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/****************************************************************
The author of this software (_dtoa, strtod) is David M. Gay.
Please send bug reports to
David M. Gay
Bell Laboratories, Room 2C-463
600 Mountain Avenue
Murray Hill, NJ 07974-2070
U.S.A.
dmg@research.bell-labs.com
*/
#include <stdlib.h>
#include <string.h>
#define _RESEARCH_SOURCE
#include <errno.h>
#include <float.h>
#include <math.h>
#define CONST const
/*
* #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.
*/
#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
typedef union {
double d;
unsigned long ul[2];
} Dul;
#ifdef IEEE_8087
#define word0(x) ((x).ul[1])
#define word1(x) ((x).ul[0])
#else
#define word0(x) ((x).ul[0])
#define word1(x) ((x).ul[1])
#endif
#ifdef Unsigned_Shifts
#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
#else
#define Sign_Extend(a,b) /*no-op*/
#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
#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
struct
Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
unsigned long x[1];
};
typedef struct Bigint Bigint;
/* This routines shouldn't be visible externally */
extern Bigint *_Balloc(int);
extern void _Bfree(Bigint *);
extern Bigint *_multadd(Bigint *, int, int);
extern int _hi0bits(unsigned long);
extern Bigint *_mult(Bigint *, Bigint *);
extern Bigint *_pow5mult(Bigint *, int);
extern Bigint *_lshift(Bigint *, int);
extern int _cmp(Bigint *, Bigint *);
extern Bigint *_diff(Bigint *, Bigint *);
extern Bigint *_d2b(double, int *, int *);
extern Bigint *_i2b(int);
extern double _tens[], _bigtens[], _tinytens[];
#ifdef IEEE_Arith
#define n_bigtens 5
#else
#ifdef IBM
#define n_bigtens 3
#else
#define n_bigtens 2
#endif
#endif
#define Balloc(x) _Balloc(x)
#define Bfree(x) _Bfree(x)
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
y->wds*sizeof(long) + 2*sizeof(int))
#define multadd(x,y,z) _multadd(x,y,z)
#define hi0bits(x) _hi0bits(x)
#define i2b(x) _i2b(x)
#define mult(x,y) _mult(x,y)
#define pow5mult(x,y) _pow5mult(x,y)
#define lshift(x,y) _lshift(x,y)
#define cmp(x,y) _cmp(x,y)
#define diff(x,y) _diff(x,y)
#define d2b(x,y,z) _d2b(x,y,z)
#define tens _tens
#define bigtens _bigtens
#define tinytens _tinytens
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