prdtoa.c

Netscape NSPR库源码

/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* 
 * The contents of this file are subject to the Mozilla 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/MPL/
 * 
 * Software distributed under the License is distributed on an "AS
 * IS" basis, WITHOUT WARRANTY OF ANY KIND, either express or
 * implied. See the License for the specific language governing
 * rights and limitations under the License.
 * 
 * The Original Code is the Netscape Portable Runtime (NSPR).
 * 
 * The Initial Developer of the Original Code is Netscape
 * Communications Corporation.  Portions created by Netscape are 
 * Copyright (C) 1998-2000 Netscape Communications Corporation.  All
 * Rights Reserved.
 * 
 * Contributor(s):
 * 
 * Alternatively, the contents of this file may be used under the
 * terms of the GNU General Public License Version 2 or later (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 MPL,
 * 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 MPL or the
 * GPL.
 */

#include "primpl.h"

/****************************************************************
 *
 * The author of this software is David M. Gay.
 *
 * Copyright (c) 1991 by AT&T.
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose without fee is hereby granted, provided that this entire notice
 * is included in all copies of any software which is or includes a copy
 * or modification of this software and in all copies of the supporting
 * documentation for such software.
 *
 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
 *
 ***************************************************************/

/* Please send bug reports to
	David M. Gay
	AT&T Bell Laboratories, Room 2C-463
	600 Mountain Avenue
	Murray Hill, NJ 07974-2070
	U.S.A.
	[e-mail] or research!dmg
 */

/* PR_strtod for IEEE-, VAX-, and IBM-arithmetic machines.
 *
 * This PR_strtod returns a nearest machine number to the input decimal
 * string (or sets the error code to PR_RANGE_ERROR).  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 Long int on machines with 32-bit ints and 64-bit longs.
 * #define Sudden_Underflow for IEEE-format machines without gradual
 *	underflow (i.e., that flush to zero on underflow).
 * #define IBM for IBM mainframe-style floating-point arithmetic.
 * #define VAX for VAX-style floating-point arithmetic.
 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
 * #define No_leftright to omit left-right logic in fast floating-point
 *	computation of PR_dtoa.
 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
 *	that use extended-precision instructions to compute rounded
 *	products and quotients) with IBM.
 * #define ROUND_BIASED for IEEE-format with biased rounding.
 * #define Inaccurate_Divide for IEEE-format with correctly rounded
 *	products but inaccurate quotients, e.g., for Intel i860.
 * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
 *	integer arithmetic.  Whether this speeds things up or slows things
 *	down depends on the machine and the number being converted.
 * #define KR_headers for old-style C function headers.
 * #define Bad_float_h if your system lacks a float.h or if it does not
 *	define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
 *	FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
 *	if memory is available and otherwise does something you deem
 *	appropriate.  If MALLOC is undefined, malloc will be invoked
 *	directly -- and assumed always to succeed.
 */
#if  defined(IS_LITTLE_ENDIAN)
#define IEEE_8087
#else
#define IEEE_MC68k
#endif

#ifndef Long
#if PR_BYTES_PER_LONG == 4
#define Long long
#elif PR_BYTES_PER_INT == 4
#define Long int
#else
#error "No suitable type for Long"
#endif
#endif

#ifdef DEBUG_DTOA
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#else
#define Bug(x)
#endif

#include "stdlib.h"
#include "string.h"

#ifdef MALLOC
extern void *MALLOC(size_t);
#else
#define MALLOC PR_MALLOC
#endif

#ifdef Bad_float_h
#undef __STDC__
#ifdef IEEE_MC68k
#define IEEE_ARITHMETIC
#endif
#ifdef IEEE_8087
#define IEEE_ARITHMETIC
#endif

#ifdef IEEE_ARITHMETIC
#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
#endif

#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define FLT_ROUNDS 0
#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 FLT_ROUNDS 1
#define DBL_MAX 1.7014118346046923e+38
#endif

#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif
#else
#include "float.h"
#endif
#ifndef __MATH_H__
#include "math.h"
#endif

#ifndef CONST
#define CONST const
#endif

#ifdef Unsigned_Shifts
#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
#else
#define Sign_Extend(a,b) /*no-op*/
#endif

#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM)	!= 1
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
#endif

#ifdef IEEE_8087
#define word0(x) ((unsigned Long *)&x)[1]
#define word1(x) ((unsigned Long *)&x)[0]
#else
#define word0(x) ((unsigned Long *)&x)[0]
#define word1(x) ((unsigned Long *)&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) + 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) */

#if defined(IEEE_8087) + defined(IEEE_MC68k)
#define Exp_shift  20
#define Exp_shift1 20
#define Exp_msk1    0x100000
#define Exp_msk11   0x100000
#define Exp_mask  0x7ff00000
#define P 53
#define Bias 1023
#define IEEE_Arith
#define Emin (-1022)
#define Exp_1  0x3ff00000
#define Exp_11 0x3ff00000
#define Ebits 11
#define Frac_mask  0xfffff
#define Frac_mask1 0xfffff
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask  0xfffff
#define Bndry_mask1 0xfffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
#else
#undef  Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#define Exp_shift  24
#define Exp_shift1 24
#define Exp_msk1   0x1000000
#define Exp_msk11  0x1000000
#define Exp_mask  0x7f000000
#define P 14
#define Bias 65
#define Exp_1  0x41000000
#define Exp_11 0x41000000
#define Ebits 8	/* exponent has 7 bits, but 8 is the right value in b2d */
#define Frac_mask  0xffffff
#define Frac_mask1 0xffffff
#define Bletch 4
#define Ten_pmax 22
#define Bndry_mask  0xefffff
#define Bndry_mask1 0xffffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 4
#define Tiny0 0x100000
#define Tiny1 0
#define Quick_max 14
#define Int_max 15
#else /* VAX */
#define Exp_shift  23
#define Exp_shift1 7
#define Exp_msk1    0x80
#define Exp_msk11   0x800000
#define Exp_mask  0x7f80
#define P 56
#define Bias 129
#define Exp_1  0x40800000
#define Exp_11 0x4080
#define Ebits 8
#define Frac_mask  0x7fffff
#define Frac_mask1 0xffff007f
#define Ten_pmax 24
#define Bletch 2
#define Bndry_mask  0xffff007f
#define Bndry_mask1 0xffff007f
#define LSB 0x10000
#define Sign_bit 0x8000
#define Log2P 1
#define Tiny0 0x80
#define Tiny1 0
#define Quick_max 15
#define Int_max 15
#endif
#endif

#ifndef IEEE_Arith
#define ROUND_BIASED
#endif

#ifdef RND_PRODQUOT
#define rounded_product(a,b) a = rnd_prod(a, b)
#define rounded_quotient(a,b) a = rnd_quot(a, b)
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 Just_16
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
 * This makes some inner loops simpler and sometimes saves work
 * during multiplications, but it often seems to make things slightly
 * slower.  Hence the default is now to store 32 bits per Long.
 */
#ifndef Pack_32
#define Pack_32
#endif
#endif

#define Kmax 15

/*
 * Note: if you ever change struct Bigint, make sure that the
 * definition of the Bcopy(x,y) macro is still correct.
 */
struct Bigint {
	struct Bigint *next;
	PRInt32 k, maxwds, sign, wds;
	unsigned Long x[1];
};

typedef struct Bigint Bigint;

static Bigint *freelist[Kmax+1];

static PRLock *freelist_lock;

static Bigint *Balloc(PRInt32 k)
{
	PRInt32 x;
	Bigint *rv;

	PR_Lock(freelist_lock);
	if ((rv = freelist[k]) != NULL) {
		freelist[k] = rv->next;
	}
	PR_Unlock(freelist_lock);
	if (rv == NULL) {
		x = 1 << k;
		rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
		rv->k = k;
		rv->maxwds = x;
	}
	rv->sign = rv->wds = 0;
	return rv;
}

static void Bfree (Bigint *v)
{
	if (v) {
		PR_Lock(freelist_lock);
		v->next = freelist[v->k];
		freelist[v->k] = v;
		PR_Unlock(freelist_lock);
	}
}

/*
 * The definition of the Bcopy macro is highly dependent on the
 * ordering of members in struct Bigint.
 */
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
						  y->wds*sizeof(Long) + 2*sizeof(PRInt32))

static Bigint *multadd(Bigint *b, PRInt32 m, PRInt32 a)	/* multiply by m and add a */
{
	PRInt32 i, wds;
	unsigned Long *x, y;
#ifdef Pack_32
	unsigned Long xi, z;
#endif
	Bigint *b1;

	wds = b->wds;
	x = b->x;
	i = 0;
	do {
#ifdef Pack_32
		xi = *x;
		y = (xi & 0xffff) * m + a;
		z = (xi >> 16) * m + (y >> 16);
		a = (PRInt32)(z >> 16);
		*x++ = (z << 16) + (y & 0xffff);
#else
		y = *x * m + a;
		a = (PRInt32)(y >> 16);
		*x++ = y & 0xffff;
#endif
	}
	while(++i < wds);
	if (a) {
		if (wds >= b->maxwds) {
			b1 = Balloc(b->k+1);
			Bcopy(b1, b);
			Bfree(b);
			b = b1;
		}
		b->x[wds++] = a;
		b->wds = wds;
	}
	return b;
}

static Bigint *s2b(CONST char *s, PRInt32 nd0, PRInt32 nd, unsigned Long y9)
{
	Bigint *b;
	PRInt32 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 PRInt32 hi0bits(register unsigned Long x)
{
	register PRInt32 k = 0;

	if (!(x & 0xffff0000)) {
		k = 16;
		x <<= 16;
	}
	if (!(x & 0xff000000)) {
		k += 8;
		x <<= 8;
	}
	if (!(x & 0xf0000000)) {
		k += 4;
		x <<= 4;
	}
	if (!(x & 0xc0000000)) {
		k += 2;
		x <<= 2;
	}
	if (!(x & 0x80000000)) {
		k++;
		if (!(x & 0x40000000))
			return 32;
	}
	return k;
}

static PRInt32 lo0bits(unsigned Long *y)
{
	register PRInt32 k;
	register unsigned Long x = *y;

	if (x & 7) {
		if (x & 1)
			return 0;
		if (x & 2) {
			*y = x >> 1;
			return 1;
		}
		*y = x >> 2;
		return 2;
	}
	k = 0;
	if (!(x & 0xffff)) {
		k = 16;
		x >>= 16;
	}
	if (!(x & 0xff)) {
		k += 8;
		x >>= 8;
	}
	if (!(x & 0xf)) {
		k += 4;
		x >>= 4;
	}
	if (!(x & 0x3)) {
		k += 2;
		x >>= 2;
	}
	if (!(x & 1)) {
		k++;
		x >>= 1;
		if (!x & 1)
			return 32;
	}
	*y = x;
	return k;
}

static Bigint *i2b(PRInt32 i)
{
	Bigint *b;

	b = Balloc(1);
	b->x[0] = i;
	b->wds = 1;
	return b;
}

static Bigint *mult(CONST Bigint *a, CONST Bigint *b)
{
	CONST Bigint *t;
	Bigint *c;
	PRInt32 k, wa, wb, wc;
	unsigned Long carry, y, z;
	unsigned Long *xc, *xc0, *xce;
	CONST unsigned Long *x, *xa, *xae, *xb, *xbe;
#ifdef Pack_32
	unsigned Long 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 Pack_32
	for(; xb < xbe; xb++, xc0++) {
		if ((y = *xb & 0xffff) != 0) {
			x = xa;
			xc = xc0;
			carry = 0;
			do {
				z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
				carry = z >> 16;
				z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
				carry = z2 >> 16;
				Storeinc(xc, z2, z);
			}
			while(x < xae);
			*xc = carry;
		}
		if ((y = *xb >> 16) != 0) {
			x = xa;
			xc = xc0;
			carry = 0;
			z2 = *xc;
			do {
				z = (*x & 0xffff) * y + (*xc >> 16) + carry;
				carry = z >> 16;
				Storeinc(xc, z, z2);
				z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
				carry = z2 >> 16;
			}
			while(x < xae);
			*xc = z2;
		}
	}
#else
	for(; xb < xbe; xc0++) {
		if (y = *xb++) {
			x = xa;
			xc = xc0;
			carry = 0;
			do {
				z = *x++ * y + *xc + carry;
				carry = z >> 16;
				*xc++ = z & 0xffff;
			}
			while(x < xae);
			*xc = carry;
		}
	}
#endif
	for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
	c->wds = wc;
	return c;
}

/*
 * '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