5mult(b, j, &TI);
}
else
b = __gdtoa_pow5mult(b, b5, &TI);
}
S = __gdtoa_i2b(1, &TI);
if (s5 > 0)
S = __gdtoa_pow5mult(S, s5, &TI);
/* 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 __gdtoa_quorem, so it
* can do shifts and ors to compute the numerator for q.
*/
i = ((s5 ? hi0bits(S->x[S->wds-1]) : ULbits - 1) - s2 - 4) & kmask;
m2 += i;
if ((b2 += i) > 0)
b = __gdtoa_lshift(b, b2, &TI);
if ((s2 += i) > 0)
S = __gdtoa_lshift(S, s2, &TI);
if (k_check) {
if (__gdtoa_cmp(b,S) < 0) {
k--;
b = __gdtoa_multadd(b, 10, 0, &TI); /* we botched the k estimate */
if (leftright)
mhi = __gdtoa_multadd(mhi, 10, 0, &TI);
ilim = ilim1;
}
}
if (ilim <= 0 && mode > 2) {
if (ilim < 0 || __gdtoa_cmp(b,S = __gdtoa_multadd(S,5,0,&TI)) <= 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 = __gdtoa_lshift(mhi, m2, &TI);
/* Compute mlo -- check for special case
* that d is a normalized power of 2.
*/
mlo = mhi;
if (spec_case) {
mhi = __gdtoa_Balloc(mhi->k, &TI);
Bcopy(mhi, mlo);
mhi = __gdtoa_lshift(mhi, 1, &TI);
}
for(i = 1;;i++) {
dig = __gdtoa_quorem(b,S) + '0';
/* Do we yet have the shortest decimal string
* that will round to d?
*/
j = __gdtoa_cmp(b, mlo);
delta = __gdtoa_diff(S, mhi, &TI);
j1 = delta->sign ? 1 : __gdtoa_cmp(b, delta);
__gdtoa_Bfree(delta, &TI);
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;
}
if (j < 0 || (j == 0 && !mode && !(bits[0] & 1))) {
if (rdir && (b->wds > 1 || b->x[0])) {
if (rdir == 2) {
inex = STRTOG_Inexlo;
goto accept;
}
while (__gdtoa_cmp(S,mhi) > 0) {
*s++ = dig;
mhi1 = __gdtoa_multadd(mhi, 10, 0, &TI);
if (mlo == mhi)
mlo = mhi1;
mhi = mhi1;
b = __gdtoa_multadd(b, 10, 0, &TI);
dig = __gdtoa_quorem(b,S) + '0';
}
if (dig++ == '9')
goto round_9_up;
inex = STRTOG_Inexhi;
goto accept;
}
if (j1 > 0) {
b = __gdtoa_lshift(b, 1, &TI);
j1 = __gdtoa_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 = __gdtoa_multadd(b, 10, 0, &TI);
if (mlo == mhi)
mlo = mhi = __gdtoa_multadd(mhi, 10, 0, &TI);
else {
mlo = __gdtoa_multadd(mlo, 10, 0, &TI);
mhi = __gdtoa_multadd(mhi, 10, 0, &TI);
}
}
}
else
for(i = 1;; i++) {
*s++ = dig = __gdtoa_quorem(b,S) + '0';
if (i >= ilim)
break;
b = __gdtoa_multadd(b, 10, 0, &TI);
}
/* Round off last digit */
if (rdir) {
if (rdir == 2 || (b->wds <= 1 && !b->x[0]))
goto chopzeros;
goto roundoff;
}
b = __gdtoa_lshift(b, 1, &TI);
j = __gdtoa_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;
}
ret:
__gdtoa_Bfree(S, &TI);
if (mhi) {
if (mlo && mlo != mhi)
__gdtoa_Bfree(mlo, &TI);
__gdtoa_Bfree(mhi, &TI);
}
ret1:
while(s > s0 && s[-1] == '0')
--s;
__gdtoa_Bfree(b, &TI);
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
*kindp |= inex;
return s0;
}