import newlib-2000-02-17 snapshot

newlib/libm/math/math.tex

@@ -0,0 +1,199 @@
+@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 Cygnus C Support 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 math/wcosh.def
+
+@page
+@include math/serf.def
+
+@page
+@include math/wexp.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 math/sisnan.def
+
+@page
+@include math/sldexp.def
+
+@page
+@include math/wlog.def
+
+@page
+@include math/wlog10.def
+
+@page
+@include math/wpow.def
+
+@page
+@include math/wremainder.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