mirror of
https://git.FreeBSD.org/src.git
synced 2024-12-24 11:29:10 +00:00
19797b2256
Discussed with: ru
117 lines
3.3 KiB
Groff
117 lines
3.3 KiB
Groff
.\" 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 .
|