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 .