gamma, gammaf, lgamma, lgammaf, gamma_r, gammaf_r, lgamma_r, lgammaf_r, tgamma, and tgammaf—logarithmic and plain gamma functions #include <math.h>
double gamma(double x);
float gammaf(float x);
double lgamma(double x);
float lgammaf(float x);
double gamma_r(double x, int *signgamp);
float gammaf_r(float x, int *signgamp);
double lgamma_r(double x, int *signgamp);
float lgammaf_r(float x, int *signgamp);
double tgamma(double x);
float tgammaf(float x);
Description
gamma calculates
the natural logarithm of the gamma function of x. The gamma function
(exp(gamma(x))) is a generalization of factorial, and retains
the property that
exp(gamma(N)) is equivalent to N*exp(gamma(N-1)).
Accordingly, the results of the gamma function itself grow very
quickly. gamma is defined as
the natural log of the gamma function, rather than the gamma function
itself,
to extend the useful range of results representable.
The sign of the result is returned in the global variable signgam,
which is declared in math.h.
gammaf performs the same calculation as gamma, but uses and
returns float values.
lgamma and lgammaf are alternate names for gamma and
gammaf. The use of lgamma instead of gamma is a reminder
that these functions compute the log of the gamma function, rather
than the gamma function itself.
The functions gamma_r, gammaf_r, lgamma_r, and
lgammaf_r are just like gamma, gammaf, lgamma, and
lgammaf, respectively, but take an additional argument. This
additional argument is a pointer to an integer. This additional
argument is used to return the sign of the result, and the global
variable signgam is not used. These functions may be used for
reentrant calls (but they will still set the global variable errno
if an error occurs).
tgamma and tgammaf are the "true gamma" functions, returning
the gamma function of x–without a logarithm.
(They are apparently so named because of the prior existence of the old,
poorly-named gamma functions which returned the log of gamma up
through BSD 4.2.)
Returns
When x is a nonpositive integer, gamma returns HUGE_VAL
and errno is set to EDOM. If the result overflows, gamma
returns HUGE_VAL and errno is set to ERANGE.
You can modify this error treatment using matherr.
Portability
gamma nor gammaf is ANSI C. It is better not to use either
of these; use lgamma or tgamma instead.lgamma, lgammaf, tgamma, and tgammaf are nominally C standard
in terms of the base return values, although the matherr error-handling
is not standard, nor is the signgam global for lgamma.