/* Declarations for math functions. Copyright (C) 1991-1993,1995-1999,2001,2002 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. */ /* * ISO C99 Standard: 7.12 Mathematics <math.h> */ #ifndef _MATH_H #define _MATH_H 1 #include <features.h> __BEGIN_DECLS /* Get machine-dependent HUGE_VAL value (returned on overflow). On all IEEE754 machines, this is +Infinity. */ #include <bits/huge_val.h> /* Get machine-dependent NAN value (returned for some domain errors). */ #ifdef __USE_ISOC99 # include <bits/nan.h> #endif /* Get general and ISO C99 specific information. */ #include <bits/mathdef.h> /* The file <bits/mathcalls.h> contains the prototypes for all the actual math functions. These macros are used for those prototypes, so we can easily declare each function as both `name' and `__name', and can declare the float versions `namef' and `__namef'. */ #define __MATHCALL(function,suffix, args) \ __MATHDECL (_Mdouble_,function,suffix, args) #define __MATHDECL(type, function,suffix, args) \ __MATHDECL_1(type, function,suffix, args); \ __MATHDECL_1(type, __CONCAT(__,function),suffix, args) #define __MATHCALLX(function,suffix, args, attrib) \ __MATHDECLX (_Mdouble_,function,suffix, args, attrib) #define __MATHDECLX(type, function,suffix, args, attrib) \ __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \ __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib) #define __MATHDECL_1(type, function,suffix, args) \ extern type __MATH_PRECNAME(function,suffix) args __THROW #define _Mdouble_ double #define __MATH_PRECNAME(name,r) __CONCAT(name,r) # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD # define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD #include <bits/mathcalls.h> #undef _Mdouble_ #undef _Mdouble_BEGIN_NAMESPACE #undef _Mdouble_END_NAMESPACE #undef __MATH_PRECNAME #if defined __USE_MISC || defined __USE_ISOC99 /* Include the file of declarations again, this time using `float' instead of `double' and appending f to each function name. */ # ifndef _Mfloat_ # define _Mfloat_ float # endif # define _Mdouble_ _Mfloat_ # ifdef __STDC__ # define __MATH_PRECNAME(name,r) name##f##r # else # define __MATH_PRECNAME(name,r) name/**/f/**/r # endif # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 # include <bits/mathcalls.h> # undef _Mdouble_ # undef _Mdouble_BEGIN_NAMESPACE # undef _Mdouble_END_NAMESPACE # undef __MATH_PRECNAME # if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH /* Include the file of declarations again, this time using `long double' instead of `double' and appending l to each function name. */ # ifndef _Mlong_double_ # define _Mlong_double_ long double # endif # define _Mdouble_ _Mlong_double_ # ifdef __STDC__ # define __MATH_PRECNAME(name,r) name##l##r # else # define __MATH_PRECNAME(name,r) name/**/l/**/r # endif # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99 # define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99 # include <bits/mathcalls.h> # undef _Mdouble_ # undef _Mdouble_BEGIN_NAMESPACE # undef _Mdouble_END_NAMESPACE # undef __MATH_PRECNAME # endif /* __STDC__ || __GNUC__ */ #endif /* Use misc or ISO C99. */ #undef __MATHDECL_1 #undef __MATHDECL #undef __MATHCALL #if defined __USE_MISC || defined __USE_XOPEN /* This variable is used by `gamma' and `lgamma'. */ extern int signgam; #endif /* ISO C99 defines some generic macros which work on any data type. */ #if __USE_ISOC99 /* Get the architecture specific values describing the floating-point evaluation. The following symbols will get defined: float_t floating-point type at least as wide as `float' used to evaluate `float' expressions double_t floating-point type at least as wide as `double' used to evaluate `double' expressions FLT_EVAL_METHOD Defined to 0 if `float_t' is `float' and `double_t' is `double' 1 if `float_t' and `double_t' are `double' 2 if `float_t' and `double_t' are `long double' else `float_t' and `double_t' are unspecified INFINITY representation of the infinity value of type `float' FP_FAST_FMA FP_FAST_FMAF FP_FAST_FMAL If defined it indicates that the `fma' function generally executes about as fast as a multiply and an add. This macro is defined only iff the `fma' function is implemented directly with a hardware multiply-add instructions. FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'. FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'. DECIMAL_DIG Number of decimal digits supported by conversion between decimal and all internal floating-point formats. */ /* All floating-point numbers can be put in one of these categories. */ enum { FP_NAN, # define FP_NAN FP_NAN FP_INFINITE, # define FP_INFINITE FP_INFINITE FP_ZERO, # define FP_ZERO FP_ZERO FP_SUBNORMAL, # define FP_SUBNORMAL FP_SUBNORMAL FP_NORMAL # define FP_NORMAL FP_NORMAL }; /* Return number of classification appropriate for X. */ # ifdef __NO_LONG_DOUBLE_MATH # define fpclassify(x) \ (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x)) # else # define fpclassify(x) \ (sizeof (x) == sizeof (float) \ ? __fpclassifyf (x) \ : sizeof (x) == sizeof (double) \ ? __fpclassify (x) : __fpclassifyl (x)) # endif /* Return nonzero value if sign of X is negative. */ # ifdef __NO_LONG_DOUBLE_MATH # define signbit(x) \ (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x)) # else # define signbit(x) \ (sizeof (x) == sizeof (float) \ ? __signbitf (x) \ : sizeof (x) == sizeof (double) \ ? __signbit (x) : __signbitl (x)) # endif /* Return nonzero value if X is not +-Inf or NaN. */ # ifdef __NO_LONG_DOUBLE_MATH # define isfinite(x) \ (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x)) # else # define isfinite(x) \ (sizeof (x) == sizeof (float) \ ? __finitef (x) \ : sizeof (x) == sizeof (double) \ ? __finite (x) : __finitel (x)) # endif /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */ # define isnormal(x) (fpclassify (x) == FP_NORMAL) /* Return nonzero value if X is a NaN. We could use `fpclassify' but we already have this functions `__isnan' and it is faster. */ # ifdef __NO_LONG_DOUBLE_MATH # define isnan(x) \ (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x)) # else # define isnan(x) \ (sizeof (x) == sizeof (float) \ ? __isnanf (x) \ : sizeof (x) == sizeof (double) \ ? __isnan (x) : __isnanl (x)) # endif /* Return nonzero value is X is positive or negative infinity. */ # ifdef __NO_LONG_DOUBLE_MATH # define isinf(x) \ (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x)) # else # define isinf(x) \ (sizeof (x) == sizeof (float) \ ? __isinff (x) \ : sizeof (x) == sizeof (double) \ ? __isinf (x) : __isinfl (x)) # endif /* Bitmasks for the math_errhandling macro. */ # define MATH_ERRNO 1 /* errno set by math functions. */ # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */ #endif /* Use ISO C99. */ #ifdef __USE_MISC /* Support for various different standard error handling behaviors. */ typedef enum { _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */ _SVID_, /* According to System V, release 4. */ _XOPEN_, /* Nowadays also Unix98. */ _POSIX_, _ISOC_ /* Actually this is ISO C99. */ } _LIB_VERSION_TYPE; /* This variable can be changed at run-time to any of the values above to affect floating point error handling behavior (it may also be necessary to change the hardware FPU exception settings). */ extern _LIB_VERSION_TYPE _LIB_VERSION; #endif #ifdef __USE_SVID /* In SVID error handling, `matherr' is called with this description of the exceptional condition. We have a problem when using C++ since `exception' is a reserved name in C++. */ # ifdef __cplusplus struct __exception # else struct exception # endif { int type; char *name; double arg1; double arg2; double retval; }; # ifdef __cplusplus extern int matherr (struct __exception *__exc) throw (); # else extern int matherr (struct exception *__exc); # endif # define X_TLOSS 1.41484755040568800000e+16 /* Types of exceptions in the `type' field. */ # define DOMAIN 1 # define SING 2 # define OVERFLOW 3 # define UNDERFLOW 4 # define TLOSS 5 # define PLOSS 6 /* SVID mode specifies returning this large value instead of infinity. */ # define HUGE 3.40282347e+38F #else /* !SVID */ # ifdef __USE_XOPEN /* X/Open wants another strange constant. */ # define MAXFLOAT 3.40282347e+38F # endif #endif /* SVID */ /* Some useful constants. */ #if defined __USE_BSD || defined __USE_XOPEN # define M_E 2.7182818284590452354 /* e */ # define M_LOG2E 1.4426950408889634074 /* log_2 e */ # define M_LOG10E 0.43429448190325182765 /* log_10 e */ # define M_LN2 0.69314718055994530942 /* log_e 2 */ # define M_LN10 2.30258509299404568402 /* log_e 10 */ # define M_PI 3.14159265358979323846 /* pi */ # define M_PI_2 1.57079632679489661923 /* pi/2 */ # define M_PI_4 0.78539816339744830962 /* pi/4 */ # define M_1_PI 0.31830988618379067154 /* 1/pi */ # define M_2_PI 0.63661977236758134308 /* 2/pi */ # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ #endif /* The above constants are not adequate for computation using `long double's. Therefore we provide as an extension constants with similar names as a GNU extension. Provide enough digits for the 128-bit IEEE quad. */ #ifdef __USE_GNU # define M_El 2.7182818284590452353602874713526625L /* e */ # define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */ # define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ # define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ # define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ # define M_PIl 3.1415926535897932384626433832795029L /* pi */ # define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ # define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ # define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ # define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ # define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ # define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ # define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ #endif /* When compiling in strict ISO C compatible mode we must not use the inline functions since they, among other things, do not set the `errno' variable correctly. */ #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES # define __NO_MATH_INLINES 1 #endif /* Get machine-dependent inline versions (if there are any). */ #ifdef __USE_EXTERN_INLINES # include <bits/mathinline.h> #endif #if __USE_ISOC99 /* ISO C99 defines some macros to compare number while taking care for unordered numbers. Since many FPUs provide special instructions to support these operations and these tests are defined in <bits/mathinline.h>, we define the generic macros at this late point and only if they are not defined yet. */ /* Return nonzero value if X is greater than Y. */ # ifndef isgreater # define isgreater(x, y) \ (__extension__ \ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered (__x, __y) && __x > __y; })) # endif /* Return nonzero value if X is greater than or equal to Y. */ # ifndef isgreaterequal # define isgreaterequal(x, y) \ (__extension__ \ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered (__x, __y) && __x >= __y; })) # endif /* Return nonzero value if X is less than Y. */ # ifndef isless # define isless(x, y) \ (__extension__ \ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered (__x, __y) && __x < __y; })) # endif /* Return nonzero value if X is less than or equal to Y. */ # ifndef islessequal # define islessequal(x, y) \ (__extension__ \ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered (__x, __y) && __x <= __y; })) # endif /* Return nonzero value if either X is less than Y or Y is less than X. */ # ifndef islessgreater # define islessgreater(x, y) \ (__extension__ \ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \ !isunordered (__x, __y) && (__x < __y || __y < __x); })) # endif /* Return nonzero value if arguments are unordered. */ # ifndef isunordered # define isunordered(u, v) \ (__extension__ \ ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \ fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; })) # endif #endif __END_DECLS #endif /* math.h */