LGAMMA(3)                  POSIX Programmer's Manual                 LGAMMA(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
       lgamma, lgammaf, lgammal, signgam -- log gamma function

SSYYNNOOPPSSIISS
       #include <math.h>

       double lgamma(double _x);
       float lgammaf(float _x);
       long double lgammal(long double _x);
       extern int signgam;

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.1-2008
       defers to the ISO C standard.

       These functions shall compute _l_o_g__e |<Gamma>(_x)| where <Gamma>(_x) is
       defined as <<iinnfti0engirtayl>>_e_^ -_t_t_^ _x-1_d_t.  The argument _x need not be a non-
       positive integer (<Gamma>(_x) is defined over the reals, except the non-
       positive integers).

       If _x is NaN, -Inf, or a negative integer, the value of _s_i_g_n_g_a_m is
       unspecified.

       These functions need not be thread-safe.

       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
       logarithmic gamma of _x.

       If _x is a non-positive integer, a pole error shall occur and _l_g_a_m_m_a(),
       _l_g_a_m_m_a_f(), and _l_g_a_m_m_a_l() shall return +HUGE_VAL, +HUGE_VALF, and
       +HUGE_VALL, respectively.

       If the correct value would cause overflow, a range error shall occur
       and _l_g_a_m_m_a(), _l_g_a_m_m_a_f(), and _l_g_a_m_m_a_l() shall return +-HUGE_VAL,
       +-HUGE_VALF, and +-HUGE_VALL (having the same sign as the correct
       value), respectively.

       If _x is NaN, a NaN shall be returned.

       If _x is 1 or 2, +0 shall be returned.

       If _x is +-Inf, +Inf shall be returned.

EERRRROORRSS
       These functions shall fail if:

       Pole Error  The _x argument is a negative integer or 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 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.

       _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
       None.

FFUUTTUURREE DDIIRREECCTTIIOONNSS
       None.

SSEEEE AALLSSOO
       _e_x_p(), _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(), _i_s_n_a_n()

       The Base Definitions volume of POSIX.1-2008, _S_e_c_t_i_o_n _4_._1_9, _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, 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                            LGAMMA(3)
