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 .