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.\" Copyright (c) 2005 David Schultz <das@FreeBSD.org>
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" $FreeBSD$
.\"
.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 6.0 .
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