This file documents an ANSI-C conforming mathematical subroutine
library.
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LIBM
****
* Menu:
* Math:: The mathematical functions (`math.h').
* Reentrancy:: The functions in libm are not reentrant by default.
* Index::
1 Mathematical Functions (`math.h')
***********************************
This chapter groups a wide variety of mathematical functions. The corresponding definitions and declarations are in `math.h'. Two definitions from `math.h' are of particular interest.
1. The representation of infinity as a `double' is defined as
`HUGE_VAL'; this number is returned on overflow by many functions.
2. The structure `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 `matherr'; see the section on `matherr' for details.
Since the error handling code calls `fputs', the mathematical
subroutines require stubs or minimal implementations for the same list
of OS subroutines as `fputs': `close', `fstat', `isatty', `lseek',
`read', `sbrk', `write'. *Note System Calls: (libc.info)syscalls, 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 `fastmath.h' instead of
`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
1.1 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 `_LIB_VERSION', defined in `math.h'. It may be set to one of the following constants defined in `math.h': `_IEEE_', `_POSIX_', `_XOPEN_', or `_SVID_'. The `_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 `matherr' function is never called, no warning
messages are printed, and `errno' is never set.
In POSIX mode, `errno' is set correctly, but the `matherr' function
is never called and no warning messages are printed.
In X/Open mode, `errno' is set correctly, and `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, `errno' is set correctly, `matherr'
is called, and, if `matherr' returns 0, warning messages are printed
for some errors. For example, by default `log(-1.0)' writes this
message on standard error output:
log: DOMAIN error
The library is set to X/Open mode by default.
2 Reentrancy Properties of `libm'
*********************************
When a libm function detects an exceptional case, `errno' may be set, the `matherr' function may be called, and a error message may be written to the standard error stream. This behavior may not be reentrant.
With reentrant C libraries like the Red Hat newlib C library,
`errno' is a macro which expands to the per-thread error value. This
makes it thread safe.
When the user provides his own `matherr' function it must be
reentrant for the math library as a whole to be reentrant.
In normal debugged programs, there are usually no math subroutine
errors--and therefore no assignments to `errno' and no `matherr' calls;
in that situation, the math functions behave reentrantly.
Index
*****