IEEE Std 1003.1-2008, 2016 Edition

Copyright © 2001-2016 The IEEE and The Open Group

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 POSIX.1-2008 defers to the ISO C standard.These functions shall compute Γ(

x) where Γ(x) is defined as_{}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 the gamma of

x.If

xis a negative integer, a^{[CX]}domain error may occur and either a NaN (if supported) or an implementation-defined value shall be returned.^{[MX]}On systems that support the IEC 60559 Floating-Point option, a domain error shall occur and a NaN shall be returned.If

xis ±0,tgamma(),tgammaf(), andtgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively.^{[MX]}On systems that support the IEC 60559 Floating-Point option, a pole error shall occur; otherwise, a^{[CX]}pole error may occur.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.If the correct value would cause underflow,

^{[MXX]}and is not representable, a range error may occur, andtgamma(),tgammaf(), andtgammal() shall return^{[MXX]}0.0, or (if IEC 60559 Floating-Point is not supported) an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

^{[MXX]}If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.If

xis subnormal and 1/xis representable, 1/xshould be returned.

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

xis +Inf,xshall be returned.If

xis -Inf, a domain error shall occur, and a NaN shall be returned.

These functions shall fail if:

- Domain Error
^{[MX]}The value ofxis a negative integer, orxis -Inf.If the integer expression (

math_errhandling& MATH_ERRNO) is non-zero, thenerrnoshall 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, thenerrnoshall 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, thenerrnoshall be set to [ERANGE]. If the integer expression (math_errhandling& MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.These functions may fail if:

- Domain Error
- The value of
xis a negative integer.If the integer expression (

math_errhandling& MATH_ERRNO) is non-zero, thenerrnoshall 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
- The value of
xis zero.If the integer expression (

math_errhandling& MATH_ERRNO) is non-zero, thenerrnoshall 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 result underflows.
If the integer expression (

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

None.

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,lgammaXBD

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.

ISO/IEC 9899:1999 standard, Technical Corrigendum 2 #52 (SD5-XSH-ERN-85) is applied.

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0660 [68], XSH/TC1-2008/0661 [320], and XSH/TC1-2008/0662 [68] are applied.

POSIX.1-2008, Technical Corrigendum 2, XSH/TC2-2008/0367 [604] and XSH/TC2-2008/0368 [630] are applied.

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