/**************************************************************** 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 #include #define _RESEARCH_SOURCE #include #include #include #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