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



PPRROOLLOOGG
       This manual page is part of the POSIX Programmer's Manual.  The OS
       implementation of this interface may differ (consult the corresponding
       OS manual page for details of OS behavior), or the interface may not be
       implemented on OS.

NNAAMMEE
       tgamma, tgammaf, tgammal -- compute gamma() function

SSYYNNOOPPSSIISS
       #include <math.h>

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

DDEESSCCRRIIPPTTIIOONN
       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>(_x) where <Gamma>(_x) is defined as
       <<iinnfti0engirtayl>>_e_^ -_t_t_^ _x-1_d_t.

       An application wishing to check for error situations should set _e_r_r_n_o
       to zero and call _f_e_c_l_e_a_r_e_x_c_e_p_t(FE_ALL_EXCEPT) before calling these
       functions. On return, if _e_r_r_n_o is non-zero or _f_e_t_e_s_t_e_x_c_e_p_t(FE_INVALID |
       FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
       occurred.

RREETTUURRNN VVAALLUUEE
       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, _t_g_a_m_m_a(), _t_g_a_m_m_a_f(), and _t_g_a_m_m_a_l() 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 _t_g_a_m_m_a(), _t_g_a_m_m_a_f(), and _t_g_a_m_m_a_l() 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 _t_g_a_m_m_a(), _t_g_a_m_m_a_f(), and _t_g_a_m_m_a_l() 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.

EERRRROORRSS
       These functions shall fail if:

       Domain Error
                   The value of _x is a negative integer, or _x is -Inf.

                   If the integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO)
                   is non-zero, then _e_r_r_n_o shall be set to [[EEDDOOMM]].  If the
                   integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & 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 (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO)
                   is non-zero, then _e_r_r_n_o shall be set to [[EERRAANNGGEE]].  If the
                   integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & 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 (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO)
                   is non-zero, then _e_r_r_n_o shall be set to [[EERRAANNGGEE]].  If the
                   integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & 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 (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO)
                   is non-zero, then _e_r_r_n_o shall be set to [[EEDDOOMM]].  If the
                   integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & 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 (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO)
                   is non-zero, then _e_r_r_n_o shall be set to [[EERRAANNGGEE]].  If the
                   integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & 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 (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO)
                   is non-zero, then _e_r_r_n_o shall be set to [[EERRAANNGGEE]].  If the
                   integer expression (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERREXCEPT) is
                   non-zero, then the underflow floating-point exception shall
                   be raised.

       _T_h_e _f_o_l_l_o_w_i_n_g _s_e_c_t_i_o_n_s _a_r_e _i_n_f_o_r_m_a_t_i_v_e_.

EEXXAAMMPPLLEESS
       None.

AAPPPPLLIICCAATTIIOONN UUSSAAGGEE
       On error, the expressions (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERRNO) and
       (_m_a_t_h___e_r_r_h_a_n_d_l_i_n_g & MATH_ERREXCEPT) are independent of each other, but
       at least one of them must be non-zero.

RRAATTIIOONNAALLEE
       This function is named _t_g_a_m_m_a() in order to avoid conflicts with the
       historical _g_a_m_m_a() and _l_g_a_m_m_a() functions.

FFUUTTUURREE DDIIRREECCTTIIOONNSS
       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.

SSEEEE AALLSSOO
       _f_e_c_l_e_a_r_e_x_c_e_p_t(), _f_e_t_e_s_t_e_x_c_e_p_t(), _l_g_a_m_m_a()

       The Base Definitions volume of POSIX.1-2017, _S_e_c_t_i_o_n _4_._2_0, _T_r_e_a_t_m_e_n_t _o_f
       _E_r_r_o_r _C_o_n_d_i_t_i_o_n_s _f_o_r _M_a_t_h_e_m_a_t_i_c_a_l _F_u_n_c_t_i_o_n_s, <<mmaatthh..hh>>

CCOOPPYYRRIIGGHHTT
       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(3)
