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PROLOG | NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | EXAMPLES | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT |
TGAMMA(3P) POSIX Programmer's Manual TGAMMA(3P)
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
#include <math.h>
double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);
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.
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.
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.
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
historical gamma() and lgamma() 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(3p), fetestexcept(3p), lgamma(3p)
The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment
of Error Conditions for Mathematical Functions, math.h(0p)
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 .
IEEE/The Open Group 2013 TGAMMA(3P)
Pages that refer to this page: math.h(0p)