* Re: [9fans] fp crash
2013-01-29 0:08 ` erik quanstrom
@ 2013-01-29 1:41 ` erik quanstrom
2013-01-29 3:27 ` Charles Forsyth
0 siblings, 1 reply; 8+ messages in thread
From: erik quanstrom @ 2013-01-29 1:41 UTC (permalink / raw)
To: 9fans
[-- Attachment #1: Type: text/plain, Size: 137 bytes --]
here's a stab at dtoa() that works for arm & amd64.
the diff is very noisy, but it does prevent aliasing by
... not aliasing.
- erik
[-- Attachment #2: dtoa.c --]
[-- Type: text/plain, Size: 25147 bytes --]
/* derived from /netlib/fp/dtoa.c assuming IEEE, Standard C */
/* kudos to dmg@bell-labs.com, gripes to ehg@bell-labs.com */
/* Let x be the exact mathematical number defined by a decimal
* string s. Then atof(s) is the round-nearest-even IEEE
* floating point value.
* Let y be an IEEE floating point value and let s be the string
* printed as %.17g. Then atof(s) is exactly y.
*/
#include <u.h>
#include <libc.h>
static Lock _dtoalk[2];
#define ACQUIRE_DTOA_LOCK(n) lock(&_dtoalk[n])
#define FREE_DTOA_LOCK(n) unlock(&_dtoalk[n])
#define PRIVATE_mem ((2000+sizeof(double)-1)/sizeof(double))
static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
#define FLT_ROUNDS 1
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
#define fpword0(x) ((x).hi)
#define fpword1(x) ((x).lo)
/* Ten_pmax = floor(P*log(2)/log(5)) */
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
#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 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 Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#define rounded_product(a,b) a *= b
#define rounded_quotient(a,b) a /= b
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff
#define FFFFFFFF 0xffffffffUL
#undef ULint
#define Kmax 15
struct
Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
unsigned int x[1];
};
typedef struct Bigint Bigint;
static Bigint *freelist[Kmax+1];
static Bigint *
Balloc(int k)
{
int x;
Bigint * rv;
unsigned int len;
assert(k < nelem(freelist));
ACQUIRE_DTOA_LOCK(0);
if (rv = freelist[k]) {
freelist[k] = rv->next;
} else {
x = 1 << k;
len = (sizeof(Bigint) + (x - 1) * sizeof(unsigned int) + sizeof(double) -1)
/ sizeof(double);
if (pmem_next - private_mem + len <= PRIVATE_mem) {
rv = (Bigint * )pmem_next;
pmem_next += len;
} else
rv = (Bigint * )malloc(len * sizeof(double));
rv->k = k;
rv->maxwds = x;
}
FREE_DTOA_LOCK(0);
rv->sign = rv->wds = 0;
return rv;
}
static void
Bfree(Bigint *v)
{
if (v) {
ACQUIRE_DTOA_LOCK(0);
v->next = freelist[v->k];
freelist[v->k] = v;
FREE_DTOA_LOCK(0);
}
}
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
y->wds*sizeof(int) + 2*sizeof(int))
static Bigint *
multadd(Bigint *b, int m, int a) /* multiply by m and add a */
{
int i, wds;
unsigned int carry, *x, y;
unsigned int xi, z;
Bigint * b1;
wds = b->wds;
x = b->x;
i = 0;
carry = a;
do {
xi = *x;
y = (xi & 0xffff) * m + carry;
z = (xi >> 16) * m + (y >> 16);
carry = z >> 16;
*x++ = (z << 16) + (y & 0xffff);
} while (++i < wds);
if (carry) {
if (wds >= b->maxwds) {
b1 = Balloc(b->k + 1);
Bcopy(b1, b);
Bfree(b);
b = b1;
}
b->x[wds++] = carry;
b->wds = wds;
}
return b;
}
static Bigint *
s2b(const char *s, int nd0, int nd, unsigned int y9)
{
Bigint * b;
int i, k;
int x, y;
x = (nd + 8) / 9;
for (k = 0, y = 1; x > y; y <<= 1, k++)
;
b = Balloc(k);
b->x[0] = y9;
b->wds = 1;
i = 9;
if (9 < nd0) {
s += 9;
do
b = multadd(b, 10, *s++ - '0');
while (++i < nd0);
s++;
} else
s += 10;
for (; i < nd; i++)
b = multadd(b, 10, *s++ - '0');
return b;
}
static int
hi0bits(register unsigned int x)
{
register 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 int *y)
{
register int k;
register unsigned int 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 int * x, *xa, *xae, *xb, *xbe, *xc, *xc0;
unsigned int y;
unsigned int carry, z;
unsigned int z2;
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;
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;
}
}
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 */
ACQUIRE_DTOA_LOCK(1);
if (!(p5 = p5s)) {
p5 = p5s = i2b(625);
p5->next = 0;
}
FREE_DTOA_LOCK(1);
}
for (; ; ) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1))
break;
if (!(p51 = p5->next)) {
ACQUIRE_DTOA_LOCK(1);
if (!(p51 = p5->next)) {
p51 = p5->next = mult(p5, p5);
p51->next = 0;
}
FREE_DTOA_LOCK(1);
}
p5 = p51;
}
return b;
}
static Bigint *
lshift(Bigint *b, int k)
{
int i, k1, n, n1;
Bigint * b1;
unsigned int * x, *x1, *xe, z;
n = k >> 5;
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;
if (k &= 0x1f) {
k1 = 32 - k;
z = 0;
do {
*x1++ = *x << k | z;
z = *x++ >> k1;
} while (x < xe);
if (*x1 = z)
++n1;
} else
do
*x1++ = *x++;
while (x < xe);
b1->wds = n1 - 1;
Bfree(b);
return b1;
}
static int
cmp(Bigint *a, Bigint *b)
{
unsigned int * xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
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;
unsigned int * xa, *xae, *xb, *xbe, *xc;
unsigned int borrow, y;
unsigned int z;
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;
do {
y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(xc, z, y);
} while (xb < xbe);
while (xa < xae) {
y = (*xa & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*xa++ >> 16) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(xc, z, y);
}
while (!*--xc)
wa--;
c->wds = wa;
return c;
}
static FPdbleword
b2d(Bigint *a, int *e)
{
unsigned int * xa, *xa0, w, y, z;
int k;
FPdbleword d;
xa0 = a->x;
xa = xa0 + a->wds;
y = *--xa;
k = hi0bits(y);
*e = 32 - k;
if (k < Ebits) {
d.hi = Exp_1 | y >> Ebits - k;
w = xa > xa0 ? *--xa : 0;
d.lo = y << (32 - Ebits) + k | w >> Ebits - k;
goto ret_d;
}
z = xa > xa0 ? *--xa : 0;
if (k -= Ebits) {
d.hi = Exp_1 | y << k | z >> 32 - k;
y = xa > xa0 ? *--xa : 0;
d.lo = z << k | y >> 32 - k;
} else {
d.hi = Exp_1 | y;
d.lo = z;
}
ret_d:
return d;
}
static Bigint *
d2b(FPdbleword d, int *e, int *bits)
{
Bigint * b;
int de, k;
unsigned int * x, y, z;
#define d0 d.hi
#define d1 d.lo
b = Balloc(1);
x = b->x;
z = d0 & Frac_mask;
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
de = (int)(d0 >> Exp_shift);
z |= Exp_msk11;
if (y = d1) {
if (k = lo0bits(&y)) {
x[0] = y | z << 32 - k;
z >>= k;
} else
x[0] = y;
b->wds = (x[1] = z) ? 2 : 1;
} else {
k = lo0bits(&z);
x[0] = z;
b->wds = 1;
k += 32;
}
*e = de - Bias - (P - 1) + k;
*bits = P - k;
return b;
}
#undef d0
#undef d1
static double
ratio(Bigint *a, Bigint *b)
{
FPdbleword da, db;
int k, ka, kb;
da = b2d(a, &ka);
db = b2d(b, &kb);
k = ka - kb + 32 * (a->wds - b->wds);
if (k > 0)
da.hi += k * Exp_msk1;
else {
k = -k;
da.hi += k * Exp_msk1;
}
return da.x / db.x;
}
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
};
static const double
bigtens[] = {
1e16, 1e32, 1e64, 1e128, 1e256 };
static const double tinytens[] = {
1e-16, 1e-32, 1e-64, 1e-128,
9007199254740992.e-256
};
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
#define Scale_Bit 0x10
#define n_bigtens 5
#define NAN_WORD0 0x7ff80000
#define NAN_WORD1 0
static int
match(const char **sp, char *t)
{
int c, d;
const char * s = *sp;
while (d = *t++) {
if ((c = *++s) >= 'A' && c <= 'Z')
c += 'a' - 'A';
if (c != d)
return 0;
}
*sp = s + 1;
return 1;
}
static int
quorem(Bigint *b, Bigint *S)
{
int n;
unsigned int * bx, *bxe, q, *sx, *sxe;
unsigned int borrow, carry, y, ys;
unsigned int si, z, zs;
n = S->wds;
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 */
if (q) {
borrow = 0;
carry = 0;
do {
si = *sx++;
ys = (si & 0xffff) * q + carry;
zs = (si >> 16) * q + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
} 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 {
si = *sx++;
ys = (si & 0xffff) + carry;
zs = (si >> 16) + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
} while (sx <= sxe);
bx = b->x;
bxe = bx + n;
if (!*bxe) {
while (--bxe > bx && !*bxe)
--n;
b->wds = n;
}
}
return q;
}
static char *
rv_alloc(int i)
{
int j, k, *r;
j = sizeof(unsigned int);
for (k = 0;
sizeof(Bigint) - sizeof(unsigned int) - sizeof(int) + j <= i;
j <<= 1)
k++;
r = (int * )Balloc(k);
*r = k;
return
(char *)(r + 1);
}
static char *
nrv_alloc(char *s, char **rve, int n)
{
char *rv, *t;
t = rv = rv_alloc(n);
while (*t = *s++)
t++;
if (rve)
*rve = t;
return rv;
}
/* freedtoa(s) must be used to free values s returned by dtoa
* when MULTIPLE_THREADS is #defined. It should be used in all cases,
* but for consistency with earlier versions of dtoa, it is optional
* when MULTIPLE_THREADS is not defined.
*/
void
freedtoa(char *s)
{
Bigint * b = (Bigint * )((int *)s - 1);
b->maxwds = 1 << (b->k = *(int * )b);
Bfree(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. 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 int
* 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, ilim0, ilim1,
j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
spec_case, try_quick;
int L;
Bigint * b, *b1, *delta, *mlo=nil, *mhi, *S;
double ds;
FPdbleword dx, d2, eps;
char *s, *s0;
dx.x = d;
if (fpword0(dx) & Sign_bit) {
/* set sign for everything, including 0's and NaNs */
*sign = 1;
fpword0(dx) &= ~Sign_bit; /* clear sign bit */
d = dx.x;
} else
*sign = 0;
if ((fpword0(dx) & Exp_mask) == Exp_mask) {
/* Infinity or NaN */
*decpt = 9999;
if (!fpword1(dx) && !(fpword0(dx) & 0xfffff))
return nrv_alloc("Infinity", rve, 8);
return nrv_alloc("NaN", rve, 3);
}
if (!d) {
*decpt = 1;
return nrv_alloc("0", rve, 1);
}
b = d2b(dx, &be, &bbits);
i = (int)(fpword0(dx) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
d2 = dx;
fpword0(d2) &= Frac_mask1;
fpword0(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;
ds = (d2.x - 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;
}
assert(k < 100);
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:
default:
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;
}
s = s0 = rv_alloc(i);
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
/* Try to get by with floating-point arithmetic. */
i = 0;
d2.x = 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 (j1 = -k) {
d *= tens[j1 & 0xf];
for (j = j1 >> 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.x = ieps * d + 7.;
fpword0(eps) -= (P - 1) * Exp_msk1;
if (ilim == 0) {
S = mhi = 0;
d -= 5.;
if (d > eps.x)
goto one_digit;
if (d < -eps.x)
goto no_digits;
goto fast_failed;
}
/* Generate ilim digits, then fix them up. */
eps.x *= tens[ilim-1];
for (i = 1; ; i++, d *= 10.) {
L = d;
d -= L;
*s++ = '0' + (int)L;
if (i == ilim) {
if (d > 0.5 + eps.x)
goto bump_up;
else if (d < 0.5 - eps.x) {
while (*--s == '0')
;
s++;
goto ret1;
}
break;
}
}
fast_failed:
s = s0;
d = d2.x;
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 = d / ds;
d -= L * ds;
*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 =
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. */
spec_case = 0;
if (mode < 2) {
dx.x = d;
if (!fpword1(dx) && !(fpword0(dx) & Bndry_mask)
) {
/* 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.
*/
if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
i = 32 - i;
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);
j1 = delta->sign ? 1 : cmp(b, delta);
Bfree(delta);
dx.x = d;
if (j1 == 0 && !mode && !(fpword1(dx) & 1)) {
if (dig == '9')
goto round_9_up;
if (j > 0)
dig++;
*s++ = dig;
goto ret;
}
if (j < 0 || j == 0 && !mode
&& !(fpword1(dx) & 1)
) {
if (j1 > 0) {
b = lshift(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(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);
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
return s0;
}
^ permalink raw reply [flat|nested] 8+ messages in thread