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nuttx/lib/lib_dtoa.c
patacongo 2840124ed7 Add floating point support to printf 
git-svn-id: svn://svn.code.sf.net/p/nuttx/code/trunk@2656 42af7a65-404d-4744-a932-0658087f49c3
2010-05-08 03:10:51 +00:00

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/****************************************************************************
* lib/lib_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 <stdlib.h>
#include <stdint.h>
#include <string.h>
/****************************************************************************
* Pre-processor Definitions
****************************************************************************/
#ifdef 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 Int_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
{
struct Bigint *next;
int k, maxwds, sign, wds;
unsigned long x[1];
};
typedef struct Bigint Bigint;
/****************************************************************************
* Private Data
****************************************************************************/
static Bigint *freelist[Kmax + 1];
/****************************************************************************
* Private Functions
****************************************************************************/
static Bigint *Balloc(int k)
{
int x;
Bigint *rv;
if ((rv = freelist[k]))
{
freelist[k] = rv->next;
}
else
{
x = 1 << k;
rv = (Bigint *) malloc(sizeof(Bigint) + (x - 1) * sizeof(long));
rv->k = k;
rv->maxwds = x;
}
rv->sign = rv->wds = 0;
return rv;
}
static void Bfree(Bigint * v)
{
if (v)
{
v->next = freelist[v->k];
freelist[v->k] = v;
}
}
/* multiply by m and add a */
static Bigint *multadd(Bigint * b, int m, int a)
{
int i, wds;
unsigned long *x, y;
#ifdef Pack_32
unsigned long xi, z;
#endif
Bigint *b1;
wds = b->wds;
x = b->x;
i = 0;
do
{
#ifdef Pack_32
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)
{
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))
{
k = 16;
x <<= 16;
}
if (!(x & 0xff000000))
{
k += 8;
x <<= 8;
}
if (!(x & 0xf0000000))
{
k += 4;
x <<= 4;
}
if (!(x & 0xc0000000))
{
k += 2;
x <<= 2;
}
if (!(x & 0x80000000))
{
k++;
if (!(x & 0x40000000))
{
return 32;
}
}
return k;
}
static int lo0bits(unsigned long *y)
{
int k;
unsigned long x = *y;
if (x & 7)
{
if (x & 1)
{
return 0;
}
if (x & 2)
{
*y = x >> 1;
return 1;
}
*y = x >> 2;
return 2;
}
k = 0;
if (!(x & 0xffff))
{
k = 16;
x >>= 16;
}
if (!(x & 0xff))
{
k += 8;
x >>= 8;
}
if (!(x & 0xf))
{
k += 4;
x >>= 4;
}
if (!(x & 0x3))
{
k += 2;
x >>= 2;
}
if (!(x & 1))
{
k++;
x >>= 1;
if (!x & 1)
{
return 32;
}
}
*y = x;
return k;
}
static Bigint *i2b(int i)
{
Bigint *b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
static Bigint *mult(Bigint * a, Bigint * b)
{
Bigint *c;
int k, wa, wb, wc;
unsigned long carry, y, z;
unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
#ifdef Pack_32
uint32_t z2;
#endif
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 Pack_32
for (; xb < xbe; xb++, xc0++)
{
if ((y = *xb & 0xffff))
{
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; --wc);
c->wds = wc;
return c;
}
static Bigint *p5s;
static Bigint *pow5mult(Bigint * b, int k)
{
Bigint *b1, *p5, *p51;
int i;
static int p05[3] = { 5, 25, 125 };
if ((i = k & 3))
b = multadd(b, p05[i - 1], 0);
if (!(k >>= 2))
{
return b;
}
if (!(p5 = p5s))
{
/* first time */
p5 = p5s = i2b(625);
p5->next = 0;
}
for (;;)
{
if (k & 1)
{
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1))
{
break;
}
if (!(p51 = p5->next))
{
p51 = p5->next = mult(p5, p5);
p51->next = 0;
}
p5 = p51;
}
return b;
}
static Bigint *lshift(Bigint * b, int k)
{
int i, k1, n, n1;
Bigint *b1;
unsigned long *x, *x1, *xe, z;
#ifdef Pack_32
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 Pack_32
if (k &= 0x1f)
{
k1 = 32 - k;
z = 0;
do
{
*x1++ = *x << k | z;
z = *x++ >> k1;
}
while (x < xe);
if ((*x1 = z))
{
++n1;
}
}
#else
if (k &= 0xf)
{
k1 = 16 - k;
z = 0;
do
{
*x1++ = ((*x << k) & 0xffff) | z;
z = *x++ >> k1;
}
while (x < xe);
if ((*x1 = z))
{
++n1;
}
}
#endif
else
do
{
*x1++ = *x++;
}
while (x < xe);
b1->wds = n1 - 1;
Bfree(b);
return b1;
}
static int cmp(Bigint * a, Bigint * b)
{
unsigned long *xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
#ifdef CONFIG_DEBUG_LIB
if (i > 1 && !a->x[i - 1])
{
ldbg("cmp called with a->x[a->wds-1] == 0\n");
}
if (j > 1 && !b->x[j - 1])
{
ldbg("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 Bigint *diff(Bigint * a, Bigint * b)
{
Bigint *c;
int i, wa, wb;
long borrow, y; /* We need signed shifts here. */
unsigned long *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
int32_t z;
#endif
i = cmp(a, b);
if (!i)
{
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 Pack_32
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)
wa--;
c->wds = wa;
return c;
}
static Bigint *d2b(double d, int *e, int *bits)
{
Bigint *b;
int de, i, k;
unsigned long *x, y, z;
#ifdef Pack_32
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 */
if ((de = (int)(word0(d) >> Exp_shift)))
z |= Exp_msk1;
#ifdef Pack_32
if ((y = word1(d)))
{
if ((k = lo0bits(&y)))
{
x[0] = y | z << (32 - k);
z >>= k;
}
else
x[0] = y;
i = b->wds = (x[1] = z) ? 2 : 1;
}
else
{
#ifdef CONFIG_DEBUG_LIB
if (!z)
{
ldbg("Zero passed to d2b\n");
}
#endif
k = lo0bits(&z);
x[0] = z;
i = b->wds = 1;
k += 32;
}
#else
if ((y = word1(d)))
{
if ((k = lo0bits(&y)))
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)
{
ldbg("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)
{
*e = de - Bias - (P - 1) + k;
*bits = P - k;
}
else
{
*e = de - Bias - (P - 1) + 1 + k;
#ifdef Pack_32
*bits = 32 * i - hi0bits(x[i - 1]);
#else
*bits = (i + 2) * 16 - hi0bits(x[i]);
#endif
}
return b;
}
static const double tens[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1e20, 1e21, 1e22
};
#ifdef IEEE_Arith
static const double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
# define n_bigtens 5
#else
static const double bigtens[] = { 1e16, 1e32 };
static const double tinytens[] = { 1e-16, 1e-32 };
# define n_bigtens 2
#endif
static int quorem(Bigint * b, Bigint * S)
{
int n;
long borrow, y;
unsigned long carry, q, ys;
unsigned long *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
int32_t z;
uint32_t si, zs;
#endif
n = S->wds;
#ifdef CONFIG_DEBUG_LIB
if (b->wds > n)
{
ldbg("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)
{
ldbg("oversized quotient in quorem\n");
}
#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;
}
/****************************************************************************
* 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.
*/
char *__dtoa(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 = 0, ilim0, ilim1 = 0,
j, j_1, k, k0, k_check, leftright, m2, m5, s2, s5, spec_case = 0, try_quick;
long L;
int denorm;
unsigned long x;
Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
double d2, ds, eps;
char *s, *s0;
static Bigint *result;
static int result_k;
if (result)
{
result->k = result_k;
result->maxwds = 1 << result_k;
Bfree(result);
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)
# 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
if (!d)
{
*decpt = 1;
s = "0";
if (rve)
*rve = s + 1;
return s;
}
b = d2b(d, &be, &bbits);
if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))))
{
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;
/* 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(unsigned long);
for (result_k = 0; (signed)(sizeof(Bigint) - sizeof(unsigned long) + j) <= i;
j <<= 1)
result_k++;
result = Balloc(result_k);
s = s0 = (char *)result;
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)
{
/* prevent overflows */
j &= Bletch - 1;
d /= bigtens[n_bigtens - 1];
ieps++;
}
for (; j; j >>= 1, i++)
if (j & 1)
{
ieps++;
ds *= 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)
{
ieps++;
d *= 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)
{
S = mhi = 0;
d -= 5.;
if (d > eps)
goto one_digit;
if (d < -eps)
goto no_digits;
goto fast_failed;
}
#ifndef 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;
*s++ = '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;
*s++ = '0' + (int)L;
if (i == ilim)
{
if (d > 0.5 + eps)
goto bump_up;
else if (d < 0.5 - eps)
{
while (*--s == '0');
s++;
goto ret1;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = s0;
d = 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 || 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
*s++ = '0' + (int)L;
if (i == ilim)
{
d += d;
if (d > ds || (d == ds && (L & 1)))
{
bump_up:
while (*--s == '9')
if (s == s0)
{
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
if (!(d *= 10.))
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))
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) && !(word0(d) & Bndry_mask) && word0(d) & Exp_mask)
{
/* 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(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:
*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);
j_1 = delta->sign ? 1 : cmp(b, delta);
Bfree(delta);
#ifndef ROUND_BIASED
if (j_1 == 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 ((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;
}
*s++ = dig;
goto ret;
}
if (j_1 > 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(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 (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 (*--s == '9')
if (s == s0)
{
k++;
*s++ = '1';
goto ret;
}
++*s++;
}
else
{
while (*--s == '0');
s++;
}
ret:
Bfree(S);
if (mhi)
{
if (mlo && mlo != mhi)
Bfree(mlo);
Bfree(mhi);
}
ret1:
Bfree(b);
if (s == s0)
{ /* don't return empty string */
*s++ = '0';
k = 0;
}
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
return s0;
}
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