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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input elemnum.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1991.
@
<<*>>=
<<license>>
--
-- Test numeric evaluation of elementary functions. SMW June 26, 1991.
)clear all
)set break resume
x := 0.7::Float
[exp log x]
[log exp x]
[sin asin x, cos acos x, tan atan x, cot acot x]
[asin sin x, acos cos x, atan tan x, acot cot x, acsc csc x, asec sec x ]
[sinh asinh x, tanh atanh x, csch acsch x,sech asech x]
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
--Should give errors:
--acsc x
--asec x
--acosh x
--acoth x
x := 1.1::Float
[exp log x]
[log exp x]
[ tan atan x, cot acot x, csc acsc x, sec asec x ]
[asin sin x, acos cos x, atan tan x, acot cot x, acsc csc x, asec sec x ]
[sinh asinh x,cosh acosh x, coth acoth x,csch acsch x ]
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
--Should give errors:
--asin x
--acos x
--atanh x
--asech x
x := 0.7::DoubleFloat
[exp log x]
[log exp x]
[sin asin x, cos acos x, tan atan x, cot acot x]
[asin sin x, acos cos x, atan tan x, acot cot x, acsc csc x, asec sec x ]
[sinh asinh x, tanh atanh x, csch acsch x,sech asech x]
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
--Should give errors:
--acsc x
--asec x
--acosh x
--acoth x
x := 1.1::DoubleFloat
[exp log x]
[log exp x]
[ tan atan x, cot acot x, csc acsc x, sec asec x ]
[asin sin x, acos cos x, atan tan x, acot cot x, acsc csc x, asec sec x ]
[sinh asinh x,cosh acosh x, coth acoth x,csch acsch x ]
[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
--Should give errors:
--asin x
--acos x
--atanh x
--asech x
qtest(a,b,n) ==
m1 := if n = 1 or n = 4 then 0 else 1
s1 := if n = 1 or n = 4 then 1 else -1
s2 := if n = 1 or n = 2 then 1 else -1
x := complex(s1*a, s2*b)
[x- exp log x, _
x- sin asin x, x- cos acos x, x- tan atan x , _
x- csc acsc x, x- sec asec x, x- cot acot x , _
x- sinh asinh x, x- cosh acosh x, x- tanh atanh x , _
x- csch acsch x, x- sech asech x, x- coth acoth x , _
x- log exp x, _
x- asin sin x, x- s1*acos cos x, x- atan tan x , _
x- acsc csc x, x- s1*asec sec x, x- acot cot x + m1*%pi, _
x- asinh sinh x, x- s1*acosh cosh x, x- atanh tanh x , _
x- acsch csch x, x- s1*asech sech x, x- acoth coth x ]
qerr(l) ==
reduce(+, [norm v for v in l])/#l
sa := 0.7::DoubleFloat
sb := 1.1::DoubleFloat
ba := 0.7::Float
bb := 1.1::Float
qtest(sa, sb, 1)
qerr %
qtest(ba, bb, 1)
qerr %
qtest(sa, sb, 2)
qerr %
qtest(ba, bb, 2)
qerr %
qtest(sa, sb, 3)
qerr %
qtest(ba, bb, 3)
qerr %
qtest(sa, sb, 4)
qerr %
qtest(ba, bb, 4)
qerr %
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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