tgamma(3p) — Linux manual page

PROLOG | NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | EXAMPLES | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT

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

PROLOG         top

       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         top

       tgamma, tgammaf, tgammal — compute gamma() function

SYNOPSIS         top

       #include <math.h>

       double tgamma(double x);
       float tgammaf(float x);
       long double tgammal(long double x);

DESCRIPTION         top

       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.

RETURN VALUE         top

       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         top

       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         top

       None.

APPLICATION USAGE         top

       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         top

       This function is named tgamma() in order to avoid conflicts with
       the historical gamma() and lgamma() functions.

FUTURE DIRECTIONS         top

       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         top

       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)

COPYRIGHT         top

       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:https://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)