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.1-2024 defers to the ISO C standard.

These functions shall compute Γ(x) where Γ(x) is defined as \(\int_0^{\infty} e^{-t} t^{x-1} d t\)

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 the gamma of x.

If x is a negative integer, either a domain error or a pole error may occur and either a NaN (if supported) or ±Inf (if supported), respectively, 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.

If x is subnormal and 1/ x is representable, 1/ x should 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 or a negative integer.

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.

EXAMPLES

None.

APPLICATION USAGE

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

None.

SEE ALSO

feclearexcept , fetestexcept , lgamma

XBD 4.23 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.

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

Issue 8

Austin Group Defect 1461 is applied, changing the requirements for a negative integer argument to match the ISO C standard.