TGAMMA(3P) | POSIX Programmer's Manual | TGAMMA(3P) |

# 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(doublex); float tgammaf(floatx); long double tgammal(long doublex);

# 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.1‐2017 defers to the ISO C standard.

These functions shall compute $\Gamma \left(x\right)$ where $\Gamma \left(x\right)$ is defined as $\underset{0}{\overset{\infty}{\int}}e^-tt^x-1\mathrm{dt}$ .

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 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.

# 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

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.1‐2017, *Section
4.20*, *Treatment of Error Conditions for Mathematical Functions*,
**<math.h>**

# COPYRIGHT

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, 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 .

2017 | IEEE/The Open Group |