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 (con-
       sult 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 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  inte-
       ger  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 inte-
       ger 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, Copy-
       right (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.open-
       group.org/unix/online.html .



IEEE/The Open Group                                           2003                                                       FMA(3P)