FMA(3)                     POSIX Programmer's Manual                    FMA(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
       fma, fmaf, fmal -- floating-point multiply-add

SSYYNNOOPPSSIISS
       #include <math.h>

       double fma(double _x, double _y, double _z);
       float fmaf(float _x, float _y, float _z);
       long double fmal(long double _x, long double _y, long double _z);

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 (_x * _y) + _z, rounded as one ternary
       operation: they shall compute the value (as if) to infinite precision
       and round once to the result format, according to the rounding mode
       characterized by the value of FLT_ROUNDS.

       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 (_x * _y) + _z,
       rounded as one ternary operation.

       If the result overflows or underflows, a range error may occur.  On
       systems that support the IEC 60559 Floating-Point option, if the result
       overflows a range error shall occur.

       If _x or _y are NaN, a NaN shall be returned.

       If _x multiplied by _y is an exact infinity and _z is also an infinity but
       with the opposite sign, a domain error shall occur, and either a NaN
       (if supported), or an implementation-defined value shall be returned.

       If one of _x and _y is infinite, the other is zero, and _z is not a NaN, a
       domain error shall occur, and either a NaN (if supported), or an
       implementation-defined value shall be returned.

       If one of _x and _y is infinite, the other is zero, and _z is a NaN, a NaN
       shall be returned and a domain error may occur.

       If _x*_y is not 0*Inf nor Inf*0 and _z is a NaN, a NaN shall be returned.

EERRRROORRSS
       These functions shall fail if:

       Domain Error
                   The value of _x*_y+_z is invalid, or the value _x*_y is invalid
                   and _z is not a NaN.

                   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.

       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.

       These functions may fail if:

       Domain Error
                   The value _x*_y is invalid and _z is a NaN.

                   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.

       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.

       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
       In many cases, clever use of floating (_f_u_s_e_d) multiply-add leads to
       much improved code; but its unexpected use by the compiler can
       undermine carefully written code. The FP_CONTRACT macro can be used to
       disallow use of floating multiply-add; and the _f_m_a() function
       guarantees its use where desired. Many current machines provide
       hardware floating multiply-add instructions; software implementation
       can be used for others.

FFUUTTUURREE DDIIRREECCTTIIOONNSS
       None.

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()

       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                               FMA(3)
