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nuttx/libs/libc/stdio/legacy_dtoa.c

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/****************************************************************************
* libs/libc/stdio/legacy_dtoa.c
*
* This file was ported to NuttX by Yolande Cates.
*
* Copyright (c) 1990, 1993
* The Regents of the University of California. All rights reserved.
*
* This code is derived from software contributed to Berkeley by
* Chris Torek.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the University of
* California, Berkeley and its contributors.
* 4. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
****************************************************************************/
/****************************************************************************
* Included Files
****************************************************************************/
#include <nuttx/config.h>
#include <stdint.h>
#include <string.h>
#include "libc.h"
/****************************************************************************
* Pre-processor Definitions
****************************************************************************/
#ifdef CONFIG_DTOA_UNSIGNED_SHIFTS
# define SIGN_EXTEND(a,b) if (b < 0) a |= 0xffff0000;
#else
# define SIGN_EXTEND(a,b) /* no-op */
#endif
#ifdef CONFIG_ENDIAN_BIG
# define WORD0(x) ((uint32_t *)&x)[0]
# define WORD1(x) ((uint32_t *)&x)[1]
#else
# define WORD0(x) ((uint32_t *)&x)[1]
# define WORD1(x) ((uint32_t *)&x)[0]
#endif
#ifdef CONFIG_ENDIAN_BIG
# define STOREINC(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
((unsigned short *)a)[1] = (unsigned short)c, a++)
#else
# define STOREINC(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
((unsigned short *)a)[0] = (unsigned short)c, a++)
#endif
#define EXP_SHIFT 20
#define EXP_SHIFT1 20
#define EXP_MSK1 0x100000
#define EXP_MSK11 0x100000
#define EXP_MASK 0x7ff00000
#define P 53
#define BIAS 1023
#define IEEE_ARITH
#define EMIN (-1022)
#define EXP_1 0x3ff00000
#define EXP_11 0x3ff00000
#define EBITS 11
#define FRAC_MASK 0xfffff
#define FRAC_MASK1 0xfffff
#define TEN_PMAX 22
#define BLETCH 0x10
#define BNDRY_MASK 0xfffff
#define BNDRY_MASK1 0xfffff
#define LSB 1
#define SIGN_BIT 0x80000000
#define LOG2P 1
#define TINY0 0
#define TINY1 1
#define QUICK_MAX 14
#define SMALL_MAX 14
#define INFINITE(x) (WORD0(x) == 0x7ff00000) /* sufficient test for here */
#define KMAX 15
#define BCOPY(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
y->wds*sizeof(long) + 2*sizeof(int))
/****************************************************************************
* Private Type Definitions
****************************************************************************/
struct bigint_s
{
FAR struct bigint_s *next;
int k;
int maxwds;
int sign;
int wds;
unsigned long x[1];
};
typedef struct bigint_s bigint_t;
/****************************************************************************
* Private Data
****************************************************************************/
/* REVISIT: __dtoa is not thread safe due to thse two global variables.
* Options:
*
* 1. Allocate on stack. g_freelist is rather large, however.. around 275
* bytes (it could be shrunk a little by using stdint types instead of int.
* 2. Semaphore protect the global variables and handle interrupt level
* calls as a special case (perhaps refusing them? Or having a duplicate
* set of variables, one for tasks and one for interrupt usage)
*/
static FAR bigint_t *g_freelist[KMAX + 1];
static FAR bigint_t *g_p5s;
#ifdef IEEE_ARITH
static const double_t g_bigtens[] =
{
1e16, 1e32, 1e64, 1e128, 1e256
};
# define n_bigtens 5
#else
static const double_t g_bigtens[] =
{
1e16, 1e32
};
# define n_bigtens 2
#endif
/****************************************************************************
* Private Functions
****************************************************************************/
static FAR bigint_t *balloc(int k)
{
FAR bigint_t *rv;
int x;
if ((rv = g_freelist[k]))
{
g_freelist[k] = rv->next;
}
else
{
x = 1 << k;
rv = (FAR bigint_t *)
lib_malloc(sizeof(bigint_t) + (x - 1) * sizeof(long));
rv->k = k;
rv->maxwds = x;
}
rv->sign = 0;
rv->wds = 0;
return rv;
}
static void bfree(FAR bigint_t *v)
{
if (v != NULL)
{
v->next = g_freelist[v->k];
g_freelist[v->k] = v;
}
}
/* Multiply by m and add a */
static FAR bigint_t *multadd(FAR bigint_t *b, int m, int a)
{
FAR bigint_t *b1;
FAR unsigned long *x;
unsigned long y;
#ifdef CONFIG_DTOA_PACK32
unsigned long xi;
unsigned long z;
#endif
int wds;
int i;
wds = b->wds;
x = b->x;
i = 0;
do
{
#ifdef CONFIG_DTOA_PACK32
xi = *x;
y = (xi & 0xffff) * m + a;
z = (xi >> 16) * m + (y >> 16);
a = (int)(z >> 16);
*x++ = (z << 16) + (y & 0xffff);
#else
y = *x * m + a;
a = (int)(y >> 16);
*x++ = y & 0xffff;
#endif
}
while (++i < wds);
if (a != 0)
{
if (wds >= b->maxwds)
{
b1 = balloc(b->k + 1);
BCOPY(b1, b);
bfree(b);
b = b1;
}
b->x[wds++] = a;
b->wds = wds;
}
return b;
}
static int hi0bits(unsigned long x)
{
int k = 0;
if ((x & 0xffff0000) == 0)
{
k = 16;
x <<= 16;
}
if ((x & 0xff000000) == 0)
{
k += 8;
x <<= 8;
}
if ((x & 0xf0000000) == 0)
{
k += 4;
x <<= 4;
}
if ((x & 0xc0000000) == 0)
{
k += 2;
x <<= 2;
}
if ((x & 0x80000000) == 0)
{
k++;
if ((x & 0x40000000) == 0)
{
return 32;
}
}
return k;
}
static int lo0bits(FAR unsigned long *y)
{
unsigned long x = *y;
int k;
if ((x & 7) != 0)
{
if (x & 1)
{
return 0;
}
if ((x & 2) != 0)
{
*y = x >> 1;
return 1;
}
*y = x >> 2;
return 2;
}
k = 0;
if ((x & 0xffff) == 0)
{
k = 16;
x >>= 16;
}
if ((x & 0xff) == 0)
{
k += 8;
x >>= 8;
}
if ((x & 0xf) == 0)
{
k += 4;
x >>= 4;
}
if ((x & 0x3) == 0)
{
k += 2;
x >>= 2;
}
if ((x & 1) == 0)
{
k++;
x >>= 1;
if ((!x & 1) != 0)
{
return 32;
}
}
*y = x;
return k;
}
static FAR bigint_t *i2b(int i)
{
FAR bigint_t *b;
b = balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
static FAR bigint_t *mult(FAR bigint_t *a, FAR bigint_t *b)
{
FAR bigint_t *c;
FAR unsigned long *x;
FAR unsigned long *xa;
FAR unsigned long *xae;
FAR unsigned long *xb;
FAR unsigned long *xbe;
FAR unsigned long *xc;
FAR unsigned long *xc0;
unsigned long carry;
unsigned long y;
unsigned long z;
#ifdef CONFIG_DTOA_PACK32
uint32_t z2;
#endif
int k;
int wa;
int wb;
int wc;
if (a->wds < b->wds)
{
c = a;
a = b;
b = c;
}
k = a->k;
wa = a->wds;
wb = b->wds;
wc = wa + wb;
if (wc > a->maxwds)
{
k++;
}
c = balloc(k);
for (x = c->x, xa = x + wc; x < xa; x++)
{
*x = 0;
}
xa = a->x;
xae = xa + wa;
xb = b->x;
xbe = xb + wb;
xc0 = c->x;
#ifdef CONFIG_DTOA_PACK32
for (; xb < xbe; xb++, xc0++)
{
if ((y = *xb & 0xffff) != 0)
{
x = xa;
xc = xc0;
carry = 0;
do
{
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
STOREINC(xc, z2, z);
}
while (x < xae);
*xc = carry;
}
if ((y = *xb >> 16))
{
x = xa;
xc = xc0;
carry = 0;
z2 = *xc;
do
{
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
STOREINC(xc, z, z2);
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
carry = z2 >> 16;
}
while (x < xae);
*xc = z2;
}
}
#else
for (; xb < xbe; xc0++)
{
if ((y = *xb++))
{
x = xa;
xc = xc0;
carry = 0;
do
{
z = *x++ * y + *xc + carry;
carry = z >> 16;
*xc++ = z & 0xffff;
}
while (x < xae);
*xc = carry;
}
}
#endif
for (xc0 = c->x, xc = xc0 + wc; wc > 0 && *--xc == 0; --wc);
c->wds = wc;
return c;
}
static FAR bigint_t *pow5mult(FAR bigint_t *b, int k)
{
FAR bigint_t *b1;
FAR bigint_t *p5;
FAR bigint_t *p51;
static int p05[3] =
{
5, 25, 125
};
int i;
if ((i = k & 3) != 0)
{
b = multadd(b, p05[i - 1], 0);
}
if ((k >>= 2) == 0)
{
return b;
}
if ((p5 = g_p5s) == 0)
{
/* First time */
g_p5s = i2b(625);
p5 = g_p5s;
p5->next = 0;
}
for (; ; )
{
if ((k & 1) != 0)
{
b1 = mult(b, p5);
bfree(b);
b = b1;
}
if ((k >>= 1) == 0)
{
break;
}
if ((p51 = p5->next) == 0)
{
p5->next = mult(p5, p5);
p51 = p5->next;
p51->next = 0;
}
p5 = p51;
}
return b;
}
static FAR bigint_t *lshift(FAR bigint_t *b, int k)
{
FAR bigint_t *b1;
FAR unsigned long *x;
FAR unsigned long *x1;
FAR unsigned long *xe;
unsigned long z;
int i;
int k1;
int n;
int n1;
#ifdef CONFIG_DTOA_PACK32
n = k >> 5;
#else
n = k >> 4;
#endif
k1 = b->k;
n1 = n + b->wds + 1;
for (i = b->maxwds; n1 > i; i <<= 1)
{
k1++;
}
b1 = balloc(k1);
x1 = b1->x;
for (i = 0; i < n; i++)
{
*x1++ = 0;
}
x = b->x;
xe = x + b->wds;
#ifdef CONFIG_DTOA_PACK32
if ((k &= 0x1f) != 0)
{
k1 = 32 - k;
z = 0;
do
{
*x1++ = *x << k | z;
z = *x++ >> k1;
}
while (x < xe);
if ((*x1 = z) != 0)
{
++n1;
}
}
#else
if ((k &= 0xf) != 0)
{
k1 = 16 - k;
z = 0;
do
{
*x1++ = ((*x << k) & 0xffff) | z;
z = *x++ >> k1;
}
while (x < xe);
if ((*x1 = z) != 0)
{
++n1;
}
}
#endif
else
{
do
{
*x1++ = *x++;
}
while (x < xe);
}
b1->wds = n1 - 1;
bfree(b);
return b1;
}
static int cmp(FAR bigint_t *a, FAR bigint_t *b)
{
FAR unsigned long *xa;
FAR unsigned long *xa0;
FAR unsigned long *xb;
FAR unsigned long *xb0;
int i;
int j;
i = a->wds;
j = b->wds;
#ifdef CONFIG_DEBUG_LIB
if (i > 1 && a->x[i - 1] == 0)
{
lerr("ERROR: cmp called with a->x[a->wds-1] == 0\n");
}
if (j > 1 && b->x[j - 1] == 0)
{
lerr("ERROR: cmp called with b->x[b->wds-1] == 0\n");
}
#endif
if (i -= j)
{
return i;
}
xa0 = a->x;
xa = xa0 + j;
xb0 = b->x;
xb = xb0 + j;
for (; ; )
{
if (*--xa != *--xb)
{
return *xa < *xb ? -1 : 1;
}
if (xa <= xa0)
{
break;
}
}
return 0;
}
static FAR bigint_t *diff(FAR bigint_t *a, FAR bigint_t *b)
{
FAR bigint_t *c;
FAR unsigned long *xa;
FAR unsigned long *xae;
FAR unsigned long *xb;
FAR unsigned long *xbe;
FAR unsigned long *xc;
long borrow; /* We need signed shifts here. */
long y;
#ifdef CONFIG_DTOA_PACK32
int32_t z;
#endif
int i;
int wa;
int wb;
i = cmp(a, b);
if (i == 0)
{
c = balloc(0);
c->wds = 1;
c->x[0] = 0;
return c;
}
if (i < 0)
{
c = a;
a = b;
b = c;
i = 1;
}
else
{
i = 0;
}
c = balloc(a->k);
c->sign = i;
wa = a->wds;
xa = a->x;
xae = xa + wa;
wb = b->wds;
xb = b->x;
xbe = xb + wb;
xc = c->x;
borrow = 0;
#ifdef CONFIG_DTOA_PACK32
do
{
y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
borrow = y >> 16;
SIGN_EXTEND(borrow, y);
z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
borrow = z >> 16;
SIGN_EXTEND(borrow, z);
STOREINC(xc, z, y);
}
while (xb < xbe);
while (xa < xae)
{
y = (*xa & 0xffff) + borrow;
borrow = y >> 16;
SIGN_EXTEND(borrow, y);
z = (*xa++ >> 16) + borrow;
borrow = z >> 16;
SIGN_EXTEND(borrow, z);
STOREINC(xc, z, y);
}
#else
do
{
y = *xa++ - *xb++ + borrow;
borrow = y >> 16;
SIGN_EXTEND(borrow, y);
*xc++ = y & 0xffff;
}
while (xb < xbe);
while (xa < xae)
{
y = *xa++ + borrow;
borrow = y >> 16;
SIGN_EXTEND(borrow, y);
*xc++ = y & 0xffff;
}
#endif
while (*--xc == 0)
{
wa--;
}
c->wds = wa;
return c;
}
static FAR bigint_t *d2b(double_t d, int *e, int *bits)
{
FAR bigint_t *b;
FAR unsigned long *x;
unsigned long y;
unsigned long z;
int de;
int i;
int k;
#ifdef CONFIG_DTOA_PACK32
b = balloc(1);
#else
b = balloc(2);
#endif
x = b->x;
z = WORD0(d) & FRAC_MASK;
WORD0(d) &= 0x7fffffff; /* Clear sign bit, which we ignore */
de = (int)(WORD0(d) >> EXP_SHIFT);
if (de != 0)
{
z |= EXP_MSK1;
}
#ifdef CONFIG_DTOA_PACK32
if ((y = WORD1(d)) != 0)
{
if ((k = lo0bits(&y)) != 0)
{
x[0] = y | z << (32 - k);
z >>= k;
}
else
{
x[0] = y;
}
b->wds = (x[1] = z) ? 2 : 1;
i = b->wds;
}
else
{
#ifdef CONFIG_DEBUG_LIB
if (z == 0)
{
lerr("ERROR: Zero passed to d2b\n");
}
#endif
k = lo0bits(&z);
x[0] = z;
i = b->wds = 1;
k += 32;
}
#else
if ((y = WORD1(d)) != 0)
{
if ((k = lo0bits(&y)) != 0)
if (k >= 16)
{
x[0] = y | ((z << (32 - k)) & 0xffff);
x[1] = z >> (k - 16) & 0xffff;
x[2] = z >> k;
i = 2;
}
else
{
x[0] = y & 0xffff;
x[1] = (y >> 16) | ((z << (16 - k)) & 0xffff);
x[2] = z >> k & 0xffff;
x[3] = z >> (k + 16);
i = 3;
}
else
{
x[0] = y & 0xffff;
x[1] = y >> 16;
x[2] = z & 0xffff;
x[3] = z >> 16;
i = 3;
}
}
else
{
#ifdef CONFIG_DEBUG_LIB
if (z == 0)
{
lerr("ERROR: Zero passed to d2b\n");
}
#endif
k = lo0bits(&z);
if (k >= 16)
{
x[0] = z;
i = 0;
}
else
{
x[0] = z & 0xffff;
x[1] = z >> 16;
i = 1;
}
k += 32;
}
while (!x[i])
{
--i;
}
b->wds = i + 1;
#endif
if (de != 0)
{
*e = de - BIAS - (P - 1) + k;
*bits = P - k;
}
else
{
*e = de - BIAS - (P - 1) + 1 + k;
#ifdef CONFIG_DTOA_PACK32
*bits = 32 * i - hi0bits(x[i - 1]);
#else
*bits = (i + 2) * 16 - hi0bits(x[i]);
#endif
}
return b;
}
static const double_t tens[] =
{
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1e20, 1e21, 1e22
};
static int quorem(FAR bigint_t *b, FAR bigint_t *s)
{
long borrow;
long y;
unsigned long carry;
unsigned long q;
unsigned long ys;
FAR unsigned long *bx;
FAR unsigned long *bxe;
FAR unsigned long *sx;
FAR unsigned long *sxe;
#ifdef CONFIG_DTOA_PACK32
int32_t z;
uint32_t si;
uint32_t zs;
#endif
int n;
n = s->wds;
#ifdef CONFIG_DEBUG_LIB
if (b->wds > n)
{
lerr("ERROR: oversize b in quorem\n");
}
#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 CONFIG_DEBUG_LIB
if (q > 9)
{
lerr("ERROR: oversized quotient in quorem\n");
}
#endif
if (q != 0)
{
borrow = 0;
carry = 0;
do
{
#ifdef CONFIG_DTOA_PACK32
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 == 0)
{
bx = b->x;
while (--bxe > bx && *bxe == 0)
{
--n;
}
b->wds = n;
}
}
if (cmp(b, s) >= 0)
{
q++;
borrow = 0;
carry = 0;
bx = b->x;
sx = s->x;
do
{
#ifdef CONFIG_DTOA_PACK32
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 == 0)
{
while (--bxe > bx && *bxe == 0)
{
--n;
}
b->wds = n;
}
}
return q;
}
/****************************************************************************
* Public Functions
****************************************************************************/
/* 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 int32_t
* calculation.
*/
FAR char *__dtoa(double_t d, int mode, int ndigits, FAR int *decpt,
FAR int *sign, FAR 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.
*/
static FAR bigint_t *result;
static int result_k;
FAR bigint_t *b;
FAR bigint_t *b1;
FAR bigint_t *delta;
FAR bigint_t *mlo = NULL;
FAR bigint_t *mhi;
FAR bigint_t *s;
FAR char *st;
FAR char *st0;
double_t d2;
double_t ds;
double_t eps;
long l;
unsigned long x;
int denorm;
int bbits;
int b2;
int b5;
int be;
int dig;
int i;
int ieps;
int ilim = 0;
int ilim0;
int ilim1 = 0;
int j;
int j_1;
int k;
int k0;
int k_check;
int leftright;
int m2;
int m5;
int s2;
int s5;
int spec_case = 0;
int try_quick;
if (result != 0)
{
result->k = result_k;
result->maxwds = 1 << result_k;
bfree(result);
result = 0;
}
if ((WORD0(d) & SIGN_BIT) != 0)
{
/* 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)
# ifdef IEEE_ARITH
if ((WORD0(d) & EXP_MASK) == EXP_MASK)
#else
if (WORD0(d) == 0x8000)
#endif
{
/* Infinity or NaN */
*decpt = 9999;
st =
#ifdef IEEE_ARITH
!WORD1(d) && !(WORD0(d) & 0xfffff) ? "Infinity" :
#endif
"NaN";
if (rve != NULL)
{
*rve =
#ifdef IEEE_ARITH
st[3] ? st + 8 :
#endif
st + 3;
}
return st;
}
#endif
if (d == 0)
{
*decpt = 1;
st = "0";
if (rve != NULL)
{
*rve = st + 1;
}
return st;
}
b = d2b(d, &be, &bbits);
i = (int)(WORD0(d) >> EXP_SHIFT1 & (EXP_MASK >> EXP_SHIFT1));
if (i != 0)
{
d2 = d;
WORD0(d2) &= FRAC_MASK1;
WORD0(d2) |= 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 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;
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);
d2 = x;
WORD0(d2) -= 31 * EXP_MSK1; /* Adjust exponent */
i -= (BIAS + (P - 1) - 1) + 1;
denorm = 1;
}
ds = (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 (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;
}
i = ndigits;
ilim1 = i;
ilim = i;
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 (result_k = 0;
(signed)(sizeof(bigint_t) - sizeof(unsigned long) + j) <= i;
j <<= 1)
{
result_k++;
}
result = balloc(result_k);
st0 = (FAR char *)result;
st = st0;
if (ilim >= 0 && ilim <= QUICK_MAX && try_quick)
{
/* Try to get by with floating-point arithmetic. */
i = 0;
d2 = d;
k0 = k;
ilim0 = ilim;
ieps = 2; /* Conservative */
if (k > 0)
{
ds = tens[k & 0xf];
j = k >> 4;
if ((j & BLETCH) != 0)
{
/* Prevent overflows */
j &= BLETCH - 1;
d /= g_bigtens[n_bigtens - 1];
ieps++;
}
for (; j; j >>= 1, i++)
{
if (j & 1)
{
ieps++;
ds *= g_bigtens[i];
}
}
d /= ds;
}
else if ((j_1 = -k))
{
d *= tens[j_1 & 0xf];
for (j = j_1 >> 4; j; j >>= 1, i++)
{
if ((j & 1) != 0)
{
ieps++;
d *= g_bigtens[i];
}
}
}
if (k_check && d < 1. && ilim > 0)
{
if (ilim1 <= 0)
{
goto fast_failed;
}
ilim = ilim1;
k--;
d *= 10.;
ieps++;
}
eps = ieps * d + 7.;
WORD0(eps) -= (P - 1) * EXP_MSK1;
if (ilim == 0)
{
mhi = 0;
s = 0;
d -= 5.;
if (d > eps)
{
goto one_digit;
}
if (d < -eps)
{
goto no_digits;
}
goto fast_failed;
}
#ifndef CONFIG_DTOA_NO_LEFTRIGHT
if (leftright)
{
/* Use Steele & White method of only generating digits needed. */
eps = 0.5 / tens[ilim - 1] - eps;
for (i = 0; ; )
{
l = (int)d;
d -= l;
*st++ = '0' + (int)l;
if (d < eps)
{
goto ret1;
}
if (1. - d < eps)
{
goto bump_up;
}
if (++i >= ilim)
{
break;
}
eps *= 10.;
d *= 10.;
}
}
else
{
#endif
/* Generate ilim digits, then fix them up. */
eps *= tens[ilim - 1];
for (i = 1; ; i++, d *= 10.)
{
l = (int)d;
d -= l;
*st++ = '0' + (int)l;
if (i == ilim)
{
if (d > 0.5 + eps)
{
goto bump_up;
}
else if (d < 0.5 - eps)
{
while (*--st == '0')
{
}
st++;
goto ret1;
}
break;
}
}
#ifndef CONFIG_DTOA_NO_LEFTRIGHT
}
#endif
fast_failed:
st = st0;
d = d2;
k = k0;
ilim = ilim0;
}
/* Do we have a "small" integer? */
if (be >= 0 && k <= SMALL_MAX)
{
/* Yes. */
ds = tens[k];
if (ndigits < 0 && ilim <= 0)
{
s = mhi = 0;
if (ilim < 0 || d <= 5 * ds)
{
goto no_digits;
}
goto one_digit;
}
for (i = 1; ; i++)
{
l = (int)(d / ds);
d -= l * ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, l will usually be high by 1 */
if (d < 0)
{
l--;
d += ds;
}
#endif
*st++ = '0' + (int)l;
if (i == ilim)
{
d += d;
if (d > ds || (d == ds && (l & 1)))
{
bump_up:
while (*--st == '9')
{
if (st == st0)
{
k++;
*st = '0';
break;
}
}
++*st++;
}
break;
}
if ((d *= 10.) == 0)
{
break;
}
}
goto ret1;
}
m2 = b2;
m5 = b5;
mhi = mlo = 0;
if (leftright)
{
if (mode < 2)
{
i = denorm ? be + (BIAS + (P - 1) - 1 + 1) : 1 + P - bbits;
}
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(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. */
if (mode < 2)
{
if (WORD1(d) == 0 && (WORD0(d) & BNDRY_MASK) == 0 &&
(WORD0(d) & EXP_MASK) != 0)
{
/* 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 CONFIG_DTOA_PACK32
i = ((s5 ? 32 - hi0bits(s->x[s->wds - 1]) : 1) + s2) & 0x1f;
if (i != 0)
{
i = 32 - i;
}
#else
i = ((s5 ? 32 - hi0bits(s->x[s->wds - 1]) : 1) + s2) & 0xf;
if (i != 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 > 2)
{
if (ilim < 0 || cmp(b, s = multadd(s, 5, 0)) <= 0)
{
/* no digits, fcvt style */
no_digits:
k = -1 - ndigits;
goto ret;
}
one_digit:
*st++ = '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);
j_1 = delta->sign ? 1 : cmp(b, delta);
bfree(delta);
#ifndef CONFIG_DTOA_ROUND_BIASED
if (j_1 == 0 && !mode && !(WORD1(d) & 1))
{
if (dig == '9')
{
goto round_9_up;
}
if (j > 0)
{
dig++;
}
*st++ = dig;
goto ret;
}
#endif
if (j < 0 || (j == 0 && !mode
#ifndef CONFIG_DTOA_ROUND_BIASED
&& ((WORD1(d) & 1) == 0)
#endif
))
{
if ((j_1 > 0))
{
b = lshift(b, 1);
j_1 = cmp(b, s);
if ((j_1 > 0 || (j_1 == 0 && (dig & 1))) && dig++ == '9')
{
goto round_9_up;
}
}
*st++ = dig;
goto ret;
}
if (j_1 > 0)
{
if (dig == '9')
{
/* Possible if i == 1 */
round_9_up:
*st++ = '9';
goto roundoff;
}
*st++ = dig + 1;
goto ret;
}
*st++ = dig;
if (i == ilim)
{
break;
}
b = multadd(b, 10, 0);
if (mlo == mhi)
{
mhi = multadd(mhi, 10, 0);
mlo = mhi;
}
else
{
mlo = multadd(mlo, 10, 0);
mhi = multadd(mhi, 10, 0);
}
}
}
else
{
for (i = 1; ; i++)
{
*st++ = dig = quorem(b, s) + '0';
if (i >= ilim)
{
break;
}
b = multadd(b, 10, 0);
}
}
/* Round off last digit */
b = lshift(b, 1);
j = cmp(b, s);
if (j > 0 || (j == 0 && (dig & 1)))
{
roundoff:
while (*--st == '9')
{
if (st == st0)
{
k++;
*st++ = '1';
goto ret;
}
}
++*st++;
}
else
{
while (*--st == '0')
{
}
st++;
}
ret:
bfree(s);
if (mhi)
{
if (mlo && mlo != mhi)
{
bfree(mlo);
}
bfree(mhi);
}
ret1:
bfree(b);
if (st == st0)
{
/* Don't return empty string */
*st++ = '0';
k = 0;
}
*st = 0;
*decpt = k + 1;
if (rve != NULL)
{
*rve = st;
}
return st0;
}
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