\" $NetBSD: fma.3,v 1.3 2017/09/27 10:12:47 maya Exp $
\" Copyright (c) 2005 David Schultz <
[email protected]>
\" 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: head/lib/msun/man/fma.3 152755 2005-11-24 09:25:10Z joel $
\"
Dd September 27, 2017
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 .
The
Fn fma ,
Fn fmaf
and
Fn fmal
routines were imported into
Nx
in
Nx 7.0 .
