Log gamma function
#include <math.h> double lgamma( double x ); double lgamma_r( double x, int* signgamp); float lgammaf( float x ); float lgammaf_r( float x, int* signgamp); long double lgammal( long double x ); long double lgammal_r( long double x, int* signgamp); extern int signgam;
The lgamma*() and lgamma*_r() functions return the natural log (ln) of the Γ function. These functions return ln|Γ(x)|, where Γ(x) is defined as follows:
The results converge when x is between 0.0 and 1.0. The Γ function has the property:
Γ(N) = Γ(N-1)×N
The lgamma* functions compute the log because the Γ function grows very quickly.
The lgamma() and lgammaf() functions use the external integer signgam to return the sign of Γ(x), while lgamma_r() and lgammaf_r() use the user-allocated space addressed by signgamp.
g = signgam * exp( lgamma( x ));
to compute g = Γ(x)'. Instead, compute lgamma() first:
lg = lgamma(x); g = signgam * exp( lg );
Note that Γ(x) must overflow when x is large enough, underflow when -x is large enough, and generate a division by 0 exception at the singularities x a nonpositive integer.
To check for error situations, use feclearexcept() and fetestexcept(). For example:
ln|Γ(x)|
If: | These functions return: | Errors: |
---|---|---|
x is 1.0 or 2.0 | 0.0 | — |
x is a non-positive integer | Inf | FE_DIVBYZERO |
x is ±Inf | Inf | — |
x is NaN | NaN | — |
The correct value would cause overflow | Inf | FE_OVERFLOW |
These functions raise FE_INEXACT if the FPU reports that the result can't be exactly represented as a floating-point number.
#include <stdio.h> #include <fenv.h> #include <inttypes.h> #include <math.h> #include <stdlib.h> int main(int argc, char** argv) { double a, b; int except_flags; a = 0.5; feclearexcept(FE_ALL_EXCEPT); b = lgamma(a); except_flags = fetestexcept(FE_ALL_EXCEPT); if(except_flags) { /* An error occurred; handle it appropriately. */ } printf("lgamma(%f) = %f \n", a, b); return EXIT_SUCCESS; }
produces the output:
lgamma(0.500000) = 0.572365 0
lgamma(), lgammaf(), and lgammal() are ANSI, POSIX 1003.1; lgamma_r(), lgammaf_r(), and lgammal_r() are QNX Neutrino
Safety: | |
---|---|
Cancellation point | No |
Interrupt handler | No |
Signal handler | No |
Thread | Yes |