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Reformat the list of math and trigo functions #107

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e7fe6c3
Reformat the list of math and trigo functions
gmantele Aug 18, 2026
e897f53
Update the change log
gmantele Aug 19, 2026
afbdef8
Move colons inside \item arguments
mbtaylor Aug 25, 2026
2f98137
Fix ugly HTML arg formatting from last commit
mbtaylor Aug 25, 2026
7d5b5a8
A more compact way to present math and trigo functions
gmantele Sep 25, 2026
80ceaa0
Fix HTML formatting error for mod(x,y) definition
mbtaylor Sep 25, 2026
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339 changes: 131 additions & 208 deletions ADQL.tex
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Expand Up @@ -14,6 +14,10 @@

\usepackage{hyperref}

% Redefine description blocks so that the definition is always on a new line instead of being just after the label:
\usepackage{enumitem} \SetLabelAlign{parleft}{\parbox[t]\textwidth{#1}}
\setdescription{ align=parleft, style=nextline }

% Macros for referring to IVOA standards and notes.
\input{ivoa-cite.tex}

Expand All @@ -36,9 +40,8 @@
\author{Alexander Szalay}

\editor[http://wiki.ivoa.net/twiki/bin/view/IVOA/GregoryMantelet]{Grégory Mantelet}
\editor[http://wiki.ivoa.net/twiki/bin/view/IVOA/DaveMorris]{Dave Morris}

\previousversion[http://www.ivoa.net/Documents/ADQL/2.0]{ADQL-2.0}
\previousversion[https://www.ivoa.net/Documents/ADQL/20231215/]{ADQL-2.1}

\begin{document}

Expand Down Expand Up @@ -597,213 +600,125 @@ \subsection{Mathematical and Trigonometrical Functions}

ADQL declares a list of reserved keywords \SectionSee{sec:keywords} which include
the mathematical and trigonometrical function names. Their syntax,
usage and description are detailed in tables~\ref{table:math.functions}
and \ref{table:trig.functions}.

\begin{table}[tpb]\footnotesize
\begin{tabular}{|p{0.20\textwidth}|p{0.125\textwidth}|p{0.125\textwidth}|p{0.55\textwidth}|}

\hline
\textbf{Name} &
\textbf{Argument \newline datatype} &
\textbf{Return \newline datatype} &
\textbf{Description}
\tabularnewline

\hline
abs(x) &
\textit{x} double &
double &
Returns the absolute value of \textit{x}.
\tabularnewline

\hline
ceiling(x) &
\textit{x} double &
double &
Returns the smallest integer that is not less than \textit{x}.
\tabularnewline

\hline
degrees(x) &
\textit{x} double &
double &
Converts the angle \textit{x} from radians to degrees.
\tabularnewline

\hline
exp(x) &
\textit{x} double &
double &
Returns Euler’s number \textit{e} raised to the power of \textit{x}.
\tabularnewline

\hline
floor(x) &
\textit{x} double &
double &
Returns the largest integer that is not greater than \textit{x}.
\tabularnewline

\hline
log(x) &
\textit{x} double &
double &
Returns the natural logarithm (base \textit{e}) of \textit{x}. The value of \textit{x} must be greater than zero.
\tabularnewline

\hline
log10(x) &
\textit{x} double &
double &
Returns the base 10 logarithm of \textit{x}. The value of \textit{x} must be greater than zero.
\tabularnewline

\hline
mod(x,y) &
\textit{x} double,
\newline
\textit{y} double &
double &
Returns the remainder \textit{r} of \textit{x/y} as a double,
where:
\begin{itemize}
\item \textit{r} has the same sign as \textit{x}
\item |\textit{r}| is less than |\textit{y}|
usage and description are detailed in below.

\subsubsection{Mathematical Functions}

\begin{description}
\item[\texttt{abs(x)}]
\texttt{double abs(double x)} \\
Returns the absolute value of x.

\item[\texttt{ceiling(x)}]
\texttt{double ceiling(double x)} \\
Returns the smallest integer that is not less than \textit{x}.

\item[\texttt{degrees(x)}]
\texttt{double degrees(double x)} \\
Converts the angle \textit{x} from radians to degrees.

\item[\texttt{exp(x)}]
\texttt{double exp(double x)} \\
Returns Euler’s number \textit{e} raised to the power of \textit{x}.

\item[\texttt{floor(x)}]
\texttt{double floor(double x)} \\
Returns the largest integer that is not greater than \textit{x}.

\item[\texttt{log(x)}]
\texttt{double log(double x)} \\
Returns the natural logarithm (base \textit{e}) of \textit{x}. The value of \textit{x} must be greater than zero.

\item[\texttt{log10(x)}]
\texttt{double log10(double x)} \\
Returns the base 10 logarithm of \textit{x}. The value of \textit{x} must be greater than zero.

\item[\texttt{mod(x,y)}]
\texttt{double mod(double x, double y)} \\
Returns the remainder \textit{r} of \textit{x/y} as a double,
where:
\begin{itemize}
\item \textit{r} has the same sign as \textit{x}
\item \textit{$|r|$} is less than \textit{$|y|$}
\item \textit{x} = (\textit{f} * \textit{y}) + \textit{r} for a given integer \textit{f}
\end{itemize}
\tabularnewline

\hline
pi() &
&
double &
The numeric constant \(\pi\).
\tabularnewline

\hline
power(x,y) &
\textit{x} double,
\newline
\textit{y} double &
double &
Returns the value of \textit{x} raised to the power of \textit{y}.
\tabularnewline

\hline
radians(x) &
\textit{x} double &
double &
Converts the angle \textit{x} from degrees to radians.
\tabularnewline

\hline
sqrt(x) &
\textit{x} double &
double &
Returns the positive square root of \textit{x}.
\tabularnewline

\hline
rand(x) &
\textit{x} double &
double &
Returns a random value between 0.0 and 1.0.
The optional argument, \textit{x}, originally intended to provide a random seed,
has undefined semantics. Query writers are advised to omit this argument.
\tabularnewline

\hline
round(x,n) &
\textit{x} double,
\newline
\textit{n} integer &
double &
Rounds \textit{x} to \textit{n} decimal places.
The integer \textit{n} is optional and defaults to 0 if not specified.
A negative value of \textit{n} will round to the left of the decimal point.
\tabularnewline

\hline
truncate(x, n) &
\textit{x} double
\newline
\textit{n} integer &
double &
Truncates \textit{x} to \textit{n} decimal places.
The integer \textit{n} is optional and defaults to 0 if not specified.
\tabularnewline
\hline
\end{tabular}
\caption{Mathematical functions}
\label{table:math.functions}
\end{table}

\begin{table}[tbh]\footnotesize
\begin{tabular}{|p{0.20\textwidth}|p{0.125\textwidth}|p{0.125\textwidth}|p{0.55\textwidth}|}

\hline
\textbf{Name} &
\textbf{Argument \newline datatype} &
\textbf{Return \newline datatype} &
\textbf{Description}
\tabularnewline

\hline
acos(x) &
\textit{x} double &
double &
Returns the arc cosine of \textit{x}, in the range of 0 through \(\pi\) radians. The absolute value of \textit{x} must be less than or equal to 1.0.
\tabularnewline

\hline
asin(x) &
\textit{x} double &
double &
Returns the arc sine of \textit{x}, in the range of -\(\pi\)/2 through \(\pi\)/2 radians. The absolute value of \textit{x} must be less than or equal to 1.0.
\tabularnewline

\hline
atan(x) &
\textit{x} double &
double &
Returns the arc tangent of \textit{x} , in the range of -\(\pi\)/2 through \(\pi\)/2 radians.
\tabularnewline

\hline
atan2(y,x) &
\textit{x} double,
\newline
\textit{y} double &
double &
Converts rectangular coordinates \textit{x,y} to polar angle. It computes the arc tangent of \textit{y/x} in the range of –\(\pi\) through \(\pi\) radians.
\tabularnewline

\hline
cos(x) &
\textit{x} double &
double &
Returns the cosine of the angle \textit{x} in radians, in the range of -1.0 through 1.0.
\tabularnewline

\hline
sin(x) &
\textit{x} double &
double &
Returns the sine of the angle \textit{x} in radians, in the range of -1.0 through 1.0.
\tabularnewline

\hline
tan(x) &
\textit{x} double &
double &
Returns the tangent of the angle \textit{x} in radians.
\tabularnewline
\hline
\end{tabular}
\caption{Trigonometrical functions}
\label{table:trig.functions}
\end{table}
\end{itemize}

\item[\texttt{pi()}]
\texttt{double pi()} \\
The numeric constant \(\pi\).

\item[\texttt{power(x,y)}]
\texttt{double power(double x, double y)} \\
Returns the value of \textit{x} raised to the power of \textit{y}.

\item[\texttt{radians(x)}]
\texttt{double radians(double x)} \\
Converts the angle \textit{x} from degrees to radians.

\item[\texttt{sqrt(x)}]
\texttt{double sqrt(double x)} \\
Returns the positive square root of \textit{x}.

\item[\texttt{rand(x)}]
\texttt{double rand(double x)} \\
Returns a random value between 0.0 and 1.0.
The optional argument, \textit{x}, originally intended to provide a
random seed, has undefined semantics. Query writers are advised to omit
this argument.

\item[\texttt{round(x,n)}]
\texttt{double round(double x, integer n)} \\
Rounds \textit{x} to \textit{n} decimal places.
The integer \textit{n} is optional and defaults to 0 if not specified.
A negative value of \textit{n} will round to the left of the decimal
point.

\item[\texttt{truncate(x, n)}]
\texttt{double truncate(double x, integer n)} \\
Truncates \textit{x} to \textit{n} decimal places.
The integer \textit{n} is optional and defaults to 0 if not specified.
\end{description}

\subsubsection{Trigonometrical Functions}

\begin{description}
\item[\texttt{acos(x)}]
\texttt{double acos(double x)} \\
Returns the arc cosine of \textit{x}, in the range of 0 through
\(\pi\) radians. The absolute value of \textit{x} must be less than or
equal to 1.0.

\item[\texttt{asin(x)}]
\texttt{double asin(double x)} \\
Returns the arc sine of \textit{x}, in the range of -\(\pi\)/2 through
\(\pi\)/2 radians. The absolute value of \textit{x} must be less than or
equal to 1.0.

\item[\texttt{atan(x)}]
\texttt{double atan(double x)} \\
Returns the arc tangent of \textit{x} , in the range of -\(\pi\)/2
through \(\pi\)/2 radians.

\item[\texttt{atan2(y,x)}]
\texttt{double atan2(double y, double x)} \\
Converts rectangular coordinates \textit{x,y} to polar angle. It
computes the arc tangent of \textit{y/x} in the range of –\(\pi\)
through \(\pi\) radians.

\item[\texttt{cos(x)}]
\texttt{double cos(double x)} \\
Returns the cosine of the angle \textit{x} in radians, in the range of
-1.0 through 1.0.

\item[\texttt{sin(x)}]
\texttt{double sin(double x)} \\
Returns the sine of the angle \textit{x} in radians, in the range of
-1.0 through 1.0.

\item[\texttt{tan(x)}]
\texttt{double tan(double x)} \\
Returns the tangent of the angle \textit{x} in radians.
\end{description}

\section{Type system}
\label{sec:types}
Expand Down Expand Up @@ -2931,6 +2846,14 @@ \subsection{Between 2.1 and 2.2}
\begin{itemize}
\item Erratum 1 - Addition of auxiliary files for the BNF grammar
\end{itemize}
\item \textbf{General}
\begin{itemize}
\item \textbf{Updated}
\begin{itemize}
\item Convert the tables for mathematical and trigonometrical
functions into lists (see \SectionRef{sec:math.functions})
\end{itemize}
\end{itemize}
\end{itemize}

\subsection{Between 2.0 and 2.1}
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2 changes: 2 additions & 0 deletions README.md
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Expand Up @@ -21,6 +21,8 @@ specific to astronomy.

## Status?

_**The version presently available in this repository is WD-2.2.**_

The last stable version is
**[REC-2.1](http://www.ivoa.net/documents/latest/ADQL.html)**.

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