lgamma, lgammaf, lgammal

C

Language

Headers

Type support

Program utilities

Variadic function support

Error handling

Dynamic memory management

Date and time utilities

Strings library

Algorithms

Numerics

Input/output support

Localization support

Atomic operations (C11)

Thread support (C11)

Technical Specifications

Numerics

Common mathematical functions

Floating-point environment

Complex number arithmetics

Random number generation

Type-generic math

Common mathematical functions

Functions
Basic operations
abslabsllabsimaxabs (C99) fabs divldivlldivimaxdiv (C99) fmod	remainder (C99) remquo (C99) fma (C99) fmax (C99) fmin (C99) fdim (C99) nannanfnanl (C99)(C99)(C99)
Exponential functions
exp exp2 (C99) expm1 (C99)	log log10 log1p (C99) log2 (C99)
Power functions
sqrt cbrt (C99)	hypot (C99) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C99) acosh (C99) atanh (C99)
Error and gamma functions
erf (C99) erfc (C99)	lgamma (C99) tgamma (C99)
Nearest integer floating point operations
ceil floor roundlroundllround (C99)(C99)(C99)	trunc (C99) nearbyint (C99) rintlrintllrint (C99)(C99)(C99)
Floating point manipulation functions
ldexp scalbnscalbln (C99)(C99) ilogb (C99) logb (C99)	frexp modf nextafternexttoward (C99)(C99) copysign (C99)
Classification
fpclassify (C99) isfinite (C99) isinf (C99) isnan (C99) isnormal (C99) signbit (C99)	isgreater (C99) isgreaterequal (C99) isless (C99) islessequal (C99) islessgreater (C99) isunordered (C99)
Types
div_tldiv_tlldiv_timaxdiv_t (C99)(C99)	float_tdouble_t (C99)(C99)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C99)(C99) FP_FAST_FMAFFP_FAST_FMAFP_FAST_FMAL (C99)(C99)(C99) math_errhandlingMATH_ERRNOMATH_ERRNOEXCEPT (C99)(C99)(C99)	INFINITY (C99) NAN (C99) FP_ILOGB0FP_ILOGBNAN (C99)(C99) FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99)

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|
0targ-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

tgammatgammaftgammal (C99)(C99)(C99)

computes gamma function (function)

External links

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