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newlib-cygwin/newlib/libc/stdlib/dtoa.c
Matt Joyce ea99f21ce6 Add --enable-newlib-reent-thread-local option 
By default, Newlib uses a huge object of type struct _reent to store
thread-specific data.  This object is returned by __getreent() if the
__DYNAMIC_REENT__ Newlib configuration option is defined.

The reentrancy structure contains for example errno and the standard input,
output, and error file streams.  This means that if an application only uses
errno it has a dependency on the file stream support even if it does not use
it.  This is an issue for lower end targets and applications which need to
qualify the software according to safety standards (for example ECSS-E-ST-40C,
ECSS-Q-ST-80C, IEC 61508, ISO 26262, DO-178, DO-330, DO-333).

If the new _REENT_THREAD_LOCAL configuration option is enabled, then struct
_reent is replaced by dedicated thread-local objects for each struct _reent
member.  The thread-local objects are defined in translation units which use
the corresponding object.
2022-07-13 06:55:46 +02:00

864 lines
18 KiB
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/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991 by AT&T.
*
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
* is included in all copies of any software which is or includes a copy
* or modification of this software and in all copies of the supporting
* documentation for such software.
*
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*
***************************************************************/
/* Please send bug reports to
David M. Gay
AT&T Bell Laboratories, Room 2C-463
600 Mountain Avenue
Murray Hill, NJ 07974-2070
U.S.A.
dmg@research.att.com or research!dmg
*/
#include <_ansi.h>
#include <stdlib.h>
#include <reent.h>
#include <string.h>
#include "mprec.h"
#ifdef _REENT_THREAD_LOCAL
_Thread_local struct _Bigint *_tls_mp_result;
_Thread_local int _tls_mp_result_k;
#endif
static int
quorem (_Bigint * b, _Bigint * S)
{
int n;
__Long borrow, y;
__ULong carry, q, ys;
__ULong *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
__Long z;
__ULong si, zs;
#endif
n = S->_wds;
#ifdef DEBUG
/*debug*/ if (b->_wds > n)
/*debug*/ Bug ("oversize b in quorem");
#endif
if (b->_wds < n)
return 0;
sx = S->_x;
sxe = sx + --n;
bx = b->_x;
bxe = bx + n;
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
#ifdef DEBUG
/*debug*/ if (q > 9)
/*debug*/ Bug ("oversized quotient in quorem");
#endif
if (q)
{
borrow = 0;
carry = 0;
do
{
#ifdef Pack_32
si = *sx++;
ys = (si & 0xffff) * q + carry;
zs = (si >> 16) * q + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
z = (*bx >> 16) - (zs & 0xffff) + borrow;
borrow = z >> 16;
Sign_Extend (borrow, z);
Storeinc (bx, z, y);
#else
ys = *sx++ * q + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
*bx++ = y & 0xffff;
#endif
}
while (sx <= sxe);
if (!*bxe)
{
bx = b->_x;
while (--bxe > bx && !*bxe)
--n;
b->_wds = n;
}
}
if (cmp (b, S) >= 0)
{
q++;
borrow = 0;
carry = 0;
bx = b->_x;
sx = S->_x;
do
{
#ifdef Pack_32
si = *sx++;
ys = (si & 0xffff) + carry;
zs = (si >> 16) + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
z = (*bx >> 16) - (zs & 0xffff) + borrow;
borrow = z >> 16;
Sign_Extend (borrow, z);
Storeinc (bx, z, y);
#else
ys = *sx++ + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
*bx++ = y & 0xffff;
#endif
}
while (sx <= sxe);
bx = b->_x;
bxe = bx + n;
if (!*bxe)
{
while (--bxe > bx && !*bxe)
--n;
b->_wds = n;
}
}
return q;
}
/* 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. 92-101].
*
* 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 *
_dtoa_r (struct _reent *ptr,
double _d,
int mode,
int ndigits,
int *decpt,
int *sign,
char **rve)
{
/* 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 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, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0,
k_check, leftright, m2, m5, s2, s5, spec_case, try_quick;
union double_union d, d2, eps;
__Long L;
#ifndef Sudden_Underflow
int denorm;
__ULong x;
#endif
_Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
double ds;
char *s, *s0;
d.d = _d;
_REENT_CHECK_MP(ptr);
if (_REENT_MP_RESULT(ptr))
{
_REENT_MP_RESULT(ptr)->_k = _REENT_MP_RESULT_K(ptr);
_REENT_MP_RESULT(ptr)->_maxwds = 1 << _REENT_MP_RESULT_K(ptr);
Bfree (ptr, _REENT_MP_RESULT(ptr));
_REENT_MP_RESULT(ptr) = 0;
}
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 = 9999;
s =
#ifdef IEEE_Arith
!word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" :
#endif
"NaN";
if (rve)
*rve =
#ifdef IEEE_Arith
s[3] ? s + 8 :
#endif
s + 3;
return s;
}
#endif
#ifdef IBM
d.d += 0; /* normalize */
#endif
if (!d.d)
{
*decpt = 1;
s = "0";
if (rve)
*rve = s + 1;
return s;
}
b = d2b (ptr, d.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
d2.d = d.d;
word0 (d2) &= Frac_mask1;
word0 (d2) |= Exp_11;
#ifdef IBM
if (j = 11 - hi0bits (word0 (d2) & Frac_mask))
d2.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.)
*/
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);
#if defined (_DOUBLE_IS_32BITS)
x = word0 (d) << (32 - i);
#else
x = (i > 32) ? (word0 (d) << (64 - i)) | (word1 (d) >> (i - 32))
: (word1 (d) << (32 - i));
#endif
d2.d = x;
word0 (d2) -= 31 * Exp_msk1; /* adjust exponent */
i -= (Bias + (P - 1) - 1) + 1;
denorm = 1;
}
#endif
#if defined (_DOUBLE_IS_32BITS)
ds = (d2.d - 1.5) * 0.289529651 + 0.176091269 + i * 0.30103001;
#else
ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
#endif
k = (int) ds;
if (ds < 0. && ds != k)
k--; /* want k = floor(ds) */
k_check = 1;
if (k >= 0 && k <= Ten_pmax)
{
if (d.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;
ilim = ilim1 = -1;
switch (mode)
{
case 0:
case 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;
}
j = sizeof (__ULong);
for (_REENT_MP_RESULT_K(ptr) = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i;
j <<= 1)
_REENT_MP_RESULT_K(ptr)++;
_REENT_MP_RESULT(ptr) = eBalloc (ptr, _REENT_MP_RESULT_K(ptr));
s = s0 = (char *) _REENT_MP_RESULT(ptr);
if (ilim >= 0 && ilim <= Quick_max && try_quick)
{
/* Try to get by with floating-point arithmetic. */
i = 0;
d2.d = d.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;
d.d /= bigtens[n_bigtens - 1];
ieps++;
}
for (; j; j >>= 1, i++)
if (j & 1)
{
ieps++;
ds *= bigtens[i];
}
d.d /= ds;
}
else if ((j1 = -k) != 0)
{
d.d *= tens[j1 & 0xf];
for (j = j1 >> 4; j; j >>= 1, i++)
if (j & 1)
{
ieps++;
d.d *= bigtens[i];
}
}
if (k_check && d.d < 1. && ilim > 0)
{
if (ilim1 <= 0)
goto fast_failed;
ilim = ilim1;
k--;
d.d *= 10.;
ieps++;
}
eps.d = ieps * d.d + 7.;
word0 (eps) -= (P - 1) * Exp_msk1;
if (ilim == 0)
{
S = mhi = 0;
d.d -= 5.;
if (d.d > eps.d)
goto one_digit;
if (d.d < -eps.d)
goto no_digits;
goto fast_failed;
}
#ifndef No_leftright
if (leftright)
{
/* Use Steele & White method of only
* generating digits needed.
*/
eps.d = 0.5 / tens[ilim - 1] - eps.d;
for (i = 0;;)
{
L = d.d;
d.d -= L;
*s++ = '0' + (int) L;
if (d.d < eps.d)
goto ret1;
if (1. - d.d < eps.d)
goto bump_up;
if (++i >= ilim)
break;
eps.d *= 10.;
d.d *= 10.;
}
}
else
{
#endif
/* Generate ilim digits, then fix them up. */
eps.d *= tens[ilim - 1];
for (i = 1;; i++, d.d *= 10.)
{
L = d.d;
d.d -= L;
*s++ = '0' + (int) L;
if (i == ilim)
{
if (d.d > 0.5 + eps.d)
goto bump_up;
else if (d.d < 0.5 - eps.d)
{
while (*--s == '0');
s++;
goto ret1;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = s0;
d.d = d2.d;
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 || d.d <= 5 * ds)
goto no_digits;
goto one_digit;
}
for (i = 1;; i++)
{
L = d.d / ds;
d.d -= L * ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (d.d < 0)
{
L--;
d.d += ds;
}
#endif
*s++ = '0' + (int) L;
if (i == ilim)
{
d.d += d.d;
if ((d.d > ds) || ((d.d == ds) && (L & 1)))
{
bump_up:
while (*--s == '9')
if (s == s0)
{
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
if (!(d.d *= 10.))
break;
}
goto ret1;
}
m2 = b2;
m5 = b5;
mhi = mlo = 0;
if (leftright)
{
if (mode < 2)
{
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
}
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 (ptr, 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 (ptr, mhi, m5);
b1 = mult (ptr, mhi, b);
Bfree (ptr, b);
b = b1;
}
if ((j = b5 - m5) != 0)
b = pow5mult (ptr, b, j);
}
else
b = pow5mult (ptr, b, b5);
}
S = i2b (ptr, 1);
if (s5 > 0)
S = pow5mult (ptr, S, s5);
/* Check for special case that d is a normalized power of 2. */
spec_case = 0;
if (mode < 2)
{
if (!word1 (d) && !(word0 (d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0 (d) & Exp_mask
#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 (ptr, b, b2);
if (s2 > 0)
S = lshift (ptr, S, s2);
if (k_check)
{
if (cmp (b, S) < 0)
{
k--;
b = multadd (ptr, b, 10, 0); /* we botched the k estimate */
if (leftright)
mhi = multadd (ptr, mhi, 10, 0);
ilim = ilim1;
}
}
if (ilim <= 0 && mode > 2)
{
if (ilim < 0 || cmp (b, S = multadd (ptr, 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 (ptr, mhi, m2);
/* Compute mlo -- check for special case
* that d is a normalized power of 2.
*/
mlo = mhi;
if (spec_case)
{
mhi = eBalloc (ptr, mhi->_k);
Bcopy (mhi, mlo);
mhi = lshift (ptr, 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 (ptr, S, mhi);
j1 = delta->_sign ? 1 : cmp (b, delta);
Bfree (ptr, delta);
#ifndef ROUND_BIASED
if (j1 == 0 && !mode && !(word1 (d) & 1))
{
if (dig == '9')
goto round_9_up;
if (j > 0)
dig++;
*s++ = dig;
goto ret;
}
#endif
if ((j < 0) || ((j == 0) && !mode
#ifndef ROUND_BIASED
&& !(word1 (d) & 1)
#endif
))
{
if (j1 > 0)
{
b = lshift (ptr, b, 1);
j1 = cmp (b, S);
if (((j1 > 0) || ((j1 == 0) && (dig & 1)))
&& dig++ == '9')
goto round_9_up;
}
*s++ = dig;
goto ret;
}
if (j1 > 0)
{
if (dig == '9')
{ /* possible if i == 1 */
round_9_up:
*s++ = '9';
goto roundoff;
}
*s++ = dig + 1;
goto ret;
}
*s++ = dig;
if (i == ilim)
break;
b = multadd (ptr, b, 10, 0);
if (mlo == mhi)
mlo = mhi = multadd (ptr, mhi, 10, 0);
else
{
mlo = multadd (ptr, mlo, 10, 0);
mhi = multadd (ptr, mhi, 10, 0);
}
}
}
else
for (i = 1;; i++)
{
*s++ = dig = quorem (b, S) + '0';
if (i >= ilim)
break;
b = multadd (ptr, b, 10, 0);
}
/* Round off last digit */
b = lshift (ptr, 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
{
while (*--s == '0');
s++;
}
ret:
Bfree (ptr, S);
if (mhi)
{
if (mlo && mlo != mhi)
Bfree (ptr, mlo);
Bfree (ptr, mhi);
}
ret1:
Bfree (ptr, b);
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
return s0;
}
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