NAME
fma,
fmaf,
fmal —
fused multiply-add
LIBRARY
Math Library (libm, -lm)
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
The
fma(),
fmaf(), and
fmal() functions return
(x * y) + z,
computed with only one rounding error. Using the ordinary multiplication and
addition operators, by contrast, results in two roundings: one for the
intermediate product and one for the final result.
For instance, the expression
1.2e100 * 2.0e208 - 1.4e308
produces infinity due to overflow in the intermediate product, whereas
fma(1.2e100, 2.0e208, -1.4e308) returns approximately
1.0e308.
The fused multiply-add operation is often used to improve the accuracy of
calculations such as dot products. It may also be used to improve performance
on machines that implement it natively. The macros
FP_FAST_FMA
,
FP_FAST_FMAF
and
FP_FAST_FMAL
may be defined in
<math.h> to indicate that
fma(),
fmaf(), and
fmal() (respectively) have comparable or faster speed than a
multiply operation followed by an add operation.
IMPLEMENTATION NOTES
In general, these routines will behave as one would expect if
x
* y + z were computed with unbounded precision and range, then rounded
to the precision of the return type. However, on some platforms, if
z is NaN, these functions may not raise an exception
even when the computation of
x * y would have
otherwise generated an invalid exception.
SEE ALSO
fenv(3),
math(3)
STANDARDS
The
fma(),
fmaf(), and
fmal() functions conform to
ISO/IEC
9899:1999 (“ISO C99”). A fused multiply-add operation
with virtually identical characteristics appears in IEEE draft standard 754R.
HISTORY
The
fma() and
fmaf() routines first appeared
in
FreeBSD 5.4, and
fmal() appeared
in
FreeBSD 6.0. The
fma(),
fmaf() and
fmal() routines where imported
into
NetBSD in
NetBSD
7.0.