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gecko-dev/js/src/jsdtoa.c
mccabe%netscape.com e2e7c63c10 Changes to allow Spider Monkey to be compiled under C++. 
Courtesy Bill Gibbons <bill@gibbons.org>

His comments:

Here are the changes to JSRef to make it compile either as C or C++. Mostly the changes are to add missing casts (since C++ doesn't have implict conversion from void* to other pointer types nor implicit casts from ints to enumerations) plus a few random things like the use of "private" as a variable name.

There are a few other minor bug fixes; in particular:

  * A long statement with and'ed conditions is reformatted to make it easier to remove other builtin objects (e.g. Date).

  * A #if was added to jsscript.c for the JS_HAS_SCRIPT_OBJECT off case.

  * In jsmath a #ifdef was changed to #if.

My notes also mention...

  * jsobj.c should include jsopcode.h

  * jsfun.c - doesn't link if JS_HAS_ARGS_OBJECT is off

  * jsarray.c - a reference to js_ValueToSource should be conditional on JS_HAS_TOSOURCE

r=mccabe
2000-02-02 01:10:31 +00:00

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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public
* License Version 1.1 (the "License"); you may not use this file
* except in compliance with the License. You may obtain a copy of
* the License at http://www.mozilla.org/NPL/
*
* Software distributed under the License is distributed on an "AS
* IS" basis, WITHOUT WARRANTY OF ANY KIND, either express oqr
* implied. See the License for the specific language governing
* rights and limitations under the License.
*
* The Original Code is Mozilla Communicator client code, released
* March 31, 1998.
*
* The Initial Developer of the Original Code is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All
* Rights Reserved.
*
* Contributor(s):
*
* Alternatively, the contents of this file may be used under the
* terms of the GNU Public License (the "GPL"), in which case the
* provisions of the GPL are applicable instead of those above.
* If you wish to allow use of your version of this file only
* under the terms of the GPL and not to allow others to use your
* version of this file under the NPL, indicate your decision by
* deleting the provisions above and replace them with the notice
* and other provisions required by the GPL. If you do not delete
* the provisions above, a recipient may use your version of this
* file under either the NPL or the GPL.
*/
/*
* Portable double to alphanumeric string and back converters.
*/
#include "jsstddef.h"
#include "jslibmath.h"
#include "jstypes.h"
#include "jsdtoa.h"
#include "jsprf.h"
#include "jsutil.h" /* Added by JSIFY */
#ifdef JS_THREADSAFE
#include "prlock.h"
#endif
/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991 by Lucent Technologies.
*
* 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 LUCENT 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
Bell Laboratories, Room 2C-463
600 Mountain Avenue
Murray Hill, NJ 07974-0636
U.S.A.
dmg@bell-labs.com
*/
/* On a machine with IEEE extended-precision registers, it is
* necessary to specify double-precision (53-bit) rounding precision
* before invoking strtod or dtoa. If the machine uses (the equivalent
* of) Intel 80x87 arithmetic, the call
* _control87(PC_53, MCW_PC);
* does this with many compilers. Whether this or another call is
* appropriate depends on the compiler; for this to work, it may be
* necessary to #include "float.h" or another system-dependent header
* file.
*/
/* strtod for IEEE-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 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_8087 for IEEE-arithmetic machines where the least
* significant byte has the lowest address.
* #define IEEE_MC68k 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 No_leftright to omit left-right logic in fast floating-point
* computation of JS_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 JS_HAVE_LONG_LONG on machines that have a "long long"
* integer type (of >= 64 bits). If long long is available and the name is
* something other than "long long", #define Llong to be the name,
* and if "unsigned Llong" does not work as an unsigned version of
* Llong, #define #ULLong to be the corresponding unsigned type.
* #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.
* #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
* memory allocations from a private pool of memory when possible.
* When used, the private pool is PRIVATE_MEM bytes long: 2000 bytes,
* unless #defined to be a different length. This default length
* suffices to get rid of MALLOC calls except for unusual cases,
* such as decimal-to-binary conversion of a very long string of
* digits.
* #define INFNAN_CHECK on IEEE systems to cause strtod to check for
* Infinity and NaN (case insensitively). On some systems (e.g.,
* some HP systems), it may be necessary to #define NAN_WORD0
* appropriately -- to the most significant word of a quiet NaN.
* (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
* #define MULTIPLE_THREADS if the system offers preemptively scheduled
* multiple threads. In this case, you must provide (or suitably
* #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
* by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
* in pow5mult, ensures lazy evaluation of only one copy of high
* powers of 5; omitting this lock would introduce a small
* probability of wasting memory, but would otherwise be harmless.)
* You must also invoke freedtoa(s) to free the value s returned by
* dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
* #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
* avoids underflows on inputs whose result does not underflow.
*/
#ifdef IS_LITTLE_ENDIAN
#define IEEE_8087
#else
#define IEEE_MC68k
#endif
#ifndef Long
#define Long int32
#endif
#ifndef ULong
#define ULong uint32
#endif
#define Bug(errorMessageString) JS_ASSERT(!errorMessageString)
#include "stdlib.h"
#include "string.h"
#ifdef MALLOC
extern void *MALLOC(size_t);
#else
#define MALLOC malloc
#endif
#define Omit_Private_Memory
/* Private memory currently doesn't work with JS_THREADSAFE */
#ifndef Omit_Private_Memory
#ifndef PRIVATE_MEM
#define PRIVATE_MEM 2000
#endif
#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
#endif
#include "errno.h"
#ifdef Bad_float_h
#undef __STDC__
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#define FLT_ROUNDS 1
#define DBL_MAX 1.7976931348623157e+308
#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
#ifndef CONST
#define CONST const
#endif
#if defined(IEEE_8087) + defined(IEEE_MC68k) != 1
Exactly one of IEEE_8087 or IEEE_MC68k should be defined.
#endif
/* Stefan Hanske <sh990154@mail.uni-greifswald.de> reports:
* ARM is a little endian architecture but 64 bit double words are stored
* differently: the 32 bit words are in little endian byte order, the two words
* are stored in big endian`s way.
*/
#if defined (IEEE_8087) && !defined(__arm)
#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
/* 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_8087)
#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) */
#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
#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
#ifndef NO_IEEE_Scale
#define Avoid_Underflow
#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 JS_HAVE_LONG_LONG
#undef ULLong
#else /* long long available */
#ifndef Llong
#define Llong JSInt64
#endif
#ifndef ULLong
#define ULLong JSUint64
#endif
#endif /* JS_HAVE_LONG_LONG */
#ifdef JS_THREADSAFE
#define MULTIPLE_THREADS
static PRLock *freelist_lock;
#define ACQUIRE_DTOA_LOCK(n) PR_Lock(freelist_lock)
#define FREE_DTOA_LOCK(n) PR_Unlock(freelist_lock)
#else
#undef MULTIPLE_THREADS
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
#define FREE_DTOA_LOCK(n) /*nothing*/
#endif
#define Kmax 15
struct Bigint {
struct Bigint *next; /* Free list link */
int32 k; /* lg2(maxwds) */
int32 maxwds; /* Number of words allocated for x */
int32 sign; /* Zero if positive, 1 if negative. Ignored by most Bigint routines! */
int32 wds; /* Actual number of words. If value is nonzero, the most significant word must be nonzero. */
ULong x[1]; /* wds words of number in little endian order */
};
typedef struct Bigint Bigint;
static Bigint *freelist[Kmax+1];
/* Allocate a Bigint with 2^k words. */
static Bigint *Balloc(int32 k)
{
int32 x;
Bigint *rv;
#ifndef Omit_Private_Memory
uint32 len;
#endif
ACQUIRE_DTOA_LOCK(0);
if ((rv = freelist[k]) != NULL)
freelist[k] = rv->next;
FREE_DTOA_LOCK(0);
if (rv == NULL) {
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;
}
rv->sign = rv->wds = 0;
return rv;
}
static void Bfree(Bigint *v)
{
if (v) {
ACQUIRE_DTOA_LOCK(0);
v->next = freelist[v->k];
freelist[v->k] = v;
FREE_DTOA_LOCK(0);
}
}
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
y->wds*sizeof(Long) + 2*sizeof(int32))
/* Return b*m + a. Deallocate the old b. Both a and m must be between 0 and 65535 inclusive. */
static Bigint *multadd(Bigint *b, int32 m, int32 a)
{
int32 i, wds;
#ifdef ULLong
ULong *x;
ULLong carry, y;
#else
ULong carry, *x, y;
ULong xi, z;
#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 & 0xffffffffUL);
#else
xi = *x;
y = (xi & 0xffff) * m + carry;
z = (xi >> 16) * m + (y >> 16);
carry = z >> 16;
*x++ = (z << 16) + (y & 0xffff);
#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;
}
static Bigint *s2b(CONST char *s, int32 nd0, int32 nd, ULong y9)
{
Bigint *b;
int32 i, k;
Long x, y;
x = (nd + 8) / 9;
for(k = 0, y = 1; x > y; y <<= 1, k++) ;
b = Balloc(k);
b->x[0] = y9;
b->wds = 1;
i = 9;
if (9 < nd0) {
s += 9;
do b = multadd(b, 10, *s++ - '0');
while(++i < nd0);
s++;
}
else
s += 10;
for(; i < nd; i++)
b = multadd(b, 10, *s++ - '0');
return b;
}
/* Return the number (0 through 32) of most significant zero bits in x. */
static int32 hi0bits(register ULong x)
{
register int32 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;
}
/* Return the number (0 through 32) of least significant zero bits in y.
* Also shift y to the right past these 0 through 32 zeros so that y's
* least significant bit will be set unless y was originally zero. */
static int32 lo0bits(ULong *y)
{
register int32 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;
}
/* Return a new Bigint with the given integer value, which must be nonnegative. */
static Bigint *i2b(int32 i)
{
Bigint *b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
/* Return a newly allocated product of a and b. */
static Bigint *mult(CONST Bigint *a, CONST Bigint *b)
{
CONST Bigint *t;
Bigint *c;
int32 k, wa, wb, wc;
ULong y;
ULong *xc, *xc0, *xce;
CONST ULong *x, *xa, *xae, *xb, *xbe;
#ifdef ULLong
ULLong carry, z;
#else
ULong carry, z;
ULong z2;
#endif
if (a->wds < b->wds) {
t = a;
a = b;
b = t;
}
k = a->k;
wa = a->wds;
wb = b->wds;
wc = wa + wb;
if (wc > a->maxwds)
k++;
c = Balloc(k);
for(xc = c->x, xce = xc + wc; xc < xce; xc++)
*xc = 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 & 0xffffffffUL);
}
while(x < xae);
*xc = (ULong)carry;
}
}
#else
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;
}
}
#endif
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds = wc;
return c;
}
/*
* 'p5s' points to a linked list of Bigints that are powers of 5.
* This list grows on demand, and it can only grow: it won't change
* in any other way. So if we read 'p5s' or the 'next' field of
* some Bigint on the list, and it is not NULL, we know it won't
* change to NULL or some other value. Only when the value of
* 'p5s' or 'next' is NULL do we need to acquire the lock and add
* a new Bigint to the list.
*/
static Bigint *p5s;
#ifdef JS_THREADSAFE
static PRLock *p5s_lock;
#endif
/* Return b * 5^k. Deallocate the old b. k must be nonnegative. */
static Bigint *pow5mult(Bigint *b, int32 k)
{
Bigint *b1, *p5, *p51;
int32 i;
static CONST int32 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)) {
#ifdef JS_THREADSAFE
/*
* We take great care to not call i2b() and Bfree()
* while holding the lock.
*/
Bigint *wasted_effort = NULL;
p5 = i2b(625);
/* lock and check again */
PR_Lock(p5s_lock);
if (!p5s) {
/* first time */
p5s = p5;
p5->next = 0;
} else {
/* some other thread just beat us */
wasted_effort = p5;
p5 = p5s;
}
PR_Unlock(p5s_lock);
if (wasted_effort) {
Bfree(wasted_effort);
}
#else
/* first time */
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 JS_THREADSAFE
Bigint *wasted_effort = NULL;
p51 = mult(p5, p5);
PR_Lock(p5s_lock);
if (!p5->next) {
p5->next = p51;
p51->next = 0;
} else {
wasted_effort = p51;
p51 = p5->next;
}
PR_Unlock(p5s_lock);
if (wasted_effort) {
Bfree(wasted_effort);
}
#else
p51 = p5->next = mult(p5,p5);
p51->next = 0;
#endif
}
p5 = p51;
}
return b;
}
/* Return b * 2^k. Deallocate the old b. k must be nonnegative. */
static Bigint *lshift(Bigint *b, int32 k)
{
int32 i, k1, n, n1;
Bigint *b1;
ULong *x, *x1, *xe, z;
n = k >> 5;
k1 = b->k;
n1 = n + b->wds + 1;
for(i = b->maxwds; n1 > i; i <<= 1)
k1++;
b1 = Balloc(k1);
x1 = b1->x;
for(i = 0; i < n; i++)
*x1++ = 0;
x = b->x;
xe = x + b->wds;
if (k &= 0x1f) {
k1 = 32 - k;
z = 0;
do {
*x1++ = *x << k | z;
z = *x++ >> k1;
}
while(x < xe);
if ((*x1 = z) != 0)
++n1;
}
else do
*x1++ = *x++;
while(x < xe);
b1->wds = n1 - 1;
Bfree(b);
return b1;
}
/* Return -1, 0, or 1 depending on whether a<b, a==b, or a>b, respectively. */
static int32 cmp(Bigint *a, Bigint *b)
{
ULong *xa, *xa0, *xb, *xb0;
int32 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(Bigint *a, Bigint *b)
{
Bigint *c;
int32 i, wa, wb;
ULong *xa, *xae, *xb, *xbe, *xc;
#ifdef ULLong
ULLong borrow, y;
#else
ULong borrow, y;
ULong z;
#endif
i = cmp(a,b);
if (!i) {
c = Balloc(0);
c->wds = 1;
c->x[0] = 0;
return c;
}
if (i < 0) {
c = a;
a = b;
b = c;
i = 1;
}
else
i = 0;
c = Balloc(a->k);
c->sign = i;
wa = a->wds;
xa = a->x;
xae = xa + wa;
wb = b->wds;
xb = b->x;
xbe = xb + wb;
xc = c->x;
borrow = 0;
#ifdef ULLong
do {
y = (ULLong)*xa++ - *xb++ - borrow;
borrow = y >> 32 & 1UL;
*xc++ = (ULong)(y & 0xffffffffUL);
}
while(xb < xbe);
while(xa < xae) {
y = *xa++ - borrow;
borrow = y >> 32 & 1UL;
*xc++ = (ULong)(y & 0xffffffffUL);
}
#else
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);
}
#endif
while(!*--xc)
wa--;
c->wds = wa;
return c;
}
/* Return the absolute difference between x and the adjacent greater-magnitude double number (ignoring exponent overflows). */
static double ulp(double x)
{
register Long L;
double a;
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef Sudden_Underflow
if (L > 0) {
#endif
word0(a) = L;
word1(a) = 0;
#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
return a;
}
static double b2d(Bigint *a, int32 *e)
{
ULong *xa, *xa0, w, y, z;
int32 k;
double d;
#define d0 word0(d)
#define d1 word1(d)
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;
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;
}
ret_d:
#undef d0
#undef d1
return d;
}
/* Convert d into the form b*2^e, where b is an odd integer. b is the returned
* Bigint and e is the returned binary exponent. Return the number of significant
* bits in b in bits. d must be finite and nonzero. */
static Bigint *d2b(double d, int32 *e, int32 *bits)
{
Bigint *b;
int32 de, i, k;
ULong *x, y, z;
#define d0 word0(d)
#define d1 word1(d)
b = Balloc(1);
x = b->x;
z = d0 & Frac_mask;
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
de = (int32)(d0 >> Exp_shift);
z |= Exp_msk11;
#else
if ((de = (int32)(d0 >> Exp_shift)) != 0)
z |= Exp_msk1;
#endif
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 {
JS_ASSERT(z);
k = lo0bits(&z);
x[0] = z;
i = b->wds = 1;
k += 32;
}
#ifndef Sudden_Underflow
if (de) {
#endif
*e = de - Bias - (P-1) + k;
*bits = P - k;
#ifndef Sudden_Underflow
}
else {
*e = de - Bias - (P-1) + 1 + k;
*bits = 32*i - hi0bits(x[i-1]);
}
#endif
return b;
}
#undef d0
#undef d1
static double ratio(Bigint *a, Bigint *b)
{
double da, db;
int32 k, ka, kb;
da = b2d(a, &ka);
db = b2d(b, &kb);
k = ka - kb + 32*(a->wds - b->wds);
if (k > 0)
word0(da) += k*Exp_msk1;
else {
k = -k;
word0(db) += k*Exp_msk1;
}
return da / 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
};
static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
#ifdef Avoid_Underflow
9007199254740992.e-256
#else
1e-256
#endif
};
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
#define Scale_Bit 0x10
#define n_bigtens 5
#ifdef INFNAN_CHECK
#ifndef NAN_WORD0
#define NAN_WORD0 0x7ff80000
#endif
#ifndef NAN_WORD1
#define NAN_WORD1 0
#endif
static int match(CONST char **sp, char *t)
{
int c, d;
CONST char *s = *sp;
while(d = *t++) {
if ((c = *++s) >= 'A' && c <= 'Z')
c += 'a' - 'A';
if (c != d)
return 0;
}
*sp = s + 1;
return 1;
}
#endif /* INFNAN_CHECK */
#ifdef JS_THREADSAFE
static JSBool initialized = JS_FALSE;
/* hacked replica of nspr _PR_InitDtoa */
static void InitDtoa(void)
{
freelist_lock = PR_NewLock();
p5s_lock = PR_NewLock();
initialized = JS_TRUE;
}
#endif
/* nspr2 watcom bug ifdef omitted */
JS_FRIEND_API(double)
JS_strtod(CONST char *s00, char **se)
{
int32 scale;
int32 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, *bb1, *bd, *bd0, *bs, *delta;
#ifdef JS_THREADSAFE
if (!initialized) InitDtoa();
#endif
bb = bd = bs = delta = NULL;
sign = nz0 = nz = 0;
rv = 0.;
for(s = s00;;s++) switch(*s) {
case '-':
sign = 1;
/* no break */
case '+':
if (*++s)
goto break2;
/* no break */
case 0:
s = s00;
goto ret;
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;
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) {
s = s00;
goto ret;
}
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)
/* Avoid confusion from exponents
* so large that e might overflow.
*/
e = 19999; /* safe for 16 bit ints */
else
e = (int32)L;
if (esign)
e = -e;
}
else
e = 0;
}
else
s = s00;
}
if (!nd) {
if (!nz && !nz0) {
#ifdef INFNAN_CHECK
/* Check for Nan and Infinity */
switch(c) {
case 'i':
case 'I':
if (match(&s,"nfinity")) {
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;
goto ret;
}
}
#endif /* INFNAN_CHECK */
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;
rv = y;
if (k > 9)
rv = tens[k - 9] * 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) {
/* rv = */ rounded_product(rv, tens[e]);
goto ret;
}
i = DBL_DIG - nd;
if (e <= Ten_pmax + i) {
/* A fancier test would sometimes let us do
* this for larger i values.
*/
e -= i;
rv *= tens[i];
/* rv = */ rounded_product(rv, tens[e]);
goto ret;
}
}
#ifndef Inaccurate_Divide
else if (e >= -Ten_pmax) {
/* rv = */ rounded_quotient(rv, tens[-e]);
goto ret;
}
#endif
}
e1 += nd - k;
scale = 0;
/* Get starting approximation = rv * 10**e1 */
if (e1 > 0) {
if ((i = e1 & 15) != 0)
rv *= tens[i];
if (e1 &= ~15) {
if (e1 > DBL_MAX_10_EXP) {
ovfl:
errno = ERANGE;
#ifdef __STDC__
rv = HUGE_VAL;
#else
/* Can't trust HUGE_VAL */
word0(rv) = Exp_mask;
word1(rv) = 0;
#endif
if (bd0)
goto retfree;
goto ret;
}
e1 >>= 4;
for(j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1)
rv *= bigtens[j];
/* The last multiplication could overflow. */
word0(rv) -= P*Exp_msk1;
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)
rv /= tens[i];
if (e1 &= ~15) {
e1 >>= 4;
if (e1 >= 1 << n_bigtens)
goto undfl;
#ifdef Avoid_Underflow
if (e1 & Scale_Bit)
scale = P;
for(j = 0; e1 > 0; j++, e1 >>= 1)
if (e1 & 1)
rv *= tinytens[j];
if (scale && (j = P + 1 - ((word0(rv) & Exp_mask)
>> Exp_shift)) > 0) {
/* scaled rv is denormal; zap j low bits */
if (j >= 32) {
word1(rv) = 0;
word0(rv) &= 0xffffffff << (j-32);
if (!word0(rv))
word0(rv) = 1;
}
else
word1(rv) &= 0xffffffff << j;
}
#else
for(j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1)
rv *= tinytens[j];
/* The last multiplication could underflow. */
rv0 = rv;
rv *= tinytens[j];
if (!rv) {
rv = 2.*rv0;
rv *= tinytens[j];
#endif
if (!rv) {
undfl:
rv = 0.;
errno = ERANGE;
if (bd0)
goto retfree;
goto ret;
}
#ifndef Avoid_Underflow
word0(rv) = Tiny0;
word1(rv) = Tiny1;
/* The refinement below will clean
* this approximation up.
*/
}
#endif
}
}
/* 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(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
j = P + 1 - bbbits;
#else
#ifdef Avoid_Underflow
j = bbe - scale;
#else
j = bbe;
#endif
i = j + bbbits - 1; /* logb(rv) */
if (i < Emin) /* denormal */
j += P - Emin;
else
j = P + 1 - bbbits;
#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);
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
#ifdef Avoid_Underflow
|| (word0(rv) & Exp_mask) <= Exp_msk1 + P*Exp_msk1
#else
|| (word0(rv) & Exp_mask) <= Exp_msk1
#endif
) {
#ifdef Avoid_Underflow
if (!delta->x[0] && delta->wds == 1)
dsign = 2;
#endif
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;
word1(rv) = 0;
#ifdef Avoid_Underflow
dsign = 0;
#endif
break;
}
}
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
#ifdef Avoid_Underflow
dsign = 2;
#endif
drop_down:
/* boundary case -- decrement exponent */
#ifdef Sudden_Underflow
L = word0(rv) & Exp_mask;
if (L <= Exp_msk1)
goto undfl;
L -= Exp_msk1;
#else
L = (word0(rv) & Exp_mask) - Exp_msk1;
#endif
word0(rv) = L | Bndry_mask1;
word1(rv) = 0xffffffff;
break;
}
#ifndef ROUND_BIASED
if (!(word1(rv) & LSB))
break;
#endif
if (dsign)
rv += ulp(rv);
#ifndef ROUND_BIASED
else {
rv -= ulp(rv);
#ifndef Sudden_Underflow
if (!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 {
/* 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)) {
rv0 = rv;
word0(rv) -= P*Exp_msk1;
adj = aadj1 * ulp(rv);
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) {
rv0 = rv;
word0(rv) += P*Exp_msk1;
adj = aadj1 * ulp(rv);
rv += adj;
if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
{
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(rv);
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 .
*/
#ifdef Avoid_Underflow
if (y <= P*Exp_msk1 && aadj > 1.)
#else
if (y <= (P-1)*Exp_msk1 && aadj > 1.)
#endif
{
aadj1 = (double)(int32)(aadj + 0.5);
if (!dsign)
aadj1 = -aadj1;
}
#ifdef Avoid_Underflow
if (scale && y <= P*Exp_msk1)
word0(aadj1) += (P+1)*Exp_msk1 - y;
#endif
adj = aadj1 * ulp(rv);
rv += adj;
#endif
}
z = word0(rv) & Exp_mask;
#ifdef Avoid_Underflow
if (!scale)
#endif
if (y == z) {
/* Can we stop now? */
L = (Long)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);
}
#ifdef Avoid_Underflow
if (scale) {
word0(rv0) = Exp_1 - P*Exp_msk1;
word1(rv0) = 0;
if ((word0(rv) & Exp_mask) <= P*Exp_msk1
&& word1(rv) & 1
&& dsign != 2) {
if (dsign) {
#ifdef Sudden_Underflow
/* rv will be 0, but this would give the */
/* right result if only rv *= rv0 worked. */
word0(rv) += P*Exp_msk1;
word0(rv0) = Exp_1 - 2*P*Exp_msk1;
#endif
rv += ulp(rv);
}
else
word1(rv) &= ~1;
}
rv *= rv0;
}
#endif /* Avoid_Underflow */
retfree:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(bd0);
Bfree(delta);
ret:
if (se)
*se = (char *)s;
return sign ? -rv : rv;
}
/* Return floor(b/2^k) and set b to be the remainder. The returned quotient must be less than 2^32. */
static uint32 quorem2(Bigint *b, int32 k)
{
ULong mask;
ULong result;
ULong *bx, *bxe;
int32 w;
int32 n = k >> 5;
k &= 0x1F;
mask = (1<<k) - 1;
w = b->wds - n;
if (w <= 0)
return 0;
JS_ASSERT(w <= 2);
bx = b->x;
bxe = bx + n;
result = *bxe >> k;
*bxe &= mask;
if (w == 2) {
JS_ASSERT(!(bxe[1] & ~mask));
if (k)
result |= bxe[1] << (32 - k);
}
n++;
while (!*bxe && bxe != bx) {
n--;
bxe--;
}
b->wds = n;
return result;
}
/* Return floor(b/S) and set b to be the remainder. As added restrictions, b must not have
* more words than S, the most significant word of S must not start with a 1 bit, and the
* returned quotient must be less than 36. */
static int32 quorem(Bigint *b, Bigint *S)
{
int32 n;
ULong *bx, *bxe, q, *sx, *sxe;
#ifdef ULLong
ULLong borrow, carry, y, ys;
#else
ULong borrow, carry, y, ys;
ULong si, z, zs;
#endif
n = S->wds;
JS_ASSERT(b->wds <= n);
if (b->wds < n)
return 0;
sx = S->x;
sxe = sx + --n;
bx = b->x;
bxe = bx + n;
JS_ASSERT(*sxe <= 0x7FFFFFFF);
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
JS_ASSERT(q < 36);
if (q) {
borrow = 0;
carry = 0;
do {
#ifdef ULLong
ys = *sx++ * (ULLong)q + carry;
carry = ys >> 32;
y = *bx - (ys & 0xffffffffUL) - borrow;
borrow = y >> 32 & 1UL;
*bx++ = (ULong)(y & 0xffffffffUL);
#else
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);
#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 & 0xffffffffUL) - borrow;
borrow = y >> 32 & 1UL;
*bx++ = (ULong)(y & 0xffffffffUL);
#else
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);
#endif
} while(sx <= sxe);
bx = b->x;
bxe = bx + n;
if (!*bxe) {
while(--bxe > bx && !*bxe)
--n;
b->wds = n;
}
}
return (int32)q;
}
/* 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.
*/
/* Always emits at least one digit. */
/* If biasUp is set, then rounding in modes 2 and 3 will round away from zero
* when the number is exactly halfway between two representable values. For example,
* rounding 2.5 to zero digits after the decimal point will return 3 and not 2.
* 2.49 will still round to 2, and 2.51 will still round to 3. */
/* bufsize should be at least 20 for modes 0 and 1. For the other modes,
* bufsize should be two greater than the maximum number of output characters expected. */
static JSBool
JS_dtoa(double d, int mode, JSBool biasUp, int ndigits,
int *decpt, int *sign, char **rve, char *buf, size_t bufsize)
{
/* 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.
*/
int32 bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
spec_case, try_quick;
Long L;
#ifndef Sudden_Underflow
int32 denorm;
ULong x;
#endif
Bigint *b, *b1, *delta, *mlo, *mhi, *S;
double d2, ds, eps;
char *s;
#ifdef JS_THREADSAFE
if (!initialized) InitDtoa();
#endif
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 ((word0(d) & Exp_mask) == Exp_mask) {
/* Infinity or NaN */
*decpt = 9999;
s = !word1(d) && !(word0(d) & Frac_mask) ? "Infinity" : "NaN";
if ((s[0] == 'I' && bufsize < 9) || (s[0] == 'N' && bufsize < 4)) {
JS_ASSERT(JS_FALSE);
/* JS_SetError(JS_BUFFER_OVERFLOW_ERROR, 0); */
return JS_FALSE;
}
strcpy(buf, s);
if (rve) {
*rve = buf[3] ? buf + 8 : buf + 3;
JS_ASSERT(**rve == '\0');
}
return JS_TRUE;
}
if (!d) {
no_digits:
*decpt = 1;
if (bufsize < 2) {
JS_ASSERT(JS_FALSE);
/* JS_SetError(JS_BUFFER_OVERFLOW_ERROR, 0); */
return JS_FALSE;
}
buf[0] = '0'; buf[1] = '\0'; /* copy "0" to buffer */
if (rve)
*rve = buf + 1;
return JS_TRUE;
}
b = d2b(d, &be, &bbits);
#ifdef Sudden_Underflow
i = (int32)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
if ((i = (int32)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
#endif
d2 = d;
word0(d2) &= Frac_mask1;
word0(d2) |= Exp_11;
/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
* log10(x) = log(x) / log(10)
* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
*
* This suggests computing an approximation k to log10(d) by
*
* k = (i - Bias)*0.301029995663981
* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
*
* We want k to be too large rather than too small.
* The error in the first-order Taylor series approximation
* is in our favor, so we just round up the constant enough
* to compensate for any error in the multiplication of
* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
* adding 1e-13 to the constant term more than suffices.
* Hence we adjust the constant term to 0.1760912590558.
* (We could get a more accurate k by invoking log10,
* but this is probably not worthwhile.)
*/
i -= Bias;
#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);
d2 = x;
word0(d2) -= 31*Exp_msk1; /* adjust exponent */
i -= (Bias + (P-1) - 1) + 1;
denorm = 1;
}
#endif
/* At this point d = f*2^i, where 1 <= f < 2. d2 is an approximation of f. */
ds = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
k = (int32)ds;
if (ds < 0. && ds != k)
k--; /* want k = floor(ds) */
k_check = 1;
if (k >= 0 && k <= Ten_pmax) {
if (d < tens[k])
k--;
k_check = 0;
}
/* At this point floor(log10(d)) <= k <= floor(log10(d))+1.
If k_check is zero, we're guaranteed that k = floor(log10(d)). */
j = bbits - i - 1;
/* At this point d = b/2^j, where b is an odd integer. */
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;
}
/* At this point d/10^k = (b * 2^b2 * 5^b5) / (2^s2 * 5^s5), where b is an odd integer,
b2 >= 0, b5 >= 0, s2 >= 0, and s5 >= 0. */
if (mode < 0 || mode > 9)
mode = 0;
try_quick = 1;
if (mode > 5) {
mode -= 4;
try_quick = 0;
}
leftright = 1;
ilim = ilim1 = 0;
switch(mode) {
case 0:
case 1:
ilim = ilim1 = -1;
i = 18;
ndigits = 0;
break;
case 2:
leftright = 0;
/* no break */
case 4:
if (ndigits <= 0)
ndigits = 1;
ilim = ilim1 = i = ndigits;
break;
case 3:
leftright = 0;
/* no break */
case 5:
i = ndigits + k + 1;
ilim = i;
ilim1 = i - 1;
if (i <= 0)
i = 1;
}
/* ilim is the maximum number of significant digits we want, based on k and ndigits. */
/* ilim1 is the maximum number of significant digits we want, based on k and ndigits,
when it turns out that k was computed too high by one. */
/* Ensure space for at least i+1 characters, including trailing null. */
if (bufsize <= (size_t)i) {
Bfree(b);
JS_ASSERT(JS_FALSE);
return JS_FALSE;
}
s = buf;
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
/* Try to get by with floating-point arithmetic. */
i = 0;
d2 = d;
k0 = k;
ilim0 = ilim;
ieps = 2; /* conservative */
/* Divide d by 10^k, keeping track of the roundoff error and avoiding overflows. */
if (k > 0) {
ds = tens[k&0xf];
j = k >> 4;
if (j & Bletch) {
/* prevent overflows */
j &= Bletch - 1;
d /= bigtens[n_bigtens-1];
ieps++;
}
for(; j; j >>= 1, i++)
if (j & 1) {
ieps++;
ds *= bigtens[i];
}
d /= ds;
}
else if ((j1 = -k) != 0) {
d *= tens[j1 & 0xf];
for(j = j1 >> 4; j; j >>= 1, i++)
if (j & 1) {
ieps++;
d *= bigtens[i];
}
}
/* Check that k was computed correctly. */
if (k_check && d < 1. && ilim > 0) {
if (ilim1 <= 0)
goto fast_failed;
ilim = ilim1;
k--;
d *= 10.;
ieps++;
}
/* eps bounds the cumulative error. */
eps = ieps*d + 7.;
word0(eps) -= (P-1)*Exp_msk1;
if (ilim == 0) {
S = mhi = 0;
d -= 5.;
if (d > eps)
goto one_digit;
if (d < -eps)
goto no_digits;
goto fast_failed;
}
#ifndef No_leftright
if (leftright) {
/* Use Steele & White method of only
* generating digits needed.
*/
eps = 0.5/tens[ilim-1] - eps;
for(i = 0;;) {
L = (Long)d;
d -= L;
*s++ = '0' + (char)L;
if (d < eps)
goto ret1;
if (1. - d < eps)
goto bump_up;
if (++i >= ilim)
break;
eps *= 10.;
d *= 10.;
}
}
else {
#endif
/* Generate ilim digits, then fix them up. */
eps *= tens[ilim-1];
for(i = 1;; i++, d *= 10.) {
L = (Long)d;
d -= L;
*s++ = '0' + (char)L;
if (i == ilim) {
if (d > 0.5 + eps)
goto bump_up;
else if (d < 0.5 - eps) {
while(*--s == '0') ;
s++;
goto ret1;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = buf;
d = d2;
k = k0;
ilim = ilim0;
}
/* Do we have a "small" integer? */
if (be >= 0 && k <= Int_max) {
/* Yes. */
ds = tens[k];
if (ndigits < 0 && ilim <= 0) {
S = mhi = 0;
if (ilim < 0 || d < 5*ds || (!biasUp && d == 5*ds))
goto no_digits;
goto one_digit;
}
for(i = 1;; i++) {
L = (Long) (d / ds);
d -= L*ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (d < 0) {
L--;
d += ds;
}
#endif
*s++ = '0' + (char)L;
if (i == ilim) {
d += d;
if ((d > ds) || (d == ds && (L & 1 || biasUp))) {
bump_up:
while(*--s == '9')
if (s == buf) {
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
if (!(d *= 10.))
break;
}
goto ret1;
}
m2 = b2;
m5 = b5;
mhi = mlo = 0;
if (leftright) {
if (mode < 2) {
i =
#ifndef Sudden_Underflow
denorm ? be + (Bias + (P-1) - 1 + 1) :
#endif
1 + P - bbits;
/* i is 1 plus the number of trailing zero bits in d's significand. Thus,
(2^m2 * 5^m5) / (2^(s2+i) * 5^s5) = (1/2 lsb of d)/10^k. */
}
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;
}
/* (2^m2 * 5^m5) / (2^(s2+i) * 5^s5) = (1/2 * 10^(1-ilim))/10^k. */
}
b2 += i;
s2 += i;
mhi = i2b(1);
/* (mhi * 2^m2 * 5^m5) / (2^s2 * 5^s5) = one-half of last printed (when mode >= 2) or
input (when mode < 2) significant digit, divided by 10^k. */
}
/* We still have d/10^k = (b * 2^b2 * 5^b5) / (2^s2 * 5^s5). Reduce common factors in
b2, m2, and s2 without changing the equalities. */
if (m2 > 0 && s2 > 0) {
i = m2 < s2 ? m2 : s2;
b2 -= i;
m2 -= i;
s2 -= i;
}
/* Fold b5 into b and m5 into mhi. */
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);
}
/* Now we have d/10^k = (b * 2^b2) / (2^s2 * 5^s5) and
(mhi * 2^m2) / (2^s2 * 5^s5) = one-half of last printed or input significant digit, divided by 10^k. */
S = i2b(1);
if (s5 > 0)
S = pow5mult(S, s5);
/* Now we have d/10^k = (b * 2^b2) / (S * 2^s2) and
(mhi * 2^m2) / (S * 2^s2) = one-half of last printed or input significant digit, divided by 10^k. */
/* Check for special case that d is a normalized power of 2. */
spec_case = 0;
if (mode < 2) {
if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0(d) & (Exp_mask & Exp_mask << 1)
#endif
) {
/* The special case. Here we want to be within a quarter of the last input
significant digit instead of one half of it when the decimal output string's value is less than d. */
b2 += Log2P;
s2 += Log2P;
spec_case = 1;
}
}
/* Arrange for convenient computation of quotients:
* shift left if necessary so divisor has 4 leading 0 bits.
*
* Perhaps we should just compute leading 28 bits of S once
* and for all and pass them and a shift to quorem, so it
* can do shifts and ors to compute the numerator for q.
*/
if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
i = 32 - i;
/* i is the number of leading zero bits in the most significant word of S*2^s2. */
if (i > 4) {
i -= 4;
b2 += i;
m2 += i;
s2 += i;
}
else if (i < 4) {
i += 28;
b2 += i;
m2 += i;
s2 += i;
}
/* Now S*2^s2 has exactly four leading zero bits in its most significant word. */
if (b2 > 0)
b = lshift(b, b2);
if (s2 > 0)
S = lshift(S, s2);
/* Now we have d/10^k = b/S and
(mhi * 2^m2) / S = maximum acceptable error, divided by 10^k. */
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;
}
}
/* At this point 1 <= d/10^k = b/S < 10. */
if (ilim <= 0 && mode > 2) {
/* We're doing fixed-mode output and d is less than the minimum nonzero output in this mode.
Output either zero or the minimum nonzero output depending on which is closer to d. */
if (ilim < 0 || (i = cmp(b,S = multadd(S,5,0))) < 0 || (i == 0 && !biasUp)) {
/* Always emit at least one digit. If the number appears to be zero
using the current mode, then emit one '0' digit and set decpt to 1. */
/*no_digits:
k = -1 - ndigits;
goto ret; */
goto no_digits;
}
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);
}
/* mlo/S = maximum acceptable error, divided by 10^k, if the output is less than d. */
/* mhi/S = maximum acceptable error, divided by 10^k, if the output is greater than d. */
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);
/* j is b/S compared with mlo/S. */
delta = diff(S, mhi);
j1 = delta->sign ? 1 : cmp(b, delta);
Bfree(delta);
/* j1 is b/S compared with 1 - mhi/S. */
#ifndef ROUND_BIASED
if (j1 == 0 && !mode && !(word1(d) & 1)) {
if (dig == '9')
goto round_9_up;
if (j > 0)
dig++;
*s++ = (char)dig;
goto ret;
}
#endif
if ((j < 0) || (j == 0 && !mode
#ifndef ROUND_BIASED
&& !(word1(d) & 1)
#endif
)) {
if (j1 > 0) {
/* Either dig or dig+1 would work here as the least significant decimal digit.
Use whichever would produce a decimal value closer to d. */
b = lshift(b, 1);
j1 = cmp(b, S);
if (((j1 > 0) || (j1 == 0 && (dig & 1 || biasUp)))
&& (dig++ == '9'))
goto round_9_up;
}
*s++ = (char)dig;
goto ret;
}
if (j1 > 0) {
if (dig == '9') { /* possible if i == 1 */
round_9_up:
*s++ = '9';
goto roundoff;
}
*s++ = dig + 1;
goto ret;
}
*s++ = (char)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++ = (char)(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 || biasUp))) {
roundoff:
while(*--s == '9')
if (s == buf) {
k++;
*s++ = '1';
goto ret;
}
++*s++;
}
else {
/* Strip trailing zeros */
while(*--s == '0') ;
s++;
}
ret:
Bfree(S);
if (mhi) {
if (mlo && mlo != mhi)
Bfree(mlo);
Bfree(mhi);
}
ret1:
Bfree(b);
JS_ASSERT(s < buf + bufsize);
*s = '\0';
if (rve)
*rve = s;
*decpt = k + 1;
return JS_TRUE;
}
/* Mapping of JSDToStrMode -> JS_dtoa mode */
static const int dtoaModes[] = {
0, /* DTOSTR_STANDARD */
0, /* DTOSTR_STANDARD_EXPONENTIAL, */
3, /* DTOSTR_FIXED, */
2, /* DTOSTR_EXPONENTIAL, */
2}; /* DTOSTR_PRECISION */
JS_FRIEND_API(char *)
JS_dtostr(char *buffer, size_t bufferSize, JSDToStrMode mode, int precision, double d)
{
int decPt; /* Position of decimal point relative to first digit returned by JS_dtoa */
int sign; /* Nonzero if the sign bit was set in d */
int nDigits; /* Number of significand digits returned by JS_dtoa */
char *numBegin = buffer+2; /* Pointer to the digits returned by JS_dtoa; the +2 leaves space for */
/* the sign and/or decimal point */
char *numEnd; /* Pointer past the digits returned by JS_dtoa */
JS_ASSERT(bufferSize >= (size_t)(mode <= DTOSTR_STANDARD_EXPONENTIAL ? DTOSTR_STANDARD_BUFFER_SIZE :
DTOSTR_VARIABLE_BUFFER_SIZE(precision)));
if (mode == DTOSTR_FIXED && (d >= 1e21 || d <= -1e21))
mode = DTOSTR_STANDARD; /* Change mode here rather than below because the buffer may not be large enough to hold a large integer. */
if (!JS_dtoa(d, dtoaModes[mode], mode >= DTOSTR_FIXED, precision, &decPt, &sign, &numEnd, numBegin, bufferSize-2))
return 0;
nDigits = numEnd - numBegin;
/* If Infinity, -Infinity, or NaN, return the string regardless of the mode. */
if (decPt != 9999) {
JSBool exponentialNotation = JS_FALSE;
int minNDigits = 0; /* Minimum number of significand digits required by mode and precision */
char *p;
char *q;
switch (mode) {
case DTOSTR_STANDARD:
if (decPt < -5 || decPt > 21)
exponentialNotation = JS_TRUE;
else
minNDigits = decPt;
break;
case DTOSTR_FIXED:
if (precision >= 0)
minNDigits = decPt + precision;
else
minNDigits = decPt;
break;
case DTOSTR_EXPONENTIAL:
JS_ASSERT(precision > 0);
minNDigits = precision;
/* Fall through */
case DTOSTR_STANDARD_EXPONENTIAL:
exponentialNotation = JS_TRUE;
break;
case DTOSTR_PRECISION:
JS_ASSERT(precision > 0);
minNDigits = precision;
if (decPt < -5 || decPt > precision)
exponentialNotation = JS_TRUE;
break;
}
/* If the number has fewer than minNDigits, pad it with zeros at the end */
if (nDigits < minNDigits) {
p = numBegin + minNDigits;
nDigits = minNDigits;
do {
*numEnd++ = '0';
} while (numEnd != p);
*numEnd = '\0';
}
if (exponentialNotation) {
/* Insert a decimal point if more than one significand digit */
if (nDigits != 1) {
numBegin--;
numBegin[0] = numBegin[1];
numBegin[1] = '.';
}
JS_snprintf(numEnd, bufferSize - (numEnd - buffer), "e%+d", decPt-1);
} else if (decPt != nDigits) {
/* Some kind of a fraction in fixed notation */
JS_ASSERT(decPt <= nDigits);
if (decPt > 0) {
/* dd...dd . dd...dd */
p = --numBegin;
do {
*p = p[1];
p++;
} while (--decPt);
*p = '.';
} else {
/* 0 . 00...00dd...dd */
p = numEnd;
numEnd += 1 - decPt;
q = numEnd;
JS_ASSERT(numEnd < buffer + bufferSize);
*numEnd = '\0';
while (p != numBegin)
*--q = *--p;
for (p = numBegin + 1; p != q; p++)
*p = '0';
*numBegin = '.';
*--numBegin = '0';
}
}
}
/* If negative and neither -0.0 nor NaN, output a leading '-'. */
if (sign &&
!(word0(d) == Sign_bit && word1(d) == 0) &&
!((word0(d) & Exp_mask) == Exp_mask &&
(word1(d) || (word0(d) & Frac_mask)))) {
*--numBegin = '-';
}
return numBegin;
}
/* Let b = floor(b / divisor), and return the remainder. b must be nonnegative.
* divisor must be between 1 and 65536.
* This function cannot run out of memory. */
static uint32
divrem(Bigint *b, uint32 divisor)
{
int32 n = b->wds;
uint32 remainder = 0;
ULong *bx;
ULong *bp;
JS_ASSERT(divisor > 0 && divisor <= 65536);
if (!n)
return 0; /* b is zero */
bx = b->x;
bp = bx + n;
do {
ULong a = *--bp;
ULong dividend = remainder << 16 | a >> 16;
ULong quotientHi = dividend / divisor;
ULong quotientLo;
remainder = dividend - quotientHi*divisor;
JS_ASSERT(quotientHi <= 0xFFFF && remainder < divisor);
dividend = remainder << 16 | (a & 0xFFFF);
quotientLo = dividend / divisor;
remainder = dividend - quotientLo*divisor;
JS_ASSERT(quotientLo <= 0xFFFF && remainder < divisor);
*bp = quotientHi << 16 | quotientLo;
} while (bp != bx);
/* Decrease the size of the number if its most significant word is now zero. */
if (bx[n-1] == 0)
b->wds--;
return remainder;
}
/* "-0.0000...(1073 zeros after decimal point)...0001\0" is the longest string that we could produce,
* which occurs when printing -5e-324 in binary. We could compute a better estimate of the size of
* the output string and malloc fewer bytes depending on d and base, but why bother? */
#define DTOBASESTR_BUFFER_SIZE 1078
#define BASEDIGIT(digit) ((char)(((digit) >= 10) ? 'a' - 10 + (digit) : '0' + (digit)))
JS_FRIEND_API(char *)
JS_dtobasestr(int base, double d)
{
char *buffer; /* The output string */
char *p; /* Pointer to current position in the buffer */
char *pInt; /* Pointer to the beginning of the integer part of the string */
char *q;
uint32 digit;
double di; /* d truncated to an integer */
double df; /* The fractional part of d */
JS_ASSERT(base >= 2 && base <= 36);
buffer = (char*) malloc(DTOBASESTR_BUFFER_SIZE);
if (buffer) {
p = buffer;
if (d < 0.0
#ifdef XP_PC
&& !((word0(d) & Exp_mask) == Exp_mask && ((word0(d) & Frac_mask) || word1(d))) /* Visual C++ doesn't know how to compare against NaN */
#endif
) {
*p++ = '-';
d = -d;
}
/* Check for Infinity and NaN */
if ((word0(d) & Exp_mask) == Exp_mask) {
strcpy(p, !word1(d) && !(word0(d) & Frac_mask) ? "Infinity" : "NaN");
return buffer;
}
/* Output the integer part of d with the digits in reverse order. */
pInt = p;
di = fd_floor(d);
if (di <= 4294967295.0) {
uint32 n = (uint32)di;
if (n)
do {
uint32 m = n / base;
digit = n - m*base;
n = m;
JS_ASSERT(digit < (uint32)base);
*p++ = BASEDIGIT(digit);
} while (n);
else *p++ = '0';
} else {
/* XXX We really should check for null here, but none of the routines we call is out-of-memory-safe,
* so this change would need to be made pervasively in this file. */
int32 e;
int32 bits; /* Number of significant bits in di; not used. */
Bigint *b = d2b(di, &e, &bits);
b = lshift(b, e);
do {
digit = divrem(b, base);
JS_ASSERT(digit < (uint32)base);
*p++ = BASEDIGIT(digit);
} while (b->wds);
Bfree(b);
}
/* Reverse the digits of the integer part of d. */
q = p-1;
while (q > pInt) {
char ch = *pInt;
*pInt++ = *q;
*q-- = ch;
}
df = d - di;
if (df != 0.0) {
/* We have a fraction. */
int32 e, bbits, s2, done;
Bigint *b, *s, *mlo, *mhi;
*p++ = '.';
b = d2b(df, &e, &bbits);
JS_ASSERT(e < 0);
/* At this point df = b * 2^e. e must be less than zero because 0 < df < 1. */
s2 = -(int32)(word0(d) >> Exp_shift1 & Exp_mask>>Exp_shift1);
#ifndef Sudden_Underflow
if (!s2)
s2 = -1;
#endif
s2 += Bias + P;
/* 1/2^s2 = (nextDouble(d) - d)/2 */
JS_ASSERT(-s2 < e);
mlo = i2b(1);
mhi = mlo;
if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0(d) & (Exp_mask & Exp_mask << 1)
#endif
) {
/* The special case. Here we want to be within a quarter of the last input
significant digit instead of one half of it when the output string's value is less than d. */
s2 += Log2P;
mhi = i2b(1<<Log2P);
}
b = lshift(b, e + s2);
s = i2b(1);
s = lshift(s, s2);
/* At this point we have the following:
* s = 2^s2;
* 1 > df = b/2^s2 > 0;
* (d - prevDouble(d))/2 = mlo/2^s2;
* (nextDouble(d) - d)/2 = mhi/2^s2. */
done = JS_FALSE;
do {
int32 j, j1;
Bigint *delta;
b = multadd(b, base, 0);
digit = quorem2(b, s2);
if (mlo == mhi)
mlo = mhi = multadd(mlo, base, 0);
else {
mlo = multadd(mlo, base, 0);
mhi = multadd(mhi, base, 0);
}
/* Do we yet have the shortest string that will round to d? */
j = cmp(b, mlo);
/* j is b/2^s2 compared with mlo/2^s2. */
delta = diff(s, mhi);
j1 = delta->sign ? 1 : cmp(b, delta);
Bfree(delta);
/* j1 is b/2^s2 compared with 1 - mhi/2^s2. */
#ifndef ROUND_BIASED
if (j1 == 0 && !(word1(d) & 1)) {
if (j > 0)
digit++;
done = JS_TRUE;
} else
#endif
if (j < 0 || (j == 0
#ifndef ROUND_BIASED
&& !(word1(d) & 1)
#endif
)) {
if (j1 > 0) {
/* Either dig or dig+1 would work here as the least significant digit.
Use whichever would produce an output value closer to d. */
b = lshift(b, 1);
j1 = cmp(b, s);
if (j1 > 0) /* The even test (|| (j1 == 0 && (digit & 1))) is not here because it messes up odd base output
* such as 3.5 in base 3. */
digit++;
}
done = JS_TRUE;
} else if (j1 > 0) {
digit++;
done = JS_TRUE;
}
JS_ASSERT(digit < (uint32)base);
*p++ = BASEDIGIT(digit);
} while (!done);
Bfree(b);
Bfree(s);
if (mlo != mhi)
Bfree(mlo);
Bfree(mhi);
}
JS_ASSERT(p < buffer + DTOBASESTR_BUFFER_SIZE);
*p = '\0';
}
return buffer;
}
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