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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra functions.spad}
\author{Brian Dupee}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{domain BFUNCT BasicFunctions}
<<domain BFUNCT BasicFunctions>>=
)abbrev domain BFUNCT BasicFunctions
++ Author: Brian Dupee
++ Date Created: August 1994
++ Date Last Updated: April 1996
++ Basic Operations: bfKeys, bfEntry
++ Description: A Domain which implements a table containing details of
++ points at which particular functions have evaluation problems.
DF ==> DoubleFloat
SDF ==> Stream DoubleFloat
RS ==> Record(zeros: SDF, ones: SDF, singularities: SDF)
BasicFunctions(): E == I where
E ==> SetCategory with
bfKeys:() -> List Symbol
++ bfKeys() returns the names of each function in the
++ \axiomType{BasicFunctions} table
bfEntry:Symbol -> RS
++ bfEntry(k) returns the entry in the \axiomType{BasicFunctions} table
++ corresponding to \spad{k}
finiteAggregate
I ==> add
Rep := Table(Symbol,RS)
import Rep, SDF
f(x:DF):DF ==
positive?(x) => -x
-x+1
bf():$ ==
import RS
dpi := pi()$DF
ndpi:SDF := map(#1*dpi,(z := generate(f,0))) -- [n pi for n in Z]
n1dpi:SDF := map(-(2*(#1)-1)*dpi/2,z) -- [(n+1) pi /2]
n2dpi:SDF := map(2*#1*dpi,z) -- [2 n pi for n in Z]
n3dpi:SDF := map(-(4*(#1)-1)*dpi/4,z)
n4dpi:SDF := map(-(4*(#1)-1)*dpi/2,z)
sinEntry:RS := [ndpi, n4dpi, empty()$SDF]
cosEntry:RS := [n1dpi, n2dpi, esdf := empty()$SDF]
tanEntry:RS := [ndpi, n3dpi, n1dpi]
asinEntry:RS := [construct([0$DF])$SDF,
construct([float(8414709848078965,-16,10)$DF]), esdf]
acosEntry:RS := [construct([1$DF])$SDF,
construct([float(54030230586813977,-17,10)$DF]), esdf]
atanEntry:RS := [construct([0$DF])$SDF,
construct([float(15574077246549023,-16,10)$DF]), esdf]
secEntry:RS := [esdf, n2dpi, n1dpi]
cscEntry:RS := [esdf, n4dpi, ndpi]
cotEntry:RS := [n1dpi, n3dpi, ndpi]
logEntry:RS := [construct([1$DF])$SDF,esdf, construct([0$DF])$SDF]
entryList:List(Record(key:Symbol,entry:RS)) :=
[[sin@Symbol, sinEntry], [cos@Symbol, cosEntry],
[tan@Symbol, tanEntry], [sec@Symbol, secEntry],
[csc@Symbol, cscEntry], [cot@Symbol, cotEntry],
[asin@Symbol, asinEntry], [acos@Symbol, acosEntry],
[atan@Symbol, atanEntry], [log@Symbol, logEntry]]
construct(entryList)$Rep
bfKeys():List Symbol == keys(bf())$Rep
bfEntry(k:Symbol):RS == qelt(bf(),k)$Rep
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
-- - Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- - 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.
--
-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 COPYRIGHT OWNER
--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.
@
<<*>>=
<<license>>
<<domain BFUNCT BasicFunctions>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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