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114 lines
3.3 KiB
Groff
114 lines
3.3 KiB
Groff
.\" Copyright (c) 2005 David Schultz <das@FreeBSD.org>
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.Dd January 22, 2005
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.Dt FMA 3
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.Os
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.Sh NAME
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.Nm fma ,
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.Nm fmaf ,
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.Nm fmal
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.Nd fused multiply-add
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In math.h
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.Ft double
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.Fn fma "double x" "double y" "double z"
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.Ft float
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.Fn fmaf "float x" "float y" "float z"
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.Ft long double
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.Fn fmal "long double x" "long double y" "long double z"
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.Sh DESCRIPTION
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The
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.Fn fma ,
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.Fn fmaf ,
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and
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.Fn fmal
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functions return
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.No "(x * y) + z" ,
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computed with only one rounding error.
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Using the ordinary multiplication and addition operators, by contrast,
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results in two roundings: one for the intermediate product and one for
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the final result.
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.Pp
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For instance, the expression
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.No "1.2e100 * 2.0e208 - 1.4e308"
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produces \*(If due to overflow in the intermediate product, whereas
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.No "fma(1.2e100, 2.0e208, -1.4e308)"
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returns approximately 1.0e308.
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.Pp
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The fused multiply-add operation is often used to improve the
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accuracy of calculations such as dot products.
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It may also be used to improve performance on machines that implement
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it natively.
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The macros
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.Dv FP_FAST_FMA ,
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.Dv FP_FAST_FMAF
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and
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.Dv FP_FAST_FMAL
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may be defined in
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.In math.h
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to indicate that
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.Fn fma ,
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.Fn fmaf ,
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and
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.Fn fmal
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(respectively) have comparable or faster speed than a multiply
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operation followed by an add operation.
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.Sh IMPLEMENTATION NOTES
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In general, these routines will behave as one would expect if
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.No "x * y + z"
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were computed with unbounded precision and range,
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then rounded to the precision of the return type.
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However, on some platforms, if
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.Fa z
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is \*(Na, these functions may not raise an exception even
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when the computation of
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.No "x * y"
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would have otherwise generated an invalid exception.
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.Sh SEE ALSO
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.Xr fenv 3 ,
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.Xr math 3
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.Sh STANDARDS
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The
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.Fn fma ,
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.Fn fmaf ,
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and
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.Fn fmal
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functions conform to
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.St -isoC-99 .
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A fused multiply-add operation with virtually identical
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characteristics appears in IEEE draft standard 754R.
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.Sh HISTORY
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The
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.Fn fma
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and
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.Fn fmaf
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routines first appeared in
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.Fx 5.4 ,
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and
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.Fn fmal
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appeared in
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.Fx 6.0 .
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