The Open Group Base Specifications Issue 7
IEEE Std 1003.1-2008
Copyright © 2001-2008 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] [Option Start] 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. [Option End]

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] [Option Start]  domain [Option End] error may occur and either a NaN (if supported) or an implementation-defined value shall be returned. [MX] [Option Start]  On systems that support the IEC 60559 Floating-Point option, a domain error shall occur and a NaN shall be returned. [Option End]

If x is ±0, tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively. [MX] [Option Start]  On systems that support the IEC 60559 Floating-Point option, a pole error shall occur; [Option End]
otherwise, a [CX] [Option Start]  pole [Option End] 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.

[MX] [Option Start] 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 either a NaN (if supported), or an implementation-defined value shall be returned. [Option End]

ERRORS

These functions shall fail if:

Domain Error
[MX] [Option Start] 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. [Option End]

Pole Error
[MX] [Option Start] 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. [Option End]

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.


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.

End of informative text.

 

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