# Manual Pages  — LGAMMA

### NAME

lgamma, lgamma_r, lgammaf, lgammaf_r, lgammal, lgammal_r, gamma, gamma_r, gammaf, gammaf_r, tgamma, tgammaf, tgammal, – log gamma functions, gamma function

### LIBRARY

Math Library (libm, -lm)

### SYNOPSIS

`#include <math.h>`

extern int signgam;

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);

double
gamma(double x);

double
gamma_r(double x, int *signgamp);

float
gammaf(float x);

float
gammaf_r(float x, int *signgamp);

long double
tgamma(double x);

float
tgammaf(float x);

long double
tgammal(long double x);

### DESCRIPTION

lgamma(x), lgammaf(x), and lgammal(x) return ln|Γ(x)| where
```Γ(x) = ∫0∞ tx-1 e-t dt  for x > 0 and
Γ(x) = π/(Γ(1-x)sin(πx))        for x < 1.
```
return ln|Γ(x)|. The external integer signgam returns the sign of Γ(x).

lgamma_r(x, signgamp), lgammaf_r(x, signgamp), and lgammal_r(x, signgamp) provide the same functionality as lgamma(x), lgammaf(x), and lgammal(x), but the caller must provide an integer to store the sign of Γ(x).

The tgamma(x), tgammaf(x), and tgammal(x) functions return Γ(x), with no effect on signgam.

gamma(), gammaf(), gamma_r(), and gammaf_r() are deprecated aliases for lgamma(), lgammaf(), lgamma_r(), and lgammaf_r(), respectively.

### IDIOSYNCRASIES

Do not use the expression "signgam*exp(lgamma(x))" to compute g := Γ(x). Instead use a program like this (in C):
```lg = lgamma(x); g = signgam*exp(lg);
```

Only after lgamma() or lgammaf() has returned can signgam be correct.

For arguments in its range, tgamma() is preferred, as for positive arguments it is accurate to within one unit in the last place. Exponentiation of lgamma() will lose up to 10 significant bits.

### RETURN VALUES

gamma(), gammaf(), gammal(), gamma_r(), gammaf_r(), gammal_r(), lgamma(), lgammaf(), lgammal(), lgamma_r(), lgammaf_r(), and lgammal_r() return appropriate values unless an argument is out of range. Overflow will occur for sufficiently large positive values, and non-positive integers. For large non-integer negative values, tgamma() will underflow.

### BUGS

To conform with newer C/C++ standards, a stub implementation for tgammal was committed to the math library, where tgammal is mapped to tgamma. Thus, the numerical accuracy is at most that of the 53-bit double precision implementation.

### STANDARDS

The lgamma(), lgammaf(), lgammal(), tgamma(), tgammaf(), and tgammal() functions are expected to conform to ISO/IEC 9899:1999 ("ISO C99").

### HISTORY

The lgamma() function appeared in BSD 4.3 . The gamma() function appeared in BSD 4.4 as a function which computed Γ(x). This version was used in FreeBSD 1.1 . The name gamma() was originally dedicated to the lgamma() function, and that usage was restored by switching to Sun's fdlibm in FreeBSD 1.1.5 . The tgamma() function appeared in FreeBSD 5.0 .

 LGAMMA (3) December 8, 2017