lgamma, lgammaf, lgammal
<math.h>
<tgmath.h>
lgammal is called. Otherwise, if arg has integer type or the type double, lgamma is called. Otherwise, lgammaf is called.Contents
[edit] Parameters
[edit] Return value
If no errors occur, the value of the logarithm of the gamma function of arg, that is \(\log_{e}|{\int_0^\infty t^{arg-1} e^{-t} \mathsf{d}t}|\)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.
[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 <errno.h> #include <fenv.h> #include <float.h> #include <math.h> #include <stdio.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)); const 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
- C23 standard (ISO/IEC 9899:2024):
- 7.12.8.3 The lgamma functions (p: TBD)
- 7.25 Type-generic math <tgmath.h> (p: TBD)
- F.10.5.3 The lgamma functions (p: TBD)
- C17 standard (ISO/IEC 9899:2018):
- 7.12.8.3 The lgamma functions (p: 182)
- 7.25 Type-generic math <tgmath.h> (p: 272-273)
- F.10.5.3 The lgamma functions (p: 383)
- 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)