File dtoa.c¶
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/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991, 2006 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 <string.h>
#include <stdlib.h>
#include "mprec.h"
#include <stdlib.h>
#ifdef DEBUG
#include <stdio.h>
#endif
// XXX: SHOULD BE THE LAST INCLUDE HEADER
#include "memory_wrapper.hpp"
void free_Bigints (struct _Jv_Bigint *p);
static int
_DEFUN (quorem, (b, S), _Jv_Bigint * b _AND _Jv_Bigint * S)
{
int n;
long borrow, y;
unsigned long carry, q, ys;
unsigned long *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
long z;
unsigned long 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;
}
#ifdef DEBUG
void
print (_Jv_Bigint * b)
{
int i, wds;
unsigned long *x, y;
wds = b->_wds;
x = b->_x + wds;
i = 0;
do
{
x--;
fprintf (stderr, "%08x", *x);
}
while (++i < wds);
fprintf (stderr, "\n");
}
#endif
/* 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 *
_DEFUN (_dtoa_r, (ptr, _d, mode, ndigits, decpt, sign, rve, float_type),
struct _Jv_reent *ptr _AND double _d _AND int mode _AND int ndigits _AND int *decpt _AND int *sign _AND char
**rve _AND int float_type)
{
/*
* float_type == 0 for double precision, 1 for float.
*
* 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).
*
* > 16 ==> Floating-point arg is treated as single precision.
*
* 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, ilim0, j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, try_quick;
int ilim = 0, ilim1 = 0, spec_case = 0;
union double_union d, d2, eps;
long L;
#ifndef Sudden_Underflow
int denorm;
unsigned long x;
#endif
_Jv_Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
double ds;
char *s, *s0;
static char infinity_p[] = "Infinity", NaN_p[] = "NaN", zero_p[] = "0";
d.d = _d;
if (ptr->_result)
{
ptr->_result->_k = ptr->_result_k;
ptr->_result->_maxwds = 1 << ptr->_result_k;
Bfree (ptr, ptr->_result);
ptr->_result = 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_p :
#endif
NaN_p;
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 = zero_p; /* "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))))
{
#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 + (PREC - 1) - 1);
x = i > 32 ? word0 (d) << (64 - i) | word1 (d) >> (i - 32) : word1 (d) << (32 - i);
d2.d = x;
word0 (d2) -= 31 * Exp_msk1; /* adjust exponent */
i -= (Bias + (PREC - 1) - 1) + 1;
denorm = 1;
}
#endif
ds = (d2.d - 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 (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;
switch (mode)
{
case 0:
case 1:
ilim = ilim1 = -1;
i = 18;
ndigits = 0;
break;
case 2:
leftright = 0;
[[fallthrough]];
case 4:
if (ndigits <= 0)
ndigits = 1;
ilim = ilim1 = i = ndigits;
break;
case 3:
leftright = 0;
[[fallthrough]];
case 5:
i = ndigits + k + 1;
ilim = i;
ilim1 = i - 1;
if (i <= 0)
i = 1;
}
j = sizeof (unsigned long);
for (ptr->_result_k = 0; (int) (sizeof (_Jv_Bigint) - sizeof (unsigned long)) + j <= i; j <<= 1)
ptr->_result_k++;
ptr->_result = Balloc (ptr, ptr->_result_k);
s = s0 = (char *) ptr->_result;
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))
{
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) -= (PREC - 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 = (long) 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 = (long) 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 = (long) (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 + (PREC - 1) - 1 + 1) :
#endif
#ifdef IBM
1 + 4 * PREC - 3 - bbits + ((bbits + be - 1) & 3);
#else
1 + PREC - 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))
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. */
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;
}
else
spec_case = 0;
}
/* 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))
i = 32 - i;
#else
if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf))
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);
/* Single precision case, */
if (float_type)
mhi = lshift (ptr, mhi, 29);
/* Compute mlo -- check for special case that d is a normalized power of 2. */
mlo = mhi;
if (spec_case)
{
mhi = Balloc (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;
}
void
free_Bigints (struct _Jv_Bigint *p)
{
struct _Jv_Bigint *l = p;
while (l)
{
struct _Jv_Bigint *next = l->_next;
free (l);
l = next;
}
}
_VOID
_DEFUN (_dtoa, (_d, mode, ndigits, decpt, sign, rve, buf, float_type),
double _d _AND int mode _AND int ndigits _AND int *decpt _AND int *sign _AND char **rve _AND char *buf _AND int
float_type)
{
struct _Jv_reent reent;
char *p;
int i;
memset (&reent, 0, sizeof reent);
p = _dtoa_r (&reent, _d, mode, ndigits, decpt, sign, rve, float_type);
strcpy (buf, p);
for (i = 0; i < reent._max_k; ++i)
{
free_Bigints (reent._freelist[i]);
}
if (reent._freelist)
{
free (reent._freelist);
}
if (reent._result)
{
free (reent._result);
}
free_Bigints (reent._p5s);
}