\documentclass[nocolor,memo]{j3}
\renewcommand{\hdate}{9 August 2005}
\renewcommand{\vers}{J3/05-204r1}
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\begin{document}
\vspace{-10pt}
\begin{tabbing}
Subject: \hspace*{0.25in}\=Edits for more mathematical functions\\
From: \>Van Snyder\\
Reference: \>04-388r1, WG5/N1626-J3-019\\
\end{tabbing}
\section{Detailed specification}
Provide ACOS, ASIN, ATAN, COSH, SINH, TAN and TANH for complex type.
Provide inverse hyperbolic functions, including for complex type. In the
case of TAN, specify that the real part of the argument is regarded as a
value in radians.
\edits{04-007}
\sep\mgpar{294:25+}[Editor: Add the following three summaries in {\secfont
13.5.2 Mathematical functions} in alphabetical order:]
\begin{insum}
\item[{ACOSH(X)}]Inverse hyperbolic cosine
\end{insum}
\sep\begin{insum}
\item[{ASINH(X)}]\mgpar{294:26+}Inverse hyperbolic sine
\end{insum}
\sep\begin{insum}
\item[{ATANH(X)}]\mgpar{294:27+}Inverse hyperbolic tangent
\end{insum}
\sep\mgpar{301:10}[Editor: At the end of the {\bf Argument} paragraph of
{\secfont 13.7.3 ACOS (X)}, after ``1'' insert ``, or shall be of type
complex''.]
\sep\mgpar{301:13}[Editor: At the end of the {\bf Result value} paragraph
of {\secfont 13.7.3 ACOS (X)}, ``, expressed in radians. It''
$\Rightarrow$ ``. If it is real it is expressed in radians and''. At the
end of the paragraph insert another sentence ``If it is complex the real
part is expressed in radians and lies in the range $0 \leq$ REAL(ACOS(X))
$\leq \pi$.'']
\sep\mgpar{301:14+}{\bfseries\sffamily 13.7.3$\frac12$ ACOSH ( X )}
\desc{Inverse hyperbolic cosine function.}
\class{Elemental function.}
\argument{ X shall be of type real or complex. }
\reschar{Same as X.}
\resvalue{The result has a value equal to a processor-dependent
approximation to the inverse hyperbolic cosine function of X. If the
result is complex the imaginary part lies in the range $0 \leq$
AIMAG(ACOSH(X)) $\leq \pi$.}
\example{ ACOSH~(1.5430806) has the value 1.0 (approximately).}
\sep\mgpar{304:14}[Editor: At the end of the {\bf Argument} paragraph of
{\secfont 13.7.12 ASIN (X)}, after ``1'' insert ``, or of type
complex''.]
\sep\mgpar{304:17}[Editor: At th``, expressed in radians. It''
$\Rightarrow$ ``. If it is real it is expressed in radians and''. At the
end of the paragraph insert another sentence ``If it is complex the real
part is expressed in radians and lies in the range $-\frac\pi2 \leq$
REAL(ASIN(X)) $\leq \frac\pi2$.'']
\sep\mgpar{304:18+}{\bfseries\sffamily 13.7.12$\frac12$ ASINH ( X )}
\desc{Inverse hyperbolic sine function.}
\class{Elemental function.}
\argument{ X shall be of type real or complex. }
\reschar{Same as X.}
\resvalue{The result has a value equal to a processor-dependent
approximation to the inverse hyperbolic sine function of X. If the
result is complex the imaginary part lies in the range $-\frac\pi2 \leq$
AIMAG(ASINH(X)) $\leq \frac\pi2$.}
\example{ ASINH~(1.1752012) has the value 1.0 (approximately).}
\sep\mgpar{305:31}[Editor: At the end of the {\bf Argument} paragraph of
{\secfont 13.7.14 ATAN (X)}, after ``real'' insert ``or complex''.]
\sep\mgpar{305:34}[Editor: At the end of the {\bf Result value} paragraph
of {\secfont 13.7.14 ATAN (X)}, ``, expressed in radians, that''
$\Rightarrow$ ``. If it is real it is expressed in radians and''. Insert
another sentence at the end of the paragraph ``If is complex the real part
is expressed in radians and lies in the range $-\frac\pi2 \leq$
REAL(ATAN(X)) $\leq \frac\pi2$.'']
\sep\mgpar{306:13+}{\bfseries\sffamily 13.7.15$\frac12$ ATANH ( X )}
\desc{Inverse hyperbolic tangent function.}
\class{Elemental function.}
\argument{ X shall be of type real or complex. }
\reschar{Same as X.}
\resvalue{The result has a value equal to a processor-dependent
approximation to the inverse hyperbolic tangent function of X. If the
result is complex the imaginary part is expressed in radians and lies in
the range $-\frac\pi2 \leq$ AIMAG(ATANH(X)) $\leq \frac\pi2$.}
\example{ ATANH~(0.76159416) has the value 1.0 (approximately).}
\sep\mgpar{309:7}[Editor: At the end of the {\bf Argument} paragraph of
{\secfont 13.7.24 COSH (X)}, after ``real'' insert ``or complex''.]
\sep\mgpar{309:9}[Editor: At the end of the {\bf Result value} paragraph
of {\secfont 13.7.24 COSH (X)}, insert a sentence ``If X is of type
complex its imaginary part is regarded as a value in radians.'']
\sep\mgpar{352:15}[Editor: At the end of the {\bf Argument} paragraph of
{\secfont 13.7.111 SINH (X)}, after ``real'' insert ``or complex''.]
\sep\mgpar{352:17}[Editor: At the end of the {\bf Result value} paragraph
of {\secfont 13.7.111 SINH (X)}, insert a sentence ``If X is of type
complex its imaginary part is regarded as a value in radians.'']
\sep\mgpar{355:16}[Editor: At the end of the {\bf Argument} paragraph of
{\secfont 13.7.118 TAN (X)}, after ``real'' insert ``or complex''.]
\sep\mgpar{355:18-19}[Editor: At the end of the {\bf Result value} paragraph
of {\secfont 13.7.118 TAN (X)}, ``, with X \dots\ radians'' $\Rightarrow$
``. If X is of type real, it is regarded as a value in radians. If X is
of type complex, its real part is regarded as a value in radians''.]
\sep\mgpar{355:24}[Editor: At the end of the {\bf Argument} paragraph of
{\secfont 13.7.119 TANH (X)}, after ``real'' insert ``or complex''.]
\sep\mgpar{355:26}[Editor: At the end of the {\bf Result value} paragraph
of {\secfont 13.7.119 TANH (X)}, insert a sentence ``If X is of type
complex its imaginary part is regarded as a value in radians.'']
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