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bionic/libc/stdlib/strtod.c
Elliott Hughes 205c7887ad Clean up reentrancy cruft. 
The DNS copy of reentrant.h was unused, so remove it.

The strtod implementation can use the upstream-netbsd reentrant.h and
get a little closer to what was then upstream. (It's since been replaced
by gdtoa, and we'll have to follow at some point, but for now this doesn't
make anything any worse.)

ANDROID_CHANGES is (now) only used in the DNS code, so push the -D
down.

The <locale.h> change prevents an LP32 hack from leaking into LP64.

Change-Id: Idf30b98a59d7ca8f7c6cd6d07020b512057911ef
2014-03-13 16:17:43 -07:00

2693 lines
53 KiB
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/* $NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $ */
/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991 by AT&T.
*
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
* is included in all copies of any software which is or includes a copy
* or modification of this software and in all copies of the supporting
* documentation for such software.
*
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*
***************************************************************/
/* Please send bug reports to
David M. Gay
AT&T Bell Laboratories, Room 2C-463
600 Mountain Avenue
Murray Hill, NJ 07974-2070
U.S.A.
dmg@research.att.com or research!dmg
*/
/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
*
* This strtod returns a nearest machine number to the input decimal
* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
* broken by the IEEE round-even rule. Otherwise ties are broken by
* biased rounding (add half and chop).
*
* Inspired loosely by William D. Clinger's paper "How to Read Floating
* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
*
* Modifications:
*
* 1. We only require IEEE, IBM, or VAX double-precision
* arithmetic (not IEEE double-extended).
* 2. We get by with floating-point arithmetic in a case that
* Clinger missed -- when we're computing d * 10^n
* for a small integer d and the integer n is not too
* much larger than 22 (the maximum integer k for which
* we can represent 10^k exactly), we may be able to
* compute (d*10^k) * 10^(e-k) with just one roundoff.
* 3. Rather than a bit-at-a-time adjustment of the binary
* result in the hard case, we use floating-point
* arithmetic to determine the adjustment to within
* one bit; only in really hard cases do we need to
* compute a second residual.
* 4. Because of 3., we don't need a large table of powers of 10
* for ten-to-e (just some small tables, e.g. of 10^k
* for 0 <= k <= 22).
*/
/*
* #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
* significant byte has the lowest address.
* #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
* significant byte has the lowest address.
* #define Long int on machines with 32-bit ints and 64-bit longs.
* #define Sudden_Underflow for IEEE-format machines without gradual
* underflow (i.e., that flush to zero on underflow).
* #define IBM for IBM mainframe-style floating-point arithmetic.
* #define VAX for VAX-style floating-point arithmetic.
* #define Unsigned_Shifts if >> does treats its left operand as unsigned.
* #define No_leftright to omit left-right logic in fast floating-point
* computation of dtoa.
* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
* #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
* that use extended-precision instructions to compute rounded
* products and quotients) with IBM.
* #define ROUND_BIASED for IEEE-format with biased rounding.
* #define Inaccurate_Divide for IEEE-format with correctly rounded
* products but inaccurate quotients, e.g., for Intel i860.
* #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
* integer arithmetic. Whether this speeds things up or slows things
* down depends on the machine and the number being converted.
* #define KR_headers for old-style C function headers.
* #define Bad_float_h if your system lacks a float.h or if it does not
* define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
* FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
* #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
* if memory is available and otherwise does something you deem
* appropriate. If MALLOC is undefined, malloc will be invoked
* directly -- and assumed always to succeed.
*/
#include <sys/cdefs.h>
#if defined(LIBC_SCCS) && !defined(lint)
__RCSID("$NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $");
#endif /* LIBC_SCCS and not lint */
#define Unsigned_Shifts
#if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \
defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \
defined(__powerpc__) || defined(__sh__) || defined(__x86_64__) || \
defined(__hppa__) || \
(defined(__arm__) && defined(__VFP_FP__)) || defined(__aarch64__)
#include <endian.h>
#if BYTE_ORDER == BIG_ENDIAN
#define IEEE_BIG_ENDIAN
#else
#define IEEE_LITTLE_ENDIAN
#endif
#endif
#if defined(__arm__) && !defined(__VFP_FP__)
/*
* Although the CPU is little endian the FP has different
* byte and word endianness. The byte order is still little endian
* but the word order is big endian.
*/
#define IEEE_BIG_ENDIAN
#endif
#ifdef __vax__
#define VAX
#endif
#if defined(__hppa__) || defined(__mips__) || defined(__sh__)
#define NAN_WORD0 0x7ff40000
#else
#define NAN_WORD0 0x7ff80000
#endif
#define NAN_WORD1 0
#define Long int32_t
#define ULong u_int32_t
#ifdef DEBUG
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#endif
#ifdef __cplusplus
#include "malloc.h"
#include "memory.h"
#else
#ifndef KR_headers
#include "stdlib.h"
#include "string.h"
#include "locale.h"
#else
#include "malloc.h"
#include "memory.h"
#endif
#endif
#include "../upstream-netbsd/extern.h" /* Android-changed. */
#include "../upstream-netbsd/reentrant.h" /* Android-changed. */
#ifdef MALLOC
#ifdef KR_headers
extern char *MALLOC();
#else
extern void *MALLOC(size_t);
#endif
#else
#define MALLOC malloc
#endif
#include "ctype.h"
#include "errno.h"
#include "float.h"
#ifndef __MATH_H__
#include "math.h"
#endif
#ifdef __cplusplus
extern "C" {
#endif
#ifndef CONST
#ifdef KR_headers
#define CONST /* blank */
#else
#define CONST const
#endif
#endif
#ifdef Unsigned_Shifts
#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
#else
#define Sign_Extend(a,b) /*no-op*/
#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 ul[2];
} _double;
#define value(x) ((x).d)
#ifdef IEEE_LITTLE_ENDIAN
#define word0(x) ((x).ul[1])
#define word1(x) ((x).ul[0])
#else
#define word0(x) ((x).ul[0])
#define word1(x) ((x).ul[1])
#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) \
(((u_short *)(void *)a)[1] = \
(u_short)b, ((u_short *)(void *)a)[0] = (u_short)c, a++)
#else
#define Storeinc(a,b,c) \
(((u_short *)(void *)a)[0] = \
(u_short)b, ((u_short *)(void *)a)[1] = (u_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) */
#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
#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 */
#else
#undef Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#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 */
#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 Just_16
/* 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.
*/
#ifndef Pack_32
#define Pack_32
#endif
#endif
#define Kmax 15
#ifdef __cplusplus
extern "C" double strtod(const char *s00, char **se);
extern "C" char *__dtoa(double d, int mode, int ndigits,
int *decpt, int *sign, char **rve);
#endif
struct
Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
static Bigint *freelist[Kmax+1];
#ifdef _REENTRANT
static mutex_t freelist_mutex = MUTEX_INITIALIZER;
#endif
/* Special value used to indicate an invalid Bigint value,
* e.g. when a memory allocation fails. The idea is that we
* want to avoid introducing NULL checks everytime a bigint
* computation is performed. Also the NULL value can also be
* already used to indicate "value not initialized yet" and
* returning NULL might alter the execution code path in
* case of OOM.
*/
#define BIGINT_INVALID ((Bigint *)&bigint_invalid_value)
static const Bigint bigint_invalid_value;
/* Return BIGINT_INVALID on allocation failure.
*
* Most of the code here depends on the fact that this function
* never returns NULL.
*/
static Bigint *
Balloc
#ifdef KR_headers
(k) int k;
#else
(int k)
#endif
{
int x;
Bigint *rv;
mutex_lock(&freelist_mutex);
if ((rv = freelist[k]) != NULL) {
freelist[k] = rv->next;
}
else {
x = 1 << k;
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
if (rv == NULL) {
rv = BIGINT_INVALID;
goto EXIT;
}
rv->k = k;
rv->maxwds = x;
}
rv->sign = rv->wds = 0;
EXIT:
mutex_unlock(&freelist_mutex);
return rv;
}
static void
Bfree
#ifdef KR_headers
(v) Bigint *v;
#else
(Bigint *v)
#endif
{
if (v && v != BIGINT_INVALID) {
mutex_lock(&freelist_mutex);
v->next = freelist[v->k];
freelist[v->k] = v;
mutex_unlock(&freelist_mutex);
}
}
#define Bcopy_valid(x,y) memcpy(&(x)->sign, &(y)->sign, \
(y)->wds*sizeof(Long) + 2*sizeof(int))
#define Bcopy(x,y) Bcopy_ptr(&(x),(y))
static void
Bcopy_ptr(Bigint **px, Bigint *y)
{
if (*px == BIGINT_INVALID)
return; /* no space to store copy */
if (y == BIGINT_INVALID) {
Bfree(*px); /* invalid input */
*px = BIGINT_INVALID;
} else {
Bcopy_valid(*px,y);
}
}
static Bigint *
multadd
#ifdef KR_headers
(b, m, a) Bigint *b; int m, a;
#else
(Bigint *b, int m, int a) /* multiply by m and add a */
#endif
{
int i, wds;
ULong *x, y;
#ifdef Pack_32
ULong xi, z;
#endif
Bigint *b1;
if (b == BIGINT_INVALID)
return b;
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);
if (b1 == BIGINT_INVALID) {
Bfree(b);
return b1;
}
Bcopy_valid(b1, b);
Bfree(b);
b = b1;
}
b->x[wds++] = a;
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);
if (b == BIGINT_INVALID)
return b;
b->x[0] = y9;
b->wds = 1;
#else
b = Balloc(k+1);
if (b == BIGINT_INVALID)
return b;
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) ULong x;
#else
(ULong x)
#endif
{
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
{
int k;
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);
if (b != BIGINT_INVALID) {
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 carry, y, z;
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
#ifdef Pack_32
ULong z2;
#endif
if (a == BIGINT_INVALID || b == BIGINT_INVALID)
return BIGINT_INVALID;
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);
if (c == BIGINT_INVALID)
return c;
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) != 0) {
x = xa;
xc = xc0;
carry = 0;
do {
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
Storeinc(xc, z2, z);
}
while(x < xae);
*xc = carry;
}
if ((y = *xb >> 16) != 0) {
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 pthread_mutex_t p5s_mutex = PTHREAD_MUTEX_INITIALIZER;
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 const int p05[3] = { 5, 25, 125 };
if (b == BIGINT_INVALID)
return b;
if ((i = k & 3) != 0)
b = multadd(b, p05[i-1], 0);
if (!(k = (unsigned int) k >> 2))
return b;
mutex_lock(&p5s_mutex);
if (!(p5 = p5s)) {
/* first time */
p5 = i2b(625);
if (p5 == BIGINT_INVALID) {
Bfree(b);
mutex_unlock(&p5s_mutex);
return p5;
}
p5s = p5;
p5->next = 0;
}
for(;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k = (unsigned int) k >> 1))
break;
if (!(p51 = p5->next)) {
p51 = mult(p5,p5);
if (p51 == BIGINT_INVALID) {
Bfree(b);
mutex_unlock(&p5s_mutex);
return p51;
}
p5->next = p51;
p51->next = 0;
}
p5 = p51;
}
mutex_unlock(&p5s_mutex);
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;
if (b == BIGINT_INVALID)
return b;
#ifdef Pack_32
n = (unsigned int)k >> 5;
#else
n = (unsigned int)k >> 4;
#endif
k1 = b->k;
n1 = n + b->wds + 1;
for(i = b->maxwds; n1 > i; i <<= 1)
k1++;
b1 = Balloc(k1);
if (b1 == BIGINT_INVALID) {
Bfree(b);
return b1;
}
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;
}
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;
if (a == BIGINT_INVALID || b == BIGINT_INVALID)
#ifdef DEBUG
Bug("cmp called with a or b invalid");
#else
return 0; /* equal - the best we can do right now */
#endif
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;
Long borrow, y; /* We need signed shifts here. */
ULong *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
Long z;
#endif
if (a == BIGINT_INVALID || b == BIGINT_INVALID)
return BIGINT_INVALID;
i = cmp(a,b);
if (!i) {
c = Balloc(0);
if (c != BIGINT_INVALID) {
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);
if (c == BIGINT_INVALID)
return c;
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 = (ULong)y >> 16;
Sign_Extend(borrow, y);
z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
borrow = (ULong)z >> 16;
Sign_Extend(borrow, z);
Storeinc(xc, z, y);
}
while(xb < xbe);
while(xa < xae) {
y = (*xa & 0xffff) + borrow;
borrow = (ULong)y >> 16;
Sign_Extend(borrow, y);
z = (*xa++ >> 16) + borrow;
borrow = (ULong)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 double
ulp
#ifdef KR_headers
(_x) double _x;
#else
(double _x)
#endif
{
_double x;
Long L;
_double a;
value(x) = _x;
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef Sudden_Underflow
if (L > 0) {
#endif
#ifdef IBM
L |= Exp_msk1 >> 4;
#endif
word0(a) = L;
word1(a) = 0;
#ifndef Sudden_Underflow
}
else {
L = (ULong)-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
return value(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
if (a == BIGINT_INVALID)
return NAN;
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 value(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, i, k;
ULong *x, y, z;
_double d;
#ifdef VAX
ULong d0, d1;
#endif
value(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
if (b == BIGINT_INVALID)
return b;
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;
i = b->wds = (x[1] = z) ? 2 : 1;
}
else {
#ifdef DEBUG
if (!z)
Bug("Zero passed to d2b");
#endif
k = lo0bits(&z);
x[0] = z;
i = 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;
if (a == BIGINT_INVALID || b == BIGINT_INVALID)
return NAN; /* for lack of better value ? */
value(da) = b2d(a, &ka);
value(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)
da *= 1 << k;
}
else {
k = -k;
word0(db) += (k >> 2)*Exp_msk1;
if (k &= 3)
db *= 1 << k;
}
#else
if (k > 0)
word0(da) += k*Exp_msk1;
else {
k = -k;
word0(db) += k*Exp_msk1;
}
#endif
return value(da) / value(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
};
#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
#ifdef IBM
static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
#define n_bigtens 3
#else
static CONST double bigtens[] = { 1e16, 1e32 };
static CONST double tinytens[] = { 1e-16, 1e-32 };
#define n_bigtens 2
#endif
#endif
double
strtod
#ifdef KR_headers
(s00, se) CONST char *s00; char **se;
#else
(CONST char *s00, char **se)
#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;
_double rv, rv0;
Long L;
ULong y, z;
Bigint *bb1, *bd0;
Bigint *bb = NULL, *bd = NULL, *bs = NULL, *delta = NULL;/* pacify gcc */
CONST char decimal_point = '.';
#if 0 /* BEGIN android-changed: no localeconv. */
#ifndef KR_headers
CONST char decimal_point = localeconv()->decimal_point[0];
#else
CONST char decimal_point = '.';
#endif
#endif /* END android-changed */
sign = nz0 = nz = 0;
value(rv) = 0.;
for(s = s00; isspace((unsigned char) *s); s++)
;
if (*s == '-') {
sign = 1;
s++;
} else if (*s == '+') {
s++;
}
if (*s == '\0') {
s = s00;
goto ret;
}
/* "INF" or "INFINITY" */
if (tolower((unsigned char)*s) == 'i' && strncasecmp(s, "inf", 3) == 0) {
if (strncasecmp(s + 3, "inity", 5) == 0)
s += 8;
else
s += 3;
value(rv) = HUGE_VAL;
goto ret;
}
#ifdef IEEE_Arith
/* "NAN" or "NAN(n-char-sequence-opt)" */
if (tolower((unsigned char)*s) == 'n' && strncasecmp(s, "nan", 3) == 0) {
/* Build a quiet NaN. */
word0(rv) = NAN_WORD0;
word1(rv) = NAN_WORD1;
s+= 3;
/* Don't interpret (n-char-sequence-opt), for now. */
if (*s == '(') {
s0 = s;
for (s++; *s != ')' && *s != '\0'; s++)
;
if (*s == ')')
s++; /* Skip over closing paren ... */
else
s = s0; /* ... otherwise go back. */
}
goto ret;
}
#endif
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;
if (c == decimal_point) {
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) {
s = s00;
goto ret;
}
s00 = s;
esign = 0;
switch(c = *++s) {
case '-':
esign = 1;
/* FALLTHROUGH */
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)
/* Avoid confusion from exponents
* so large that e might overflow.
*/
e = 19999; /* safe for 16 bit ints */
else
e = (int)L;
if (esign)
e = -e;
}
else
e = 0;
}
else
s = s00;
}
if (!nd) {
if (!nz && !nz0)
s = s00;
goto ret;
}
e1 = e -= nf;
/* Now we have nd0 digits, starting at s0, followed by a
* decimal point, followed by nd-nd0 digits. The number we're
* after is the integer represented by those digits times
* 10**e */
if (!nd0)
nd0 = nd;
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
value(rv) = y;
if (k > 9)
value(rv) = tens[k - 9] * value(rv) + z;
bd0 = 0;
if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
&& FLT_ROUNDS == 1
#endif
) {
if (!e)
goto ret;
if (e > 0) {
if (e <= Ten_pmax) {
#ifdef VAX
goto vax_ovfl_check;
#else
/* value(rv) = */ rounded_product(value(rv),
tens[e]);
goto ret;
#endif
}
i = DBL_DIG - nd;
if (e <= Ten_pmax + i) {
/* A fancier test would sometimes let us do
* this for larger i values.
*/
e -= i;
value(rv) *= tens[i];
#ifdef VAX
/* VAX exponent range is so narrow we must
* worry about overflow here...
*/
vax_ovfl_check:
word0(rv) -= P*Exp_msk1;
/* value(rv) = */ rounded_product(value(rv),
tens[e]);
if ((word0(rv) & Exp_mask)
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
goto ovfl;
word0(rv) += P*Exp_msk1;
#else
/* value(rv) = */ rounded_product(value(rv),
tens[e]);
#endif
goto ret;
}
}
#ifndef Inaccurate_Divide
else if (e >= -Ten_pmax) {
/* value(rv) = */ rounded_quotient(value(rv),
tens[-e]);
goto ret;
}
#endif
}
e1 += nd - k;
/* Get starting approximation = rv * 10**e1 */
if (e1 > 0) {
if ((i = e1 & 15) != 0)
value(rv) *= tens[i];
if (e1 &= ~15) {
if (e1 > DBL_MAX_10_EXP) {
ovfl:
errno = ERANGE;
value(rv) = HUGE_VAL;
if (bd0)
goto retfree;
goto ret;
}
if ((e1 = (unsigned int)e1 >> 4) != 0) {
for(j = 0; e1 > 1; j++,
e1 = (unsigned int)e1 >> 1)
if (e1 & 1)
value(rv) *= bigtens[j];
/* The last multiplication could overflow. */
word0(rv) -= P*Exp_msk1;
value(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)) {
/* set to largest number */
/* (Can't trust DBL_MAX) */
word0(rv) = Big0;
word1(rv) = Big1;
}
else
word0(rv) += P*Exp_msk1;
}
}
}
else if (e1 < 0) {
e1 = -e1;
if ((i = e1 & 15) != 0)
value(rv) /= tens[i];
if (e1 &= ~15) {
e1 = (unsigned int)e1 >> 4;
if (e1 >= 1 << n_bigtens)
goto undfl;
for(j = 0; e1 > 1; j++,
e1 = (unsigned int)e1 >> 1)
if (e1 & 1)
value(rv) *= tinytens[j];
/* The last multiplication could underflow. */
value(rv0) = value(rv);
value(rv) *= tinytens[j];
if (!value(rv)) {
value(rv) = 2.*value(rv0);
value(rv) *= tinytens[j];
if (!value(rv)) {
undfl:
value(rv) = 0.;
errno = ERANGE;
if (bd0)
goto retfree;
goto ret;
}
word0(rv) = Tiny0;
word1(rv) = Tiny1;
/* The refinement below will clean
* this approximation up.
*/
}
}
}
/* Now the hard part -- adjusting rv to the correct value.*/
/* Put digits into bd: true value = bd * 10^e */
bd0 = s2b(s0, nd0, nd, y);
for(;;) {
bd = Balloc(bd0->k);
Bcopy(bd, bd0);
bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
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 Sudden_Underflow
#ifdef IBM
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
j = P + 1 - bbbits;
#endif
#else
i = bbe + bbbits - 1; /* logb(rv) */
if (i < Emin) /* denormal */
j = bbe + (P-Emin);
else
j = P + 1 - bbbits;
#endif
bb2 += j;
bd2 += j;
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);
if (i < 0) {
/* Error is less than half an ulp -- check for
* special case of mantissa a power of two.
*/
if (dsign || word1(rv) || word0(rv) & Bndry_mask)
break;
delta = lshift(delta,Log2P);
if (cmp(delta, bs) > 0)
goto drop_down;
break;
}
if (i == 0) {
/* exactly half-way between */
if (dsign) {
if ((word0(rv) & Bndry_mask1) == Bndry_mask1
&& word1(rv) == 0xffffffff) {
/*boundary case -- increment exponent*/
word0(rv) = (word0(rv) & Exp_mask)
+ Exp_msk1
#ifdef IBM
| Exp_msk1 >> 4
#endif
;
word1(rv) = 0;
break;
}
}
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
drop_down:
/* boundary case -- decrement exponent */
#ifdef Sudden_Underflow
L = word0(rv) & Exp_mask;
#ifdef IBM
if (L < Exp_msk1)
#else
if (L <= Exp_msk1)
#endif
goto undfl;
L -= Exp_msk1;
#else
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)
value(rv) += ulp(value(rv));
#ifndef ROUND_BIASED
else {
value(rv) -= ulp(value(rv));
#ifndef Sudden_Underflow
if (!value(rv))
goto undfl;
#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 {
/* special case -- power of FLT_RADIX to be */
/* rounded down... */
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(FLT_ROUNDS) {
case 2: /* towards +infinity */
aadj1 -= 0.5;
break;
case 0: /* towards 0 */
case 3: /* towards -infinity */
aadj1 += 0.5;
}
#else
if (FLT_ROUNDS == 0)
aadj1 += 0.5;
#endif
}
y = word0(rv) & Exp_mask;
/* Check for overflow */
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
value(rv0) = value(rv);
word0(rv) -= P*Exp_msk1;
adj = aadj1 * ulp(value(rv));
value(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 Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
value(rv0) = value(rv);
word0(rv) += P*Exp_msk1;
adj = aadj1 * ulp(value(rv));
value(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(value(rv));
value(rv) += adj;
}
#else
/* Compute adj so that the IEEE rounding rules will
* correctly round rv + adj in some half-way cases.
* If rv * ulp(rv) is denormalized (i.e.,
* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
* trouble from bits lost to denormalization;
* example: 1.2e-307 .
*/
if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
aadj1 = (double)(int)(aadj + 0.5);
if (!dsign)
aadj1 = -aadj1;
}
adj = aadj1 * ulp(value(rv));
value(rv) += adj;
#endif
}
z = word0(rv) & Exp_mask;
if (y == z) {
/* Can we stop now? */
L = aadj;
aadj -= L;
/* The tolerances below are conservative. */
if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
if (aadj < .4999999 || aadj > .5000001)
break;
}
else if (aadj < .4999999/FLT_RADIX)
break;
}
cont:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(delta);
}
retfree:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(bd0);
Bfree(delta);
ret:
if (se)
/* LINTED interface specification */
*se = (char *)s;
return sign ? -value(rv) : value(rv);
}
static int
quorem
#ifdef KR_headers
(b, S) Bigint *b, *S;
#else
(Bigint *b, Bigint *S)
#endif
{
int n;
Long borrow, y;
ULong carry, q, ys;
ULong *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
Long z;
ULong si, zs;
#endif
if (b == BIGINT_INVALID || S == BIGINT_INVALID)
return 0;
n = S->wds;
#ifdef DEBUG
/*debug*/ if (b->wds > n)
/*debug*/ 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); /* ensure q <= true quotient */
#ifdef DEBUG
/*debug*/ if (q > 9)
/*debug*/ Bug("oversized quotient in quorem");
#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 = (ULong)y >> 16;
Sign_Extend(borrow, y);
z = (*bx >> 16) - (zs & 0xffff) + borrow;
borrow = (ULong)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 = (ULong)y >> 16;
Sign_Extend(borrow, y);
z = (*bx >> 16) - (zs & 0xffff) + borrow;
borrow = (ULong)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;
}
/* 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
#ifdef KR_headers
freedtoa(s) char *s;
#else
freedtoa(char *s)
#endif
{
free(s);
}
/* 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 Long
* calculation.
*/
__LIBC_HIDDEN__ 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
{
/* 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, ilim0,
j, jj1, k, k0, k_check, leftright, m2, m5, s2, s5,
try_quick;
int ilim = 0, ilim1 = 0, spec_case = 0; /* pacify gcc */
Long L;
#ifndef Sudden_Underflow
int denorm;
ULong x;
#endif
Bigint *b, *b1, *delta, *mhi, *S;
Bigint *mlo = NULL; /* pacify gcc */
double ds;
char *s, *s0;
Bigint *result = NULL;
int result_k = 0;
_double d, d2, eps;
value(d) = _d;
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) + defined(VAX)
#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";
result = Balloc(strlen(s)+1);
if (result == BIGINT_INVALID)
return NULL;
s0 = (char *)(void *)result;
strcpy(s0, s);
if (rve)
*rve =
#ifdef IEEE_Arith
s0[3] ? s0 + 8 :
#endif
s0 + 3;
return s0;
}
#endif
#ifdef IBM
value(d) += 0; /* normalize */
#endif
if (!value(d)) {
*decpt = 1;
result = Balloc(2);
if (result == BIGINT_INVALID)
return NULL;
s0 = (char *)(void *)result;
strcpy(s0, "0");
if (rve)
*rve = s0 + 1;
return s0;
}
b = d2b(value(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))) != 0) {
#endif
value(d2) = value(d);
word0(d2) &= Frac_mask1;
word0(d2) |= Exp_11;
#ifdef IBM
if (j = 11 - hi0bits(word0(d2) & Frac_mask))
value(d2) /= 1 << j;
#endif
/* 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;
#ifdef IBM
i <<= 2;
i += j;
#endif
#ifndef Sudden_Underflow
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);
value(d2) = x;
word0(d2) -= 31*Exp_msk1; /* adjust exponent */
i -= (Bias + (P-1) - 1) + 1;
denorm = 1;
}
#endif
ds = (value(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 (value(d) < tens[k])
k--;
k_check = 0;
}
j = bbits - i - 1;
if (j >= 0) {
b2 = 0;
s2 = j;
}
else {
b2 = -j;
s2 = 0;
}
if (k >= 0) {
b5 = 0;
s5 = k;
s2 += k;
}
else {
b2 -= k;
b5 = -k;
s5 = 0;
}
if (mode < 0 || mode > 9)
mode = 0;
try_quick = 1;
if (mode > 5) {
mode -= 4;
try_quick = 0;
}
leftright = 1;
switch(mode) {
case 0:
case 1:
ilim = ilim1 = -1;
i = 18;
ndigits = 0;
break;
case 2:
leftright = 0;
/* FALLTHROUGH */
case 4:
if (ndigits <= 0)
ndigits = 1;
ilim = ilim1 = i = ndigits;
break;
case 3:
leftright = 0;
/* FALLTHROUGH */
case 5:
i = ndigits + k + 1;
ilim = i;
ilim1 = i - 1;
if (i <= 0)
i = 1;
}
j = sizeof(ULong);
for(result_k = 0; (int)(sizeof(Bigint) - sizeof(ULong)) + j <= i;
j <<= 1) result_k++;
// this is really a ugly hack, the code uses Balloc
// instead of malloc, but casts the result into a char*
// it seems the only reason to do that is due to the
// complicated way the block size need to be computed
// buuurk....
result = Balloc(result_k);
if (result == BIGINT_INVALID) {
Bfree(b);
return NULL;
}
s = s0 = (char *)(void *)result;
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
/* Try to get by with floating-point arithmetic. */
i = 0;
value(d2) = value(d);
k0 = k;
ilim0 = ilim;
ieps = 2; /* conservative */
if (k > 0) {
ds = tens[k&0xf];
j = (unsigned int)k >> 4;
if (j & Bletch) {
/* prevent overflows */
j &= Bletch - 1;
value(d) /= bigtens[n_bigtens-1];
ieps++;
}
for(; j; j = (unsigned int)j >> 1, i++)
if (j & 1) {
ieps++;
ds *= bigtens[i];
}
value(d) /= ds;
}
else if ((jj1 = -k) != 0) {
value(d) *= tens[jj1 & 0xf];
for(j = (unsigned int)jj1 >> 4; j;
j = (unsigned int)j >> 1, i++)
if (j & 1) {
ieps++;
value(d) *= bigtens[i];
}
}
if (k_check && value(d) < 1. && ilim > 0) {
if (ilim1 <= 0)
goto fast_failed;
ilim = ilim1;
k--;
value(d) *= 10.;
ieps++;
}
value(eps) = ieps*value(d) + 7.;
word0(eps) -= (P-1)*Exp_msk1;
if (ilim == 0) {
S = mhi = 0;
value(d) -= 5.;
if (value(d) > value(eps))
goto one_digit;
if (value(d) < -value(eps))
goto no_digits;
goto fast_failed;
}
#ifndef No_leftright
if (leftright) {
/* Use Steele & White method of only
* generating digits needed.
*/
value(eps) = 0.5/tens[ilim-1] - value(eps);
for(i = 0;;) {
L = value(d);
value(d) -= L;
*s++ = '0' + (int)L;
if (value(d) < value(eps))
goto ret1;
if (1. - value(d) < value(eps))
goto bump_up;
if (++i >= ilim)
break;
value(eps) *= 10.;
value(d) *= 10.;
}
}
else {
#endif
/* Generate ilim digits, then fix them up. */
value(eps) *= tens[ilim-1];
for(i = 1;; i++, value(d) *= 10.) {
L = value(d);
value(d) -= L;
*s++ = '0' + (int)L;
if (i == ilim) {
if (value(d) > 0.5 + value(eps))
goto bump_up;
else if (value(d) < 0.5 - value(eps)) {
while(*--s == '0');
s++;
goto ret1;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = s0;
value(d) = value(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 || value(d) <= 5*ds)
goto no_digits;
goto one_digit;
}
for(i = 1;; i++) {
L = value(d) / ds;
value(d) -= L*ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (value(d) < 0) {
L--;
value(d) += ds;
}
#endif
*s++ = '0' + (int)L;
if (i == ilim) {
value(d) += value(d);
if (value(d) > ds || (value(d) == ds && L & 1)) {
bump_up:
while(*--s == '9')
if (s == s0) {
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
if (!(value(d) *= 10.))
break;
}
goto ret1;
}
m2 = b2;
m5 = b5;
mhi = mlo = 0;
if (leftright) {
if (mode < 2) {
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
}
else {
j = ilim - 1;
if (m5 >= j)
m5 -= j;
else {
s5 += j -= m5;
b5 += j;
m5 = 0;
}
if ((i = ilim) < 0) {
m2 -= i;
i = 0;
}
}
b2 += i;
s2 += i;
mhi = i2b(1);
}
if (m2 > 0 && s2 > 0) {
i = m2 < s2 ? m2 : s2;
b2 -= i;
m2 -= i;
s2 -= i;
}
if (b5 > 0) {
if (leftright) {
if (m5 > 0) {
mhi = pow5mult(mhi, m5);
b1 = mult(mhi, b);
Bfree(b);
b = b1;
}
if ((j = b5 - m5) != 0)
b = pow5mult(b, j);
}
else
b = pow5mult(b, b5);
}
S = i2b(1);
if (s5 > 0)
S = pow5mult(S, s5);
/* Check for special case that d is a normalized power of 2. */
if (mode < 2) {
if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0(d) & Exp_mask
#endif
) {
/* 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.
*/
if (S == BIGINT_INVALID) {
i = 0;
} else {
#ifdef Pack_32
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
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);
jj1 = delta->sign ? 1 : cmp(b, delta);
Bfree(delta);
#ifndef ROUND_BIASED
if (jj1 == 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 (jj1 > 0) {
b = lshift(b, 1);
jj1 = cmp(b, S);
if ((jj1 > 0 || (jj1 == 0 && dig & 1))
&& dig++ == '9')
goto round_9_up;
}
*s++ = dig;
goto ret;
}
if (jj1 > 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;
}
#ifdef __cplusplus
}
#endif
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