TGAMMA(P) POSIX Programmer's Manual TGAMMA(P)NAME
tgamma, tgammaf, tgammal - compute gamma() function
SYNOPSIS
#include <math.h>
double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);
DESCRIPTION
These functions shall compute the gamma() function of x.
An application wishing to check for error situations should set errno
to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
functions. On return, if errno is non-zero or fetestexcept(FE_INVALID
| FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
occurred.
RETURN VALUE
Upon successful completion, these functions shall return Gamma( x).
If x is a negative integer, a domain error shall occur, and either a
NaN (if supported), or an implementation-defined value shall be
returned.
If the correct value would cause overflow, a range error shall occur
and tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL,
±HUGE_VALF, or ±HUGE_VALL, respectively, with the same sign as the cor‐
rect value of the function.
If x is NaN, a NaN shall be returned.
If x is +Inf, x shall be returned.
If x is ±0, a pole error shall occur, and tgamma(), tgammaf(), and
tgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respec‐
tively.
If x is -Inf, a domain error shall occur, and either a NaN (if sup‐
ported), or an implementation-defined value shall be returned.
ERRORS
These functions shall fail if:
Domain Error
The value of x is a negative integer, or x is -Inf.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
then errno shall be set to [EDOM]. If the integer expression
(math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid
floating-point exception shall be raised.
Pole Error
The value of x is zero.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
then errno shall be set to [ERANGE]. If the integer expression
(math_errhandling & MATH_ERREXCEPT) is non-zero, then the divide-by-
zero floating-point exception shall be raised.
Range Error
The value overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
then errno shall be set to [ERANGE]. If the integer expression
(math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow
floating-point exception shall be raised.
The following sections are informative.
EXAMPLES
None.
APPLICATION USAGE
For IEEE Std 754-1985 double, overflow happens when 0 < x < 1/DBL_MAX,
and 171.7 < x.
On error, the expressions (math_errhandling & MATH_ERRNO) and
(math_errhandling & MATH_ERREXCEPT) are independent of each other, but
at least one of them must be non-zero.
RATIONALE
This function is named tgamma() in order to avoid conflicts with the
historical gamma() and lgamma() functions.
FUTURE DIRECTIONS
It is possible that the error response for a negative integer argument
may be changed to a pole error and a return value of ±Inf.
SEE ALSOfeclearexcept() , fetestexcept() , lgamma() , the Base Definitions vol‐
ume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Condi‐
tions for Mathematical Functions, <math.h>
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group. In the
event of any discrepancy between this version and the original IEEE and
The Open Group Standard, the original IEEE and The Open Group Standard
is the referee document. The original Standard can be obtained online
at http://www.opengroup.org/unix/online.html .
IEEE/The Open Group 2003 TGAMMA(P)
