/* @(#)fdlibm.h 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* REDHAT LOCAL: Include files. */ #include <math.h> #include <sys/types.h> #include <machine/ieeefp.h> /* REDHAT LOCAL: Default to XOPEN_MODE. */ #define _XOPEN_MODE /* Most routines need to check whether a float is finite, infinite, or not a number, and many need to know whether the result of an operation will overflow. These conditions depend on whether the largest exponent is used for NaNs & infinities, or whether it's used for finite numbers. The macros below wrap up that kind of information: FLT_UWORD_IS_FINITE(X) True if a positive float with bitmask X is finite. FLT_UWORD_IS_NAN(X) True if a positive float with bitmask X is not a number. FLT_UWORD_IS_INFINITE(X) True if a positive float with bitmask X is +infinity. FLT_UWORD_MAX The bitmask of FLT_MAX. FLT_UWORD_HALF_MAX The bitmask of FLT_MAX/2. FLT_UWORD_EXP_MAX The bitmask of the largest finite exponent (129 if the largest exponent is used for finite numbers, 128 otherwise). FLT_UWORD_LOG_MAX The bitmask of log(FLT_MAX), rounded down. This value is the largest input that can be passed to exp() without producing overflow. FLT_UWORD_LOG_2MAX The bitmask of log(2*FLT_MAX), rounded down. This value is the largest input than can be passed to cosh() without producing overflow. FLT_LARGEST_EXP The largest biased exponent that can be used for finite numbers (255 if the largest exponent is used for finite numbers, 254 otherwise) */ #ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL #define FLT_UWORD_IS_FINITE(x) 1 #define FLT_UWORD_IS_NAN(x) 0 #define FLT_UWORD_IS_INFINITE(x) 0 #define FLT_UWORD_MAX 0x7fffffff #define FLT_UWORD_EXP_MAX 0x43010000 #define FLT_UWORD_LOG_MAX 0x42b2d4fc #define FLT_UWORD_LOG_2MAX 0x42b437e0 #define HUGE ((float)0X1.FFFFFEP128) #else #define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L) #define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L) #define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L) #define FLT_UWORD_MAX 0x7f7fffffL #define FLT_UWORD_EXP_MAX 0x43000000 #define FLT_UWORD_LOG_MAX 0x42b17217 #define FLT_UWORD_LOG_2MAX 0x42b2d4fc #define HUGE ((float)3.40282346638528860e+38) #endif #define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1L<<23)) #define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23) /* Many routines check for zero and subnormal numbers. Such things depend on whether the target supports denormals or not: FLT_UWORD_IS_ZERO(X) True if a positive float with bitmask X is +0. Without denormals, any float with a zero exponent is a +0 representation. With denormals, the only +0 representation is a 0 bitmask. FLT_UWORD_IS_SUBNORMAL(X) True if a non-zero positive float with bitmask X is subnormal. (Routines should check for zeros first.) FLT_UWORD_MIN The bitmask of the smallest float above +0. Call this number REAL_FLT_MIN... FLT_UWORD_EXP_MIN The bitmask of the float representation of REAL_FLT_MIN's exponent. FLT_UWORD_LOG_MIN The bitmask of |log(REAL_FLT_MIN)|, rounding down. FLT_SMALLEST_EXP REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported, -22 if they are). */ #ifdef _FLT_NO_DENORMALS #define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L) #define FLT_UWORD_IS_SUBNORMAL(x) 0 #define FLT_UWORD_MIN 0x00800000 #define FLT_UWORD_EXP_MIN 0x42fc0000 #define FLT_UWORD_LOG_MIN 0x42aeac50 #define FLT_SMALLEST_EXP 1 #else #define FLT_UWORD_IS_ZERO(x) ((x)==0) #define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L) #define FLT_UWORD_MIN 0x00000001 #define FLT_UWORD_EXP_MIN 0x43160000 #define FLT_UWORD_LOG_MIN 0x42cff1b5 #define FLT_SMALLEST_EXP -22 #endif #ifdef __STDC__ #undef __P #define __P(p) p #else #define __P(p) () #endif /* * set X_TLOSS = pi*2**52, which is possibly defined in <values.h> * (one may replace the following line by "#include <values.h>") */ #define X_TLOSS 1.41484755040568800000e+16 /* Functions that are not documented, and are not in <math.h>. */ #ifdef _SCALB_INT extern double scalb __P((double, int)); #else extern double scalb __P((double, double)); #endif extern double significand __P((double)); /* ieee style elementary functions */ extern double __ieee754_sqrt __P((double)); extern double __ieee754_acos __P((double)); extern double __ieee754_acosh __P((double)); extern double __ieee754_log __P((double)); extern double __ieee754_atanh __P((double)); extern double __ieee754_asin __P((double)); extern double __ieee754_atan2 __P((double,double)); extern double __ieee754_exp __P((double)); extern double __ieee754_cosh __P((double)); extern double __ieee754_fmod __P((double,double)); extern double __ieee754_pow __P((double,double)); extern double __ieee754_lgamma_r __P((double,int *)); extern double __ieee754_gamma_r __P((double,int *)); extern double __ieee754_log10 __P((double)); extern double __ieee754_sinh __P((double)); extern double __ieee754_hypot __P((double,double)); extern double __ieee754_j0 __P((double)); extern double __ieee754_j1 __P((double)); extern double __ieee754_y0 __P((double)); extern double __ieee754_y1 __P((double)); extern double __ieee754_jn __P((int,double)); extern double __ieee754_yn __P((int,double)); extern double __ieee754_remainder __P((double,double)); extern __int32_t __ieee754_rem_pio2 __P((double,double*)); #ifdef _SCALB_INT extern double __ieee754_scalb __P((double,int)); #else extern double __ieee754_scalb __P((double,double)); #endif /* fdlibm kernel function */ extern double __kernel_standard __P((double,double,int)); extern double __kernel_sin __P((double,double,int)); extern double __kernel_cos __P((double,double)); extern double __kernel_tan __P((double,double,int)); extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const __int32_t*)); /* Undocumented float functions. */ #ifdef _SCALB_INT extern float scalbf __P((float, int)); #else extern float scalbf __P((float, float)); #endif extern float significandf __P((float)); /* ieee style elementary float functions */ extern float __ieee754_sqrtf __P((float)); extern float __ieee754_acosf __P((float)); extern float __ieee754_acoshf __P((float)); extern float __ieee754_logf __P((float)); extern float __ieee754_atanhf __P((float)); extern float __ieee754_asinf __P((float)); extern float __ieee754_atan2f __P((float,float)); extern float __ieee754_expf __P((float)); extern float __ieee754_coshf __P((float)); extern float __ieee754_fmodf __P((float,float)); extern float __ieee754_powf __P((float,float)); extern float __ieee754_lgammaf_r __P((float,int *)); extern float __ieee754_gammaf_r __P((float,int *)); extern float __ieee754_log10f __P((float)); extern float __ieee754_sinhf __P((float)); extern float __ieee754_hypotf __P((float,float)); extern float __ieee754_j0f __P((float)); extern float __ieee754_j1f __P((float)); extern float __ieee754_y0f __P((float)); extern float __ieee754_y1f __P((float)); extern float __ieee754_jnf __P((int,float)); extern float __ieee754_ynf __P((int,float)); extern float __ieee754_remainderf __P((float,float)); extern __int32_t __ieee754_rem_pio2f __P((float,float*)); #ifdef _SCALB_INT extern float __ieee754_scalbf __P((float,int)); #else extern float __ieee754_scalbf __P((float,float)); #endif /* float versions of fdlibm kernel functions */ extern float __kernel_sinf __P((float,float,int)); extern float __kernel_cosf __P((float,float)); extern float __kernel_tanf __P((float,float,int)); extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __int32_t*)); /* The original code used statements like n0 = ((*(int*)&one)>>29)^1; * index of high word * ix0 = *(n0+(int*)&x); * high word of x * ix1 = *((1-n0)+(int*)&x); * low word of x * to dig two 32 bit words out of the 64 bit IEEE floating point value. That is non-ANSI, and, moreover, the gcc instruction scheduler gets it wrong. We instead use the following macros. Unlike the original code, we determine the endianness at compile time, not at run time; I don't see much benefit to selecting endianness at run time. */ #ifndef __IEEE_BIG_ENDIAN #ifndef __IEEE_LITTLE_ENDIAN #error Must define endianness #endif #endif /* A union which permits us to convert between a double and two 32 bit ints. */ #ifdef __IEEE_BIG_ENDIAN typedef union { double value; struct { __uint32_t msw; __uint32_t lsw; } parts; } ieee_double_shape_type; #endif #ifdef __IEEE_LITTLE_ENDIAN typedef union { double value; struct { __uint32_t lsw; __uint32_t msw; } parts; } ieee_double_shape_type; #endif /* Get two 32 bit ints from a double. */ #define EXTRACT_WORDS(ix0,ix1,d) \ do { \ ieee_double_shape_type ew_u; \ ew_u.value = (d); \ (ix0) = ew_u.parts.msw; \ (ix1) = ew_u.parts.lsw; \ } while (0) /* Get the more significant 32 bit int from a double. */ #define GET_HIGH_WORD(i,d) \ do { \ ieee_double_shape_type gh_u; \ gh_u.value = (d); \ (i) = gh_u.parts.msw; \ } while (0) /* Get the less significant 32 bit int from a double. */ #define GET_LOW_WORD(i,d) \ do { \ ieee_double_shape_type gl_u; \ gl_u.value = (d); \ (i) = gl_u.parts.lsw; \ } while (0) /* Set a double from two 32 bit ints. */ #define INSERT_WORDS(d,ix0,ix1) \ do { \ ieee_double_shape_type iw_u; \ iw_u.parts.msw = (ix0); \ iw_u.parts.lsw = (ix1); \ (d) = iw_u.value; \ } while (0) /* Set the more significant 32 bits of a double from an int. */ #define SET_HIGH_WORD(d,v) \ do { \ ieee_double_shape_type sh_u; \ sh_u.value = (d); \ sh_u.parts.msw = (v); \ (d) = sh_u.value; \ } while (0) /* Set the less significant 32 bits of a double from an int. */ #define SET_LOW_WORD(d,v) \ do { \ ieee_double_shape_type sl_u; \ sl_u.value = (d); \ sl_u.parts.lsw = (v); \ (d) = sl_u.value; \ } while (0) /* A union which permits us to convert between a float and a 32 bit int. */ typedef union { float value; __uint32_t word; } ieee_float_shape_type; /* Get a 32 bit int from a float. */ #define GET_FLOAT_WORD(i,d) \ do { \ ieee_float_shape_type gf_u; \ gf_u.value = (d); \ (i) = gf_u.word; \ } while (0) /* Set a float from a 32 bit int. */ #define SET_FLOAT_WORD(d,i) \ do { \ ieee_float_shape_type sf_u; \ sf_u.word = (i); \ (d) = sf_u.value; \ } while (0) /* Macros to avoid undefined behaviour that can arise if the amount of a shift is exactly equal to the size of the shifted operand. */ #define SAFE_LEFT_SHIFT(op,amt) \ (((amt) < 8 * sizeof(op)) ? ((op) << (amt)) : 0) #define SAFE_RIGHT_SHIFT(op,amt) \ (((amt) < 8 * sizeof(op)) ? ((op) >> (amt)) : 0) #ifdef _COMPLEX_H /* * Quoting from ISO/IEC 9899:TC2: * * 6.2.5.13 Types * Each complex type has the same representation and alignment requirements as * an array type containing exactly two elements of the corresponding real type; * the first element is equal to the real part, and the second element to the * imaginary part, of the complex number. */ typedef union { float complex z; float parts[2]; } float_complex; typedef union { double complex z; double parts[2]; } double_complex; typedef union { long double complex z; long double parts[2]; } long_double_complex; #define REAL_PART(z) ((z).parts[0]) #define IMAG_PART(z) ((z).parts[1]) #endif /* _COMPLEX_H */