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@node Math

@chapter Mathematical Functions (@file{math.h})

This chapter groups a wide variety of mathematical functions.  The

corresponding definitions and declarations are in @file{math.h}.

Two definitions from @file{math.h} are of particular interest.

@enumerate

@item

The representation of infinity as a @code{double} is defined as

@code{HUGE_VAL}; this number is returned on overflow by many functions.

@item

The structure @code{exception} is used when you write customized error

handlers for the mathematical functions.  You can customize error

handling for most of these functions by defining your own version of

@code{matherr}; see the section on @code{matherr} for details.

@end enumerate

@cindex system calls

@cindex support subroutines

@cindex stubs

@cindex OS stubs

Since the error handling code calls @code{fputs}, the mathematical

subroutines require stubs or minimal implementations for the same list

of OS subroutines as @code{fputs}: @code{close}, @code{fstat},

@code{isatty}, @code{lseek}, @code{read}, @code{sbrk}, @code{write}.

@xref{syscalls,,System Calls, libc.info, The Red Hat newlib C Library},

for a discussion and for sample minimal implementations of these support

subroutines.

Alternative declarations of the mathematical functions, which exploit

specific machine capabilities to operate faster---but generally have

less error checking and may reflect additional limitations on some

machines---are available when you include @file{fastmath.h} instead of

@file{math.h}.

@menu

* version::     Version of library

* acos::        Arccosine

* acosh::       Inverse hyperbolic cosine

* asin::        Arcsine

* asinh::       Inverse hyperbolic sine

* atan::        Arctangent

* atan2::       Arctangent of y/x

* atanh::       Inverse hyperbolic tangent

* jN::          Bessel functions  (jN, yN)

* cbrt::        Cube root

* copysign::    Sign of Y, magnitude of X

* cosh::        Hyperbolic cosine

* erf::         Error function  (erf, erfc)

* exp::         Exponential

* expm1::       Exponential of x, - 1

* fabs::        Absolute value (magnitude)

* floor::       Floor and ceiling  (floor, ceil)

* fmod::        Floating-point remainder (modulo)

* frexp::       Split floating-point number

* gamma::       Logarithmic gamma function

* hypot::       Distance from origin

* ilogb::       Get exponent

* infinity::    Floating infinity

* isnan::       Check type of number

* ldexp::       Load exponent

* log::         Natural logarithms

* log10::       Base 10 logarithms

* log1p::       Log of 1 + X

* matherr::     Modifiable math error handler

* modf::        Split fractional and integer parts

* nan::         Floating Not a Number

* nextafter::   Get next representable number

* pow::         X to the power Y

* remainder::   remainder of X divided by Y

* scalbn::      scalbn

* sin::         Sine or cosine (sin, cos)

* sinh::        Hyperbolic sine

* sqrt::        Positive square root

* tan::         Tangent

* tanh::        Hyperbolic tangent

@end menu

@page

@node version

@section Version of library

There are four different versions of the math library routines: IEEE,

POSIX, X/Open, or SVID.  The version may be selected at runtime by

setting the global variable @code{_LIB_VERSION}, defined in

@file{math.h}.  It may be set to one of the following constants defined

in @file{math.h}: @code{_IEEE_}, @code{_POSIX_}, @code{_XOPEN_}, or

@code{_SVID_}.  The @code{_LIB_VERSION} variable is not specific to any

thread, and changing it will affect all threads.

The versions of the library differ only in how errors are handled.

In IEEE mode, the @code{matherr} function is never called, no warning

messages are printed, and @code{errno} is never set.

In POSIX mode, @code{errno} is set correctly, but the @code{matherr}

function is never called and no warning messages are printed.

In X/Open mode, @code{errno} is set correctly, and @code{matherr} is

called, but warning message are not printed.

In SVID mode, functions which overflow return 3.40282346638528860e+38,

the maximum single-precision floating-point value, rather than infinity.

Also, @code{errno} is set correctly, @code{matherr} is called, and, if

@code{matherr} returns 0, warning messages are printed for some errors.

For example, by default @samp{log(-1.0)} writes this message on standard

error output:

@example

log: DOMAIN error

@end example

The library is set to X/Open mode by default.

@page

@include math/wacos.def

@page

@include math/wacosh.def

@page

@include math/wasin.def

@page

@include math/sasinh.def

@page

@include math/satan.def

@page

@include math/watan2.def

@page

@include math/watanh.def

@page

@include math/wj0.def

@page

@include common/scbrt.def

@page

@include common/scopysign.def

@page

@include math/wcosh.def

@page

@include math/serf.def

@page

@include math/wexp.def

@page

@include common/sexpm1.def

@page

@include math/sfabs.def

@page

@include math/sfloor.def

@page

@include math/wfmod.def

@page

@include math/sfrexp.def

@page

@include math/wgamma.def

@page

@include math/whypot.def

@page

@include common/silogb.def

@page

@include common/sinfinity.def

@page

@include common/sisnan.def

@page

@include math/sldexp.def

@page

@include math/wlog.def

@page

@include math/wlog10.def

@page

@include common/slog1p.def

@page

@include common/smatherr.def

@page

@include common/smodf.def

@page

@include common/snan.def

@page

@include common/snextafter.def

@page

@include math/wpow.def

@page

@include math/wremainder.def

@page

@include common/sscalbn.def

@page

@include math/wsqrt.def

@page

@include math/ssin.def

@page

@include math/wsinh.def

@page

@include math/stan.def

@page

@include math/stanh.def