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.1‐2008 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         top

       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         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

       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         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.1‐2008, Section 4.19, 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, 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)