IEEE Std 1003.1, 2004 Edition

Copyright © 2001-2004 The IEEE and The Open Group, All Rights reserved.

tgamma, tgammaf, tgammal - compute gamma() function

#include <math.h>

double tgamma(doublex);

float tgammaf(floatx);

long double tgammal(long doublex);

^{[CX]}The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of IEEE Std 1003.1-2001 defers to the ISO C standard.These functions shall compute the

gamma() function ofx.An application wishing to check for error situations should set

errnoto zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrnois non-zero orfetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

Upon successful completion, these functions shall return

Gamma(x).If

xis a negative integer, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.If the correct value would cause overflow, a range error shall occur and

tgamma(),tgammaf(), andtgammal() shall return ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL, respectively, with the same sign as the correct value of the function.

^{[MX]}Ifxis NaN, a NaN shall be returned.If

xis +Inf,xshall be returned.If

xis ±0, a pole error shall occur, andtgamma(),tgammaf(), andtgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively.If

xis -Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.

These functions shall fail if:

- Domain Error
- The value of
xis a negative integer,^{[MX]}orxis -Inf.If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then

errnoshall be set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised.- Pole Error
^{[MX]}The value ofxis zero.If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then

errnoshall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the divide-by-zero floating-point exception shall be raised.

- Range Error
- The value overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then

errnoshall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

None.

For IEEE Std 754-1985

double, overflow happens when 0 <x< 1/DBL_MAX, and 171.7 <x.On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

This function is named

tgamma() in order to avoid conflicts with the historicalgamma() andlgamma() functions.

It is possible that the error response for a negative integer argument may be changed to a pole error and a return value of ±Inf.

feclearexcept(),fetestexcept(),lgamma(), the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions,<math.h>

First released in Issue 6. Derived from the ISO/IEC 9899:1999 standard.

IEEE Std 1003.1-2001/Cor 1-2002, item XSH/TC1/D6/65 is applied, correcting the third paragraph in the RETURN VALUE section.

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