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drasko |
/* Declarations for math functions.
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Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006
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Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, write to the Free
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Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 USA. */
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/*
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* ISO C99 Standard: 7.12 Mathematics <math.h>
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*/
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#ifndef _MATH_H
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#define _MATH_H 1
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#include <features.h>
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__BEGIN_DECLS
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/* Get machine-dependent HUGE_VAL value (returned on overflow).
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On all IEEE754 machines, this is +Infinity. */
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#include <bits/huge_val.h>
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#ifdef __USE_ISOC99
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# include <bits/huge_valf.h>
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# include <bits/huge_vall.h>
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/* Get machine-dependent INFINITY value. */
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# include <bits/inf.h>
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/* Get machine-dependent NAN value (returned for some domain errors). */
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# include <bits/nan.h>
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#endif /* __USE_ISOC99 */
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/* Get general and ISO C99 specific information. */
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#include <bits/mathdef.h>
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/* The file <bits/mathcalls.h> contains the prototypes for all the
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actual math functions. These macros are used for those prototypes,
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so we can easily declare each function as both `name' and `__name',
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and can declare the float versions `namef' and `__namef'. */
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#define __MATHCALL(function,suffix, args) \
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__MATHDECL (_Mdouble_,function,suffix, args)
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#define __MATHDECL(type, function,suffix, args) \
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__MATHDECL_1(type, function,suffix, args); \
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__MATHDECL_1(type, __CONCAT(__,function),suffix, args)
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#define __MATHCALLX(function,suffix, args, attrib) \
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__MATHDECLX (_Mdouble_,function,suffix, args, attrib)
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#define __MATHDECLX(type, function,suffix, args, attrib) \
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__MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
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__MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
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#define __MATHDECL_1(type, function,suffix, args) \
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extern type __MATH_PRECNAME(function,suffix) args __THROW
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#define _Mdouble_ double
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#define __MATH_PRECNAME(name,r) __CONCAT(name,r)
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# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
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# define _Mdouble_END_NAMESPACE __END_NAMESPACE_STD
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#include <bits/mathcalls.h>
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#undef _Mdouble_
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#undef _Mdouble_BEGIN_NAMESPACE
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#undef _Mdouble_END_NAMESPACE
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#undef __MATH_PRECNAME
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#if defined __USE_MISC || defined __USE_ISOC99
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/* Include the file of declarations again, this time using `float'
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instead of `double' and appending f to each function name. */
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# ifndef _Mfloat_
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# define _Mfloat_ float
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# endif
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# define _Mdouble_ _Mfloat_
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# ifdef __STDC__
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# define __MATH_PRECNAME(name,r) name##f##r
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# else
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# define __MATH_PRECNAME(name,r) name/**/f/**/r
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# endif
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# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
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# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
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# include <bits/mathcalls.h>
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# undef _Mdouble_
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# undef _Mdouble_BEGIN_NAMESPACE
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# undef _Mdouble_END_NAMESPACE
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# undef __MATH_PRECNAME
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# if (__STDC__ - 0 || __GNUC__ - 0) \
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&& (!defined __NO_LONG_DOUBLE_MATH || defined __LDBL_COMPAT)
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# ifdef __LDBL_COMPAT
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# ifdef __USE_ISOC99
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extern float __nldbl_nexttowardf (float __x, long double __y)
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__THROW __attribute__ ((__const__));
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# ifdef __REDIRECT_NTH
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extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
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__nldbl_nexttowardf)
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__attribute__ ((__const__));
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extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
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nextafter) __attribute__ ((__const__));
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extern long double __REDIRECT_NTH (nexttowardl,
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(long double __x, long double __y),
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nextafter) __attribute__ ((__const__));
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# endif
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# endif
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/* Include the file of declarations again, this time using `long double'
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instead of `double' and appending l to each function name. */
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# undef __MATHDECL_1
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# define __MATHDECL_2(type, function,suffix, args, alias) \
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extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
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args, alias)
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# define __MATHDECL_1(type, function,suffix, args) \
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__MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
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# endif
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# ifndef _Mlong_double_
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# define _Mlong_double_ long double
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# endif
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# define _Mdouble_ _Mlong_double_
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# ifdef __STDC__
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# define __MATH_PRECNAME(name,r) name##l##r
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# else
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# define __MATH_PRECNAME(name,r) name/**/l/**/r
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# endif
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# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
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# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
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# include <bits/mathcalls.h>
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# undef _Mdouble_
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# undef _Mdouble_BEGIN_NAMESPACE
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# undef _Mdouble_END_NAMESPACE
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# undef __MATH_PRECNAME
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# endif /* __STDC__ || __GNUC__ */
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#endif /* Use misc or ISO C99. */
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#undef __MATHDECL_1
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#undef __MATHDECL
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#undef __MATHCALL
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#if defined __USE_MISC || defined __USE_XOPEN
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/* This variable is used by `gamma' and `lgamma'. */
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extern int signgam;
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#endif
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/* ISO C99 defines some generic macros which work on any data type. */
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#ifdef __USE_ISOC99
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/* Get the architecture specific values describing the floating-point
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evaluation. The following symbols will get defined:
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float_t floating-point type at least as wide as `float' used
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to evaluate `float' expressions
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double_t floating-point type at least as wide as `double' used
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to evaluate `double' expressions
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FLT_EVAL_METHOD
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Defined to
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1 if `float_t' and `double_t' are `double'
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2 if `float_t' and `double_t' are `long double'
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else `float_t' and `double_t' are unspecified
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INFINITY representation of the infinity value of type `float'
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FP_FAST_FMA
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FP_FAST_FMAF
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FP_FAST_FMAL
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If defined it indicates that the `fma' function
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generally executes about as fast as a multiply and an add.
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This macro is defined only iff the `fma' function is
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implemented directly with a hardware multiply-add instructions.
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FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
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FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
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DECIMAL_DIG Number of decimal digits supported by conversion between
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decimal and all internal floating-point formats.
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*/
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/* All floating-point numbers can be put in one of these categories. */
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enum
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{
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FP_NAN,
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# define FP_NAN FP_NAN
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FP_INFINITE,
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# define FP_INFINITE FP_INFINITE
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FP_ZERO,
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# define FP_ZERO FP_ZERO
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FP_SUBNORMAL,
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# define FP_SUBNORMAL FP_SUBNORMAL
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FP_NORMAL
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# define FP_NORMAL FP_NORMAL
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};
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/* Return number of classification appropriate for X. */
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# ifdef __NO_LONG_DOUBLE_MATH
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# define fpclassify(x) \
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(sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
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# else
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# define fpclassify(x) \
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(sizeof (x) == sizeof (float) \
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? __fpclassifyf (x) \
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: sizeof (x) == sizeof (double) \
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? __fpclassify (x) : __fpclassifyl (x))
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# endif
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/* Return nonzero value if sign of X is negative. */
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# ifdef __NO_LONG_DOUBLE_MATH
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# define signbit(x) \
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(sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
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# else
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# define signbit(x) \
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(sizeof (x) == sizeof (float) \
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? __signbitf (x) \
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: sizeof (x) == sizeof (double) \
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? __signbit (x) : __signbitl (x))
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# endif
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/* Return nonzero value if X is not +-Inf or NaN. */
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# ifdef __NO_LONG_DOUBLE_MATH
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# define isfinite(x) \
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(sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
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# else
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# define isfinite(x) \
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(sizeof (x) == sizeof (float) \
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? __finitef (x) \
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: sizeof (x) == sizeof (double) \
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? __finite (x) : __finitel (x))
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# endif
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/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
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# define isnormal(x) (fpclassify (x) == FP_NORMAL)
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/* Return nonzero value if X is a NaN. We could use `fpclassify' but
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we already have this functions `__isnan' and it is faster. */
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# ifdef __NO_LONG_DOUBLE_MATH
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# define isnan(x) \
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(sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
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# else
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# define isnan(x) \
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(sizeof (x) == sizeof (float) \
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? __isnanf (x) \
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: sizeof (x) == sizeof (double) \
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? __isnan (x) : __isnanl (x))
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# endif
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/* Return nonzero value is X is positive or negative infinity. */
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# ifdef __NO_LONG_DOUBLE_MATH
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# define isinf(x) \
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(sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
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# else
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# define isinf(x) \
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(sizeof (x) == sizeof (float) \
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? __isinff (x) \
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: sizeof (x) == sizeof (double) \
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| 273 |
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? __isinf (x) : __isinfl (x))
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# endif
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| 275 |
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| 276 |
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/* Bitmasks for the math_errhandling macro. */
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| 277 |
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# define MATH_ERRNO 1 /* errno set by math functions. */
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# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
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| 280 |
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#endif /* Use ISO C99. */
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| 282 |
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#ifdef __USE_MISC
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| 283 |
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/* Support for various different standard error handling behaviors. */
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| 284 |
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typedef enum
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{
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| 286 |
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_IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
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| 287 |
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_SVID_, /* According to System V, release 4. */
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_XOPEN_, /* Nowadays also Unix98. */
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_POSIX_,
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_ISOC_ /* Actually this is ISO C99. */
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| 291 |
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} _LIB_VERSION_TYPE;
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| 293 |
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/* This variable can be changed at run-time to any of the values above to
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affect floating point error handling behavior (it may also be necessary
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| 295 |
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to change the hardware FPU exception settings). */
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| 296 |
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extern _LIB_VERSION_TYPE _LIB_VERSION;
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#endif
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| 299 |
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| 300 |
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#ifdef __USE_SVID
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/* In SVID error handling, `matherr' is called with this description
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of the exceptional condition.
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| 304 |
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We have a problem when using C++ since `exception' is a reserved
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name in C++. */
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# ifdef __cplusplus
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struct __exception
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# else
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struct exception
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| 310 |
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# endif
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| 311 |
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{
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| 312 |
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int type;
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| 313 |
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char *name;
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| 314 |
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double arg1;
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| 315 |
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double arg2;
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double retval;
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| 317 |
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};
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| 318 |
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| 319 |
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# ifdef __cplusplus
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extern int matherr (struct __exception *__exc) throw ();
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# else
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| 322 |
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extern int matherr (struct exception *__exc);
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| 323 |
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# endif
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| 324 |
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| 325 |
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# define X_TLOSS 1.41484755040568800000e+16
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| 326 |
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| 327 |
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/* Types of exceptions in the `type' field. */
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| 328 |
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# define DOMAIN 1
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| 329 |
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# define SING 2
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|
|
# define OVERFLOW 3
|
| 331 |
|
|
# define UNDERFLOW 4
|
| 332 |
|
|
# define TLOSS 5
|
| 333 |
|
|
# define PLOSS 6
|
| 334 |
|
|
|
| 335 |
|
|
/* SVID mode specifies returning this large value instead of infinity. */
|
| 336 |
|
|
# define HUGE 3.40282347e+38F
|
| 337 |
|
|
|
| 338 |
|
|
#else /* !SVID */
|
| 339 |
|
|
|
| 340 |
|
|
# ifdef __USE_XOPEN
|
| 341 |
|
|
/* X/Open wants another strange constant. */
|
| 342 |
|
|
# define MAXFLOAT 3.40282347e+38F
|
| 343 |
|
|
# endif
|
| 344 |
|
|
|
| 345 |
|
|
#endif /* SVID */
|
| 346 |
|
|
|
| 347 |
|
|
|
| 348 |
|
|
/* Some useful constants. */
|
| 349 |
|
|
#if defined __USE_BSD || defined __USE_XOPEN
|
| 350 |
|
|
# define M_E 2.7182818284590452354 /* e */
|
| 351 |
|
|
# define M_LOG2E 1.4426950408889634074 /* log_2 e */
|
| 352 |
|
|
# define M_LOG10E 0.43429448190325182765 /* log_10 e */
|
| 353 |
|
|
# define M_LN2 0.69314718055994530942 /* log_e 2 */
|
| 354 |
|
|
# define M_LN10 2.30258509299404568402 /* log_e 10 */
|
| 355 |
|
|
# define M_PI 3.14159265358979323846 /* pi */
|
| 356 |
|
|
# define M_PI_2 1.57079632679489661923 /* pi/2 */
|
| 357 |
|
|
# define M_PI_4 0.78539816339744830962 /* pi/4 */
|
| 358 |
|
|
# define M_1_PI 0.31830988618379067154 /* 1/pi */
|
| 359 |
|
|
# define M_2_PI 0.63661977236758134308 /* 2/pi */
|
| 360 |
|
|
# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
|
| 361 |
|
|
# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
|
| 362 |
|
|
# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
|
| 363 |
|
|
#endif
|
| 364 |
|
|
|
| 365 |
|
|
/* The above constants are not adequate for computation using `long double's.
|
| 366 |
|
|
Therefore we provide as an extension constants with similar names as a
|
| 367 |
|
|
GNU extension. Provide enough digits for the 128-bit IEEE quad. */
|
| 368 |
|
|
#ifdef __USE_GNU
|
| 369 |
|
|
# define M_El 2.7182818284590452353602874713526625L /* e */
|
| 370 |
|
|
# define M_LOG2El 1.4426950408889634073599246810018921L /* log_2 e */
|
| 371 |
|
|
# define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */
|
| 372 |
|
|
# define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */
|
| 373 |
|
|
# define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */
|
| 374 |
|
|
# define M_PIl 3.1415926535897932384626433832795029L /* pi */
|
| 375 |
|
|
# define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
|
| 376 |
|
|
# define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
|
| 377 |
|
|
# define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
|
| 378 |
|
|
# define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
|
| 379 |
|
|
# define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
|
| 380 |
|
|
# define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */
|
| 381 |
|
|
# define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */
|
| 382 |
|
|
#endif
|
| 383 |
|
|
|
| 384 |
|
|
|
| 385 |
|
|
/* When compiling in strict ISO C compatible mode we must not use the
|
| 386 |
|
|
inline functions since they, among other things, do not set the
|
| 387 |
|
|
`errno' variable correctly. */
|
| 388 |
|
|
#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
|
| 389 |
|
|
# define __NO_MATH_INLINES 1
|
| 390 |
|
|
#endif
|
| 391 |
|
|
|
| 392 |
|
|
#if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
|
| 393 |
|
|
/* ISO C99 defines some macros to compare number while taking care for
|
| 394 |
|
|
unordered numbers. Many FPUs provide special instructions to support
|
| 395 |
|
|
these operations. Generic support in GCC for these as builtins went
|
| 396 |
|
|
in before 3.0.0, but not all cpus added their patterns. We define
|
| 397 |
|
|
versions that use the builtins here, and <bits/mathinline.h> will
|
| 398 |
|
|
undef/redefine as appropriate for the specific GCC version in use. */
|
| 399 |
|
|
# define isgreater(x, y) __builtin_isgreater(x, y)
|
| 400 |
|
|
# define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
|
| 401 |
|
|
# define isless(x, y) __builtin_isless(x, y)
|
| 402 |
|
|
# define islessequal(x, y) __builtin_islessequal(x, y)
|
| 403 |
|
|
# define islessgreater(x, y) __builtin_islessgreater(x, y)
|
| 404 |
|
|
# define isunordered(u, v) __builtin_isunordered(u, v)
|
| 405 |
|
|
#endif
|
| 406 |
|
|
|
| 407 |
|
|
/* Get machine-dependent inline versions (if there are any). */
|
| 408 |
|
|
#ifdef __USE_EXTERN_INLINES
|
| 409 |
|
|
# include <bits/mathinline.h>
|
| 410 |
|
|
#endif
|
| 411 |
|
|
|
| 412 |
|
|
#ifdef __USE_ISOC99
|
| 413 |
|
|
/* If we've still got undefined comparison macros, provide defaults. */
|
| 414 |
|
|
|
| 415 |
|
|
/* Return nonzero value if X is greater than Y. */
|
| 416 |
|
|
# ifndef isgreater
|
| 417 |
|
|
# define isgreater(x, y) \
|
| 418 |
|
|
(__extension__ \
|
| 419 |
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
| 420 |
|
|
!isunordered (__x, __y) && __x > __y; }))
|
| 421 |
|
|
# endif
|
| 422 |
|
|
|
| 423 |
|
|
/* Return nonzero value if X is greater than or equal to Y. */
|
| 424 |
|
|
# ifndef isgreaterequal
|
| 425 |
|
|
# define isgreaterequal(x, y) \
|
| 426 |
|
|
(__extension__ \
|
| 427 |
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
| 428 |
|
|
!isunordered (__x, __y) && __x >= __y; }))
|
| 429 |
|
|
# endif
|
| 430 |
|
|
|
| 431 |
|
|
/* Return nonzero value if X is less than Y. */
|
| 432 |
|
|
# ifndef isless
|
| 433 |
|
|
# define isless(x, y) \
|
| 434 |
|
|
(__extension__ \
|
| 435 |
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
| 436 |
|
|
!isunordered (__x, __y) && __x < __y; }))
|
| 437 |
|
|
# endif
|
| 438 |
|
|
|
| 439 |
|
|
/* Return nonzero value if X is less than or equal to Y. */
|
| 440 |
|
|
# ifndef islessequal
|
| 441 |
|
|
# define islessequal(x, y) \
|
| 442 |
|
|
(__extension__ \
|
| 443 |
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
| 444 |
|
|
!isunordered (__x, __y) && __x <= __y; }))
|
| 445 |
|
|
# endif
|
| 446 |
|
|
|
| 447 |
|
|
/* Return nonzero value if either X is less than Y or Y is less than X. */
|
| 448 |
|
|
# ifndef islessgreater
|
| 449 |
|
|
# define islessgreater(x, y) \
|
| 450 |
|
|
(__extension__ \
|
| 451 |
|
|
({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
|
| 452 |
|
|
!isunordered (__x, __y) && (__x < __y || __y < __x); }))
|
| 453 |
|
|
# endif
|
| 454 |
|
|
|
| 455 |
|
|
/* Return nonzero value if arguments are unordered. */
|
| 456 |
|
|
# ifndef isunordered
|
| 457 |
|
|
# define isunordered(u, v) \
|
| 458 |
|
|
(__extension__ \
|
| 459 |
|
|
({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
|
| 460 |
|
|
fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
|
| 461 |
|
|
# endif
|
| 462 |
|
|
|
| 463 |
|
|
#endif
|
| 464 |
|
|
|
| 465 |
|
|
__END_DECLS
|
| 466 |
|
|
|
| 467 |
|
|
|
| 468 |
|
|
#endif /* math.h */
|
