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%2Ftgamma.html | 83 ++++++++++++++++++++++++++++++++++ 1 file changed, 83 insertions(+) create mode 100644 devdocs/c/numeric%2Fmath%2Ftgamma.html (limited to 'devdocs/c/numeric%2Fmath%2Ftgamma.html') diff --git a/devdocs/c/numeric%2Fmath%2Ftgamma.html b/devdocs/c/numeric%2Fmath%2Ftgamma.html new file mode 100644 index 00000000..5b7fec6f --- /dev/null +++ b/devdocs/c/numeric%2Fmath%2Ftgamma.html @@ -0,0 +1,83 @@ +

tgamma, tgammaf, tgammal

Defined in header <math.h> 
float       tgammaf( float arg );
+		 (1) (since C99) 
double      tgamma( double arg );
+		 (2) (since C99) 
long double tgammal( long double arg );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define tgamma( arg )
+		 (4) (since C99)
+1-3) Computes the gamma function of arg.
+4) Type-generic macro: If arg has type long double, tgammal is called. Otherwise, if arg has integer type or the type double, tgamma is called. Otherwise, tgammaf is called.

Parameters

+ +
arg - floating point value

Return value

If no errors occur, the value of the gamma function of arg, that is \(\Gamma(\mathtt{arg}) = \displaystyle\int_0^\infty\!\! t^{\mathtt{arg}-1} e^{-t}\, dt\)∫∞0targ-1 e-t dt, is returned.

+

If a domain error occurs, an implementation-defined value (NaN where supported) 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.

+

If a range error due to underflow occurs, the correct value (after rounding) 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 or a domain error may occur.

+

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

+

Notes

If arg is a natural number, tgamma(arg) is the factorial of arg - 1. Many implementations calculate the exact integer-domain factorial if the argument is a sufficiently small integer.

+

For IEEE-compatible type double, overflow happens if 0 < x < 1/DBL_MAX or if x > 171.7.

+

POSIX requires that a pole error occurs if the argument is zero, but a domain error occurs when the argument is a negative integer. It also specifies that in future, domain errors may be replaced by pole errors for negative integer arguments (in which case the return value in those cases would change from NaN to ±∞).

+

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("tgamma(10) = %f, 9!=%f\n", tgamma(10), 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9.0);
+    printf("tgamma(0.5) = %f, sqrt(pi) = %f\n", tgamma(0.5), sqrt(acos(-1)));
+ 
+    // special values
+    printf("tgamma(+Inf) = %f\n", tgamma(INFINITY));
+ 
+    // error handling
+    errno = 0; feclearexcept(FE_ALL_EXCEPT);
+    printf("tgamma(-1) = %f\n", tgamma(-1));
+    if (errno == ERANGE)
+        perror("    errno == ERANGE");
+    else
+        if (errno == EDOM)   perror("    errno == EDOM");
+    if (fetestexcept(FE_DIVBYZERO))
+        puts("    FE_DIVBYZERO raised");
+    else if (fetestexcept(FE_INVALID))
+        puts("    FE_INVALID raised");
+}

Possible output:

+
tgamma(10) = 362880.000000, 9!=362880.000000
+tgamma(0.5) = 1.772454, sqrt(pi) = 1.772454
+tgamma(+Inf) = inf
+tgamma(-1) = nan
+    errno == EDOM: Numerical argument out of domain
+    FE_INVALID raised

References

See also

+ +
+
(C99)(C99)(C99)
 computes natural (base-e) logarithm of the gamma function
(function)
C++ documentation for tgamma
+ +
+Weisstein, Eric W. "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/tgamma +

+
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