314 lines
8.7 KiB
C
314 lines
8.7 KiB
C
|
/****************************************************************
|
||
|
|
*
|
||
|
|
* 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.
|
||
|
|
dmg@research.att.com or research!dmg
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include <ieeefp.h>
|
||
|
|
#include <math.h>
|
||
|
|
#include <float.h>
|
||
|
|
#include <errno.h>
|
||
|
|
#include <sys/config.h>
|
||
|
|
|
||
|
|
#ifdef __IEEE_LITTLE_ENDIAN
|
||
|
|
#define IEEE_8087
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifdef __IEEE_BIG_ENDIAN
|
||
|
|
#define IEEE_MC68k
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifdef __Z8000__
|
||
|
|
#define Just_16
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifdef DEBUG
|
||
|
|
#include "stdio.h"
|
||
|
|
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifdef Unsigned_Shifts
|
||
|
|
#define Sign_Extend(a,b) if (b < 0) a |= (__uint32_t)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
|
||
|
|
|
||
|
|
/* If we are going to examine or modify specific bits in a double using
|
||
|
|
the word0 and/or word1 macros, then we must wrap the double inside
|
||
|
|
a union. This is necessary to avoid undefined behavior according to
|
||
|
|
the ANSI C spec. */
|
||
|
|
union double_union
|
||
|
|
{
|
||
|
|
double d;
|
||
|
|
__uint32_t i[2];
|
||
|
|
};
|
||
|
|
|
||
|
|
#ifdef IEEE_8087
|
||
|
|
#define word0(x) (x.i[1])
|
||
|
|
#define word1(x) (x.i[0])
|
||
|
|
#else
|
||
|
|
#define word0(x) (x.i[0])
|
||
|
|
#define word1(x) (x.i[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)
|
||
|
|
#if defined (_DOUBLE_IS_32BITS)
|
||
|
|
#define Exp_shift 23
|
||
|
|
#define Exp_shift1 23
|
||
|
|
#define Exp_msk1 ((__uint32_t)0x00800000L)
|
||
|
|
#define Exp_msk11 ((__uint32_t)0x00800000L)
|
||
|
|
#define Exp_mask ((__uint32_t)0x7f800000L)
|
||
|
|
#define P 24
|
||
|
|
#define Bias 127
|
||
|
|
#if 0
|
||
|
|
#define IEEE_Arith /* it is, but the code doesn't handle IEEE singles yet */
|
||
|
|
#endif
|
||
|
|
#define Emin (-126)
|
||
|
|
#define Exp_1 ((__uint32_t)0x3f800000L)
|
||
|
|
#define Exp_11 ((__uint32_t)0x3f800000L)
|
||
|
|
#define Ebits 8
|
||
|
|
#define Frac_mask ((__uint32_t)0x007fffffL)
|
||
|
|
#define Frac_mask1 ((__uint32_t)0x007fffffL)
|
||
|
|
#define Ten_pmax 10
|
||
|
|
#define Sign_bit ((__uint32_t)0x80000000L)
|
||
|
|
#define Ten_pmax 10
|
||
|
|
#define Bletch 2
|
||
|
|
#define Bndry_mask ((__uint32_t)0x007fffffL)
|
||
|
|
#define Bndry_mask1 ((__uint32_t)0x007fffffL)
|
||
|
|
#define LSB 1
|
||
|
|
#define Sign_bit ((__uint32_t)0x80000000L)
|
||
|
|
#define Log2P 1
|
||
|
|
#define Tiny0 0
|
||
|
|
#define Tiny1 1
|
||
|
|
#define Quick_max 5
|
||
|
|
#define Int_max 6
|
||
|
|
#define Infinite(x) (word0(x) == ((__uint32_t)0x7f800000L))
|
||
|
|
#undef word0
|
||
|
|
#undef word1
|
||
|
|
|
||
|
|
#define word0(x) (x.i[0])
|
||
|
|
#define word1(x) 0
|
||
|
|
#else
|
||
|
|
|
||
|
|
#define Exp_shift 20
|
||
|
|
#define Exp_shift1 20
|
||
|
|
#define Exp_msk1 ((__uint32_t)0x100000L)
|
||
|
|
#define Exp_msk11 ((__uint32_t)0x100000L)
|
||
|
|
#define Exp_mask ((__uint32_t)0x7ff00000L)
|
||
|
|
#define P 53
|
||
|
|
#define Bias 1023
|
||
|
|
#define IEEE_Arith
|
||
|
|
#define Emin (-1022)
|
||
|
|
#define Exp_1 ((__uint32_t)0x3ff00000L)
|
||
|
|
#define Exp_11 ((__uint32_t)0x3ff00000L)
|
||
|
|
#define Ebits 11
|
||
|
|
#define Frac_mask ((__uint32_t)0xfffffL)
|
||
|
|
#define Frac_mask1 ((__uint32_t)0xfffffL)
|
||
|
|
#define Ten_pmax 22
|
||
|
|
#define Bletch 0x10
|
||
|
|
#define Bndry_mask ((__uint32_t)0xfffffL)
|
||
|
|
#define Bndry_mask1 ((__uint32_t)0xfffffL)
|
||
|
|
#define LSB 1
|
||
|
|
#define Sign_bit ((__uint32_t)0x80000000L)
|
||
|
|
#define Log2P 1
|
||
|
|
#define Tiny0 0
|
||
|
|
#define Tiny1 1
|
||
|
|
#define Quick_max 14
|
||
|
|
#define Int_max 14
|
||
|
|
#define Infinite(x) (word0(x) == ((__uint32_t)0x7ff00000L)) /* sufficient test for here */
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#else
|
||
|
|
#undef Sudden_Underflow
|
||
|
|
#define Sudden_Underflow
|
||
|
|
#ifdef IBM
|
||
|
|
#define Exp_shift 24
|
||
|
|
#define Exp_shift1 24
|
||
|
|
#define Exp_msk1 ((__uint32_t)0x1000000L)
|
||
|
|
#define Exp_msk11 ((__uint32_t)0x1000000L)
|
||
|
|
#define Exp_mask ((__uint32_t)0x7f000000L)
|
||
|
|
#define P 14
|
||
|
|
#define Bias 65
|
||
|
|
#define Exp_1 ((__uint32_t)0x41000000L)
|
||
|
|
#define Exp_11 ((__uint32_t)0x41000000L)
|
||
|
|
#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
|
||
|
|
#define Frac_mask ((__uint32_t)0xffffffL)
|
||
|
|
#define Frac_mask1 ((__uint32_t)0xffffffL)
|
||
|
|
#define Bletch 4
|
||
|
|
#define Ten_pmax 22
|
||
|
|
#define Bndry_mask ((__uint32_t)0xefffffL)
|
||
|
|
#define Bndry_mask1 ((__uint32_t)0xffffffL)
|
||
|
|
#define LSB 1
|
||
|
|
#define Sign_bit ((__uint32_t)0x80000000L)
|
||
|
|
#define Log2P 4
|
||
|
|
#define Tiny0 ((__uint32_t)0x100000L)
|
||
|
|
#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 ((__uint32_t)0x800000L)
|
||
|
|
#define Exp_mask ((__uint32_t)0x7f80L)
|
||
|
|
#define P 56
|
||
|
|
#define Bias 129
|
||
|
|
#define Exp_1 ((__uint32_t)0x40800000L)
|
||
|
|
#define Exp_11 ((__uint32_t)0x4080L)
|
||
|
|
#define Ebits 8
|
||
|
|
#define Frac_mask ((__uint32_t)0x7fffffL)
|
||
|
|
#define Frac_mask1 ((__uint32_t)0xffff007fL)
|
||
|
|
#define Ten_pmax 24
|
||
|
|
#define Bletch 2
|
||
|
|
#define Bndry_mask ((__uint32_t)0xffff007fL)
|
||
|
|
#define Bndry_mask1 ((__uint32_t)0xffff007fL)
|
||
|
|
#define LSB ((__uint32_t)0x10000L)
|
||
|
|
#define Sign_bit ((__uint32_t)0x8000L)
|
||
|
|
#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)
|
||
|
|
#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 ((__uint32_t)0xffffffffL)
|
||
|
|
|
||
|
|
#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
|
||
|
|
|
||
|
|
|
||
|
|
#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
|
||
|
|
|
||
|
|
|
||
|
|
typedef struct _Bigint _Bigint;
|
||
|
|
|
||
|
|
#define Balloc _Balloc
|
||
|
|
#define Bfree _Bfree
|
||
|
|
#define multadd _multadd
|
||
|
|
#define s2b _s2b
|
||
|
|
#define lo0bits _lo0bits
|
||
|
|
#define hi0bits _hi0bits
|
||
|
|
#define i2b _i2b
|
||
|
|
#define mult _multiply
|
||
|
|
#define pow5mult _pow5mult
|
||
|
|
#define lshift _lshift
|
||
|
|
#define cmp __mcmp
|
||
|
|
#define diff __mdiff
|
||
|
|
#define ulp _ulp
|
||
|
|
#define b2d _b2d
|
||
|
|
#define d2b _d2b
|
||
|
|
#define ratio _ratio
|
||
|
|
|
||
|
|
#define tens __mprec_tens
|
||
|
|
#define bigtens __mprec_bigtens
|
||
|
|
#define tinytens __mprec_tinytens
|
||
|
|
|
||
|
|
struct _reent ;
|
||
|
|
double _EXFUN(ulp,(double x));
|
||
|
|
double _EXFUN(b2d,(_Bigint *a , int *e));
|
||
|
|
_Bigint * _EXFUN(Balloc,(struct _reent *p, int k));
|
||
|
|
void _EXFUN(Bfree,(struct _reent *p, _Bigint *v));
|
||
|
|
_Bigint * _EXFUN(multadd,(struct _reent *p, _Bigint *, int, int));
|
||
|
|
_Bigint * _EXFUN(s2b,(struct _reent *, const char*, int, int, __ULong));
|
||
|
|
_Bigint * _EXFUN(i2b,(struct _reent *,int));
|
||
|
|
_Bigint * _EXFUN(mult, (struct _reent *, _Bigint *, _Bigint *));
|
||
|
|
_Bigint * _EXFUN(pow5mult, (struct _reent *, _Bigint *, int k));
|
||
|
|
int _EXFUN(hi0bits,(__ULong));
|
||
|
|
int _EXFUN(lo0bits,(__ULong *));
|
||
|
|
_Bigint * _EXFUN(d2b,(struct _reent *p, double d, int *e, int *bits));
|
||
|
|
_Bigint * _EXFUN(lshift,(struct _reent *p, _Bigint *b, int k));
|
||
|
|
_Bigint * _EXFUN(diff,(struct _reent *p, _Bigint *a, _Bigint *b));
|
||
|
|
int _EXFUN(cmp,(_Bigint *a, _Bigint *b));
|
||
|
|
|
||
|
|
double _EXFUN(ratio,(_Bigint *a, _Bigint *b));
|
||
|
|
#define Bcopy(x,y) memcpy((char *)&x->_sign, (char *)&y->_sign, y->_wds*sizeof(__Long) + 2*sizeof(int))
|
||
|
|
|
||
|
|
#if defined(_DOUBLE_IS_32BITS) && defined(__v800)
|
||
|
|
#define n_bigtens 2
|
||
|
|
#else
|
||
|
|
#define n_bigtens 5
|
||
|
|
#endif
|
||
|
|
|
||
|
|
extern _CONST double tinytens[];
|
||
|
|
extern _CONST double bigtens[];
|
||
|
|
extern _CONST double tens[];
|
||
|
|
|
||
|
|
|
||
|
|
double _EXFUN(_mprec_log10,(int));
|