From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fmath%2Flgamma.html | 85 ++++++++++++++++++++++++++++++++++ 1 file changed, 85 insertions(+) create mode 100644 devdocs/c/numeric%2Fmath%2Flgamma.html (limited to 'devdocs/c/numeric%2Fmath%2Flgamma.html') diff --git a/devdocs/c/numeric%2Fmath%2Flgamma.html b/devdocs/c/numeric%2Fmath%2Flgamma.html new file mode 100644 index 00000000..5dbfcbd3 --- /dev/null +++ b/devdocs/c/numeric%2Fmath%2Flgamma.html @@ -0,0 +1,85 @@ +

lgamma, lgammaf, lgammal

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 \(\log_{e}|{\int_0^\infty t^{arg-1} e^{-t} \mathsf{d}t}|\)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.

+

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),

+

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));
+    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

References

See also

+ +
+
(C99)(C99)(C99)
 computes gamma function
(function)
C++ documentation for lgamma
+ +
+Weisstein, Eric W. "Log Gamma Function." From MathWorld — A Wolfram Web Resource.
+

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/math/lgamma +

+
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