Manual Reference Pages - FMAL (3)
- fused multiply-add
fma double x double y double z
fmaf float x float y float z
fmal long double x long double y long double z
(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 oo 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
may be defined in
to indicate that
(respectively) have comparable or faster speed than a multiply
operation followed by an add operation.
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
is NaN, these functions may not raise an exception even
when the computation of
x * y
would have otherwise generated an invalid exception.
functions conform to
A fused multiply-add operation with virtually identical
characteristics appears in IEEE draft standard 754R.
routines first appeared in
.Fx 5.4 ,
.Fx 6.0 .
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