tgamma man page
Prolog
This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.
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
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.12008 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 nonzero or fetestexcept(FE_INVALID  FE_DIVBYZERO  FE_OVERFLOW  FE_UNDERFLOW) is nonzero, an error has occurred.
Return Value
Upon successful completion, these functions shall return Gamma(x).
If x is a negative integer, a domain error may occur and either a NaN (if supported) or an implementationdefined value shall be returned. On systems that support the IEC 60559 FloatingPoint 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. On systems that support the IEC 60559 FloatingPoint option, a pole error shall occur; otherwise, a 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, and is not representable, a range error may occur, and tgamma(), tgammaf(), and tgammal() shall return 0.0, or (if IEC 60559 FloatingPoint is not supported) an implementationdefined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
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 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

The value of x is a negative integer, or x is Inf.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the invalid floatingpoint exception shall be raised.
 Pole Error

The value of x is zero.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the dividebyzero floatingpoint exception shall be raised.
 Range Error

The value overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the overflow floatingpoint 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 nonzero, then errno shall be set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the invalid floatingpoint exception shall be raised.
 Pole Error

The value of x is zero.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the dividebyzero floatingpoint exception shall be raised.
 Range Error

The result underflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the underflow floatingpoint exception shall be raised.
The following sections are informative.
Examples
None.
Application Usage
For IEEE Std 7541985 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 nonzero.
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()
The Base Definitions volume of POSIX.12008, Section 4.19, Treatment of Error Conditions for Mathematical Functions, <math.h>
Copyright
Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology  Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, Copyright (C) 2013 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. (This is POSIX.12008 with the 2013 Technical Corrigendum 1 applied.) In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.unix.org/online.html .
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