dtoa.c

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/****************************************************************************
*
*                            Open Watcom Project
*
*    Portions Copyright (c) 1983-2002 Sybase, Inc. All Rights Reserved.
*
*  ========================================================================
*
*    This file contains Original Code and/or Modifications of Original
*    Code as defined in and that are subject to the Sybase Open Watcom
*    Public License version 1.0 (the 'License'). You may not use this file
*    except in compliance with the License. BY USING THIS FILE YOU AGREE TO
*    ALL TERMS AND CONDITIONS OF THE LICENSE. A copy of the License is
*    provided with the Original Code and Modifications, and is also
*    available at www.sybase.com/developer/opensource.
*
*    The Original Code and all software distributed under the License are
*    distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER
*    EXPRESS OR IMPLIED, AND SYBASE AND ALL CONTRIBUTORS HEREBY DISCLAIM
*    ALL SUCH WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF
*    MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR
*    NON-INFRINGEMENT. Please see the License for the specific language
*    governing rights and limitations under the License.
*
*  ========================================================================
*
* Description:  WHEN YOU FIGURE OUT WHAT THIS FILE DOES, PLEASE
*               DESCRIBE IT HERE!
*
****************************************************************************/


/****************************************************************
 *
 * 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
 */

/* 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 Sudden_Underflow for IEEE-format machines without gradual
 *      underflow (i.e., that flush to zero on underflow).
 * #define IBM for IBM mainframe-style floating-point arithmetic.
 * #define VAX for VAX-style floating-point arithmetic.
 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
 * #define No_leftright to omit left-right logic in fast floating-point
 *      computation of dtoa.
 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
 *      that use extended-precision instructions to compute rounded
 *      products and quotients) with IBM.
 * #define ROUND_BIASED for IEEE-format with biased rounding.
 * #define Inaccurate_Divide for IEEE-format with correctly rounded
 *      products but inaccurate quotients, e.g., for Intel i860.
 * #define Just_16 to store 16 bits per 32-bit long when doing high-precision
 *      integer arithmetic.  Whether this speeds things up or slows things
 *      down depends on the machine and the number being converted.
 * #define KR_headers for old-style C function headers.
 */

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

#ifdef __cplusplus
extern "C" {
#include "variety.h"
#include "malloc.h"
#include "string.h"
#define CONST const
#else
#ifdef __STDC__
#include "stdlib.h"
#include "string.h"
#define CONST const
#else
#define CONST /* blank */
#include "malloc.h"
#include "string.h"
#endif
#endif

#include "errno.h"
#include "float.h"
#ifndef __MATH_H__
#include "math.h"
#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

#ifdef __cplusplus
extern "C" double strtod(const char *s00, char **se);
extern "C" char *dtoa(double d, int mode, int ndigits,
                        int *decpt, int *sign, char **rve);
#endif

 struct
Bigint {
        struct Bigint *next;
        int k, maxwds, sign, wds;
        unsigned long 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;

        if (rv = freelist[k]) {
                freelist[k] = rv->next;
                }
        else {
                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
#ifdef KR_headers
        (v) Bigint *v;
#else
        (Bigint *v)
#endif
{
        if (v) {
                v->next = freelist[v->k];
                freelist[v->k] = v;
                }
        }

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

 static Bigint *
s2b
#ifdef KR_headers
        (s, nd0, nd, y9) CONST char *s; int nd0, nd; unsigned long y9;
#else
        (CONST char *s, int nd0, int nd, unsigned long 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