path: root/math/math.h

/* Declarations for math functions.
   Copyright (C) 1991-2016 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, see
   <http://www.gnu.org/licenses/>.  */

/*
 *	ISO C99 Standard: 7.12 Mathematics	<math.h>
 */

#ifndef	_MATH_H
#define	_MATH_H	1

#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
#include <bits/libc-header-start.h>

__BEGIN_DECLS

/* Get machine-dependent vector math functions declarations.  */
#include <bits/math-vector.h>

/* Get machine-dependent HUGE_VAL value (returned on overflow).
   On all IEEE754 machines, this is +Infinity.  */
#include <bits/huge_val.h>
#ifdef __USE_ISOC99
# include <bits/huge_valf.h>
# include <bits/huge_vall.h>

/* Get machine-dependent INFINITY value.  */
# include <bits/inf.h>

/* Get machine-dependent NAN value (returned for some domain errors).  */
# include <bits/nan.h>
#endif /* __USE_ISOC99 */

#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Signaling NaN macros, if supported.  */
# if __GNUC_PREREQ (3, 3)
#  define SNANF (__builtin_nansf (""))
#  define SNAN (__builtin_nans (""))
#  define SNANL (__builtin_nansl (""))
# endif
#endif

/* 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

    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)'.

*/

#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 __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)

#define __MATHCALL_VEC(function, suffix, args) 	\
  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  __MATHCALL (function, suffix, args)

#define __MATHDECL_VEC(type, function,suffix, args) \
  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  __MATHDECL(type, function,suffix, args)

#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 __MATH_DECLARING_DOUBLE  1
#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
#undef __MATH_DECLARING_DOUBLE

#ifdef __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_
# define __MATH_PRECNAME(name,r) name##f##r
# define __MATH_DECLARING_DOUBLE  0
# 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
# undef __MATH_DECLARING_DOUBLE

# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
     || defined __LDBL_COMPAT \
     || defined _LIBC_TEST
#  ifdef __LDBL_COMPAT

#   ifdef __USE_ISOC99
extern float __nldbl_nexttowardf (float __x, long double __y)
				  __THROW __attribute__ ((__const__));
#    ifdef __REDIRECT_NTH
extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
			     __nldbl_nexttowardf)
     __attribute__ ((__const__));
extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
			      nextafter) __attribute__ ((__const__));
extern long double __REDIRECT_NTH (nexttowardl,
				   (long double __x, long double __y),
				   nextafter) __attribute__ ((__const__));
#    endif
#   endif

#   undef __MATHDECL_1
#   define __MATHDECL_2(type, function,suffix, args, alias) \
  extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
			     args, alias)
#   define __MATHDECL_1(type, function,suffix, args) \
  __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
#  endif

/* 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_
#  define __MATH_PRECNAME(name,r) name##l##r
#  define __MATH_DECLARING_DOUBLE  0
#  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
#  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
#  define __MATH_DECLARE_LDOUBLE   1
#  include <bits/mathcalls.h>
#  undef _Mdouble_
#  undef _Mdouble_BEGIN_NAMESPACE
#  undef _Mdouble_END_NAMESPACE
#  undef __MATH_PRECNAME
#  undef __MATH_DECLARING_DOUBLE

# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */

#endif	/* Use 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.  */
#ifdef __USE_ISOC99

/* All floating-point numbers can be put in one of these categories.  */
enum
  {
    FP_NAN =
# define FP_NAN 0
      FP_NAN,
    FP_INFINITE =
# define FP_INFINITE 1
      FP_INFINITE,
    FP_ZERO =
# define FP_ZERO 2
      FP_ZERO,
    FP_SUBNORMAL =
# define FP_SUBNORMAL 3
      FP_SUBNORMAL,
    FP_NORMAL =
# define FP_NORMAL 4
      FP_NORMAL
  };

/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
   so disable builtins if this is enabled.  When fixed in a newer GCC,
   the __SUPPORT_SNAN__ check may be skipped for those versions.  */

/* Return number of classification appropriate for X.  */
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__			      \
     && !defined __OPTIMIZE_SIZE__
#  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,	      \
     FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
# elif defined __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.  */
# if __GNUC_PREREQ (4,0)
#  define signbit(x) \
     (sizeof (x) == sizeof (float)                                            \
      ? __builtin_signbitf (x)