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inum200.h
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inum200.h
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/*
* Ruby's Integer part from ruby_2_0_0, r47627.
*
* These are hand copies (with few modifications) taken from original
* Ruby's code in "numeric.c" and "bignum.c," so the copyrights are
* held by matz and other contributors:
*
* Copyright (C) 1993-2014 Yukihiro Matsumoto
*
*/
/*
* copied from internal.h
*/
#define MUL_OVERFLOW_SIGNED_INTEGER_P(a, b, min, max) ( \
(a) == 0 ? 0 : \
(a) == -1 ? (b) < -(max) : \
(a) > 0 ? \
((b) > 0 ? (max) / (a) < (b) : (min) / (a) > (b)) : \
((b) > 0 ? (min) / (a) < (b) : (max) / (a) > (b)))
#define MUL_OVERFLOW_FIXNUM_P(a, b) MUL_OVERFLOW_SIGNED_INTEGER_P(a, b, FIXNUM_MIN, FIXNUM_MAX)
/*
* copied from util.c
*/
#include <errno.h>
#ifdef WORDS_BIGENDIAN
#define IEEE_BIG_ENDIAN
#else
#define IEEE_LITTLE_ENDIAN
#endif
#ifdef __vax__
#define VAX
#undef IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif
#if defined(__arm__) && !defined(__VFP_FP__)
#define IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif
#undef Long
#undef ULong
#if SIZEOF_INT == 4
#define Long int
#define ULong unsigned int
#elif SIZEOF_LONG == 4
#define Long long int
#define ULong unsigned long int
#endif
#if HAVE_LONG_LONG
#define Llong LONG_LONG
#endif
#ifdef DEBUG
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
#endif
#include "stdlib.h"
#include "string.h"
#ifdef USE_LOCALE
#include "locale.h"
#endif
#ifdef MALLOC
extern void *MALLOC(size_t);
#else
#define MALLOC malloc
#endif
#ifdef FREE
extern void FREE(void*);
#else
#define FREE free
#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_BIG_ENDIAN
#define IEEE_Arith
#endif
#ifdef IEEE_LITTLE_ENDIAN
#define IEEE_Arith
#endif
#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 /*IEEE_Arith*/
#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 /* ifndef Bad_float_h */
#include "float.h"
#endif /* Bad_float_h */
#ifndef __MATH_H__
#include "math.h"
#endif
#ifdef __cplusplus
extern "C" {
#if 0
} /* satisfy cc-mode */
#endif
#endif
#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
#endif
typedef union { double d; ULong L[2]; } U;
#ifdef YES_ALIAS
typedef double double_u;
# define dval(x) (x)
# ifdef IEEE_LITTLE_ENDIAN
# 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
typedef U double_u;
# ifdef IEEE_LITTLE_ENDIAN
# define word0(x) ((x).L[1])
# define word1(x) ((x).L[0])
# else
# define word0(x) ((x).L[0])
# define word1(x) ((x).L[1])
# endif
# define dval(x) ((x).d)
#endif
/* The following definition of Storeinc is appropriate for MIPS processors.
* An alternative that might be better on some machines is
* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
*/
#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
#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
/* #define P DBL_MANT_DIG */
/* 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) */
#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 /* debugging option */
#undef Sudden_Underflow
#endif
#endif
#ifndef Flt_Rounds
#ifdef FLT_ROUNDS
#define Flt_Rounds FLT_ROUNDS
#else
#define Flt_Rounds 1
#endif
#endif /*Flt_Rounds*/
#ifdef Honor_FLT_ROUNDS
#define Rounding rounding
#undef Check_FLT_ROUNDS
#define Check_FLT_ROUNDS
#else
#define Rounding Flt_Rounds
#endif
#else /* ifndef IEEE_Arith */
#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 /* exponent has 7 bits, but 8 is the right value in b2d */
#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 /* VAX */
#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 /* IBM, VAX */
#endif /* IEEE_Arith */
#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)))
extern double rnd_prod(double, double), rnd_quot(double, double);
#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
#define FFFFFFFF 0xffffffffUL
#ifdef NO_LONG_LONG
#undef ULLong
#ifdef Just_16
#undef Pack_32
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
* This makes some inner loops simpler and sometimes saves work
* during multiplications, but it often seems to make things slightly
* slower. Hence the default is now to store 32 bits per Long.
*/
#endif
#else /* long long available */
#ifndef Llong
#define Llong long long
#endif
#ifndef ULLong
#define ULLong unsigned Llong
#endif
#endif /* NO_LONG_LONG */
#define MULTIPLE_THREADS 1
#ifndef MULTIPLE_THREADS
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
#define FREE_DTOA_LOCK(n) /*nothing*/
#else
#define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
#define FREE_DTOA_LOCK(n) /*unused right now*/
#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(int k)
{
int x;
Bigint *rv;
#ifndef Omit_Private_Memory
size_t len;
#endif
ACQUIRE_DTOA_LOCK(0);
if (k <= Kmax && (rv = freelist[k]) != 0) {
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 (k <= Kmax && 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(Bigint *v)
{
if (v) {
if (v->k > Kmax) {
FREE(v);
return;
}
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(Bigint *b, int m, int a) /* multiply by m and add a */
{
int i, wds;
ULong *x;
#ifdef ULLong
ULLong carry, y;
#else
ULong carry, 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++ = (ULong)(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++] = (ULong)carry;
b->wds = wds;
}
return b;
}
/* removed: s2b() */
static int
hi0bits(register ULong 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(ULong *y)
{
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)
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;
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++) != 0) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * (ULLong)y + *xc + carry;
carry = z >> 32;
*xc++ = (ULong)(z & FFFFFFFF);
} while (x < xae);
*xc = (ULong)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 = (ULong)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 = (ULong)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(Bigint *b, int k)
{
Bigint *b1, *p5, *p51;
int i;
static int p05[3] = { 5, 25, 125 };
if ((i = k & 3) != 0)
b = multadd(b, p05[i-1], 0);
if (!(k >>= 2))
return b;
if (!(p5 = p5s)) {
/* first time */
#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(Bigint *b, int k)
{
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) != 0)
++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;
}
/* renamed from cmp() */
static int
bicmp(Bigint *a, Bigint *b)
{
ULong *xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
#ifdef DEBUG
if (i > 1 && !a->x[i-1])
Bug("bicmp called with a->x[a->wds-1] == 0");
if (j > 1 && !b->x[j-1])
Bug("bicmp 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(Bigint *a, Bigint *b)
{
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 = bicmp(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++ = (ULong)(y & FFFFFFFF);
} while (xb < xbe);
while (xa < xae) {
y = *xa++ - borrow;
borrow = y >> 32 & (ULong)1;
*xc++ = (ULong)(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;
}
/* removed: ulp(), b2d() */
static Bigint *
d2b(double d_, int *e, int *bits)
{
double_u d;
Bigint *b;
int de, k;
ULong *x, y, z;
#ifndef Sudden_Underflow
int i;
#endif
#ifdef VAX
ULong d0, d1;
#endif
dval(d) = d_;
#ifdef VAX
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; /* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
de = (int)(d0 >> Exp_shift);
#ifndef IBM
z |= Exp_msk11;
#endif
#else
if ((de = (int)(d0 >> Exp_shift)) != 0)
z |= Exp_msk1;
#endif
#ifdef Pack_32
if ((y = d1) != 0) {
if ((k = lo0bits(&y)) != 0) {
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