#include <config.h>
#ifdef WORDS_BIGENDIAN
#define IEEE_MC68k
#else
#define IEEE_8087
#endif
#define INFNAN_CHECK
#include "dtoa.h"
#define strtod kjs_strtod
#define dtoa kjs_dtoa
#define freedtoa kjs_freedtoa
#ifndef Long
#define Long long
#endif
#ifndef ULong
typedef unsigned Long ULong;
#endif
#ifdef DEBUG
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#endif
#include "stdlib.h"
#include "string.h"
#ifdef USE_LOCALE
#include "locale.h"
#endif
#ifdef MALLOC
#ifdef KR_headers
extern char *MALLOC();
#else
extern void *MALLOC(size_t);
#endif
#else
#define MALLOC malloc
#endif
#ifndef Omit_Private_Memory
#ifndef PRIVATE_MEM
#define PRIVATE_MEM 2304
#endif
#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
#endif
#undef IEEE_Arith
#undef Avoid_Underflow
#ifdef IEEE_MC68k
#define IEEE_Arith
#endif
#ifdef IEEE_8087
#define IEEE_Arith
#endif
#include "errno.h"
#ifdef Bad_float_h
#ifdef IEEE_Arith
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#endif
#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define DBL_MAX 7.2370055773322621e+75
#endif
#ifdef VAX
#define DBL_DIG 16
#define DBL_MAX_10_EXP 38
#define DBL_MAX_EXP 127
#define FLT_RADIX 2
#define DBL_MAX 1.7014118346046923e+38
#endif
#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif
#else
#include "float.h"
#endif
#ifndef __MATH_H__
#include "math.h"
#endif
#ifdef __cplusplus
extern "C" {
#endif
#ifndef CONST
#ifdef KR_headers
#define CONST
#else
#define CONST const
#endif
#endif
#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
#endif
typedef union { double d; ULong L[2]; } U;
#ifdef YES_ALIAS
#define dval(x) x
#ifdef IEEE_8087
#define word0(x) ((ULong *)&x)[1]
#define word1(x) ((ULong *)&x)[0]
#else
#define word0(x) ((ULong *)&x)[0]
#define word1(x) ((ULong *)&x)[1]
#endif
#else
#ifdef IEEE_8087
#define word0(x) ((U*)&x)->L[1]
#define word1(x) ((U*)&x)->L[0]
#else
#define word0(x) ((U*)&x)->L[0]
#define word1(x) ((U*)&x)->L[1]
#endif
#define dval(x) ((U*)&x)->d
#endif
#if defined(IEEE_8087) + defined(VAX)
#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
((unsigned short *)a)[0] = (unsigned short)c, a++)
#else
#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
((unsigned short *)a)[1] = (unsigned short)c, a++)
#endif
#ifdef IEEE_Arith
#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 LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#ifndef NO_IEEE_Scale
#define Avoid_Underflow
#ifdef Flush_Denorm
#undef Sudden_Underflow
#endif
#endif
#ifndef Flt_Rounds
#ifdef FLT_ROUNDS
#define Flt_Rounds FLT_ROUNDS
#else
#define Flt_Rounds 1
#endif
#endif
#ifdef Honor_FLT_ROUNDS
#define Rounding rounding
#undef Check_FLT_ROUNDS
#define Check_FLT_ROUNDS
#else
#define Rounding Flt_Rounds
#endif
#else
#undef Check_FLT_ROUNDS
#undef Honor_FLT_ROUNDS
#undef SET_INEXACT
#undef Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#undef Flt_Rounds
#define Flt_Rounds 0
#define Exp_shift 24
#define Exp_shift1 24
#define Exp_msk1 0x1000000
#define Exp_msk11 0x1000000
#define Exp_mask 0x7f000000
#define P 14
#define Bias 65
#define Exp_1 0x41000000
#define Exp_11 0x41000000
#define Ebits 8
#define Frac_mask 0xffffff
#define Frac_mask1 0xffffff
#define Bletch 4
#define Ten_pmax 22
#define Bndry_mask 0xefffff
#define Bndry_mask1 0xffffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 4
#define Tiny0 0x100000
#define Tiny1 0
#define Quick_max 14
#define Int_max 15
#else
#undef Flt_Rounds
#define Flt_Rounds 1
#define Exp_shift 23
#define Exp_shift1 7
#define Exp_msk1 0x80
#define Exp_msk11 0x800000
#define Exp_mask 0x7f80
#define P 56
#define Bias 129
#define Exp_1 0x40800000
#define Exp_11 0x4080
#define Ebits 8
#define Frac_mask 0x7fffff
#define Frac_mask1 0xffff007f
#define Ten_pmax 24
#define Bletch 2
#define Bndry_mask 0xffff007f
#define Bndry_mask1 0xffff007f
#define LSB 0x10000
#define Sign_bit 0x8000
#define Log2P 1
#define Tiny0 0x80
#define Tiny1 0
#define Quick_max 15
#define Int_max 15
#endif
#endif
#ifndef IEEE_Arith
#define ROUND_BIASED
#endif
#ifdef RND_PRODQUOT
#define rounded_product(a,b) a = rnd_prod(a, b)
#define rounded_quotient(a,b) a = rnd_quot(a, b)
#ifdef KR_headers
extern double rnd_prod(), rnd_quot();
#else
extern double rnd_prod(double, double), rnd_quot(double, double);
#endif
#else
#define rounded_product(a,b) a *= b
#define rounded_quotient(a,b) a /= b
#endif
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff
#ifndef Pack_32
#define Pack_32
#endif
#ifdef KR_headers
#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
#else
#define FFFFFFFF 0xffffffffUL
#endif
#ifdef NO_LONG_LONG
#undef ULLong
#ifdef Just_16
#undef Pack_32
#endif
#else
#ifndef Llong
#define Llong long long
#endif
#ifndef ULLong
#define ULLong unsigned Llong
#endif
#endif
#ifndef MULTIPLE_THREADS
#define ACQUIRE_DTOA_LOCK(n)
#define FREE_DTOA_LOCK(n)
#endif
#define Kmax 15
struct
Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
static Bigint *freelist[Kmax+1];
static Bigint *
Balloc
#ifdef KR_headers
(k) int k;
#else
(int k)
#endif
{
int x;
Bigint *rv;
#ifndef Omit_Private_Memory
unsigned int len;
#endif
ACQUIRE_DTOA_LOCK(0);
if ((rv = freelist[k])) {
freelist[k] = rv->next;
}
else {
x = 1 << k;
#ifdef Omit_Private_Memory
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
#else
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + 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));
#endif
rv->k = k;
rv->maxwds = x;
}
FREE_DTOA_LOCK(0);
rv->sign = rv->wds = 0;
return rv;
}
static void
Bfree
#ifdef KR_headers
(v) Bigint *v;
#else
(Bigint *v)
#endif
{
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(Long) + 2*sizeof(int))
static Bigint *
multadd
#ifdef KR_headers
(b, m, a) Bigint *b; int m, a;
#else
(Bigint *b, int m, int a)
#endif
{
int i, wds;
#ifdef ULLong
ULong *x;
ULLong carry, y;
#else
ULong carry, *x, y;
#ifdef Pack_32
ULong xi, z;
#endif
#endif
Bigint *b1;
wds = b->wds;
x = b->x;
i = 0;
carry = a;
do {
#ifdef ULLong
y = *x * (ULLong)m + carry;
carry = y >> 32;
*x++ = y & FFFFFFFF;
#else
#ifdef Pack_32
xi = *x;
y = (xi & 0xffff) * m + carry;
z = (xi >> 16) * m + (y >> 16);
carry = z >> 16;
*x++ = (z << 16) + (y & 0xffff);
#else
y = *x * m + carry;
carry = y >> 16;
*x++ = y & 0xffff;
#endif
#endif
}
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
#ifdef KR_headers
(s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
#else
(CONST char *s, int nd0, int nd, ULong y9)
#endif
{
Bigint *b;
int i, k;
Long x, y;
x = (nd + 8) / 9;
for(k = 0, y = 1; x > y; y <<= 1, k++) ;
#ifdef Pack_32
b = Balloc(k);
b->x[0] = y9;
b->wds = 1;
#else
b = Balloc(k+1);
b->x[0] = y9 & 0xffff;
b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
#endif
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
#ifdef KR_headers
(x) register ULong x;
#else
(register ULong x)
#endif
{
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
#ifdef KR_headers
(y) ULong *y;
#else
(ULong *y)
#endif
{
register int k;
register ULong 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
#ifdef KR_headers
(i) int i;
#else
(int i)
#endif
{
Bigint *b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
static Bigint *
mult
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(Bigint *a, Bigint *b)
#endif
{
Bigint *c;
int k, wa, wb, wc;
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
ULong y;
#ifdef ULLong
ULLong carry, z;
#else
ULong carry, z;
#ifdef Pack_32
ULong z2;
#endif
#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 ULLong
for(; xb < xbe; xc0++) {
if ((y = *xb++)) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * (ULLong)y + *xc + carry;
carry = z >> 32;
*xc++ = z & FFFFFFFF;
}
while(x < xae);
*xc = carry;
}
}
#else
#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
#endif
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds = wc;
return c;
}
static Bigint *p5s;
static Bigint *
pow5mult
#ifdef KR_headers
(b, k) Bigint *b; int k;
#else
(Bigint *b, int k)
#endif
{
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)) {
#ifdef MULTIPLE_THREADS
ACQUIRE_DTOA_LOCK(1);
if (!(p5 = p5s)) {
p5 = p5s = i2b(625);
p5->next = 0;
}
FREE_DTOA_LOCK(1);
#else
p5 = p5s = i2b(625);
p5->next = 0;
#endif
}
for(;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1))
break;
if (!(p51 = p5->next)) {
#ifdef MULTIPLE_THREADS
ACQUIRE_DTOA_LOCK(1);
if (!(p51 = p5->next)) {
p51 = p5->next = mult(p5,p5);
p51->next = 0;
}
FREE_DTOA_LOCK(1);
#else
p51 = p5->next = mult(p5,p5);
p51->next = 0;
#endif
}
p5 = p51;
}
return b;
}
static Bigint *
lshift
#ifdef KR_headers
(b, k) Bigint *b; int k;
#else
(Bigint *b, int k)
#endif
{
int i, k1, n, n1;
Bigint *b1;
ULong *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
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(Bigint *a, Bigint *b)
#endif
{
ULong *xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
#ifdef DEBUG
if (i > 1 && !a->x[i-1])
Bug("cmp called with a->x[a->wds-1] == 0");
if (j > 1 && !b->x[j-1])
Bug("cmp called with b->x[b->wds-1] == 0");
#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
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(Bigint *a, Bigint *b)
#endif
{
Bigint *c;
int i, wa, wb;
ULong *xa, *xae, *xb, *xbe, *xc;
#ifdef ULLong
ULLong borrow, y;
#else
ULong borrow, y;
#ifdef Pack_32
ULong z;
#endif
#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 ULLong
do {
y = (ULLong)*xa++ - *xb++ - borrow;
borrow = y >> 32 & (ULong)1;
*xc++ = y & FFFFFFFF;
}
while(xb < xbe);
while(xa < xae) {
y = *xa++ - borrow;
borrow = y >> 32 & (ULong)1;
*xc++ = y & FFFFFFFF;
}
#else
#ifdef Pack_32
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);
}
#else
do {
y = *xa++ - *xb++ - borrow;
borrow = (y & 0x10000) >> 16;
*xc++ = y & 0xffff;
}
while(xb < xbe);
while(xa < xae) {
y = *xa++ - borrow;
borrow = (y & 0x10000) >> 16;
*xc++ = y & 0xffff;
}
#endif
#endif
while(!*--xc)
wa--;
c->wds = wa;
return c;
}
static double
ulp
#ifdef KR_headers
(x) double x;
#else
(double x)
#endif
{
register Long L;
double a;
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
if (L > 0) {
#endif
#endif
#ifdef IBM
L |= Exp_msk1 >> 4;
#endif
word0(a) = L;
word1(a) = 0;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
}
else {
L = -L >> Exp_shift;
if (L < Exp_shift) {
word0(a) = 0x80000 >> L;
word1(a) = 0;
}
else {
word0(a) = 0;
L -= Exp_shift;
word1(a) = L >= 31 ? 1 : 1 << 31 - L;
}
}
#endif
#endif
return dval(a);
}
static double
b2d
#ifdef KR_headers
(a, e) Bigint *a; int *e;
#else
(Bigint *a, int *e)
#endif
{
ULong *xa, *xa0, w, y, z;
int k;
double d;
#ifdef VAX
ULong d0, d1;
#else
#define d0 word0(d)
#define d1 word1(d)
#endif
xa0 = a->x;
xa = xa0 + a->wds;
y = *--xa;
#ifdef DEBUG
if (!y) Bug("zero y in b2d");
#endif
k = hi0bits(y);
*e = 32 - k;
#ifdef Pack_32
if (k < Ebits) {
d0 = Exp_1 | y >> Ebits - k;
w = xa > xa0 ? *--xa : 0;
d1 = y << (32-Ebits) + k | w >> Ebits - k;
goto ret_d;
}
z = xa > xa0 ? *--xa : 0;
if (k -= Ebits) {
d0 = Exp_1 | y << k | z >> 32 - k;
y = xa > xa0 ? *--xa : 0;
d1 = z << k | y >> 32 - k;
}
else {
d0 = Exp_1 | y;
d1 = z;
}
#else
if (k < Ebits + 16) {
z = xa > xa0 ? *--xa : 0;
d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
w = xa > xa0 ? *--xa : 0;
y = xa > xa0 ? *--xa : 0;
d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
goto ret_d;
}
z = xa > xa0 ? *--xa : 0;
w = xa > xa0 ? *--xa : 0;
k -= Ebits + 16;
d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
y = xa > xa0 ? *--xa : 0;
d1 = w << k + 16 | y << k;
#endif
ret_d:
#ifdef VAX
word0(d) = d0 >> 16 | d0 << 16;
word1(d) = d1 >> 16 | d1 << 16;
#else
#undef d0
#undef d1
#endif
return dval(d);
}
static Bigint *
d2b
#ifdef KR_headers
(d, e, bits) double d; int *e, *bits;
#else
(double d, int *e, int *bits)
#endif
{
Bigint *b;
int de, k;
ULong *x, y, z;
#ifndef Sudden_Underflow
int i;
#endif
#ifdef VAX
ULong d0, d1;
d0 = word0(d) >> 16 | word0(d) << 16;
d1 = word1(d) >> 16 | word1(d) << 16;
#else
#define d0 word0(d)
#define d1 word1(d)
#endif
#ifdef Pack_32
b = Balloc(1);
#else
b = Balloc(2);
#endif
x = b->x;
z = d0 & Frac_mask;
d0 &= 0x7fffffff;
#ifdef Sudden_Underflow
de = (int)(d0 >> Exp_shift);
#ifndef IBM
z |= Exp_msk11;
#endif
#else
if ((de = (int)(d0 >> Exp_shift)))
z |= Exp_msk1;
#endif
#ifdef Pack_32
if ((y = d1)) {
if ((k = lo0bits(&y))) {
x[0] = y | z << 32 - k;
z >>= k;
}
else
x[0] = y;
#ifndef Sudden_Underflow
i =
#endif
b->wds = (x[1] = z) ? 2 : 1;
}
else {
#ifdef DEBUG
if (!z)
Bug("Zero passed to d2b");
#endif
k = lo0bits(&z);
x[0] = z;
#ifndef Sudden_Underflow
i =
#endif
b->wds = 1;
k += 32;
}
#else
if (y = d1) {
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 DEBUG
if (!z)
Bug("Zero passed to d2b");
#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
#ifndef Sudden_Underflow
if (de) {
#endif
#ifdef IBM
*e = (de - Bias - (P-1) << 2) + k;
*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
#else
*e = de - Bias - (P-1) + k;
*bits = P - k;
#endif
#ifndef Sudden_Underflow
}
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
}
#endif
return b;
}
#undef d0
#undef d1
static double
ratio
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(Bigint *a, Bigint *b)
#endif
{
double da, db;
int k, ka, kb;
dval(da) = b2d(a, &ka);
dval(db) = b2d(b, &kb);
#ifdef Pack_32
k = ka - kb + 32*(a->wds - b->wds);
#else
k = ka - kb + 16*(a->wds - b->wds);
#endif
#ifdef IBM
if (k > 0) {
word0(da) += (k >> 2)*Exp_msk1;
if (k &= 3)
dval(da) *= 1 << k;
}
else {
k = -k;
word0(db) += (k >> 2)*Exp_msk1;
if (k &= 3)
dval(db) *= 1 << k;
}
#else
if (k > 0)
word0(da) += k*Exp_msk1;
else {
k = -k;
word0(db) += k*Exp_msk1;
}
#endif
return dval(da) / dval(db);
}
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 VAX
, 1e23, 1e24
#endif
};
static CONST double
#ifdef IEEE_Arith
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
#ifdef Avoid_Underflow
9007199254740992.*9007199254740992.e-256
#else
1e-256
#endif
};
#define Scale_Bit 0x10
#define n_bigtens 5
#else
#ifdef IBM
bigtens[] = { 1e16, 1e32, 1e64 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
#define n_bigtens 3
#else
bigtens[] = { 1e16, 1e32 };
static CONST double tinytens[] = { 1e-16, 1e-32 };
#define n_bigtens 2
#endif
#endif
#ifndef IEEE_Arith
#undef INFNAN_CHECK
#endif
#ifdef INFNAN_CHECK
#ifndef NAN_WORD0
#define NAN_WORD0 0x7ff80000
#endif
#ifndef NAN_WORD1
#define NAN_WORD1 0
#endif
static int
match
#ifdef KR_headers
(sp, t) char **sp, *t;
#else
(CONST char **sp, CONST char *t)
#endif
{
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;
}
#ifndef No_Hex_NaN
static void
hexnan
#ifdef KR_headers
(rvp, sp) double *rvp; CONST char **sp;
#else
(double *rvp, CONST char **sp)
#endif
{
ULong c, x[2];
CONST char *s;
int havedig, udx0, xshift;
x[0] = x[1] = 0;
havedig = xshift = 0;
udx0 = 1;
s = *sp;
while((c = *(CONST unsigned char*)++s)) {
if (c >= '0' && c <= '9')
c -= '0';
else if (c >= 'a' && c <= 'f')
c += 10 - 'a';
else if (c >= 'A' && c <= 'F')
c += 10 - 'A';
else if (c <= ' ') {
if (udx0 && havedig) {
udx0 = 0;
xshift = 1;
}
continue;
}
else if ( c == ')' && havedig) {
*sp = s + 1;
break;
}
else
return;
havedig = 1;
if (xshift) {
xshift = 0;
x[0] = x[1];
x[1] = 0;
}
if (udx0)
x[0] = (x[0] << 4) | (x[1] >> 28);
x[1] = (x[1] << 4) | c;
}
if ((x[0] &= 0xfffff) || x[1]) {
word0(*rvp) = Exp_mask | x[0];
word1(*rvp) = x[1];
}
}
#endif
#endif
double
strtod
#ifdef KR_headers
(s00, se) CONST char *s00; char **se;
#else
(CONST char *s00, char **se)
#endif
{
#ifdef Avoid_Underflow
int scale;
#endif
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
CONST char *s, *s0, *s1;
double aadj, aadj1, adj, rv, rv0;
Long L;
ULong y, z;
Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
#ifdef USE_LOCALE
CONST char *s2;
#endif
sign = nz0 = nz = 0;
dval(rv) = 0.;
for(s = s00;;s++) switch(*s) {
case '-':
sign = 1;
case '+':
if (*++s)
goto break2;
case 0:
goto ret0;
case '\t':
case '\n':
case '\v':
case '\f':
case '\r':
case ' ':
continue;
default:
goto break2;
}
break2:
if (*s == '0') {
nz0 = 1;
while(*++s == '0') ;
if (!*s)
goto ret;
}
s0 = s;
y = z = 0;
for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
if (nd < 9)
y = 10*y + c - '0';
else if (nd < 16)
z = 10*z + c - '0';
nd0 = nd;
#ifdef USE_LOCALE
s1 = localeconv()->decimal_point;
if (c == *s1) {
c = '.';
if (*++s1) {
s2 = s;
for(;;) {
if (*++s2 != *s1) {
c = 0;
break;
}
if (!*++s1) {
s = s2;
break;
}
}
}
}
#endif
if (c == '.') {
c = *++s;
if (!nd) {
for(; c == '0'; c = *++s)
nz++;
if (c > '0' && c <= '9') {
s0 = s;
nf += nz;
nz = 0;
goto have_dig;
}
goto dig_done;
}
for(; c >= '0' && c <= '9'; c = *++s) {
have_dig:
nz++;
if (c -= '0') {
nf += nz;
for(i = 1; i < nz; i++)
if (nd++ < 9)
y *= 10;
else if (nd <= DBL_DIG + 1)
z *= 10;
if (nd++ < 9)
y = 10*y + c;
else if (nd <= DBL_DIG + 1)
z = 10*z + c;
nz = 0;
}
}
}
dig_done:
e = 0;
if (c == 'e' || c == 'E') {
if (!nd && !nz && !nz0) {
goto ret0;
}
s00 = s;
esign = 0;
switch(c = *++s) {
case '-':
esign = 1;
case '+':
c = *++s;
}
if (c >= '0' && c <= '9') {
while(c == '0')
c = *++s;
if (c > '0' && c <= '9') {
L = c - '0';
s1 = s;
while((c = *++s) >= '0' && c <= '9')
L = 10*L + c - '0';
if (s - s1 > 8 || L > 19999)
e = 19999;
else
e = (int)L;
if (esign)
e = -e;
}
else
e = 0;
}
else
s = s00;
}
if (!nd) {
if (!nz && !nz0) {
#ifdef INFNAN_CHECK
switch(c) {
case 'i':
case 'I':
if (match(&s,"nf")) {
--s;
if (!match(&s,"inity"))
++s;
word0(rv) = 0x7ff00000;
word1(rv) = 0;
goto ret;
}
break;
case 'n':
case 'N':
if (match(&s, "an")) {
word0(rv) = NAN_WORD0;
word1(rv) = NAN_WORD1;
#ifndef No_Hex_NaN
if (*s == '(')
hexnan(&rv, &s);
#endif
goto ret;
}
}
#endif
ret0:
s = s00;
sign = 0;
}
goto ret;
}
e1 = e -= nf;
if (!nd0)
nd0 = nd;
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
dval(rv) = y;
if (k > 9) {
#ifdef SET_INEXACT
if (k > DBL_DIG)
oldinexact = get_inexact();
#endif
dval(rv) = tens[k - 9] * dval(rv) + z;
}
bd0 = 0;
if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
#ifndef Honor_FLT_ROUNDS
&& Flt_Rounds == 1
#endif
#endif
) {
if (!e)
goto ret;
if (e > 0) {
if (e <= Ten_pmax) {
#ifdef VAX
goto vax_ovfl_check;
#else
#ifdef Honor_FLT_ROUNDS
if (sign) {
rv = -rv;
sign = 0;
}
#endif
rounded_product(dval(rv), tens[e]);
goto ret;
#endif
}
i = DBL_DIG - nd;
if (e <= Ten_pmax + i) {
#ifdef Honor_FLT_ROUNDS
if (sign) {
rv = -rv;
sign = 0;
}
#endif
e -= i;
dval(rv) *= tens[i];
#ifdef VAX
vax_ovfl_check:
word0(rv) -= P*Exp_msk1;
rounded_product(dval(rv), tens[e]);
if ((word0(rv) & Exp_mask)
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
goto ovfl;
word0(rv) += P*Exp_msk1;
#else
rounded_product(dval(rv), tens[e]);
#endif
goto ret;
}
}
#ifndef Inaccurate_Divide
else if (e >= -Ten_pmax) {
#ifdef Honor_FLT_ROUNDS
if (sign) {
rv = -rv;
sign = 0;
}
#endif
rounded_quotient(dval(rv), tens[-e]);
goto ret;
}
#endif
}
e1 += nd - k;
#ifdef IEEE_Arith
#ifdef SET_INEXACT
inexact = 1;
if (k <= DBL_DIG)
oldinexact = get_inexact();
#endif
#ifdef Avoid_Underflow
scale = 0;
#endif
#ifdef Honor_FLT_ROUNDS
if ((rounding = Flt_Rounds) >= 2) {
if (sign)
rounding = rounding == 2 ? 0 : 2;
else
if (rounding != 2)
rounding = 0;
}
#endif
#endif
if (e1 > 0) {
if ((i = e1 & 15))
dval(rv) *= tens[i];
if (e1 &= ~15) {
if (e1 > DBL_MAX_10_EXP) {
ovfl:
#ifndef NO_ERRNO
errno = ERANGE;
#endif
#ifdef IEEE_Arith
#ifdef Honor_FLT_ROUNDS
switch(rounding) {
case 0:
case 3:
word0(rv) = Big0;
word1(rv) = Big1;
break;
default:
word0(rv) = Exp_mask;
word1(rv) = 0;
}
#else
word0(rv) = Exp_mask;
word1(rv) = 0;
#endif
#ifdef SET_INEXACT
dval(rv0) = 1e300;
dval(rv0) *= dval(rv0);
#endif
#else
word0(rv) = Big0;
word1(rv) = Big1;
#endif
if (bd0)
goto retfree;
goto ret;
}
e1 >>= 4;
for(j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1)
dval(rv) *= bigtens[j];
word0(rv) -= P*Exp_msk1;
dval(rv) *= bigtens[j];
if ((z = word0(rv) & Exp_mask)
> Exp_msk1*(DBL_MAX_EXP+Bias-P))
goto ovfl;
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
word0(rv) = Big0;
word1(rv) = Big1;
}
else
word0(rv) += P*Exp_msk1;
}
}
else if (e1 < 0) {
e1 = -e1;
if ((i = e1 & 15))
dval(rv) /= tens[i];
if (e1 >>= 4) {
if (e1 >= 1 << n_bigtens)
goto undfl;
#ifdef Avoid_Underflow
if (e1 & Scale_Bit)
scale = 2*P;
for(j = 0; e1 > 0; j++, e1 >>= 1)
if (e1 & 1)
dval(rv) *= tinytens[j];
if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
>> Exp_shift)) > 0) {
if (j >= 32) {
word1(rv) = 0;
if (j >= 53)
word0(rv) = (P+2)*Exp_msk1;
else
word0(rv) &= 0xffffffff << j-32;
}
else
word1(rv) &= 0xffffffff << j;
}
#else
for(j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1)
dval(rv) *= tinytens[j];
dval(rv0) = dval(rv);
dval(rv) *= tinytens[j];
if (!dval(rv)) {
dval(rv) = 2.*dval(rv0);
dval(rv) *= tinytens[j];
#endif
if (!dval(rv)) {
undfl:
dval(rv) = 0.;
#ifndef NO_ERRNO
errno = ERANGE;
#endif
if (bd0)
goto retfree;
goto ret;
}
#ifndef Avoid_Underflow
word0(rv) = Tiny0;
word1(rv) = Tiny1;
}
#endif
}
}
bd0 = s2b(s0, nd0, nd, y);
for(;;) {
bd = Balloc(bd0->k);
Bcopy(bd, bd0);
bb = d2b(dval(rv), &bbe, &bbbits);
bs = i2b(1);
if (e >= 0) {
bb2 = bb5 = 0;
bd2 = bd5 = e;
}
else {
bb2 = bb5 = -e;
bd2 = bd5 = 0;
}
if (bbe >= 0)
bb2 += bbe;
else
bd2 -= bbe;
bs2 = bb2;
#ifdef Honor_FLT_ROUNDS
if (rounding != 1)
bs2++;
#endif
#ifdef Avoid_Underflow
j = bbe - scale;
i = j + bbbits - 1;
if (i < Emin)
j += P - Emin;
else
j = P + 1 - bbbits;
#else
#ifdef Sudden_Underflow
#ifdef IBM
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
j = P + 1 - bbbits;
#endif
#else
j = bbe;
i = j + bbbits - 1;
if (i < Emin)
j += P - Emin;
else
j = P + 1 - bbbits;
#endif
#endif
bb2 += j;
bd2 += j;
#ifdef Avoid_Underflow
bd2 += scale;
#endif
i = bb2 < bd2 ? bb2 : bd2;
if (i > bs2)
i = bs2;
if (i > 0) {
bb2 -= i;
bd2 -= i;
bs2 -= i;
}
if (bb5 > 0) {
bs = pow5mult(bs, bb5);
bb1 = mult(bs, bb);
Bfree(bb);
bb = bb1;
}
if (bb2 > 0)
bb = lshift(bb, bb2);
if (bd5 > 0)
bd = pow5mult(bd, bd5);
if (bd2 > 0)
bd = lshift(bd, bd2);
if (bs2 > 0)
bs = lshift(bs, bs2);
delta = diff(bb, bd);
dsign = delta->sign;
delta->sign = 0;
i = cmp(delta, bs);
#ifdef Honor_FLT_ROUNDS
if (rounding != 1) {
if (i < 0) {
if (!delta->x[0] && delta->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
break;
}
if (rounding) {
if (dsign) {
adj = 1.;
goto apply_adj;
}
}
else if (!dsign) {
adj = -1.;
if (!word1(rv)
&& !(word0(rv) & Frac_mask)) {
y = word0(rv) & Exp_mask;
#ifdef Avoid_Underflow
if (!scale || y > 2*P*Exp_msk1)
#else
if (y)
#endif
{
delta = lshift(delta,Log2P);
if (cmp(delta, bs) <= 0)
adj = -0.5;
}
}
apply_adj:
#ifdef Avoid_Underflow
if (scale && (y = word0(rv) & Exp_mask)
<= 2*P*Exp_msk1)
word0(adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <=
P*Exp_msk1) {
word0(rv) += P*Exp_msk1;
dval(rv) += adj*ulp(dval(rv));
word0(rv) -= P*Exp_msk1;
}
else
#endif
#endif
dval(rv) += adj*ulp(dval(rv));
}
break;
}
adj = ratio(delta, bs);
if (adj < 1.)
adj = 1.;
if (adj <= 0x7ffffffe) {
y = adj;
if (y != adj) {
if (!((rounding>>1) ^ dsign))
y++;
adj = y;
}
}
#ifdef Avoid_Underflow
if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
word0(adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
word0(rv) += P*Exp_msk1;
adj *= ulp(dval(rv));
if (dsign)
dval(rv) += adj;
else
dval(rv) -= adj;
word0(rv) -= P*Exp_msk1;
goto cont;
}
#endif
#endif
adj *= ulp(dval(rv));
if (dsign)
dval(rv) += adj;
else
dval(rv) -= adj;
goto cont;
}
#endif
if (i < 0) {
if (dsign || word1(rv) || word0(rv) & Bndry_mask
#ifdef IEEE_Arith
#ifdef Avoid_Underflow
|| (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
#else
|| (word0(rv) & Exp_mask) <= Exp_msk1
#endif
#endif
) {
#ifdef SET_INEXACT
if (!delta->x[0] && delta->wds <= 1)
inexact = 0;
#endif
break;
}
if (!delta->x[0] && delta->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
break;
}
delta = lshift(delta,Log2P);
if (cmp(delta, bs) > 0)
goto drop_down;
break;
}
if (i == 0) {
if (dsign) {
if ((word0(rv) & Bndry_mask1) == Bndry_mask1
&& word1(rv) == (
#ifdef Avoid_Underflow
(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
#endif
0xffffffff)) {
word0(rv) = (word0(rv) & Exp_mask)
+ Exp_msk1
#ifdef IBM
| Exp_msk1 >> 4
#endif
;
word1(rv) = 0;
#ifdef Avoid_Underflow
dsign = 0;
#endif
break;
}
}
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
drop_down:
#ifdef Sudden_Underflow
L = word0(rv) & Exp_mask;
#ifdef IBM
if (L < Exp_msk1)
#else
#ifdef Avoid_Underflow
if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
#else
if (L <= Exp_msk1)
#endif
#endif
goto undfl;
L -= Exp_msk1;
#else
#ifdef Avoid_Underflow
if (scale) {
L = word0(rv) & Exp_mask;
if (L <= (2*P+1)*Exp_msk1) {
if (L > (P+2)*Exp_msk1)
break;
goto undfl;
}
}
#endif
L = (word0(rv) & Exp_mask) - Exp_msk1;
#endif
word0(rv) = L | Bndry_mask1;
word1(rv) = 0xffffffff;
#ifdef IBM
goto cont;
#else
break;
#endif
}
#ifndef ROUND_BIASED
if (!(word1(rv) & LSB))
break;
#endif
if (dsign)
dval(rv) += ulp(dval(rv));
#ifndef ROUND_BIASED
else {
dval(rv) -= ulp(dval(rv));
#ifndef Sudden_Underflow
if (!dval(rv))
goto undfl;
#endif
}
#ifdef Avoid_Underflow
dsign = 1 - dsign;
#endif
#endif
break;
}
if ((aadj = ratio(delta, bs)) <= 2.) {
if (dsign)
aadj = aadj1 = 1.;
else if (word1(rv) || word0(rv) & Bndry_mask) {
#ifndef Sudden_Underflow
if (word1(rv) == Tiny1 && !word0(rv))
goto undfl;
#endif
aadj = 1.;
aadj1 = -1.;
}
else {
if (aadj < 2./FLT_RADIX)
aadj = 1./FLT_RADIX;
else
aadj *= 0.5;
aadj1 = -aadj;
}
}
else {
aadj *= 0.5;
aadj1 = dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
switch(Rounding) {
case 2:
aadj1 -= 0.5;
break;
case 0:
case 3:
aadj1 += 0.5;
}
#else
if (Flt_Rounds == 0)
aadj1 += 0.5;
#endif
}
y = word0(rv) & Exp_mask;
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
dval(rv0) = dval(rv);
word0(rv) -= P*Exp_msk1;
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
if ((word0(rv) & Exp_mask) >=
Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
if (word0(rv0) == Big0 && word1(rv0) == Big1)
goto ovfl;
word0(rv) = Big0;
word1(rv) = Big1;
goto cont;
}
else
word0(rv) += P*Exp_msk1;
}
else {
#ifdef Avoid_Underflow
if (scale && y <= 2*P*Exp_msk1) {
if (aadj <= 0x7fffffff) {
if ((z = (ULong)aadj) <= 0)
z = 1;
aadj = z;
aadj1 = dsign ? aadj : -aadj;
}
word0(aadj1) += (2*P+1)*Exp_msk1 - y;
}
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
#else
#ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
dval(rv0) = dval(rv);
word0(rv) += P*Exp_msk1;
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
#ifdef IBM
if ((word0(rv) & Exp_mask) < P*Exp_msk1)
#else
if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
#endif
{
if (word0(rv0) == Tiny0
&& word1(rv0) == Tiny1)
goto undfl;
word0(rv) = Tiny0;
word1(rv) = Tiny1;
goto cont;
}
else
word0(rv) -= P*Exp_msk1;
}
else {
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
}
#else
if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
aadj1 = (double)(int)(aadj + 0.5);
if (!dsign)
aadj1 = -aadj1;
}
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
#endif
#endif
}
z = word0(rv) & Exp_mask;
#ifndef SET_INEXACT
#ifdef Avoid_Underflow
if (!scale)
#endif
if (y == z) {
L = (Long)aadj;
aadj -= L;
if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
if (aadj < .4999999 || aadj > .5000001)
break;
}
else if (aadj < .4999999/FLT_RADIX)
break;
}
#endif
cont:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(delta);
}
#ifdef SET_INEXACT
if (inexact) {
if (!oldinexact) {
word0(rv0) = Exp_1 + (70 << Exp_shift);
word1(rv0) = 0;
dval(rv0) += 1.;
}
}
else if (!oldinexact)
clear_inexact();
#endif
#ifdef Avoid_Underflow
if (scale) {
word0(rv0) = Exp_1 - 2*P*Exp_msk1;
word1(rv0) = 0;
dval(rv) *= dval(rv0);
#ifndef NO_ERRNO
if (word0(rv) == 0 && word1(rv) == 0)
errno = ERANGE;
#endif
}
#endif
#ifdef SET_INEXACT
if (inexact && !(word0(rv) & Exp_mask)) {
dval(rv0) = 1e-300;
dval(rv0) *= dval(rv0);
}
#endif
retfree:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(bd0);
Bfree(delta);
ret:
if (se)
*se = (char *)s;
return sign ? -dval(rv) : dval(rv);
}
static int
quorem
#ifdef KR_headers
(b, S) Bigint *b, *S;
#else
(Bigint *b, Bigint *S)
#endif
{
int n;
ULong *bx, *bxe, q, *sx, *sxe;
#ifdef ULLong
ULLong borrow, carry, y, ys;
#else
ULong borrow, carry, y, ys;
#ifdef Pack_32
ULong si, z, zs;
#endif
#endif
n = S->wds;
#ifdef DEBUG
if (b->wds > n)
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);
#ifdef DEBUG
if (q > 9)
Bug("oversized quotient in quorem");
#endif
if (q) {
borrow = 0;
carry = 0;
do {
#ifdef ULLong
ys = *sx++ * (ULLong)q + carry;
carry = ys >> 32;
y = *bx - (ys & FFFFFFFF) - borrow;
borrow = y >> 32 & (ULong)1;
*bx++ = y & FFFFFFFF;
#else
#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 & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
#else
ys = *sx++ * q + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
*bx++ = y & 0xffff;
#endif
#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 ULLong
ys = *sx++ + carry;
carry = ys >> 32;
y = *bx - (ys & FFFFFFFF) - borrow;
borrow = y >> 32 & (ULong)1;
*bx++ = y & FFFFFFFF;
#else
#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 & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
#else
ys = *sx++ + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
*bx++ = y & 0xffff;
#endif
#endif
}
while(sx <= sxe);
bx = b->x;
bxe = bx + n;
if (!*bxe) {
while(--bxe > bx && !*bxe)
--n;
b->wds = n;
}
}
return q;
}
#ifndef MULTIPLE_THREADS
static char *dtoa_result;
#endif
static char *
#ifdef KR_headers
rv_alloc(i) int i;
#else
rv_alloc(int i)
#endif
{
int j, k, *r;
j = sizeof(ULong);
for(k = 0;
sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
j <<= 1)
k++;
r = (int*)Balloc(k);
*r = k;
return
#ifndef MULTIPLE_THREADS
dtoa_result =
#endif
(char *)(r+1);
}
static char *
#ifdef KR_headers
nrv_alloc(s, rve, n) char *s, **rve; int n;
#else
nrv_alloc(CONST char *s, char **rve, int n)
#endif
{
char *rv, *t;
t = rv = rv_alloc(n);
while((*t = *s++)) t++;
if (rve)
*rve = t;
return rv;
}
void
#ifdef KR_headers
freedtoa(s) char *s;
#else
freedtoa(char *s)
#endif
{
Bigint *b = (Bigint *)((int *)s - 1);
b->maxwds = 1 << (b->k = *(int*)b);
Bfree(b);
#ifndef MULTIPLE_THREADS
if (s == dtoa_result)
dtoa_result = 0;
#endif
}
char *
dtoa
#ifdef KR_headers
(d, mode, ndigits, decpt, sign, rve)
double d; int mode, ndigits, *decpt, *sign; char **rve;
#else
(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
#endif
{
int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
spec_case, try_quick;
Long L;
#ifndef Sudden_Underflow
int denorm;
ULong x;
#endif
Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
double d2, ds, eps;
char *s, *s0;
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
#ifndef MULTIPLE_THREADS
if (dtoa_result) {
freedtoa(dtoa_result);
dtoa_result = 0;
}
#endif
if (word0(d) & Sign_bit) {
*sign = 1;
word0(d) &= ~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
{
*decpt = 9999;
#ifdef IEEE_Arith
if (!word1(d) && !(word0(d) & 0xfffff))
return nrv_alloc("Infinity", rve, 8);
#endif
return nrv_alloc("NaN", rve, 3);
}
#endif
#ifdef IBM
dval(d) += 0;
#endif
if (!dval(d)) {
*decpt = 1;
return nrv_alloc("0", rve, 1);
}
#ifdef SET_INEXACT
try_quick = oldinexact = get_inexact();
inexact = 1;
#endif
#ifdef Honor_FLT_ROUNDS
if ((rounding = Flt_Rounds) >= 2) {
if (*sign)
rounding = rounding == 2 ? 0 : 2;
else
if (rounding != 2)
rounding = 0;
}
#endif
b = d2b(dval(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
dval(d2) = dval(d);
word0(d2) &= Frac_mask1;
word0(d2) |= Exp_11;
#ifdef IBM
if (j = 11 - hi0bits(word0(d2) & Frac_mask))
dval(d2) /= 1 << j;
#endif
i -= Bias;
#ifdef IBM
i <<= 2;
i += j;
#endif
#ifndef Sudden_Underflow
denorm = 0;
}
else {
i = bbits + be + (Bias + (P-1) - 1);
x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
: word1(d) << 32 - i;
dval(d2) = x;
word0(d2) -= 31*Exp_msk1;
i -= (Bias + (P-1) - 1) + 1;
denorm = 1;
}
#endif
ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
k = (int)ds;
if (ds < 0. && ds != k)
k--;
k_check = 1;
if (k >= 0 && k <= Ten_pmax) {
if (dval(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;
#ifndef SET_INEXACT
#ifdef Check_FLT_ROUNDS
try_quick = Rounding == 1;
#else
try_quick = 1;
#endif
#endif
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;
case 4:
if (ndigits <= 0)
ndigits = 1;
ilim = ilim1 = i = ndigits;
break;
case 3:
leftright = 0;
case 5:
i = ndigits + k + 1;
ilim = i;
ilim1 = i - 1;
if (i <= 0)
i = 1;
}
s = s0 = rv_alloc(i);
#ifdef Honor_FLT_ROUNDS
if (mode > 1 && rounding != 1)
leftright = 0;
#endif
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
i = 0;
dval(d2) = dval(d);
k0 = k;
ilim0 = ilim;
ieps = 2;
if (k > 0) {
ds = tens[k&0xf];
j = k >> 4;
if (j & Bletch) {
j &= Bletch - 1;
dval(d) /= bigtens[n_bigtens-1];
ieps++;
}
for(; j; j >>= 1, i++)
if (j & 1) {
ieps++;
ds *= bigtens[i];
}
dval(d) /= ds;
}
else if ((j1 = -k)) {
dval(d) *= tens[j1 & 0xf];
for(j = j1 >> 4; j; j >>= 1, i++)
if (j & 1) {
ieps++;
dval(d) *= bigtens[i];
}
}
if (k_check && dval(d) < 1. && ilim > 0) {
if (ilim1 <= 0)
goto fast_failed;
ilim = ilim1;
k--;
dval(d) *= 10.;
ieps++;
}
dval(eps) = ieps*dval(d) + 7.;
word0(eps) -= (P-1)*Exp_msk1;
if (ilim == 0) {
S = mhi = 0;
dval(d) -= 5.;
if (dval(d) > dval(eps))
goto one_digit;
if (dval(d) < -dval(eps))
goto no_digits;
goto fast_failed;
}
#ifndef No_leftright
if (leftright) {
dval(eps) = 0.5/tens[ilim-1] - dval(eps);
for(i = 0;;) {
L = (long int)dval(d);
dval(d) -= L;
*s++ = '0' + (int)L;
if (dval(d) < dval(eps))
goto ret1;
if (1. - dval(d) < dval(eps))
goto bump_up;
if (++i >= ilim)
break;
dval(eps) *= 10.;
dval(d) *= 10.;
}
}
else {
#endif
dval(eps) *= tens[ilim-1];
for(i = 1;; i++, dval(d) *= 10.) {
L = (Long)(dval(d));
if (!(dval(d) -= L))
ilim = i;
*s++ = '0' + (int)L;
if (i == ilim) {
if (dval(d) > 0.5 + dval(eps))
goto bump_up;
else if (dval(d) < 0.5 - dval(eps)) {
while(*--s == '0');
s++;
goto ret1;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = s0;
dval(d) = dval(d2);
k = k0;
ilim = ilim0;
}
if (be >= 0 && k <= Int_max) {
ds = tens[k];
if (ndigits < 0 && ilim <= 0) {
S = mhi = 0;
if (ilim < 0 || dval(d) <= 5*ds)
goto no_digits;
goto one_digit;
}
for(i = 1;; i++, dval(d) *= 10.) {
L = (Long)(dval(d) / ds);
dval(d) -= L*ds;
#ifdef Check_FLT_ROUNDS
if (dval(d) < 0) {
L--;
dval(d) += ds;
}
#endif
*s++ = '0' + (int)L;
if (!dval(d)) {
#ifdef SET_INEXACT
inexact = 0;
#endif
break;
}
if (i == ilim) {
#ifdef Honor_FLT_ROUNDS
if (mode > 1)
switch(rounding) {
case 0: goto ret1;
case 2: goto bump_up;
}
#endif
dval(d) += dval(d);
if (dval(d) > ds || dval(d) == ds && L & 1) {
bump_up:
while(*--s == '9')
if (s == s0) {
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
}
goto ret1;
}
m2 = b2;
m5 = b5;
mhi = mlo = 0;
if (leftright) {
i =
#ifndef Sudden_Underflow
denorm ? be + (Bias + (P-1) - 1 + 1) :
#endif
#ifdef IBM
1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
#else
1 + P - bbits;
#endif
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);
spec_case = 0;
if ((mode < 2 || leftright)
#ifdef Honor_FLT_ROUNDS
&& rounding == 1
#endif
) {
if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0(d) & (Exp_mask & ~Exp_msk1)
#endif
) {
b2 += Log2P;
s2 += Log2P;
spec_case = 1;
}
}
#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);
if (leftright)
mhi = multadd(mhi, 10, 0);
ilim = ilim1;
}
}
if (ilim <= 0 && (mode == 3 || mode == 5)) {
if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
no_digits:
k = -1 - ndigits;
goto ret;
}
one_digit:
*s++ = '1';
k++;
goto ret;
}
if (leftright) {
if (m2 > 0)
mhi = lshift(mhi, m2);
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';
j = cmp(b, mlo);
delta = diff(S, mhi);
j1 = delta->sign ? 1 : cmp(b, delta);
Bfree(delta);
#ifndef ROUND_BIASED
if (j1 == 0 && mode != 1 && !(word1(d) & 1)
#ifdef Honor_FLT_ROUNDS
&& rounding >= 1
#endif
) {
if (dig == '9')
goto round_9_up;
if (j > 0)
dig++;
#ifdef SET_INEXACT
else if (!b->x[0] && b->wds <= 1)
inexact = 0;
#endif
*s++ = dig;
goto ret;
}
#endif
if (j < 0 || j == 0 && mode != 1
#ifndef ROUND_BIASED
&& !(word1(d) & 1)
#endif
) {
if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
goto accept_dig;
}
#ifdef Honor_FLT_ROUNDS
if (mode > 1)
switch(rounding) {
case 0: goto accept_dig;
case 2: goto keep_dig;
}
#endif
if (j1 > 0) {
b = lshift(b, 1);
j1 = cmp(b, S);
if ((j1 > 0 || j1 == 0 && dig & 1)
&& dig++ == '9')
goto round_9_up;
}
accept_dig:
*s++ = dig;
goto ret;
}
if (j1 > 0) {
#ifdef Honor_FLT_ROUNDS
if (!rounding)
goto accept_dig;
#endif
if (dig == '9') {
round_9_up:
*s++ = '9';
goto roundoff;
}
*s++ = dig + 1;
goto ret;
}
#ifdef Honor_FLT_ROUNDS
keep_dig:
#endif
*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 (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
goto ret;
}
if (i >= ilim)
break;
b = multadd(b, 10, 0);
}
#ifdef Honor_FLT_ROUNDS
switch(rounding) {
case 0: goto trimzeros;
case 2: goto roundoff;
}
#endif
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 {
#ifdef Honor_FLT_ROUNDS
trimzeros:
#endif
while(*--s == '0');
s++;
}
ret:
Bfree(S);
if (mhi) {
if (mlo && mlo != mhi)
Bfree(mlo);
Bfree(mhi);
}
ret1:
#ifdef SET_INEXACT
if (inexact) {
if (!oldinexact) {
word0(d) = Exp_1 + (70 << Exp_shift);
word1(d) = 0;
dval(d) += 1.;
}
}
else if (!oldinexact)
clear_inexact();
#endif
Bfree(b);
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
return s0;
}
#ifdef __cplusplus
}
#endif