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 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   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 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.

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 undermine carefully written code. The FP_CONTRACT macro can be used to
       disallow  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 others.

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(P)