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PROLOG | NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | EXAMPLES | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT |
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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.1‐2017 defers to the ISO C standard.
These functions shall compute Γ(x) where Γ(x) is defined as ∞0∫e^
−tt^ x−1dt.
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 the gamma
of 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 subnormal and 1/x is representable, 1/x should 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.
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.1‐2017, Section 4.20,
Treatment of Error Conditions for Mathematical Functions,
math.h(0p)
Portions of this text are reprinted and reproduced in electronic
form from IEEE Std 1003.1-2017, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The
Open Group Base Specifications Issue 7, 2018 Edition, Copyright
(C) 2018 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 .
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 2017 TGAMMA(3P)
Pages that refer to this page: math.h(0p)
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HTML rendering created 2025-02-02 by Michael Kerrisk, author of The Linux Programming Interface. For details of in-depth Linux/UNIX system programming training courses that I teach, look here. Hosting by jambit GmbH. |
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