/**************************************************************** * * 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 #include #include #include #include #include #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_BYTES_LITTLE_ENDIAN) + 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));