.\" Copyright (c) 2005 David Schultz <das@FreeBSD.org>
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.Dd January 22, 2005
.Dt FMA 3
.Os
.Sh NAME
.Nm fma ,
.Nm fmaf ,
.Nm fmal
.Nd fused multiply-add
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn fma "double x" "double y" "double z"
.Ft float
.Fn fmaf "float x" "float y" "float z"
.Ft long double
.Fn fmal "long double x" "long double y" "long double z"
.Sh DESCRIPTION
The
.Fn fma ,
.Fn fmaf ,
and
.Fn fmal
functions return
.No "(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.
.Pp
For instance, the expression
.No "1.2e100 * 2.0e208 - 1.4e308"
produces \*(If due to overflow in the intermediate product, whereas
.No "fma(1.2e100, 2.0e208, -1.4e308)"
returns approximately 1.0e308.
.Pp
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
.Dv FP_FAST_FMA ,
.Dv FP_FAST_FMAF
and
.Dv FP_FAST_FMAL
may be defined in
.In math.h
to indicate that
.Fn fma ,
.Fn fmaf ,
and
.Fn fmal
(respectively) have comparable or faster speed than a multiply
operation followed by an add operation.
.Sh IMPLEMENTATION NOTES
In general, these routines will behave as one would expect if
.No "x * y + z"
were computed with unbounded precision and range,
then rounded to the precision of the return type.
However, on some platforms, if
.Fa z
is \*(Na, these functions may not raise an exception even
when the computation of
.No "x * y"
would have otherwise generated an invalid exception.
.Sh SEE ALSO
.Xr fenv 3 ,
.Xr math 3
.Sh STANDARDS
The
.Fn fma ,
.Fn fmaf ,
and
.Fn fmal
functions conform to
.St -isoC-99 .
A fused multiply-add operation with virtually identical
characteristics appears in IEEE draft standard 754R.
.Sh HISTORY
The
.Fn fma
and
.Fn fmaf
routines first appeared in
.Fx 5.4 ,
and
.Fn fmal
appeared in
.Fx 5.5 .