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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
/*
* This file is based on the third-party code dtoa.c. We minimize our
* modifications to third-party code to make it easy to merge new versions.
* The author of dtoa.c was not willing to add the parentheses suggested by
* GCC, so we suppress these warnings.
*/
#if (__GNUC__ > 4) || (__GNUC__ == 4 && __GNUC_MINOR__ >= 2)
# pragma GCC diagnostic ignored "-Wparentheses"
#endif
#include "primpl.h"
#include "prbit.h"
#define MULTIPLE_THREADS
#define ACQUIRE_DTOA_LOCK(n) PR_Lock(dtoa_lock[n])
#define FREE_DTOA_LOCK(n) PR_Unlock(dtoa_lock[n])
static PRLock* dtoa_lock[2];
void _PR_InitDtoa(void) {
dtoa_lock[0] = PR_NewLock();
dtoa_lock[1] = PR_NewLock();
}
void _PR_CleanupDtoa(void) {
PR_DestroyLock(dtoa_lock[0]);
dtoa_lock[0] = NULL;
PR_DestroyLock(dtoa_lock[1]);
dtoa_lock[1] = NULL;
/* FIXME: deal with freelist and p5s. */
}
#if !defined(__ARM_EABI__) && (defined(__arm) || defined(__arm__) || \
defined(__arm26__) || defined(__arm32__))
# define IEEE_ARM
#elif defined(IS_LITTLE_ENDIAN)
# define IEEE_8087
#else
# define IEEE_MC68k
#endif
#define Long PRInt32
#define ULong PRUint32
#define NO_LONG_LONG
#define No_Hex_NaN
/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991, 2000, 2001 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 (dmg at acm dot org,
* with " at " changed at "@" and " dot " changed to "."). */
/* 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-, 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_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 IEEE_ARM for IEEE-arithmetic machines where the two words
* in a double are stored in big endian order but the two shorts
* in a word are still stored in little endian order.
* #define Long int on machines with 32-bit ints and 64-bit longs.
* #define IBM for IBM mainframe-style floating-point arithmetic.
* #define VAX for VAX-style floating-point arithmetic (D_floating).
* #define No_leftright to omit left-right logic in fast floating-point
* computation of dtoa.
* #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
* and strtod and dtoa should round accordingly.
* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
* and Honor_FLT_ROUNDS is not #defined.
* #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 NO_LONG_LONG on machines that do not have a "long long"
* integer type (of >= 64 bits). On such machines, you can
* #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. 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 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. Similarly, if you
* want something other than the system's free() to be called to
* recycle memory acquired from MALLOC, #define FREE to be the
* name of the alternate routine. (FREE or free is only called in
* pathological cases, e.g., in a dtoa call after a dtoa return in
* mode 3 with thousands of digits requested.)
* #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: 2304 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. The longest string dtoa can return is about 751 bytes
* long. For conversions by strtod of strings of 800 digits and
* all dtoa conversions in single-threaded executions with 8-byte
* pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
* pointers, PRIVATE_MEM >= 7112 appears adequate.
* #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.)
* When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
* strtod also accepts (case insensitively) strings of the form
* NaN(x), where x is a string of hexadecimal digits and spaces;
* if there is only one string of hexadecimal digits, it is taken
* for the 52 fraction bits of the resulting NaN; if there are two
* or more strings of hex digits, the first is for the high 20 bits,
* the second and subsequent for the low 32 bits, with intervening
* white space ignored; but if this results in none of the 52
* fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
* and NAN_WORD1 are used instead.
* #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.
* If you #define NO_IEEE_Scale on a machine that uses IEEE-format
* floating-point numbers and flushes underflows to zero rather
* than implementing gradual underflow, then you must also #define
* Sudden_Underflow.
* #define USE_LOCALE to use the current locale's decimal_point value.
* #define SET_INEXACT if IEEE arithmetic is being used and extra
* computation should be done to set the inexact flag when the
* result is inexact and avoid setting inexact when the result
* is exact. In this case, dtoa.c must be compiled in
* an environment, perhaps provided by #include "dtoa.c" in a
* suitable wrapper, that defines two functions,
* int get_inexact(void);
* void clear_inexact(void);
* such that get_inexact() returns a nonzero value if the
* inexact bit is already set, and clear_inexact() sets the
* inexact bit to 0. When SET_INEXACT is #defined, strtod
* also does extra computations to set the underflow and overflow
* flags when appropriate (i.e., when the result is tiny and
* inexact or when it is a numeric value rounded to +-infinity).
* #define NO_ERRNO if strtod should not assign errno = ERANGE when
* the result overflows to +-Infinity or underflows to 0.
*/
#ifndef Long
# define Long long
#endif
#ifndef ULong
typedef unsigned Long ULong;
#endif
#ifdef DEBUG
# include "stdio.h"
# define Bug(x) \
{ \
fprintf(stderr, "%s\n", x); \
exit(1); \
}
#endif
#include "stdlib.h"
#include "string.h"
#ifdef USE_LOCALE
# include "locale.h"
#endif
#ifdef MALLOC
# ifdef KR_headers
extern char* MALLOC();
# else
extern void* MALLOC(size_t);
# endif
#else
# define MALLOC malloc
#endif
#ifndef Omit_Private_Memory
# ifndef PRIVATE_MEM
# define PRIVATE_MEM 2304
# endif
# define PRIVATE_mem ((PRIVATE_MEM + sizeof(double) - 1) / sizeof(double))
static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
#endif
#undef IEEE_Arith
#undef Avoid_Underflow
#ifdef IEEE_MC68k
# define IEEE_Arith
#endif
#ifdef IEEE_8087
# define IEEE_Arith
#endif
#ifdef IEEE_ARM
# define IEEE_Arith
#endif
#include "errno.h"
#ifdef Bad_float_h
# ifdef IEEE_Arith
# define DBL_DIG 15
# define DBL_MAX_10_EXP 308
# define DBL_MAX_EXP 1024
# define FLT_RADIX 2
# endif /*IEEE_Arith*/
# ifdef IBM
# define DBL_DIG 16
# define DBL_MAX_10_EXP 75
# define DBL_MAX_EXP 63
# define FLT_RADIX 16
# define DBL_MAX 7.2370055773322621e+75
# endif
# ifdef VAX
# define DBL_DIG 16
# define DBL_MAX_10_EXP 38
# define DBL_MAX_EXP 127
# define FLT_RADIX 2
# define DBL_MAX 1.7014118346046923e+38
# endif
# ifndef LONG_MAX
# define LONG_MAX 2147483647
# endif
#else /* ifndef Bad_float_h */
# include "float.h"
#endif /* Bad_float_h */
#ifndef __MATH_H__
# include "math.h"
#endif
#ifdef __cplusplus
extern "C" {
#endif
#ifndef CONST
# ifdef KR_headers
# define CONST /* blank */
# else
# define CONST const
# endif
#endif
#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_ARM) + \
defined(VAX) + defined(IBM) != \
1
Exactly one of IEEE_8087, IEEE_MC68k, IEEE_ARM, VAX, or IBM should be defined.
#endif
typedef union {
double d;
ULong L[2];
} U;
#define dval(x) (x).d
#ifdef IEEE_8087
# define word0(x) (x).L[1]
# define word1(x) (x).L[0]
#else
# define word0(x) (x).L[0]
# define word1(x) (x).L[1]
#endif
/* 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) + defined(IEEE_ARM) + defined(VAX)
# define Storeinc(a, b, c) \
(((unsigned short*)a)[1] = (unsigned short)b, \
((unsigned short*)a)[0] = (unsigned short)c, a++)
#else
# define Storeinc(a, b, c) \
(((unsigned short*)a)[0] = (unsigned short)b, \
((unsigned short*)a)[1] = (unsigned short)c, a++)
#endif
/* #define P DBL_MANT_DIG */
/* Ten_pmax = floor(P*log(2)/log(5)) */
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
#ifdef IEEE_Arith
# define Exp_shift 20
# define Exp_shift1 20
# define Exp_msk1 0x100000
# define Exp_msk11 0x100000
# define Exp_mask 0x7ff00000
# define P 53
# define Bias 1023
# define Emin (-1022)
# define Exp_1 0x3ff00000
# define Exp_11 0x3ff00000
# define Ebits 11
# define Frac_mask 0xfffff
# define Frac_mask1 0xfffff
# define Ten_pmax 22
# define Bletch 0x10
# define Bndry_mask 0xfffff
# define Bndry_mask1 0xfffff
# define LSB 1
# define Sign_bit 0x80000000
# define Log2P 1
# define Tiny0 0
# define Tiny1 1
# define Quick_max 14
# define Int_max 14
# ifndef NO_IEEE_Scale
# define Avoid_Underflow
# ifdef Flush_Denorm /* debugging option */
# undef Sudden_Underflow
# endif
# endif
# ifndef Flt_Rounds
# ifdef FLT_ROUNDS
# define Flt_Rounds FLT_ROUNDS
# else
# define Flt_Rounds 1
# endif
# endif /*Flt_Rounds*/
# ifdef Honor_FLT_ROUNDS
# define Rounding rounding
# undef Check_FLT_ROUNDS
# define Check_FLT_ROUNDS
# else
# define Rounding Flt_Rounds
# endif
#else /* ifndef IEEE_Arith */
# undef Check_FLT_ROUNDS
# undef Honor_FLT_ROUNDS
# undef SET_INEXACT
# undef Sudden_Underflow
# define Sudden_Underflow
# ifdef IBM
# undef Flt_Rounds
# define Flt_Rounds 0
# define Exp_shift 24
# define Exp_shift1 24
# define Exp_msk1 0x1000000
# define Exp_msk11 0x1000000
# define Exp_mask 0x7f000000
# define P 14
# define Bias 65
# define Exp_1 0x41000000
# define Exp_11 0x41000000
# define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
# define Frac_mask 0xffffff
# define Frac_mask1 0xffffff
# define Bletch 4
# define Ten_pmax 22
# define Bndry_mask 0xefffff
# define Bndry_mask1 0xffffff
# define LSB 1
# define Sign_bit 0x80000000
# define Log2P 4
# define Tiny0 0x100000
# define Tiny1 0
# define Quick_max 14
# define Int_max 15
# else /* VAX */
# undef Flt_Rounds
# define Flt_Rounds 1
# define Exp_shift 23
# define Exp_shift1 7
# define Exp_msk1 0x80
# define Exp_msk11 0x800000
# define Exp_mask 0x7f80
# define P 56
# define Bias 129
# define Exp_1 0x40800000
# define Exp_11 0x4080
# define Ebits 8
# define Frac_mask 0x7fffff
# define Frac_mask1 0xffff007f
# define Ten_pmax 24
# define Bletch 2
# define Bndry_mask 0xffff007f
# define Bndry_mask1 0xffff007f
# define LSB 0x10000
# define Sign_bit 0x8000
# define Log2P 1
# define Tiny0 0x80
# define Tiny1 0
# define Quick_max 15
# define Int_max 15
# endif /* IBM, VAX */
#endif /* IEEE_Arith */
#ifndef IEEE_Arith
# define ROUND_BIASED
#endif
#ifdef RND_PRODQUOT
# define rounded_product(a, b) a = rnd_prod(a, b)
# define rounded_quotient(a, b) a = rnd_quot(a, b)
# ifdef KR_headers
extern double rnd_prod(), rnd_quot();
# else
extern double rnd_prod(double, double), rnd_quot(double, double);
# endif
#else
# define rounded_product(a, b) a *= b
# define rounded_quotient(a, b) a /= b
#endif
#define Big0 (Frac_mask1 | Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
#define Big1 0xffffffff
#ifndef Pack_32
# define Pack_32
#endif
#ifdef KR_headers
# define FFFFFFFF ((((unsigned long)0xffff) << 16) | (unsigned long)0xffff)
#else
# define FFFFFFFF 0xffffffffUL
#endif
#ifdef NO_LONG_LONG
# undef ULLong
# ifdef Just_16
# undef Pack_32
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
* This makes some inner loops simpler and sometimes saves work
* during multiplications, but it often seems to make things slightly
* slower. Hence the default is now to store 32 bits per Long.
*/
# endif
#else /* long long available */
# ifndef Llong
# define Llong long long
# endif
# ifndef ULLong
# define ULLong unsigned Llong
# endif
#endif /* NO_LONG_LONG */
#ifndef MULTIPLE_THREADS
# define ACQUIRE_DTOA_LOCK(n) /*nothing*/
# define FREE_DTOA_LOCK(n) /*nothing*/
#endif
#define Kmax 7
struct Bigint {
struct Bigint* next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
static Bigint* freelist[Kmax + 1];
static Bigint* Balloc
#ifdef KR_headers
(k) int k;
#else
(int k)
#endif
{
int x;
Bigint* rv;
#ifndef Omit_Private_Memory
unsigned int len;
#endif
ACQUIRE_DTOA_LOCK(0);
/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
/* but this case seems very unlikely. */
if (k <= Kmax && (rv = freelist[k])) {
freelist[k] = rv->next;
} else {
x = 1 << k;
#ifdef Omit_Private_Memory
rv = (Bigint*)MALLOC(sizeof(Bigint) + (x - 1) * sizeof(ULong));
#else
len = (sizeof(Bigint) + (x - 1) * sizeof(ULong) + sizeof(double) - 1) /
sizeof(double);
if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
rv = (Bigint*)pmem_next;
pmem_next += len;
} else {
rv = (Bigint*)MALLOC(len * sizeof(double));
}
#endif
rv->k = k;
rv->maxwds = x;
}
FREE_DTOA_LOCK(0);
rv->sign = rv->wds = 0;
return rv;
}
static void Bfree
#ifdef KR_headers
(v) Bigint* v;
#else
(Bigint* v)
#endif
{
if (v) {
if (v->k > Kmax)
#ifdef FREE
FREE((void*)v);
#else
free((void*)v);
#endif
else {
ACQUIRE_DTOA_LOCK(0);
v->next = freelist[v->k];
freelist[v->k] = v;
FREE_DTOA_LOCK(0);
}
}
}
#define Bcopy(x, y) \
memcpy((char*)&x->sign, (char*)&y->sign, \
y->wds * sizeof(Long) + 2 * sizeof(int))
static Bigint* multadd
#ifdef KR_headers
(b, m, a) Bigint* b;
int m, a;
#else
(Bigint* b, int m, int a) /* multiply by m and add a */
#endif
{
int i, wds;
#ifdef ULLong
ULong* x;
ULLong carry, y;
#else
ULong carry, *x, y;
# ifdef Pack_32
ULong xi, z;
# endif
#endif
Bigint* b1;
wds = b->wds;
x = b->x;
i = 0;
carry = a;
do {
#ifdef ULLong
y = *x * (ULLong)m + carry;
carry = y >> 32;
*x++ = y & FFFFFFFF;
#else
# ifdef Pack_32
xi = *x;
y = (xi & 0xffff) * m + carry;
z = (xi >> 16) * m + (y >> 16);
carry = z >> 16;
*x++ = (z << 16) + (y & 0xffff);
# else
y = *x * m + carry;
carry = y >> 16;
*x++ = y & 0xffff;
# endif
#endif
} while (++i < wds);
if (carry) {
if (wds >= b->maxwds) {
b1 = Balloc(b->k + 1);
Bcopy(b1, b);
Bfree(b);
b = b1;
}
b->x[wds++] = carry;
b->wds = wds;
}
return b;
}
static Bigint* s2b
#ifdef KR_headers
(s, nd0, nd, y9) CONST char* s;
int nd0, nd;
ULong y9;
#else
(CONST char* s, int nd0, int nd, ULong y9)
#endif
{
Bigint* b;
int i, k;
Long x, y;
x = (nd + 8) / 9;
for (k = 0, y = 1; x > y; y <<= 1, k++);
#ifdef Pack_32
b = Balloc(k);
b->x[0] = y9;
b->wds = 1;
#else
b = Balloc(k + 1);
b->x[0] = y9 & 0xffff;
b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
#endif
i = 9;
if (9 < nd0) {
s += 9;
do {
b = multadd(b, 10, *s++ - '0');
} while (++i < nd0);
s++;
} else {
s += 10;
}
for (; i < nd; i++) {
b = multadd(b, 10, *s++ - '0');
}
return b;
}
static int hi0bits
#ifdef KR_headers
(x) register ULong x;
#else
(register ULong x)
#endif
{
#ifdef PR_HAVE_BUILTIN_BITSCAN32
return ((!x) ? 32 : pr_bitscan_clz32(x));
#else
register int k = 0;
if (!(x & 0xffff0000)) {
k = 16;
x <<= 16;
}
if (!(x & 0xff000000)) {
k += 8;
x <<= 8;
}
if (!(x & 0xf0000000)) {
k += 4;
x <<= 4;
}
if (!(x & 0xc0000000)) {
k += 2;
x <<= 2;
}
if (!(x & 0x80000000)) {
k++;
if (!(x & 0x40000000)) {
return 32;
}
}
return k;
#endif /* PR_HAVE_BUILTIN_BITSCAN32 */
}
static int lo0bits
#ifdef KR_headers
(y) ULong* y;
#else
(ULong* y)
#endif
{
#ifdef PR_HAVE_BUILTIN_BITSCAN32
int k;
ULong x = *y;
if (x > 1) {
*y = (x >> (k = pr_bitscan_ctz32(x)));
} else {
k = ((x ^ 1) << 5);
}
#else
register int k;
register ULong x = *y;
if (x & 7) {
if (x & 1) {
return 0;
}
if (x & 2) {
*y = x >> 1;
return 1;
}
*y = x >> 2;
return 2;
}
k = 0;
if (!(x & 0xffff)) {
k = 16;
x >>= 16;
}
if (!(x & 0xff)) {
k += 8;
x >>= 8;
}
if (!(x & 0xf)) {
k += 4;
x >>= 4;
}
if (!(x & 0x3)) {
k += 2;
x >>= 2;
}
if (!(x & 1)) {
k++;
x >>= 1;
if (!x) {
return 32;
}
}
*y = x;
#endif /* PR_HAVE_BUILTIN_BITSCAN32 */
return k;
}
static Bigint* i2b
#ifdef KR_headers
(i) int i;
#else
(int i)
#endif
{
Bigint* b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
static Bigint *mult
#ifdef KR_headers
(a, b) Bigint *a,
*b;
#else
(Bigint* a, Bigint* b)
#endif
{
Bigint* c;
int k, wa, wb, wc;
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
ULong y;
#ifdef ULLong
ULLong carry, z;
#else
ULong carry, z;
# ifdef Pack_32
ULong z2;
# endif
#endif
if (a->wds < b->wds) {
c = a;
a = b;
b = c;
}
k = a->k;
wa = a->wds;
wb = b->wds;
wc = wa + wb;
if (wc > a->maxwds) {
k++;
}
c = Balloc(k);
for (x = c->x, xa = x + wc; x < xa; x++) {
*x = 0;
}
xa = a->x;
xae = xa + wa;
xb = b->x;
xbe = xb + wb;
xc0 = c->x;
#ifdef ULLong
for (; xb < xbe; xc0++) {
if (y = *xb++) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * (ULLong)y + *xc + carry;
carry = z >> 32;
*xc++ = z & FFFFFFFF;
} while (x < xae);
*xc = carry;
}
}
#else
# ifdef Pack_32
for (; xb < xbe; xb++, xc0++) {
if (y = *xb & 0xffff) {
x = xa;
xc = xc0;
carry = 0;
do {
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
Storeinc(xc, z2, z);
} while (x < xae);
*xc = carry;
}
if (y = *xb >> 16) {
x = xa;
xc = xc0;
carry = 0;
z2 = *xc;
do {
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
Storeinc(xc, z, z2);
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
carry = z2 >> 16;
} while (x < xae);
*xc = z2;
}
}
# else
for (; xb < xbe; xc0++) {
if (y = *xb++) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * y + *xc + carry;
carry = z >> 16;
*xc++ = z & 0xffff;
} while (x < xae);
*xc = carry;
}
}
# endif
#endif
for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc);
c->wds = wc;
return c;
}
static Bigint* p5s;
static Bigint* pow5mult
#ifdef KR_headers
(b, k) Bigint* b;
int k;
#else
(Bigint* b, int k)
#endif
{
Bigint *b1, *p5, *p51;
int i;
static int p05[3] = {5, 25, 125};
if (i = k & 3) {
b = multadd(b, p05[i - 1], 0);
}
if (!(k >>= 2)) {
return b;
}
if (!(p5 = p5s)) {
/* first time */
#ifdef MULTIPLE_THREADS
ACQUIRE_DTOA_LOCK(1);
if (!(p5 = p5s)) {
p5 = p5s = i2b(625);
p5->next = 0;
}
FREE_DTOA_LOCK(1);
#else
p5 = p5s = i2b(625);
p5->next = 0;
#endif
}
for (;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1)) {
break;
}
if (!(p51 = p5->next)) {
#ifdef MULTIPLE_THREADS
ACQUIRE_DTOA_LOCK(1);
if (!(p51 = p5->next)) {
p51 = p5->next = mult(p5, p5);
p51->next = 0;
}
FREE_DTOA_LOCK(1);
#else
p51 = p5->next = mult(p5, p5);
p51->next = 0;
#endif
}
p5 = p51;
}
return b;
}
static Bigint* lshift
#ifdef KR_headers
(b, k) Bigint* b;
int k;
#else
(Bigint* b, int k)
#endif
{
int i, k1, n, n1;
Bigint* b1;
ULong *x, *x1, *xe, z;
#ifdef Pack_32
n = k >> 5;
#else
n = k >> 4;
#endif
k1 = b->k;
n1 = n + b->wds + 1;
for (i = b->maxwds; n1 > i; i <<= 1) {
k1++;
}
b1 = Balloc(k1);
x1 = b1->x;
for (i = 0; i < n; i++) {
*x1++ = 0;
}
x = b->x;
xe = x + b->wds;
#ifdef Pack_32
if (k &= 0x1f) {
k1 = 32 - k;
z = 0;
do {
*x1++ = *x << k | z;
z = *x++ >> k1;
} while (x < xe);
if (*x1 = z) {
++n1;
}
}
#else
if (k &= 0xf) {
k1 = 16 - k;
z = 0;
do {
*x1++ = *x << k & 0xffff | z;
z = *x++ >> k1;
} while (x < xe);
if (*x1 = z) {
++n1;
}
}
#endif
else
do {
*x1++ = *x++;
} while (x < xe);
b1->wds = n1 - 1;
Bfree(b);
return b1;
}
static int cmp
#ifdef KR_headers
(a, b) Bigint *a,
*b;
#else
(Bigint* a, Bigint* b)
#endif
{
ULong *xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
#ifdef DEBUG
if (i > 1 && !a->x[i - 1]) {
Bug("cmp called with a->x[a->wds-1] == 0");
}
if (j > 1 && !b->x[j - 1]) {
Bug("cmp called with b->x[b->wds-1] == 0");
}
#endif
if (i -= j) {
return i;
}
xa0 = a->x;
xa = xa0 + j;
xb0 = b->x;
xb = xb0 + j;
for (;;) {
if (*--xa != *--xb) {
return *xa < *xb ? -1 : 1;
}
if (xa <= xa0) {
break;
}
}
return 0;
}
static Bigint *diff
#ifdef KR_headers
(a, b) Bigint *a,
*b;
#else
(Bigint* a, Bigint* b)
#endif
{
Bigint* c;
int i, wa, wb;
ULong *xa, *xae, *xb, *xbe, *xc;
#ifdef ULLong
ULLong borrow, y;
#else
ULong borrow, y;
# ifdef Pack_32
ULong z;
# endif
#endif
i = cmp(a, b);
if (!i) {
c = Balloc(0);
c->wds = 1;
c->x[0] = 0;
return c;
}
if (i < 0) {
c = a;
a = b;
b = c;
i = 1;
} else {
i = 0;
}
c = Balloc(a->k);
c->sign = i;
wa = a->wds;
xa = a->x;
xae = xa + wa;
wb = b->wds;
xb = b->x;
xbe = xb + wb;
xc = c->x;
borrow = 0;
#ifdef ULLong
do {
y = (ULLong)*xa++ - *xb++ - borrow;
borrow = y >> 32 & (ULong)1;
*xc++ = y & FFFFFFFF;
} while (xb < xbe);
while (xa < xae) {
y = *xa++ - borrow;
borrow = y >> 32 & (ULong)1;
*xc++ = y & FFFFFFFF;
}
#else
# ifdef Pack_32
do {
y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(xc, z, y);
} while (xb < xbe);
while (xa < xae) {
y = (*xa & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*xa++ >> 16) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(xc, z, y);
}
# else
do {
y = *xa++ - *xb++ - borrow;
borrow = (y & 0x10000) >> 16;
*xc++ = y & 0xffff;
} while (xb < xbe);
while (xa < xae) {
y = *xa++ - borrow;
borrow = (y & 0x10000) >> 16;
*xc++ = y & 0xffff;
}
# endif
#endif
while (!*--xc) {
wa--;
}
c->wds = wa;
return c;
}
static double ulp
#ifdef KR_headers
(dx) double dx;
#else
(double dx)
#endif
{
register Long L;
U x, a;
dval(x) = dx;
L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
#ifndef Avoid_Underflow
# ifndef Sudden_Underflow
if (L > 0) {
# endif
#endif
#ifdef IBM
L |= Exp_msk1 >> 4;
#endif
word0(a) = L;
word1(a) = 0;
#ifndef Avoid_Underflow
# ifndef Sudden_Underflow
} else {
L = -L >> Exp_shift;
if (L < Exp_shift) {
word0(a) = 0x80000 >> L;
word1(a) = 0;
} else {
word0(a) = 0;
L -= Exp_shift;
word1(a) = L >= 31 ? 1 : 1 << 31 - L;
}
}
# endif
#endif
return dval(a);
}
static double b2d
#ifdef KR_headers
(a, e) Bigint* a;
int* e;
#else
(Bigint* a, int* e)
#endif
{
ULong *xa, *xa0, w, y, z;
int k;
U d;
#ifdef VAX
ULong d0, d1;
#else
# define d0 word0(d)
# define d1 word1(d)
#endif
xa0 = a->x;
xa = xa0 + a->wds;
y = *--xa;
#ifdef DEBUG
if (!y) {
Bug("zero y in b2d");
}
#endif
k = hi0bits(y);
*e = 32 - k;
#ifdef Pack_32
if (k < Ebits) {
d0 = Exp_1 | y >> Ebits - k;
w = xa > xa0 ? *--xa : 0;
d1 = y << (32 - Ebits) + k | w >> Ebits - k;
goto ret_d;
}
z = xa > xa0 ? *--xa : 0;
if (k -= Ebits) {
d0 = Exp_1 | y << k | z >> 32 - k;
y = xa > xa0 ? *--xa : 0;
d1 = z << k | y >> 32 - k;
} else {
d0 = Exp_1 | y;
d1 = z;
}
#else
if (k < Ebits + 16) {
z = xa > xa0 ? *--xa : 0;
d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
w = xa > xa0 ? *--xa : 0;
y = xa > xa0 ? *--xa : 0;
d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
goto ret_d;
}
z = xa > xa0 ? *--xa : 0;
w = xa > xa0 ? *--xa : 0;
k -= Ebits + 16;
d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
y = xa > xa0 ? *--xa : 0;
d1 = w << k + 16 | y << k;
#endif
ret_d:
#ifdef VAX
word0(d) = d0 >> 16 | d0 << 16;
word1(d) = d1 >> 16 | d1 << 16;
#else
# undef d0
# undef d1
#endif
return dval(d);
}
static Bigint* d2b
#ifdef KR_headers
(dd, e, bits) double dd;
int *e, *bits;
#else
(double dd, int* e, int* bits)
#endif
{
U d;
Bigint* b;
int de, k;
ULong *x, y, z;
#ifndef Sudden_Underflow
int i;
#endif
#ifdef VAX
ULong d0, d1;
#endif
dval(d) = dd;
#ifdef VAX
d0 = word0(d) >> 16 | word0(d) << 16;
d1 = word1(d) >> 16 | word1(d) << 16;
#else
# define d0 word0(d)
# define d1 word1(d)
#endif
#ifdef Pack_32
b = Balloc(1);
#else
b = Balloc(2);
#endif
x = b->x;
z = d0 & Frac_mask;
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
de = (int)(d0 >> Exp_shift);
# ifndef IBM
z |= Exp_msk11;
# endif
#else
if (de = (int)(d0 >> Exp_shift)) {
z |= Exp_msk1;
}
#endif
#ifdef Pack_32
if (y = d1) {
if (k = lo0bits(&y)) {
x[0] = y | z << 32 - k;
z >>= k;
} else {
x[0] = y;
}
# ifndef Sudden_Underflow
i =
# endif
b->wds = (x[1] = z) ? 2 : 1;
} else {
k = lo0bits(&z);
x[0] = z;
# ifndef Sudden_Underflow
i =
# endif
b->wds = 1;
k += 32;
}
#else
if (y = d1) {
if (k = lo0bits(&y))
if (k >= 16) {
x[0] = y | z << 32 - k & 0xffff;
x[1] = z >> k - 16 & 0xffff;
x[2] = z >> k;
i = 2;
} else {
x[0] = y & 0xffff;
x[1] = y >> 16 | z << 16 - k & 0xffff;
x[2] = z >> k & 0xffff;
x[3] = z >> k + 16;
i = 3;
}
else {
x[0] = y & 0xffff;
x[1] = y >> 16;
x[2] = z & 0xffff;
x[3] = z >> 16;
i = 3;
}
} else {
# ifdef DEBUG
if (!z) {
Bug("Zero passed to d2b");
}
# endif
k = lo0bits(&z);
if (k >= 16) {
x[0] = z;
i = 0;
} else {
x[0] = z & 0xffff;
x[1] = z >> 16;
i = 1;
}
k += 32;
}
while (!x[i]) {
--i;
}
b->wds = i + 1;
#endif
#ifndef Sudden_Underflow
if (de) {
#endif
#ifdef IBM
*e = (de - Bias - (P - 1) << 2) + k;
*bits = 4 * P + 8 - k - hi0bits(word0(d) & Frac_mask);
#else
*e = de - Bias - (P - 1) + k;
*bits = P - k;
#endif
#ifndef Sudden_Underflow
} else {
*e = de - Bias - (P - 1) + 1 + k;
# ifdef Pack_32
*bits = 32 * i - hi0bits(x[i - 1]);
# else
*bits = (i + 2) * 16 - hi0bits(x[i]);
# endif
}
#endif
return b;
}
#undef d0
#undef d1
static double ratio
#ifdef KR_headers
(a, b) Bigint *a,
*b;
#else
(Bigint* a, Bigint* b)
#endif
{
U da, db;
int k, ka, kb;
dval(da) = b2d(a, &ka);
dval(db) = b2d(b, &kb);
#ifdef Pack_32
k = ka - kb + 32 * (a->wds - b->wds);
#else
k = ka - kb + 16 * (a->wds - b->wds);
#endif
#ifdef IBM
if (k > 0) {
word0(da) += (k >> 2) * Exp_msk1;
if (k &= 3) {
dval(da) *= 1 << k;
}
} else {
k = -k;
word0(db) += (k >> 2) * Exp_msk1;
if (k &= 3) {
dval(db) *= 1 << k;
}
}
#else
if (k > 0) {
word0(da) += k * Exp_msk1;
} else {
k = -k;
word0(db) += k * Exp_msk1;
}
#endif
return dval(da) / dval(db);
}
static CONST double tens[] = {1e0,
1e1,
1e2,
1e3,
1e4,
1e5,
1e6,
1e7,
1e8,
1e9,
1e10,
1e11,
1e12,
1e13,
1e14,
1e15,
1e16,
1e17,
1e18,
1e19,
1e20,
1e21,
1e22
#ifdef VAX
,
1e23,
1e24
#endif
};
static CONST double
#ifdef IEEE_Arith
bigtens[] = {1e16, 1e32, 1e64, 1e128, 1e256};
static CONST double tinytens[] = {1e-16, 1e-32, 1e-64, 1e-128,
# ifdef Avoid_Underflow
9007199254740992. * 9007199254740992.e-256
/* = 2^106 * 1e-53 */
# 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
#else
# ifdef IBM
bigtens[] = {1e16, 1e32, 1e64};
static CONST double tinytens[] = {1e-16, 1e-32, 1e-64};
# define n_bigtens 3
# else
bigtens[] = {1e16, 1e32};
static CONST double tinytens[] = {1e-16, 1e-32};
# define n_bigtens 2
# endif
#endif
#ifndef IEEE_Arith
# undef INFNAN_CHECK
#endif
#ifdef INFNAN_CHECK
# ifndef NAN_WORD0
# define NAN_WORD0 0x7ff80000
# endif
# ifndef NAN_WORD1
# define NAN_WORD1 0
# endif
static int match
# ifdef KR_headers
(sp, t) char **sp,
*t;
# else
(CONST char** sp, char* t)
# endif
{
int c, d;
CONST char* s = *sp;
while (d = *t++) {
if ((c = *++s) >= 'A' && c <= 'Z') {
c += 'a' - 'A';
}
if (c != d) {
return 0;
}
}
*sp = s + 1;
return 1;
}
# ifndef No_Hex_NaN
static void hexnan
# ifdef KR_headers
(rvp, sp) double* rvp;
CONST char** sp;
# else
(double* rvp, CONST char** sp)
# endif
{
ULong c, x[2];
CONST char* s;
int havedig, udx0, xshift;
x[0] = x[1] = 0;
havedig = xshift = 0;
udx0 = 1;
s = *sp;
while (c = *(CONST unsigned char*)++s) {
if (c >= '0' && c <= '9') {
c -= '0';
} else if (c >= 'a' && c <= 'f') {
c += 10 - 'a';
} else if (c >= 'A' && c <= 'F') {
c += 10 - 'A';
} else if (c <= ' ') {
if (udx0 && havedig) {
udx0 = 0;
xshift = 1;
}
continue;
} else if (/*(*/ c == ')' && havedig) {
*sp = s + 1;
break;
} else {
return; /* invalid form: don't change *sp */
}
havedig = 1;
if (xshift) {
xshift = 0;
x[0] = x[1];
x[1] = 0;
}
if (udx0) {
x[0] = (x[0] << 4) | (x[1] >> 28);
}
x[1] = (x[1] << 4) | c;
}
if ((x[0] &= 0xfffff) || x[1]) {
word0(*rvp) = Exp_mask | x[0];
word1(*rvp) = x[1];
}
}
# endif /*No_Hex_NaN*/
#endif /* INFNAN_CHECK */
PR_IMPLEMENT(double)
PR_strtod
#ifdef KR_headers
(s00, se) CONST char* s00;
char** se;
#else
(CONST char* s00, char** se)
#endif
{
#ifdef Avoid_Underflow
int scale;
#endif
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e, e1, esign, i, j, k, nd,
nd0, nf, nz, nz0, sign;
CONST char *s, *s0, *s1;
double aadj, aadj1, adj;
U aadj2, rv, rv0;
Long L;
ULong y, z;
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
#ifdef USE_LOCALE
CONST char* s2;
#endif
if (!_pr_initialized) {
_PR_ImplicitInitialization();
}
sign = nz0 = nz = 0;
dval(rv) = 0.;
for (s = s00;; s++) switch (*s) {
case '-':
sign = 1;
/* no break */
case '+':
if (*++s) {
goto break2;
}
/* no break */
case 0:
goto ret0;
case '\t':
case '\n':
case '\v':
case '\f':
case '\r':
case ' ':
continue;
default:
goto break2;
}
break2:
if (*s == '0') {
nz0 = 1;
while (*++s == '0');
if (!*s) {
goto ret;
}
}
s0 = s;
y = z = 0;
for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
if (nd < 9) {
y = 10 * y + c - '0';
} else if (nd < 16) {
z = 10 * z + c - '0';
}
nd0 = nd;
#ifdef USE_LOCALE
s1 = localeconv()->decimal_point;
if (c == *s1) {
c = '.';
if (*++s1) {
s2 = s;
for (;;) {
if (*++s2 != *s1) {
c = 0;
break;
}
if (!*++s1) {
s = s2;
break;
}
}
}
}
#endif
if (c == '.') {
c = *++s;
if (!nd) {
for (; c == '0'; c = *++s) {
nz++;
}
if (c > '0' && c <= '9') {
s0 = s;
nf += nz;
nz = 0;
goto have_dig;
}
goto dig_done;
}
for (; c >= '0' && c <= '9'; c = *++s) {
have_dig:
nz++;
if (c -= '0') {
nf += nz;
for (i = 1; i < nz; i++)
if (nd++ < 9) {
y *= 10;
} else if (nd <= DBL_DIG + 1) {
z *= 10;
}
if (nd++ < 9) {
y = 10 * y + c;
} else if (nd <= DBL_DIG + 1) {
z = 10 * z + c;
}
nz = 0;
}
}
}
dig_done:
if (nd > 64 * 1024) {
goto ret0;
}
e = 0;
if (c == 'e' || c == 'E') {
if (!nd && !nz && !nz0) {
goto ret0;
}
s00 = s;
esign = 0;
switch (c = *++s) {
case '-':
esign = 1;
case '+':
c = *++s;
}
if (c >= '0' && c <= '9') {
while (c == '0') {
c = *++s;
}
if (c > '0' && c <= '9') {
L = c - '0';
s1 = s;
while ((c = *++s) >= '0' && c <= '9') {
L = 10 * L + c - '0';
}
if (s - s1 > 8 || L > 19999)
/* 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) {
#ifdef INFNAN_CHECK
/* Check for Nan and Infinity */
switch (c) {
case 'i':
case 'I':
if (match(&s, "nf")) {
--s;
if (!match(&s, "inity")) {
++s;
}
word0(rv) = 0x7ff00000;
word1(rv) = 0;
goto ret;
}
break;
case 'n':
case 'N':
if (match(&s, "an")) {
word0(rv) = NAN_WORD0;
word1(rv) = NAN_WORD1;
# ifndef No_Hex_NaN
if (*s == '(') { /*)*/
hexnan(&rv, &s);
}
# endif
goto ret;
}
}
#endif /* INFNAN_CHECK */
ret0:
s = s00;
sign = 0;
}
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;
dval(rv) = y;
if (k > 9) {
#ifdef SET_INEXACT
if (k > DBL_DIG) {
oldinexact = get_inexact();
}
#endif
dval(rv) = tens[k - 9] * dval(rv) + z;
}
bd0 = 0;
if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
# ifndef Honor_FLT_ROUNDS
&& Flt_Rounds == 1
# endif
#endif
) {
if (!e) {
goto ret;
}
if (e > 0) {
if (e <= Ten_pmax) {
#ifdef VAX
goto vax_ovfl_check;
#else
# ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign) {
rv = -rv;
sign = 0;
}
# endif
/* rv = */ rounded_product(dval(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.
*/
#ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign) {
rv = -rv;
sign = 0;
}
#endif
e -= i;
dval(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;
/* rv = */ rounded_product(dval(rv), tens[e]);
if ((word0(rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
goto ovfl;
}
word0(rv) += P * Exp_msk1;
#else
/* rv = */ rounded_product(dval(rv), tens[e]);
#endif
goto ret;
}
}
#ifndef Inaccurate_Divide
else if (e >= -Ten_pmax) {
# ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign) {
rv = -rv;
sign = 0;
}
# endif
/* rv = */ rounded_quotient(dval(rv), tens[-e]);
goto ret;
}
#endif
}
e1 += nd - k;
#ifdef IEEE_Arith
# ifdef SET_INEXACT
inexact = 1;
if (k <= DBL_DIG) {
oldinexact = get_inexact();
}
# endif
# ifdef Avoid_Underflow
scale = 0;
# endif
# ifdef Honor_FLT_ROUNDS
if ((rounding = Flt_Rounds) >= 2) {
if (sign) {
rounding = rounding == 2 ? 0 : 2;
} else if (rounding != 2) {
rounding = 0;
}
}
# endif
#endif /*IEEE_Arith*/
/* Get starting approximation = rv * 10**e1 */
if (e1 > 0) {
if (i = e1 & 15) {
dval(rv) *= tens[i];
}
if (e1 &= ~15) {
if (e1 > DBL_MAX_10_EXP) {
ovfl:
#ifndef NO_ERRNO
PR_SetError(PR_RANGE_ERROR, 0);
#endif
/* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
# ifdef Honor_FLT_ROUNDS
switch (rounding) {
case 0: /* toward 0 */
case 3: /* toward -infinity */
word0(rv) = Big0;
word1(rv) = Big1;
break;
default:
word0(rv) = Exp_mask;
word1(rv) = 0;
}
# else /*Honor_FLT_ROUNDS*/
word0(rv) = Exp_mask;
word1(rv) = 0;
# endif /*Honor_FLT_ROUNDS*/
# ifdef SET_INEXACT
/* set overflow bit */
dval(rv0) = 1e300;
dval(rv0) *= dval(rv0);
# endif
#else /*IEEE_Arith*/
word0(rv) = Big0;
word1(rv) = Big1;
#endif /*IEEE_Arith*/
if (bd0) {
goto retfree;
}
goto ret;
}
e1 >>= 4;
for (j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1) {
dval(rv) *= bigtens[j];
}
/* The last multiplication could overflow. */
word0(rv) -= P * Exp_msk1;
dval(rv) *= bigtens[j];
if ((z = word0(rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
goto ovfl;
}
if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
/* 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) {
dval(rv) /= tens[i];
}
if (e1 >>= 4) {
if (e1 >= 1 << n_bigtens) {
goto undfl;
}
#ifdef Avoid_Underflow
if (e1 & Scale_Bit) {
scale = 2 * P;
}
for (j = 0; e1 > 0; j++, e1 >>= 1)
if (e1 & 1) {
dval(rv) *= tinytens[j];
}
if (scale &&
(j = 2 * P + 1 - ((word0(rv) & Exp_mask) >> Exp_shift)) > 0) {
/* scaled rv is denormal; zap j low bits */
if (j >= 32) {
word1(rv) = 0;
if (j >= 53) {
word0(rv) = (P + 2) * Exp_msk1;
} else {
word0(rv) &= 0xffffffff << j - 32;
}
} else {
word1(rv) &= 0xffffffff << j;
}
}
#else
for (j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1) {
dval(rv) *= tinytens[j];
}
/* The last multiplication could underflow. */
dval(rv0) = dval(rv);
dval(rv) *= tinytens[j];
if (!dval(rv)) {
dval(rv) = 2. * dval(rv0);
dval(rv) *= tinytens[j];
#endif
if (!dval(rv)) {
undfl:
dval(rv) = 0.;
#ifndef NO_ERRNO
PR_SetError(PR_RANGE_ERROR, 0);
#endif
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(dval(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 Honor_FLT_ROUNDS
if (rounding != 1) {
bs2++;
}
#endif
#ifdef Avoid_Underflow
j = bbe - scale;
i = j + bbbits - 1; /* logb(rv) */
if (i < Emin) { /* denormal */
j += P - Emin;
} else {
j = P + 1 - bbbits;
}
#else /*Avoid_Underflow*/
# ifdef Sudden_Underflow
# ifdef IBM
j = 1 + 4 * P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
# else
j = P + 1 - bbbits;
# endif
# else /*Sudden_Underflow*/
j = bbe;
i = j + bbbits - 1; /* logb(rv) */
if (i < Emin) { /* denormal */
j += P - Emin;
} else {
j = P + 1 - bbbits;
}
# endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
bb2 += j;
bd2 += j;
#ifdef Avoid_Underflow
bd2 += scale;
#endif
i = bb2 < bd2 ? bb2 : bd2;
if (i > bs2) {
i = bs2;
}
if (i > 0) {
bb2 -= i;
bd2 -= i;
bs2 -= i;
}
if (bb5 > 0) {
bs = pow5mult(bs, bb5);
bb1 = mult(bs, bb);
Bfree(bb);
bb = bb1;
}
if (bb2 > 0) {
bb = lshift(bb, bb2);
}
if (bd5 > 0) {
bd = pow5mult(bd, bd5);
}
if (bd2 > 0) {
bd = lshift(bd, bd2);
}
if (bs2 > 0) {
bs = lshift(bs, bs2);
}
delta = diff(bb, bd);
dsign = delta->sign;
delta->sign = 0;
i = cmp(delta, bs);
#ifdef Honor_FLT_ROUNDS
if (rounding != 1) {
if (i < 0) {
/* Error is less than an ulp */
if (!delta->x[0] && delta->wds <= 1) {
/* exact */
# ifdef SET_INEXACT
inexact = 0;
# endif
break;
}
if (rounding) {
if (dsign) {
adj = 1.;
goto apply_adj;
}
} else if (!dsign) {
adj = -1.;
if (!word1(rv) && !(word0(rv) & Frac_mask)) {
y = word0(rv) & Exp_mask;
# ifdef Avoid_Underflow
if (!scale || y > 2 * P * Exp_msk1)
# else
if (y)
# endif
{
delta = lshift(delta, Log2P);
if (cmp(delta, bs) <= 0) {
adj = -0.5;
}
}
}
apply_adj:
# ifdef Avoid_Underflow
if (scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1) {
word0(adj) += (2 * P + 1) * Exp_msk1 - y;
}
# else
# ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P * Exp_msk1) {
word0(rv) += P * Exp_msk1;
dval(rv) += adj * ulp(dval(rv));
word0(rv) -= P * Exp_msk1;
} else
# endif /*Sudden_Underflow*/
# endif /*Avoid_Underflow*/
dval(rv) += adj * ulp(dval(rv));
}
break;
}
adj = ratio(delta, bs);
if (adj < 1.) {
adj = 1.;
}
if (adj <= 0x7ffffffe) {
/* adj = rounding ? ceil(adj) : floor(adj); */
y = adj;
if (y != adj) {
if (!((rounding >> 1) ^ dsign)) {
y++;
}
adj = y;
}
}
# ifdef Avoid_Underflow
if (scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1) {
word0(adj) += (2 * P + 1) * Exp_msk1 - y;
}
# else
# ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P * Exp_msk1) {
word0(rv) += P * Exp_msk1;
adj *= ulp(dval(rv));
if (dsign) {
dval(rv) += adj;
} else {
dval(rv) -= adj;
}
word0(rv) -= P * Exp_msk1;
goto cont;
}
# endif /*Sudden_Underflow*/
# endif /*Avoid_Underflow*/
adj *= ulp(dval(rv));
if (dsign) {
dval(rv) += adj;
} else {
dval(rv) -= adj;
}
goto cont;
}
#endif /*Honor_FLT_ROUNDS*/
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 IEEE_Arith
# ifdef Avoid_Underflow
|| (word0(rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1
# else
|| (word0(rv) & Exp_mask) <= Exp_msk1
# endif
#endif
) {
#ifdef SET_INEXACT
if (!delta->x[0] && delta->wds <= 1) {
inexact = 0;
}
#endif
break;
}
if (!delta->x[0] && delta->wds <= 1) {
/* exact result */
#ifdef SET_INEXACT
inexact = 0;
#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) ==
(
#ifdef Avoid_Underflow
(scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1)
? (0xffffffff &
(0xffffffff << (2 * P + 1 - (y >> Exp_shift))))
:
#endif
0xffffffff)) {
/*boundary case -- increment exponent*/
word0(rv) = (word0(rv) & Exp_mask) + Exp_msk1
#ifdef IBM
| Exp_msk1 >> 4
#endif
;
word1(rv) = 0;
#ifdef Avoid_Underflow
dsign = 0;
#endif
break;
}
} else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
drop_down:
/* boundary case -- decrement exponent */
#ifdef Sudden_Underflow /*{{*/
L = word0(rv) & Exp_mask;
# ifdef IBM
if (L < Exp_msk1)
# else
# ifdef Avoid_Underflow
if (L <= (scale ? (2 * P + 1) * Exp_msk1 : Exp_msk1))
# else
if (L <= Exp_msk1)
# endif /*Avoid_Underflow*/
# endif /*IBM*/
goto undfl;
L -= Exp_msk1;
#else /*Sudden_Underflow}{*/
# ifdef Avoid_Underflow
if (scale) {
L = word0(rv) & Exp_mask;
if (L <= (2 * P + 1) * Exp_msk1) {
if (L > (P + 2) * Exp_msk1)
/* round even ==> */
/* accept rv */
{
break;
}
/* rv = smallest denormal */
goto undfl;
}
}
# endif /*Avoid_Underflow*/
L = (word0(rv) & Exp_mask) - Exp_msk1;
#endif /*Sudden_Underflow}}*/
word0(rv) = L | Bndry_mask1;
word1(rv) = 0xffffffff;
#ifdef IBM
goto cont;
#else
break;
#endif
}
#ifndef ROUND_BIASED
if (!(word1(rv) & LSB)) {
break;
}
#endif
if (dsign) {
dval(rv) += ulp(dval(rv));
}
#ifndef ROUND_BIASED
else {
dval(rv) -= ulp(dval(rv));
# ifndef Sudden_Underflow
if (!dval(rv)) {
goto undfl;
}
# endif
}
# ifdef Avoid_Underflow
dsign = 1 - dsign;
# endif
#endif
break;
}
if ((aadj = ratio(delta, bs)) <= 2.) {
if (dsign) {
aadj = aadj1 = 1.;
} else if (word1(rv) || word0(rv) & Bndry_mask) {
#ifndef Sudden_Underflow
if (word1(rv) == Tiny1 && !word0(rv)) {
goto undfl;
}
#endif
aadj = 1.;
aadj1 = -1.;
} else {
/* 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 (Rounding) {
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 /*Check_FLT_ROUNDS*/
}
y = word0(rv) & Exp_mask;
/* Check for overflow */
if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) {
dval(rv0) = dval(rv);
word0(rv) -= P * Exp_msk1;
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
if ((word0(rv) & Exp_mask) >= Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
if (word0(rv0) == Big0 && word1(rv0) == Big1) {
goto ovfl;
}
word0(rv) = Big0;
word1(rv) = Big1;
goto cont;
} else {
word0(rv) += P * Exp_msk1;
}
} else {
#ifdef Avoid_Underflow
if (scale && y <= 2 * P * Exp_msk1) {
if (aadj <= 0x7fffffff) {
if ((z = aadj) <= 0) {
z = 1;
}
aadj = z;
aadj1 = dsign ? aadj : -aadj;
}
dval(aadj2) = aadj1;
word0(aadj2) += (2 * P + 1) * Exp_msk1 - y;
aadj1 = dval(aadj2);
}
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
#else
# ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P * Exp_msk1) {
dval(rv0) = dval(rv);
word0(rv) += P * Exp_msk1;
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
# ifdef IBM
if ((word0(rv) & Exp_mask) < P * Exp_msk1)
# else
if ((word0(rv) & Exp_mask) <= P * Exp_msk1)
# endif
{
if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1) {
goto undfl;
}
word0(rv) = Tiny0;
word1(rv) = Tiny1;
goto cont;
} else {
word0(rv) -= P * Exp_msk1;
}
} else {
adj = aadj1 * ulp(dval(rv));
dval(rv) += adj;
}
# else /*Sudden_Underflow*/
/* 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(dval(rv));
dval(rv) += adj;
# endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
}
z = word0(rv) & Exp_mask;
#ifndef SET_INEXACT
# 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;
}
}
#endif
cont:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(delta);
}
#ifdef SET_INEXACT
if (inexact) {
if (!oldinexact) {
word0(rv0) = Exp_1 + (70 << Exp_shift);
word1(rv0) = 0;
dval(rv0) += 1.;
}
} else if (!oldinexact) {
clear_inexact();
}
#endif
#ifdef Avoid_Underflow
if (scale) {
word0(rv0) = Exp_1 - 2 * P * Exp_msk1;
word1(rv0) = 0;
dval(rv) *= dval(rv0);
# ifndef NO_ERRNO
/* try to avoid the bug of testing an 8087 register value */
if (word0(rv) == 0 && word1(rv) == 0) {
PR_SetError(PR_RANGE_ERROR, 0);
}
# endif
}
#endif /* Avoid_Underflow */
#ifdef SET_INEXACT
if (inexact && !(word0(rv) & Exp_mask)) {
/* set underflow bit */
dval(rv0) = 1e-300;
dval(rv0) *= dval(rv0);
}
#endif
retfree: Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(bd0);
Bfree(delta);
ret: if (se) { *se = (char*)s; }
return sign ? -dval(rv) : dval(rv);
}
static int quorem
#ifdef KR_headers
(b, S)
Bigint *b, *S;
#else
(Bigint * b, Bigint * S)
#endif
{
int n;
ULong *bx, *bxe, q, *sx, *sxe;
#ifdef ULLong
ULLong borrow, carry, y, ys;
#else
ULong borrow, carry, y, ys;
# ifdef Pack_32
ULong si, z, zs;
# endif
#endif
n = S->wds;
#ifdef DEBUG
/*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 ULLong
ys = *sx++ * (ULLong)q + carry;
carry = ys >> 32;
y = *bx - (ys & FFFFFFFF) - borrow;
borrow = y >> 32 & (ULong)1;
*bx++ = y & FFFFFFFF;
#else
# ifdef Pack_32
si = *sx++;
ys = (si & 0xffff) * q + carry;
zs = (si >> 16) * q + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
# else
ys = *sx++ * q + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
*bx++ = y & 0xffff;
# endif
#endif
} while (sx <= sxe);
if (!*bxe) {
bx = b->x;
while (--bxe > bx && !*bxe) {
--n;
}
b->wds = n;
}
}
if (cmp(b, S) >= 0) {
q++;
borrow = 0;
carry = 0;
bx = b->x;
sx = S->x;
do {
#ifdef ULLong
ys = *sx++ + carry;
carry = ys >> 32;
y = *bx - (ys & FFFFFFFF) - borrow;
borrow = y >> 32 & (ULong)1;
*bx++ = y & FFFFFFFF;
#else
# ifdef Pack_32
si = *sx++;
ys = (si & 0xffff) + carry;
zs = (si >> 16) + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
# else
ys = *sx++ + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
*bx++ = y & 0xffff;
# endif
#endif
} while (sx <= sxe);
bx = b->x;
bxe = bx + n;
if (!*bxe) {
while (--bxe > bx && !*bxe) {
--n;
}
b->wds = n;
}
}
return q;
}
#ifndef MULTIPLE_THREADS
static char* dtoa_result;
#endif
static char*
#ifdef KR_headers
rv_alloc(i)
int i;
#else
rv_alloc(int i)
#endif
{
int j, k, *r;
j = sizeof(ULong);
for (k = 0; sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i; j <<= 1) {
k++;
}
r = (int*)Balloc(k);
*r = k;
return
#ifndef MULTIPLE_THREADS
dtoa_result =
#endif
(char*)(r + 1);
}
static char*
#ifdef KR_headers
nrv_alloc(s, rve, n)
char *s, **rve;
int n;
#else
nrv_alloc(char* s, char** rve, int n)
#endif
{
char *rv, *t;
t = rv = rv_alloc(n);
while (*t = *s++) {
t++;
}
if (rve) {
*rve = t;
}
return rv;
}
/* 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.
*/
static void
#ifdef KR_headers
freedtoa(s) char* s;
#else
freedtoa(char* s)
#endif
{
Bigint* b = (Bigint*)((int*)s - 1);
b->maxwds = 1 << (b->k = *(int*)b);
Bfree(b);
#ifndef MULTIPLE_THREADS
if (s == dtoa_result) {
dtoa_result = 0;
}
#endif
}
/* 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. 112-126].
*
* 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.
*/
static char* dtoa
#ifdef KR_headers
(dd, mode, ndigits, decpt, sign, rve)
double dd;
int mode, ndigits, *decpt, *sign;
char** rve;
#else
(double dd, 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.
4,5 ==> similar to 2 and 3, respectively, but (in
round-nearest mode) with the tests of mode 0 to
possibly return a shorter string that rounds to d.
With IEEE arithmetic and compilation with
-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
as modes 2 and 3 when FLT_ROUNDS != 1.
6-9 ==> Debugging modes similar to mode - 4: don't try
fast floating-point estimate (if applicable).
Values of mode other than 0-9 are treated as mode 0.
Sufficient space is allocated to the return value
to hold the suppressed trailing zeros.
*/
int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0,
k_check, leftright, m2, m5, s2, s5, spec_case, try_quick;
Long L;
#ifndef Sudden_Underflow
int denorm;
ULong x;
#endif
Bigint *b, *b1, *delta, *mlo, *mhi, *S;
U d, d2, eps;
double ds;
char *s, *s0;
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
#ifndef MULTIPLE_THREADS
if (dtoa_result) {
freedtoa(dtoa_result);
dtoa_result = 0;
}
#endif
dval(d) = dd;
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;
# ifdef IEEE_Arith
if (!word1(d) && !(word0(d) & 0xfffff)) {
return nrv_alloc("Infinity", rve, 8);
}
# endif
return nrv_alloc("NaN", rve, 3);
}
#endif
#ifdef IBM
dval(d) += 0; /* normalize */
#endif
if (!dval(d)) {
*decpt = 1;
return nrv_alloc("0", rve, 1);
}
#ifdef SET_INEXACT
try_quick = oldinexact = get_inexact();
inexact = 1;
#endif
#ifdef Honor_FLT_ROUNDS
if ((rounding = Flt_Rounds) >= 2) {
if (*sign) {
rounding = rounding == 2 ? 0 : 2;
} else if (rounding != 2) {
rounding = 0;
}
}
#endif
b = d2b(dval(d), &be, &bbits);
#ifdef Sudden_Underflow
i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
#else
if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))) {
#endif
dval(d2) = dval(d);
word0(d2) &= Frac_mask1;
word0(d2) |= Exp_11;
#ifdef IBM
if (j = 11 - hi0bits(word0(d2) & Frac_mask)) {
dval(d2) /= 1 << j;
}
#endif
/* 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;
dval(d2) = x;
word0(d2) -= 31 * Exp_msk1; /* adjust exponent */
i -= (Bias + (P - 1) - 1) + 1;
denorm = 1;
}
#endif
ds = (dval(d2) - 1.5) * 0.289529654602168 + 0.1760912590558 +
i * 0.301029995663981;
k = (int)ds;
if (ds < 0. && ds != k) {
k--; /* want k = floor(ds) */
}
k_check = 1;
if (k >= 0 && k <= Ten_pmax) {
if (dval(d) < tens[k]) {
k--;
}
k_check = 0;
}
j = bbits - i - 1;
if (j >= 0) {
b2 = 0;
s2 = j;
} else {
b2 = -j;
s2 = 0;
}
if (k >= 0) {
b5 = 0;
s5 = k;
s2 += k;
} else {
b2 -= k;
b5 = -k;
s5 = 0;
}
if (mode < 0 || mode > 9) {
mode = 0;
}
#ifndef SET_INEXACT
# ifdef Check_FLT_ROUNDS
try_quick = Rounding == 1;
# else
try_quick = 1;
# endif
#endif /*SET_INEXACT*/
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;
/* no break */
case 4:
if (ndigits <= 0) {
ndigits = 1;
}
ilim = ilim1 = i = ndigits;
break;
case 3:
leftright = 0;
/* no break */
case 5:
i = ndigits + k + 1;
ilim = i;
ilim1 = i - 1;
if (i <= 0) {
i = 1;
}
}
s = s0 = rv_alloc(i);
#ifdef Honor_FLT_ROUNDS
if (mode > 1 && rounding != 1) {
leftright = 0;
}
#endif
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
/* Try to get by with floating-point arithmetic. */
i = 0;
dval(d2) = dval(d);
k0 = k;
ilim0 = ilim;
ieps = 2; /* conservative */
if (k > 0) {
ds = tens[k & 0xf];
j = k >> 4;
if (j & Bletch) {
/* prevent overflows */
j &= Bletch - 1;
dval(d) /= bigtens[n_bigtens - 1];
ieps++;
}
for (; j; j >>= 1, i++)
if (j & 1) {
ieps++;
ds *= bigtens[i];
}
dval(d) /= ds;
} else if (j1 = -k) {
dval(d) *= tens[j1 & 0xf];
for (j = j1 >> 4; j; j >>= 1, i++)
if (j & 1) {
ieps++;
dval(d) *= bigtens[i];
}
}
if (k_check && dval(d) < 1. && ilim > 0) {
if (ilim1 <= 0) {
goto fast_failed;
}
ilim = ilim1;
k--;
dval(d) *= 10.;
ieps++;
}
dval(eps) = ieps * dval(d) + 7.;
word0(eps) -= (P - 1) * Exp_msk1;
if (ilim == 0) {
S = mhi = 0;
dval(d) -= 5.;
if (dval(d) > dval(eps)) {
goto one_digit;
}
if (dval(d) < -dval(eps)) {
goto no_digits;
}
goto fast_failed;
}
#ifndef No_leftright
if (leftright) {
/* Use Steele & White method of only
* generating digits needed.
*/
dval(eps) = 0.5 / tens[ilim - 1] - dval(eps);
for (i = 0;;) {
L = dval(d);
dval(d) -= L;
*s++ = '0' + (int)L;
if (dval(d) < dval(eps)) {
goto ret1;
}
if (1. - dval(d) < dval(eps)) {
goto bump_up;
}
if (++i >= ilim) {
break;
}
dval(eps) *= 10.;
dval(d) *= 10.;
}
} else {
#endif
/* Generate ilim digits, then fix them up. */
dval(eps) *= tens[ilim - 1];
for (i = 1;; i++, dval(d) *= 10.) {
L = (Long)(dval(d));
if (!(dval(d) -= L)) {
ilim = i;
}
*s++ = '0' + (int)L;
if (i == ilim) {
if (dval(d) > 0.5 + dval(eps)) {
goto bump_up;
} else if (dval(d) < 0.5 - dval(eps)) {
while (*--s == '0');
s++;
goto ret1;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = s0;
dval(d) = dval(d2);
k = k0;
ilim = ilim0;
}
/* 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 || dval(d) <= 5 * ds) {
goto no_digits;
}
goto one_digit;
}
for (i = 1; i <= k + 1; i++, dval(d) *= 10.) {
L = (Long)(dval(d) / ds);
dval(d) -= L * ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (dval(d) < 0) {
L--;
dval(d) += ds;
}
#endif
*s++ = '0' + (int)L;
if (!dval(d)) {
#ifdef SET_INEXACT
inexact = 0;
#endif
break;
}
if (i == ilim) {
#ifdef Honor_FLT_ROUNDS
if (mode > 1) switch (rounding) {
case 0:
goto ret1;
case 2:
goto bump_up;
}
#endif
dval(d) += dval(d);
if (dval(d) > ds || dval(d) == ds && L & 1) {
bump_up:
while (*--s == '9')
if (s == s0) {
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
}
goto ret1;
}
m2 = b2;
m5 = b5;
mhi = mlo = 0;
if (leftright) {
i =
#ifndef Sudden_Underflow
denorm ? be + (Bias + (P - 1) - 1 + 1) :
#endif
#ifdef IBM
1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3);
#else
1 + P - bbits;
#endif
b2 += i;
s2 += i;
mhi = i2b(1);
}
if (m2 > 0 && s2 > 0) {
i = m2 < s2 ? m2 : s2;
b2 -= i;
m2 -= i;
s2 -= i;
}
if (b5 > 0) {
if (leftright) {
if (m5 > 0) {
mhi = pow5mult(mhi, m5);
b1 = mult(mhi, b);
Bfree(b);
b = b1;
}
if (j = b5 - m5) {
b = pow5mult(b, j);
}
} else {
b = pow5mult(b, b5);
}
}
S = i2b(1);
if (s5 > 0) {
S = pow5mult(S, s5);
}
/* Check for special case that d is a normalized power of 2. */
spec_case = 0;
if ((mode < 2 || leftright)
#ifdef Honor_FLT_ROUNDS
&& rounding == 1
#endif
) {
if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0(d) & (Exp_mask & ~Exp_msk1)
#endif
) {
/* The special case */
b2 += Log2P;
s2 += Log2P;
spec_case = 1;
}
}
/* Arrange for convenient computation of quotients:
* shift left if necessary so divisor has 4 leading 0 bits.
*
* Perhaps we should just compute leading 28 bits of S once
* and for all and pass them and a shift to quorem, so it
* can do shifts and ors to compute the numerator for q.
*/
#ifdef Pack_32
if (i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0x1f) {
i = 32 - i;
}
#else
if (i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0xf) {
i = 16 - i;
}
#endif
if (i > 4) {
i -= 4;
b2 += i;
m2 += i;
s2 += i;
} else if (i < 4) {
i += 28;
b2 += i;
m2 += i;
s2 += i;
}
if (b2 > 0) {
b = lshift(b, b2);
}
if (s2 > 0) {
S = lshift(S, s2);
}
if (k_check) {
if (cmp(b, S) < 0) {
k--;
b = multadd(b, 10, 0); /* we botched the k estimate */
if (leftright) {
mhi = multadd(mhi, 10, 0);
}
ilim = ilim1;
}
}
if (ilim <= 0 && (mode == 3 || mode == 5)) {
if (ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0) {
/* no digits, fcvt style */
no_digits:
k = -1 - ndigits;
goto ret;
}
one_digit:
*s++ = '1';
k++;
goto ret;
}
if (leftright) {
if (m2 > 0) {
mhi = lshift(mhi, m2);
}
/* Compute mlo -- check for special case
* that d is a normalized power of 2.
*/
mlo = mhi;
if (spec_case) {
mhi = Balloc(mhi->k);
Bcopy(mhi, mlo);
mhi = lshift(mhi, Log2P);
}
for (i = 1;; i++) {
dig = quorem(b, S) + '0';
/* Do we yet have the shortest decimal string
* that will round to d?
*/
j = cmp(b, mlo);
delta = diff(S, mhi);
j1 = delta->sign ? 1 : cmp(b, delta);
Bfree(delta);
#ifndef ROUND_BIASED
if (j1 == 0 && mode != 1 && !(word1(d) & 1)
# ifdef Honor_FLT_ROUNDS
&& rounding >= 1
# endif
) {
if (dig == '9') {
goto round_9_up;
}
if (j > 0) {
dig++;
}
# ifdef SET_INEXACT
else if (!b->x[0] && b->wds <= 1) {
inexact = 0;
}
# endif
*s++ = dig;
goto ret;
}
#endif
if (j < 0 || j == 0 && mode != 1
#ifndef ROUND_BIASED
&& !(word1(d) & 1)
#endif
) {
if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
goto accept_dig;
}
#ifdef Honor_FLT_ROUNDS
if (mode > 1) switch (rounding) {
case 0:
goto accept_dig;
case 2:
goto keep_dig;
}
#endif /*Honor_FLT_ROUNDS*/
if (j1 > 0) {
b = lshift(b, 1);
j1 = cmp(b, S);
if ((j1 > 0 || j1 == 0 && dig & 1) && dig++ == '9') {
goto round_9_up;
}
}
accept_dig:
*s++ = dig;
goto ret;
}
if (j1 > 0) {
#ifdef Honor_FLT_ROUNDS
if (!rounding) {
goto accept_dig;
}
#endif
if (dig == '9') { /* possible if i == 1 */
round_9_up:
*s++ = '9';
goto roundoff;
}
*s++ = dig + 1;
goto ret;
}
#ifdef Honor_FLT_ROUNDS
keep_dig:
#endif
*s++ = dig;
if (i == ilim) {
break;
}
b = multadd(b, 10, 0);
if (mlo == mhi) {
mlo = mhi = multadd(mhi, 10, 0);
} else {
mlo = multadd(mlo, 10, 0);
mhi = multadd(mhi, 10, 0);
}
}
} else
for (i = 1;; i++) {
*s++ = dig = quorem(b, S) + '0';
if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
goto ret;
}
if (i >= ilim) {
break;
}
b = multadd(b, 10, 0);
}
/* Round off last digit */
#ifdef Honor_FLT_ROUNDS
switch (rounding) {
case 0:
goto trimzeros;
case 2:
goto roundoff;
}
#endif
b = lshift(b, 1);
j = cmp(b, S);
if (j > 0 || j == 0 && dig & 1) {
roundoff:
while (*--s == '9')
if (s == s0) {
k++;
*s++ = '1';
goto ret;
}
++*s++;
} else {
#ifdef Honor_FLT_ROUNDS
trimzeros:
#endif
while (*--s == '0');
s++;
}
ret: Bfree(S);
if (mhi) {
if (mlo && mlo != mhi) {
Bfree(mlo);
}
Bfree(mhi);
}
ret1:
#ifdef SET_INEXACT
if (inexact) {
if (!oldinexact) {
word0(d) = Exp_1 + (70 << Exp_shift);
word1(d) = 0;
dval(d) += 1.;
}
}
else if (!oldinexact) {
clear_inexact();
}
#endif
Bfree(b);
*s = 0;
*decpt = k + 1;
if (rve) {
*rve = s;
}
return s0;
}
#ifdef __cplusplus
}
#endif
PR_IMPLEMENT(PRStatus)
PR_dtoa(PRFloat64 d, PRIntn mode, PRIntn ndigits, PRIntn* decpt, PRIntn* sign,
char** rve, char* buf, PRSize bufsize) {
char* result;
PRSize resultlen;
PRStatus rv = PR_FAILURE;
if (!_pr_initialized) {
_PR_ImplicitInitialization();
}
if (mode < 0 || mode > 3) {
PR_SetError(PR_INVALID_ARGUMENT_ERROR, 0);
return rv;
}
result = dtoa(d, mode, ndigits, decpt, sign, rve);
if (!result) {
PR_SetError(PR_OUT_OF_MEMORY_ERROR, 0);
return rv;
}
resultlen = strlen(result) + 1;
if (bufsize < resultlen) {
PR_SetError(PR_BUFFER_OVERFLOW_ERROR, 0);
} else {
memcpy(buf, result, resultlen);
if (rve) {
*rve = buf + (*rve - result);
}
rv = PR_SUCCESS;
}
freedtoa(result);
return rv;
}
/*
** conversion routines for floating point
** prcsn - number of digits of precision to generate floating
** point value.
** This should be reparameterized so that you can send in a
** prcn for the positive and negative ranges. For now,
** conform to the ECMA JavaScript spec which says numbers
** less than 1e-6 are in scientific notation.
** Also, the ECMA spec says that there should always be a
** '+' or '-' after the 'e' in scientific notation
*/
PR_IMPLEMENT(void)
PR_cnvtf(char* buf, int bufsz, int prcsn, double dfval) {
PRIntn decpt, sign, numdigits;
char *num, *nump;
char* bufp = buf;
char* endnum;
U fval;
dval(fval) = dfval;
/* If anything fails, we store an empty string in 'buf' */
num = (char*)PR_MALLOC(bufsz);
if (num == NULL) {
buf[0] = '\0';
return;
}
/* XXX Why use mode 1? */
if (PR_dtoa(dval(fval), 1, prcsn, &decpt, &sign, &endnum, num, bufsz) ==
PR_FAILURE) {
buf[0] = '\0';
goto done;
}
numdigits = endnum - num;
nump = num;
if (sign && !(word0(fval) == Sign_bit && word1(fval) == 0) &&
!((word0(fval) & Exp_mask) == Exp_mask &&
(word1(fval) || (word0(fval) & 0xfffff)))) {
*bufp++ = '-';
}
if (decpt == 9999) {
while ((*bufp++ = *nump++) != 0) {
} /* nothing to execute */
goto done;
}
if (decpt > (prcsn + 1) || decpt < -(prcsn - 1) || decpt < -5) {
*bufp++ = *nump++;
if (numdigits != 1) {
*bufp++ = '.';
}
while (*nump != '\0') {
*bufp++ = *nump++;
}
*bufp++ = 'e';
PR_snprintf(bufp, bufsz - (bufp - buf), "%+d", decpt - 1);
} else if (decpt >= 0) {
if (decpt == 0) {
*bufp++ = '0';
} else {
while (decpt--) {
if (*nump != '\0') {
*bufp++ = *nump++;
} else {
*bufp++ = '0';
}
}
}
if (*nump != '\0') {
*bufp++ = '.';
while (*nump != '\0') {
*bufp++ = *nump++;
}
}
*bufp++ = '\0';
} else if (decpt < 0) {
*bufp++ = '0';
*bufp++ = '.';
while (decpt++) {
*bufp++ = '0';
}
while (*nump != '\0') {
*bufp++ = *nump++;
}
*bufp++ = '\0';
}
done:
PR_DELETE(num);
}