---
name: "lgamma"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/lgamma"
---

# lgamma(3)

log gamma function

## NAME

lgamma, lgammaf, lgammal, lgamma\_r, lgammaf\_r, lgammal\_r, signgam - log gamma function

## LIBRARY

Math library (*libm*, *-lm*)

## SYNOPSIS

```
#include <math.h>
```

**double lgamma(double** *x***);** **float lgammaf(float** *x***);** **long double lgammal(long double** *x***);**

**double lgamma\_r(double** *x***, int \****signp***);** **float lgammaf\_r(float** *x***, int \****signp***);** **long double lgammal\_r(long double** *x***, int \****signp***);**

**extern int** *signgam***;**

Feature Test Macro Requirements for glibc (see [**feature\_test\_macros**(7)](/feature_test_macros/7.md)):

```
lgamma():
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

**lgammaf**(), **lgammal**():

```
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

**lgamma\_r**(), **lgammaf\_r**(), **lgammal\_r**():

```
    /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

*signgam*:

```
    _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

## DESCRIPTION

For the definition of the Gamma function, see [**tgamma**(3)](/tgamma/3.md).

The **lgamma**(), **lgammaf**(), and **lgammal**() functions return the natural logarithm of the absolute value of the Gamma function. The sign of the Gamma function is returned in the external integer *signgam* declared in *\<math.h\>*. It is 1 when the Gamma function is positive or zero, -1 when it is negative.

Since using a constant location *signgam* is not thread-safe, the functions **lgamma\_r**(), **lgammaf\_r**(), and **lgammal\_r**() have been introduced; they return the sign via the argument *signp*.

## RETURN VALUE

On success, these functions return the natural logarithm of Gamma(x).

If *x* is a NaN, a NaN is returned.

If *x* is 1 or 2, +0 is returned.

If *x* is positive infinity or negative infinity, positive infinity is returned.

If *x* is a nonpositive integer, a pole error occurs, and the functions return +**HUGE\_VAL**, +**HUGE\_VALF**, or +**HUGE\_VALL**, respectively.

If the result overflows, a range error occurs, and the functions return **HUGE\_VAL**, **HUGE\_VALF**, or **HUGE\_VALL**, respectively, with the correct mathematical sign.

## ERRORS

See [**math\_error**(7)](/math_error/7.md) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

- Pole error: *x* is a nonpositive integer

  *errno* is set to **ERANGE** (but see BUGS). A divide-by-zero floating-point exception (**FE\_DIVBYZERO**) is raised.

- Range error: result overflow

  *errno* is set to **ERANGE**. An overflow floating-point exception (**FE\_OVERFLOW**) is raised.

## STANDARDS

- **lgamma**() **lgammaf**() **lgammal**()

  C11, POSIX.1-2008.

- *signgam*

  POSIX.1-2008.

- **lgamma\_r**() **lgammaf\_r**() **lgammal\_r**()

  None.

## HISTORY

- **lgamma**() **lgammaf**() **lgammal**()

  C99, POSIX.1-2001.

- *signgam*

  POSIX.1-2001.

- **lgamma\_r**() **lgammaf\_r**() **lgammal\_r**()

  None.

## BUGS

In glibc 2.9 and earlier, when a pole error occurs, *errno* is set to **EDOM**; instead of the POSIX-mandated **ERANGE**. Since glibc 2.10, glibc does the right thing.

## SEE ALSO

[**tgamma**(3)](/tgamma/3.md)