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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 dif-
       fer (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 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 feclearex-
       cept(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 excep-
       tion 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 excep-
       tion 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 excep-
       tion 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  indepen-
       dent 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, Stan-
       dard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base  Specifica-
       tions  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 Stan-
       dard,  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)