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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.
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
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 domain error may occur and either a NaN (if supported) or an
implementation-defined value shall be returned. 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. On systems that support the IEC 60559 Floating-Point 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 Floating-Point is not supported) an
implementation-defined 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 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 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()
The Base Definitions volume of POSIX.1‐2008, 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.1-2008 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 .
Any typographical or formatting errors that appear in this page are most likely to have been introduced
during the conversion of the source files to man page format. To report such errors, see
https://www.kernel.org/doc/man-pages/reporting_bugs.html .