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tgamma, tgammaf, tgammal - compute gamma() function

#include <math.h>

double tgamma(doublex);

float tgammaf(floatx);

long double tgammal(long doublex);

These functions shall compute the

gamma() function ofx.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

Gamma(x).If

xis a negative integer, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.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

xis NaN, a NaN shall be returned.If

xis +Inf,xshall be returned.If

xis ±0, a pole error shall occur, andtgamma(),tgammaf(), andtgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively.If

xis -Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.

These functions shall fail if:

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then

Domain Error The value of xis a negative integer, orxis -Inf.If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errnoshall 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, then errnoshall 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. errnoshall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

The following sections are informative.

None.

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.

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() ,lgamma() , the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions,<math.h>

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. 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.opengroup.org/unix/online.html .

IEEE/The Open Group |
TGAMMA (P) | 2003 |