lgamma, lgammaf, lgammal
Defined in header <math.h>
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(1) | (since C99) |
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(2) | (since C99) |
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(3) | (since C99) |
Defined in header <tgmath.h>
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(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 loge|∫∞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
#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 (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 (p: 335-337)
- F.9.5.3 The lgamma functions (p: 462)
See also
(C99)(C99)(C99) |
computes gamma function (function) |
External links
Weisstein, Eric W. "Log Gamma Function."
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