# lgamma, lgammaf, lgammal

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float lgammaf( float arg ); | (1) | (since C99)
double lgamma( double arg ); | (2) | (since C99)
long double lgammal( long double arg ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define lgamma( arg ) | (4) | (since C99)

1-3) Computes the natural logarithm of the absolute value of the gamma function of `arg`.
4) Type-generic macro: If `arg` has type long double, `lgammal` is called. Otherwise, if `arg` has integer type or the type double, `lgamma` is called. Otherwise, `lgammaf` is called.

### Parameters

arg | - | floating point value

### Return value

If no errors occur, the value of the logarithm of the gamma function of `arg`, that is log
e|∫∞
0 t arg-1
e-t dt|, is returned.

If a pole error occurs, `+HUGE_VAL`, `+HUGE_VALF`, or `+HUGE_VALL` is returned.

If a range error due to overflow occurs, `±HUGE_VAL`, `±HUGE_VALF`, or `±HUGE_VALL` is returned.

### Error handling

Errors are reported as specified in math_errhandling.

If `arg` is zero or is an integer less than zero, a pole error may occur.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- If the argument is 1, +0 is returned
- If the argument is 2, +0 is returned
- If the argument is ±0, +∞ is returned and FE_DIVBYZERO is raised
- If the argument is a negative integer, +∞ is returned and FE_DIVBYZERO is raised
- If the argument is ±∞, +∞ is returned.
- If the argument is NaN, NaN is returned

### Notes

If `arg` is a natural number, lgamma(arg) is the logarithm of the factorial of `arg-1`.

The POSIX version of lgamma is not thread-safe: each execution of the function stores the sign of the gamma function of `arg` in the static external variable `signgam`. Some implementations provide `lgamma_r`, which takes a pointer to user-provided storage for singgam as the second parameter, and is thread-safe.

There is a non-standard function named `gamma` in various implementations, but its definition is inconsistent. For example, glibc and 4.2BSD version of `gamma` executes `lgamma`, but 4.4BSD version of `gamma` executes `tgamma`.

### Example

Run this code

    #include <stdio.h>
    #include <math.h>
    #include <float.h>
    #include <errno.h>
    #include <fenv.h>
    #pragma STDC FENV_ACCESS ON
    int main(void)
    {
        printf("lgamma(10) = %f, log(9!)=%f\n", lgamma(10), log(2*3*4*5*6*7*8*9));
        double pi = acos(-1);
        printf("lgamma(0.5) = %f, log(sqrt(pi)) = %f\n", log(sqrt(pi)), lgamma(0.5));
        // special values
        printf("lgamma(1) = %f\n", lgamma(1));
        printf("lgamma(+Inf) = %f\n", lgamma(INFINITY));
        //error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("lgamma(0) = %f\n", lgamma(0));
        if(errno == ERANGE) perror("    errno == ERANGE");
        if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");
    }

Possible output:

    lgamma(10) = 12.801827, log(9!)=12.801827
    lgamma(0.5) = 0.572365, log(sqrt(pi)) = 0.572365
    lgamma(1) = 0.000000
    lgamma(+Inf) = inf
    lgamma(0) = inf
        errno == ERANGE: Numerical result out of range
        FE_DIVBYZERO raised

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.8.3 The lgamma functions (p: 250)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.5.3 The lgamma functions (p: 525)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.8.3 The lgamma functions (p: 231)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.5.3 The lgamma functions (p: 462)

### See also

tgamma tgammaf tgammal (C99)(C99)(C99) | computes gamma function (function)
C++ documentation for lgamma

### External links

Weisstein, Eric W. "Log Gamma Function." From MathWorld--A Wolfram Web Resource.
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