@node Math
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@node Math
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@chapter Mathematical Functions (@file{math.h})
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@chapter Mathematical Functions (@file{math.h})
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This chapter groups a wide variety of mathematical functions. The
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This chapter groups a wide variety of mathematical functions. The
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corresponding definitions and declarations are in @file{math.h}.
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corresponding definitions and declarations are in @file{math.h}.
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Two definitions from @file{math.h} are of particular interest.
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Two definitions from @file{math.h} are of particular interest.
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@enumerate
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@enumerate
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@item
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@item
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The representation of infinity as a @code{double} is defined as
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The representation of infinity as a @code{double} is defined as
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@code{HUGE_VAL}; this number is returned on overflow by many functions.
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@code{HUGE_VAL}; this number is returned on overflow by many functions.
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@item
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@item
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The structure @code{exception} is used when you write customized error
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The structure @code{exception} is used when you write customized error
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handlers for the mathematical functions. You can customize error
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handlers for the mathematical functions. You can customize error
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handling for most of these functions by defining your own version of
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handling for most of these functions by defining your own version of
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@code{matherr}; see the section on @code{matherr} for details.
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@code{matherr}; see the section on @code{matherr} for details.
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@end enumerate
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@end enumerate
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@cindex system calls
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@cindex system calls
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@cindex support subroutines
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@cindex support subroutines
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@cindex stubs
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@cindex stubs
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@cindex OS stubs
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@cindex OS stubs
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Since the error handling code calls @code{fputs}, the mathematical
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Since the error handling code calls @code{fputs}, the mathematical
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subroutines require stubs or minimal implementations for the same list
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subroutines require stubs or minimal implementations for the same list
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of OS subroutines as @code{fputs}: @code{close}, @code{fstat},
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of OS subroutines as @code{fputs}: @code{close}, @code{fstat},
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@code{isatty}, @code{lseek}, @code{read}, @code{sbrk}, @code{write}.
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@code{isatty}, @code{lseek}, @code{read}, @code{sbrk}, @code{write}.
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@xref{syscalls,,System Calls, libc.info, The Cygnus C Support Library},
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@xref{syscalls,,System Calls, libc.info, The Cygnus C Support Library},
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for a discussion and for sample minimal implementations of these support
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for a discussion and for sample minimal implementations of these support
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subroutines.
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subroutines.
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Alternative declarations of the mathematical functions, which exploit
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Alternative declarations of the mathematical functions, which exploit
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specific machine capabilities to operate faster---but generally have
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specific machine capabilities to operate faster---but generally have
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less error checking and may reflect additional limitations on some
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less error checking and may reflect additional limitations on some
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machines---are available when you include @file{fastmath.h} instead of
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machines---are available when you include @file{fastmath.h} instead of
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@file{math.h}.
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@file{math.h}.
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@menu
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@menu
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* version:: Version of library
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* version:: Version of library
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* acos:: Arccosine
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* acos:: Arccosine
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* acosh:: Inverse hyperbolic cosine
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* acosh:: Inverse hyperbolic cosine
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* asin:: Arcsine
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* asin:: Arcsine
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* asinh:: Inverse hyperbolic sine
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* asinh:: Inverse hyperbolic sine
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* atan:: Arctangent
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* atan:: Arctangent
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* atan2:: Arctangent of y/x
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* atan2:: Arctangent of y/x
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* atanh:: Inverse hyperbolic tangent
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* atanh:: Inverse hyperbolic tangent
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* jN:: Bessel functions (jN, yN)
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* jN:: Bessel functions (jN, yN)
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* cbrt:: Cube root
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* cbrt:: Cube root
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* copysign:: Sign of Y, magnitude of X
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* copysign:: Sign of Y, magnitude of X
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* cosh:: Hyperbolic cosine
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* cosh:: Hyperbolic cosine
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* erf:: Error function (erf, erfc)
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* erf:: Error function (erf, erfc)
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* exp:: Exponential
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* exp:: Exponential
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* expm1:: Exponential of x, - 1
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* expm1:: Exponential of x, - 1
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* fabs:: Absolute value (magnitude)
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* fabs:: Absolute value (magnitude)
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* floor:: Floor and ceiling (floor, ceil)
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* floor:: Floor and ceiling (floor, ceil)
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* fmod:: Floating-point remainder (modulo)
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* fmod:: Floating-point remainder (modulo)
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* frexp:: Split floating-point number
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* frexp:: Split floating-point number
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* gamma:: Logarithmic gamma function
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* gamma:: Logarithmic gamma function
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* hypot:: Distance from origin
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* hypot:: Distance from origin
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* ilogb:: Get exponent
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* ilogb:: Get exponent
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* infinity:: Floating infinity
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* infinity:: Floating infinity
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* isnan:: Check type of number
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* isnan:: Check type of number
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* ldexp:: Load exponent
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* ldexp:: Load exponent
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* log:: Natural logarithms
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* log:: Natural logarithms
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* log10:: Base 10 logarithms
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* log10:: Base 10 logarithms
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* log1p:: Log of 1 + X
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* log1p:: Log of 1 + X
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* matherr:: Modifiable math error handler
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* matherr:: Modifiable math error handler
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* modf:: Split fractional and integer parts
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* modf:: Split fractional and integer parts
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* nan:: Floating Not a Number
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* nan:: Floating Not a Number
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* nextafter:: Get next representable number
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* nextafter:: Get next representable number
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* pow:: X to the power Y
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* pow:: X to the power Y
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* remainder:: remainder of X divided by Y
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* remainder:: remainder of X divided by Y
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* scalbn:: scalbn
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* scalbn:: scalbn
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* sin:: Sine or cosine (sin, cos)
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* sin:: Sine or cosine (sin, cos)
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* sinh:: Hyperbolic sine
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* sinh:: Hyperbolic sine
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* sqrt:: Positive square root
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* sqrt:: Positive square root
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* tan:: Tangent
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* tan:: Tangent
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* tanh:: Hyperbolic tangent
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* tanh:: Hyperbolic tangent
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@end menu
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@end menu
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@page
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@page
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@node version
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@node version
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@section Version of library
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@section Version of library
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There are four different versions of the math library routines: IEEE,
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There are four different versions of the math library routines: IEEE,
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POSIX, X/Open, or SVID. The version may be selected at runtime by
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POSIX, X/Open, or SVID. The version may be selected at runtime by
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setting the global variable @code{_LIB_VERSION}, defined in
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setting the global variable @code{_LIB_VERSION}, defined in
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@file{math.h}. It may be set to one of the following constants defined
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@file{math.h}. It may be set to one of the following constants defined
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in @file{math.h}: @code{_IEEE_}, @code{_POSIX_}, @code{_XOPEN_}, or
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in @file{math.h}: @code{_IEEE_}, @code{_POSIX_}, @code{_XOPEN_}, or
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@code{_SVID_}. The @code{_LIB_VERSION} variable is not specific to any
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@code{_SVID_}. The @code{_LIB_VERSION} variable is not specific to any
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thread, and changing it will affect all threads.
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thread, and changing it will affect all threads.
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The versions of the library differ only in how errors are handled.
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The versions of the library differ only in how errors are handled.
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In IEEE mode, the @code{matherr} function is never called, no warning
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In IEEE mode, the @code{matherr} function is never called, no warning
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messages are printed, and @code{errno} is never set.
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messages are printed, and @code{errno} is never set.
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In POSIX mode, @code{errno} is set correctly, but the @code{matherr}
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In POSIX mode, @code{errno} is set correctly, but the @code{matherr}
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function is never called and no warning messages are printed.
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function is never called and no warning messages are printed.
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In X/Open mode, @code{errno} is set correctly, and @code{matherr} is
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In X/Open mode, @code{errno} is set correctly, and @code{matherr} is
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called, but warning message are not printed.
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called, but warning message are not printed.
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In SVID mode, functions which overflow return 3.40282346638528860e+38,
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In SVID mode, functions which overflow return 3.40282346638528860e+38,
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the maximum single precision floating point value, rather than infinity.
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the maximum single precision floating point value, rather than infinity.
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Also, @code{errno} is set correctly, @code{matherr} is called, and, if
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Also, @code{errno} is set correctly, @code{matherr} is called, and, if
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@code{matherr} returns 0, warning messages are printed for some errors.
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@code{matherr} returns 0, warning messages are printed for some errors.
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For example, by default @samp{log(-1.0)} writes this message on standard
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For example, by default @samp{log(-1.0)} writes this message on standard
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error output:
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error output:
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@example
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@example
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log: DOMAIN error
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log: DOMAIN error
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@end example
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@end example
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The library is set to X/Open mode by default.
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The library is set to X/Open mode by default.
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@page
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@page
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@include math/wacos.def
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@include math/wacos.def
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@page
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@page
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@include math/wacosh.def
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@include math/wacosh.def
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@page
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@page
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@include math/wasin.def
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@include math/wasin.def
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@page
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@page
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@include math/sasinh.def
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@include math/sasinh.def
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@page
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@page
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@include math/satan.def
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@include math/satan.def
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@page
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@page
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@include math/watan2.def
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@include math/watan2.def
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@page
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@page
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@include math/watanh.def
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@include math/watanh.def
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@page
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@page
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@include math/wj0.def
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@include math/wj0.def
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@page
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@page
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@include math/wcosh.def
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@include math/wcosh.def
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@page
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@page
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@include math/serf.def
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@include math/serf.def
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@page
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@page
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@include math/wexp.def
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@include math/wexp.def
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@page
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@page
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@include math/sfabs.def
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@include math/sfabs.def
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@page
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@page
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@include math/sfloor.def
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@include math/sfloor.def
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@page
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@page
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@include math/wfmod.def
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@include math/wfmod.def
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@page
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@page
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@include math/sfrexp.def
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@include math/sfrexp.def
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@page
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@page
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@include math/wgamma.def
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@include math/wgamma.def
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@page
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@page
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@include math/whypot.def
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@include math/whypot.def
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@page
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@page
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@include math/sisnan.def
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@include math/sisnan.def
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@page
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@page
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@include math/sldexp.def
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@include math/sldexp.def
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@page
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@page
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@include math/wlog.def
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@include math/wlog.def
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@page
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@page
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@include math/wlog10.def
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@include math/wlog10.def
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@page
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@page
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@include math/wpow.def
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@include math/wpow.def
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@page
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@page
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@include math/wremainder.def
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@include math/wremainder.def
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@page
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@page
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@include math/wsqrt.def
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@include math/wsqrt.def
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@page
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@page
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@include math/ssin.def
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@include math/ssin.def
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@page
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@page
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@include math/wsinh.def
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@include math/wsinh.def
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@page
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@page
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@include math/stan.def
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@include math/stan.def
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@page
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@page
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@include math/stanh.def
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@include math/stanh.def
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