\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}