lgamma, lgammaf, lgammal

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Common mathematical functions
Basic operations
Exponential functions
Power functions
Trigonometric and hyperbolic functions
Error and gamma functions
Nearest integer floating point operations
Floating point manipulation functions
Macro constants
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.


[edit] Parameters

arg - floating point value

[edit] Return value

If no errors occur, the value of the logarithm of the gamma function of arg, that is log
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.

[edit] 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

[edit] 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.

[edit] Example

#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
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

[edit] References

  • C11 standard (ISO/IEC 9899:2011):
  • 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):
  • The lgamma functions (p: 231)
  • 7.22 Type-generic math <tgmath.h> (p: 335-337)
  • F.9.5.3 The lgamma functions (p: 462)

[edit] See also

computes gamma function
C++ documentation for lgamma

[edit] External links

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