
FMA(P) POSIX Programmer's Manual FMA(P)
NAME
fma, fmaf, fmal  floatingpoint multiplyadd
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 nonzero,
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 implementationdefined 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 nonzero, then errno shall be
set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero,
then the invalid floatingpoint exception shall be raised.
Range Error
The result overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non
zero, then the overflow floatingpoint 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 nonzero, then errno shall be
set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero,
then the invalid floatingpoint exception shall be raised.
Range Error
The result underflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non
zero, then the underflow floatingpoint 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 nonzero.
RATIONALE
In many cases, clever use of floating (fused) multiplyadd leads to much improved code;
but its unexpected use by the compiler can undermine carefully written code. The FP_CON
TRACT macro can be used to disallow use of floating multiplyadd; and the fma() function
guarantees its use where desired. Many current machines provide hardware floating multi
plyadd instructions; software implementation can be used for others.
FUTURE DIRECTIONS
None.
SEE ALSO
feclearexcept() , fetestexcept() , the Base Definitions volume of IEEE Std 1003.12001,
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) 20012003 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 orig
inal Standard can be obtained online at http://www.opengroup.org/unix/online.html .
IEEE/The Open Group 2003 FMA(P) 
