The Open Group Base Specifications Issue 7
IEEE Std 1003.1, 2013 Edition
Copyright © 2001-2013 The IEEE and The Open Group

#### NAME

> tgamma, tgammaf, tgammal - compute gamma() function

#### SYNOPSIS

> ``#include <math.h>
> double tgamma(double` x`);
> float tgammaf(float` x`);
> long double tgammal(long double` x`);
> ``

#### DESCRIPTION

> [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 the gamma() function of x.

> An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

#### RETURN VALUE

> Upon successful completion, these functions shall return Gamma(x).

> If x is 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 x is ±0, tgamma(), tgammaf(), and tgammal() 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(), and tgammal() 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, and tgamma(), tgammaf(), and tgammal() 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.

> [MX] If x is NaN, a NaN shall be returned.

> If x is +Inf, x shall be returned.

> If x is -Inf, a domain error shall occur, and a NaN shall be returned.

#### ERRORS

> These functions shall fail if:

> Domain Error
>   [MX] The value of x is a negative integer, or x is -Inf.

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall 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 of x is zero.

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall 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 errno shall 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 x is a negative integer.

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall 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 x is zero.

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

The following sections are informative.

#### EXAMPLES

> None.

#### APPLICATION USAGE

> 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.

#### RATIONALE

> This function is named tgamma() in order to avoid conflicts with the historical gamma() and lgamma() functions.

#### FUTURE DIRECTIONS

> 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.

#### SEE ALSO

> feclearexcept, fetestexcept, lgamma

> XBD Treatment of Error Conditions for Mathematical Functions, <math.h>

#### CHANGE HISTORY

> 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.

#### Issue 7

> 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.

End of informative text.

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