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

PROLOG
       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
       fma, fmaf, fmal - floating-point multiply-add
SYNOPSIS
       #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);

DESCRIPTION
       These functions shall compute (x * y) + z, rounded as one ternary oper-
       ation:  they  shall compute the value (as if) to infinite precision and
       round once to the result format, according to the rounding mode charac-
       terized by the value of FLT_ROUNDS.
       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
       Upon  successful  completion, these functions shall return (x * y) + z,
       rounded as one ternary operation.
       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 imple-
       mentation-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.
ERRORS
       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 (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.
       Range Error
              The result 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 x* y is invalid and z is a NaN.
       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.
       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
       None.
APPLICATION USAGE
       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
       In many cases, clever use of floating  (fused)  multiply-add  leads  to
       much  improved  code; but its unexpected use by the compiler can under-
       mine carefully written code. The FP_CONTRACT macro can be used to  dis-
       allow  use  of floating multiply-add; and the fma() function guarantees
       its use where desired. Many current machines provide hardware  floating
       multiply-add instructions; software implementation can be used for oth-
       ers.
FUTURE DIRECTIONS
       None.
SEE ALSO
       feclearexcept(),  fetestexcept(),  the  Base  Definitions   volume   of
       IEEE Std 1003.1-2001,  Section  4.18, Treatment of Error Conditions for
       Mathematical Functions, <math.h>
COPYRIGHT
       Portions of this text are reprinted and reproduced in  electronic  form
       from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
       -- Portable Operating System Interface (POSIX),  The  Open  Group  Base
       Specifications  Issue  6,  Copyright  (C) 2001-2003 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 .

IEEE/The Open Group                  2003                              FMA(3P)