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%$Header: /home/dashley/cvsrep/uculib01/uculib01/doc/manual/c_afn0/c_afn0.tex,v 1.37 2010/05/12 18:35:49 dashley Exp $ |
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|
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\chapter{Arithmetic Functions} |
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|
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\label{cafn0} |
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\section{Introduction and Overview} |
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%Section tag: iov0 |
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\label{cafn0:siov0} |
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|
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This chapter documents functions that perform arithmetic. |
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|
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\begin{itemize} |
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\item \S{}\ref{cafn0:sscx0} (p. \pageref{cafn0:sscx0}) documents |
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functions that compare UCU\_UINT16 data. |
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\item \S{}\ref{cafn0:slsf0} (p. \pageref{cafn0:slsf0}) documents |
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functions that calculate or approximate functions of the form |
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$y=mx$, where $y$ is a UCU\_UINT16. |
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\item \S{}\ref{cafn0:ssre0} (p. \pageref{cafn0:ssre0}) documents |
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functions that calculate or approximate square roots. |
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\end{itemize} |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\section{UCU\_UINT16 Comparison Functions} |
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%Section tag: scx0 |
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\label{cafn0:sscx0} |
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\subsection[\emph{UcuAtU16CmpDiffAbsGtRxx(\protect\mbox{\protect$\cdot$})}] |
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{\emph{UcuAtU16CmpDiffAbsGtRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
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%Subsection tag: csx0 |
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\label{cafn0:sscx0:scsx0} |
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|
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\index{UcuAtU16CmpDiffAbsGtRxx()@\emph{UcuAtU16CmpDiffAbsGtRxx($\cdot$)}}% |
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|
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\noindent\textbf{PROTOTYPE} |
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\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item |
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\begin{verbatim} |
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UCU_BOOLEAN UcuAtU16CmpDiffAbsGtRxx( |
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UCU_UINT16 x1, |
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UCU_UINT16 x2, |
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UCU_UINT16 d |
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) |
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\end{verbatim} |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{SYNOPSIS} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item Returns UCU\_TRUE if $|x_1-x_2|>d$, or UCU\_FALSE otherwise. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{INPUTS} |
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\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
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\item \emph{\textbf{x1}}, \emph{\textbf{x2}}\\ |
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The UCU\_UINT16 arguments to compare. |
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\item \emph{\textbf{d}}\\ |
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The comparison threshold. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{OUTPUT} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item UCU\_TRUE if $|x_1-x_2|>d$, or UCU\_FALSE otherwise. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{DETAILED DESCRIPTION} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item \emph{UcuAtU16CmpDiffAbsGtRxx($\cdot$)} determines whether |
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$x_1$ and $x_2$ are more than $d$ apart. |
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\item The function is |
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typically used to detect change in a value (either negative or positive) |
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of a magnitude greater than $d$, |
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or to determine if two values are within $d$ of each other. |
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\item \emph{UcuAtU16CmpDiffAbsGtRxx($\cdot$)} is symmetric with |
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respect to its arguments: $f(x_1, x_2) \equiv f(x_2, x_1)$. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{INTERRUPT COMPATIBILITY} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item This function may be used from both non-ISR and ISR software. |
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\item This function is thread-safe. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{EXECUTION TIME} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item TBD. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{FUNCTION NAME MNEMONIC} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item \emph{U16}: arguments and return type are UCU\_UINT16. |
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\emph{Cmp}: compare. |
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\emph{Diff}: difference. |
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\emph{Abs}: absolute value. |
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\emph{Gt}: greater than. |
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\end{list} |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%\section{UCU\_SINT32 Complement and Negation Functions} |
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%\label{cafn0:scnf0} |
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% |
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% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%\subsection[\emph{UcuAtS32NegationRxx(\protect\mbox{\protect$\cdot$})}] |
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% {\emph{UcuAtS32NegationRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
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%\label{cafn0:scnf0:sstf0} |
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% |
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%\index{UcuAtS32NegationRxx()@\emph{UcuAtS32NegationRxx($\cdot$)}}% |
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% |
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%\noindent\textbf{PROTOTYPE} |
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%\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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%\item |
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%\begin{verbatim} |
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%UCU_SINT32 UcuAtS32NegationRxx( UCU_SINT32 x ) |
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%\end{verbatim} |
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%\end{list} |
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%\vspace{2.8ex} |
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% |
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%\noindent\textbf{SYNOPSIS} |
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%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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%\item Returns the 1's complement of $x$, plus 1. In most cases, this represents |
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% $-x$, but $-2^{31}$ (the most negative representable value) maps to |
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% $-2^{31}$ (this is a standard feature of the 2's complement representation of signed |
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% integers). |
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%\end{list} |
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%\vspace{2.8ex} |
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% |
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%\noindent\textbf{INPUTS} |
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%\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
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%\item \emph{\textbf{x}} \\ |
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% The UCU\_SINT32 integer to negate. |
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%\end{list} |
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%\vspace{2.8ex} |
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% |
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%\noindent\textbf{OUTPUT} |
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%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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%\item The 1's complement of $x$, plus 1 |
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%\end{list} |
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%\vspace{2.8ex} |
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% |
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%\noindent\textbf{INTERRUPT COMPATIBILITY} |
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%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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%\item This function may be used from both non-ISR and ISR software. |
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%\item This function is thread-safe. |
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%\end{list} |
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%\vspace{2.8ex} |
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% |
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%\noindent\textbf{EXECUTION TIME} |
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%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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%\item TBD. |
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%\end{list} |
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%\vspace{2.8ex} |
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% |
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%\noindent\textbf{FUNCTION NAME MNEMONIC} |
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%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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%\item \emph{Negation}: negates the argument. |
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%\end{list} |
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% |
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% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\section{UCU\_UINT16 Linear Scaling Functions, Zero Y-Intercept} |
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%Section tag: lsf0 |
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\label{cafn0:slsf0} |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\subsection[\emph{UcuAtU16LscZyiFAxdAxrRxx(\protect\mbox{\protect$\cdot$})}] |
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{\emph{UcuAtU16LscZyiFAxdAxrRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
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%Subsection tag: faa0 |
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\label{cafn0:slsf0:sfaa0} |
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|
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\index{UcuAtU16LscZyiFAxdAxrRxx()@\emph{UcuAtU16LscZyiFAxdAxrRxx($\cdot$)}}% |
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|
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\noindent\textbf{PROTOTYPE} |
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\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item |
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\begin{verbatim} |
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UCU_UINT16 UcuAtU16LscZyiFAxdAxrRxx( |
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UCU_UINT16 x, |
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UCU_UINT16 x_max, |
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UCU_UINT16 y_max |
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) |
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\end{verbatim} |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{SYNOPSIS} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item Linearly scales (or projects) from $[0, x_{max}]$ to $[0, y_{max}]$, |
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implementing the floor function (discarding any remainder resulting |
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from the division). The value calculated is |
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$\displaystyle{\left\lfloor \frac{y_{max} x}{x_{max}} \right\rfloor}$, |
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with the provision that the function output will never |
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exceed $y_{max}$. |
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|
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{INPUTS} |
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\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
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\item \emph{\textbf{x}}\\ |
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The input to scale. |
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\item \emph{\textbf{x\_max}}\\ |
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The value of $x$ that should correspond to $y_{max}$. |
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\item \emph{\textbf{y\_max}}\\ |
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The maximum output value of the function. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{OUTPUT} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item $\displaystyle{\left\lfloor \frac{y_{max} x}{x_{max}} \right\rfloor}$, with |
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a maximum of $y_{max}$. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{EXCEPTION CASES} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item If $x>x_{max}$, $y_{max}$ is returned. |
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\item If $x_{max}=0$ or $y_{max}=0$, 0 is returned. (In either of these |
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cases, it isn't possible to determine the intent of the caller, |
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so 0 is the safest return value.) |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{INTERRUPT COMPATIBILITY} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item This function may be used from both non-ISR and ISR software. |
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\item This function is thread-safe. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{EXECUTION TIME} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item TBD. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{FUNCTION NAME MNEMONIC} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item \emph{U16}: operates on and returns UCU\_UINT16. |
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\emph{Lsc}: linear scaling function. |
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\emph{Zyi}: zero $y$ intercept. |
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\emph{F}: result floored (rather than rounded). |
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\emph{Axd}: arbitrary maxima of domain. |
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\emph{Axr}: arbitrary maxima of range. |
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\end{list} |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\subsection[\emph{UcuAtU16LscZyiRAxdAxrRxx(\protect\mbox{\protect$\cdot$})}] |
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{\emph{UcuAtU16LscZyiRAxdAxrRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
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%Subsection tag: faa1 |
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\label{cafn0:slsf0:sfaa1} |
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|
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\index{UcuAtU16LscZyiRAxdAxrRxx()@\emph{UcuAtU16LscZyiRAxdAxrRxx($\cdot$)}}% |
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|
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\noindent\textbf{PROTOTYPE} |
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\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item |
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\begin{verbatim} |
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UCU_UINT16 UcuAtU16LscZyiRAxdAxrRxx( |
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UCU_UINT16 x, |
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UCU_UINT16 x_max, |
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UCU_UINT16 y_max |
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) |
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\end{verbatim} |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{SYNOPSIS} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item Linearly scales from $[0, x_{max}]$ to $[0, y_{max}]$, rounding the result |
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to the nearest integer with a downward bias. The result calculated is |
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$\displaystyle{\left\lfloor \frac{y_{max} x + \left\lfloor \displaystyle{\frac{x_{max} - 1}{2}} \right\rfloor}{x_{max}} \right\rfloor}$, |
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with the provision that the function output will never exceed $y_{max}$. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{INPUTS} |
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\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
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\item \emph{\textbf{x}}\\ |
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The input to scale. |
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\item \emph{\textbf{x\_max}}\\ |
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The value of $x$ that should correspond to $y_{max}$. |
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\item \emph{\textbf{y\_max}}\\ |
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The maximum output value of the function. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{OUTPUT} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item $\displaystyle{\left\lfloor \frac{y_{max} x + \left\lfloor \displaystyle{\frac{x_{max} - 1}{2}} \right\rfloor}{x_{max}} \right\rfloor}$, |
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with a maximum of $y_{max}$. |
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\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{EXCEPTION CASES} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item If $x>x_{max}$, $y_{max}$ is returned. |
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\item If $x_{max}=0$ or $y_{max}=0$, 0 is returned. (In either |
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of these cases, it isn't possible to determine the intent of |
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the caller, so 0 is the safest return value.) |
| 330 |
\end{list} |
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\vspace{2.8ex} |
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|
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\noindent\textbf{INTERRUPT COMPATIBILITY} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item This function may be used from both non-ISR and ISR software. |
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\item This function is thread-safe. |
| 337 |
\end{list} |
| 338 |
\vspace{2.8ex} |
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|
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\noindent\textbf{EXECUTION TIME} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item TBD. |
| 343 |
\end{list} |
| 344 |
\vspace{2.8ex} |
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|
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\noindent\textbf{FUNCTION NAME MNEMONIC} |
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\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item \emph{U16}: operates on UCU\_UINT16 operands. |
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\emph{Lsc}: linear scaling function. |
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\emph{Zyi}: zero $y$ intercept. |
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\emph{R}: result rounded to nearest integer. |
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\emph{Axd}: arbitrary maxima of domain. |
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\emph{Axr}: arbitrary maxima of range. |
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\end{list} |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\section{Ratiometric Adjustment Functions} |
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%Section tag: sraf0 |
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\label{cafn0:sraf0} |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\subsection[\emph{UcuAtU16RatAdjRRxx(\protect\mbox{\protect$\cdot$})}] |
| 369 |
{\emph{UcuAtU16RatAdjRRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 370 |
%Subsection tag: rat0 |
| 371 |
\label{cafn0:sraf0:srat0} |
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|
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\index{UcuAtU16RatAdjRRxx()@\emph{UcuAtU16RatAdjRRxx($\cdot$)}}% |
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|
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\noindent\textbf{PROTOTYPE} |
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\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
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\item |
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\begin{verbatim} |
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UCU_UINT16 UcuAtU16RatAdjRRxx( |
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UCU_UINT16 arg, |
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UCU_UINT16 arg_max, |
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UCU_UINT16 adj_in, |
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UCU_UINT16 adj_nom |
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) |
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\end{verbatim} |
| 386 |
\end{list} |
| 387 |
\vspace{2.8ex} |
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|
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\noindent\textbf{SYNOPSIS} |
| 390 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 391 |
\item Ratiometrically adjusts $arg$ according to the formula |
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$\displaystyle{\left\lfloor \frac{arg\;adj_{nom} + \left\lfloor \displaystyle{\frac{adj_{in} - 1}{2}} \right\rfloor}{adj_{in}} \right\rfloor}$, |
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with the result then clipped at $arg_{max}$. |
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\end{list} |
| 395 |
\vspace{2.8ex} |
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|
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\noindent\textbf{INPUTS} |
| 398 |
\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 399 |
\item \emph{\textbf{arg}}\\ |
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The input to scale. |
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\item \emph{\textbf{arg\_max}}\\ |
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The maximum value of $arg$ that may be returned by the function. |
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\item \emph{\textbf{adj\_in}}\\ |
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The value of the adjustment parameter that should be used for calculation. |
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\item \emph{\textbf{adj\_nom}}\\ |
| 406 |
The nominal value of the adjustment parameter that should leave $arg$ unchanged. As |
| 407 |
$adj_{in}$ increases, the value returned will decrease, and vice-versa. |
| 408 |
\end{list} |
| 409 |
\vspace{2.8ex} |
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|
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\noindent\textbf{OUTPUT} |
| 412 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 413 |
\item $\displaystyle{\left\lfloor \frac{arg\;adj_{nom} + \left\lfloor \displaystyle{\frac{adj_{in} - 1}{2}} \right\rfloor}{adj_{in}} \right\rfloor}$, |
| 414 |
with a maximum of $arg_{max}$. |
| 415 |
\end{list} |
| 416 |
\vspace{2.8ex} |
| 417 |
|
| 418 |
\noindent\textbf{EXCEPTION CASES} |
| 419 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 420 |
\item If $adj_{in}=0$ and $arg=0$, 0 is returned. |
| 421 |
\item If $adj_{in}=0$ and $arg>0$, $arg_{max}$ is returned. |
| 422 |
\item If $adj_{nom}=0$, 0 is returned. |
| 423 |
\end{list} |
| 424 |
\vspace{2.8ex} |
| 425 |
|
| 426 |
\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 427 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 428 |
\item This function may be used from both non-ISR and ISR software. |
| 429 |
\item This function is thread-safe. |
| 430 |
\end{list} |
| 431 |
\vspace{2.8ex} |
| 432 |
|
| 433 |
\noindent\textbf{EXECUTION TIME} |
| 434 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 435 |
\item TBD. |
| 436 |
\end{list} |
| 437 |
\vspace{2.8ex} |
| 438 |
|
| 439 |
\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 440 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 441 |
\item \emph{U16}: operates on UCU\_UINT16 operands. |
| 442 |
\emph{RatAdj}: ratiometric adjustment. |
| 443 |
\emph{R}: result rounded to nearest integer. |
| 444 |
\end{list} |
| 445 |
|
| 446 |
|
| 447 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 448 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 449 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 450 |
\section{Vector Functions, 2-Dimensional} |
| 451 |
\label{cafn0:svft0} |
| 452 |
|
| 453 |
|
| 454 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 455 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 456 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 457 |
%\subsection[\emph{UcuAtS32S16v2CpRxx(\protect\mbox{\protect$\cdot$})}] |
| 458 |
% {\emph{UcuAtS32S16v2CpRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 459 |
%\label{cafn0:svft0:scpt1} |
| 460 |
% |
| 461 |
%\index{UcuAtS32S16v2CpRxx()@\emph{UcuAtS32S16v2CpRxx($\cdot$)}}% |
| 462 |
% |
| 463 |
%\noindent\textbf{PROTOTYPE} |
| 464 |
%\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 465 |
%\item |
| 466 |
%\begin{verbatim} |
| 467 |
%UCU_SINT32 UcuAtS32S16v2CpRxx( |
| 468 |
% UCU_SINT16 a_x, |
| 469 |
% UCU_SINT16 a_y, |
| 470 |
% UCU_SINT16 b_x, |
| 471 |
% UCU_SINT16 b_y |
| 472 |
% ) |
| 473 |
%\end{verbatim} |
| 474 |
%\end{list} |
| 475 |
%\vspace{2.8ex} |
| 476 |
% |
| 477 |
%\noindent\textbf{SYNOPSIS} |
| 478 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 479 |
%\item Calculates the signed magnitude of the $\hat{k}$-component of the |
| 480 |
% cross-product of $\vec{a}$ and $\vec{b}$: |
| 481 |
% |
| 482 |
% \begin{equation} |
| 483 |
% \label{eq:cafn0:svft0:scpt1:01} |
| 484 |
% a_x b_y - a_y b_x . |
| 485 |
% \end{equation} |
| 486 |
%\end{list} |
| 487 |
%\vspace{2.8ex} |
| 488 |
% |
| 489 |
%\noindent\textbf{INPUTS} |
| 490 |
%\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 491 |
%\item \emph{\textbf{a\_x, a\_y, b\_x, b\_y}}\\ |
| 492 |
% The $x$ and $y$ components of the two vectors. The correct cross-product |
| 493 |
% will be returned over the entire domain of input arguments. |
| 494 |
%\end{list} |
| 495 |
%\vspace{2.8ex} |
| 496 |
% |
| 497 |
%\noindent\textbf{OUTPUT} |
| 498 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 499 |
%\item $a_x b_y - a_y b_x$. |
| 500 |
%\end{list} |
| 501 |
%\vspace{2.8ex} |
| 502 |
% |
| 503 |
%\noindent\textbf{EXCEPTION CASES} |
| 504 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 505 |
%\item None. |
| 506 |
%\end{list} |
| 507 |
%\vspace{2.8ex} |
| 508 |
% |
| 509 |
%\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 510 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 511 |
%\item This function may be used from both non-ISR and ISR software. |
| 512 |
%\item This function is thread-safe. |
| 513 |
%\end{list} |
| 514 |
%\vspace{2.8ex} |
| 515 |
% |
| 516 |
%\noindent\textbf{EXECUTION TIME} |
| 517 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 518 |
%\item TBD. |
| 519 |
%\end{list} |
| 520 |
%\vspace{2.8ex} |
| 521 |
% |
| 522 |
%\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 523 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 524 |
%\item \emph{S32}: returned value is a UCU\_SINT32. |
| 525 |
% \emph{S16v2}: operates on 2-dimensional vecotrs with UCU\_SINT16 components. |
| 526 |
% \emph{Cp}: cross-product. |
| 527 |
%\end{list} |
| 528 |
%\vspace{2.8ex} |
| 529 |
% |
| 530 |
%\noindent\textbf{DETAILED DESCRIPTION / ADDITIONAL INFORMATION} |
| 531 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 532 |
%\item The three-dimensional vector cross product is defined as |
| 533 |
% |
| 534 |
% \begin{equation} |
| 535 |
% \label{eq:cafn0:svft0:scpt1:02} |
| 536 |
% \vec{a} \times \vec{b} = \left | |
| 537 |
% { |
| 538 |
% \begin{array}{ccc} |
| 539 |
% \hat{i} & \hat{j} & \hat{k} \\ |
| 540 |
% a_x & a_y & a_z \\ |
| 541 |
% b_x & b_y & b_z |
| 542 |
% \end{array} |
| 543 |
% } |
| 544 |
% \right |. |
| 545 |
% \end{equation} |
| 546 |
%\item In two dimensions ($a_z = b_z = 0$), the vector |
| 547 |
% cross-product is defined as |
| 548 |
% |
| 549 |
% \begin{equation} |
| 550 |
% \label{eq:cafn0:svft0:scpt1:03} |
| 551 |
% \vec{a} \times \vec{b} = \left | |
| 552 |
% { |
| 553 |
% \begin{array}{ccc} |
| 554 |
% \hat{i} & \hat{j} & \hat{k} \\ |
| 555 |
% a_x & a_y & 0 \\ |
| 556 |
% b_x & b_y & 0 |
| 557 |
% \end{array} |
| 558 |
% } |
| 559 |
% \right | = \hat{k} (a_x b_y - a_y b_x) . |
| 560 |
% \end{equation} |
| 561 |
% |
| 562 |
% This function calculates the magnitude of the $\vec{k}$ component |
| 563 |
% of a 3-dimensional vector cross-product when $a_z = b_z = 0$. |
| 564 |
%\item This function returns a maximum when $a_x = b_y = a_y = -2^{15}$ |
| 565 |
% and $b_x = 2^{15} - 1$, leading to a maximum of $2^{31} - 2^{15}$. |
| 566 |
% Similarly, the minimum can be shown to be $-2^{31} + 2^{15}$\@. |
| 567 |
% Thus, the calculated result is always exact and always fits in a UCU\_SINT32. |
| 568 |
%\end{list} |
| 569 |
% |
| 570 |
% |
| 571 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 572 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 573 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 574 |
\subsection[\emph{UcuAtU16v2CpDiva2FRxx(\protect\mbox{\protect$\cdot$})}] |
| 575 |
{\emph{UcuAtU16v2CpDiva2FRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 576 |
\label{cafn0:svft0:scpt0} |
| 577 |
|
| 578 |
\index{UcuAtU16v2CpDiva2FRxx()@\emph{UcuAtU16v2CpDiva2FRxx($\cdot$)}}% |
| 579 |
|
| 580 |
\noindent\textbf{PROTOTYPE} |
| 581 |
\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 582 |
\item |
| 583 |
\begin{verbatim} |
| 584 |
UCU_UINT16 UcuAtU16v2CpDiva2FRxx( |
| 585 |
UCU_UINT16 a_x, |
| 586 |
UCU_UINT16 a_y, |
| 587 |
UCU_UINT16 b_x, |
| 588 |
UCU_UINT16 b_y |
| 589 |
) |
| 590 |
\end{verbatim} |
| 591 |
\end{list} |
| 592 |
\vspace{2.8ex} |
| 593 |
|
| 594 |
\noindent\textbf{SYNOPSIS} |
| 595 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 596 |
\item Calculates an approximation to |
| 597 |
|
| 598 |
\begin{equation} |
| 599 |
\label{eq:cafn0:svft0:scpt0:01} |
| 600 |
\left\lfloor \frac{| \vec{a} \times \vec{b} |}{| \vec{b} |} \right\rfloor |
| 601 |
= |
| 602 |
\left\lfloor \frac{| \vec{a} | | \vec{b} | \sin \theta}{| \vec{b} |} \right\rfloor , |
| 603 |
\end{equation} |
| 604 |
|
| 605 |
where $\vec{a}$ and $\vec{b}$ are in a special form as described below. |
| 606 |
\item This function is a special purpose function and not especially portable. In particular, the design |
| 607 |
of the interface is awkward. This function will eventually be replaced in the library. |
| 608 |
\end{list} |
| 609 |
\vspace{2.8ex} |
| 610 |
|
| 611 |
\noindent\textbf{INPUTS} |
| 612 |
\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 613 |
\item \emph{\textbf{a\_x, a\_y, b\_x, b\_y}}\\ |
| 614 |
The $x$ and $y$ components of the two vectors. Each is in ``excess-4096'' format, so that a value of 0 represents -4096, a value of 4096 |
| 615 |
represents 0, and a value of 8192 represents 4096. |
| 616 |
|
| 617 |
Each of these parameters are clipped into [32, 8160] by the function before any calculation |
| 618 |
is performed, representing vector component values in [-4064, 4064]. |
| 619 |
\end{list} |
| 620 |
\vspace{2.8ex} |
| 621 |
|
| 622 |
\noindent\textbf{OUTPUT} |
| 623 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 624 |
\item An approximation of |
| 625 |
$\left\lfloor \frac{| \vec{a} \times \vec{b} |}{| \vec{b} |}\right\rfloor |
| 626 |
= |
| 627 |
\left\lfloor\frac{| \vec{a} | | \vec{b} | \sin \theta}{| \vec{b} |}\right\rfloor$. |
| 628 |
The approximation is within several counts of the ideal value. |
| 629 |
\end{list} |
| 630 |
\vspace{2.8ex} |
| 631 |
|
| 632 |
\noindent\textbf{EXCEPTION CASES} |
| 633 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 634 |
\item If $\vec{b} = \vec{0}$, 0 is returned. |
| 635 |
\end{list} |
| 636 |
\vspace{2.8ex} |
| 637 |
|
| 638 |
\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 639 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 640 |
\item This function may be used from both non-ISR and ISR software. |
| 641 |
\item This function is thread-safe. |
| 642 |
\end{list} |
| 643 |
\vspace{2.8ex} |
| 644 |
|
| 645 |
\noindent\textbf{EXECUTION TIME} |
| 646 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 647 |
\item TBD. |
| 648 |
\end{list} |
| 649 |
\vspace{2.8ex} |
| 650 |
|
| 651 |
\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 652 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 653 |
\item \emph{U16v2}: operates on 2-dimensional vecotrs with UCU\_UINT16 components. |
| 654 |
\emph{Cp}: cross-product. |
| 655 |
\emph{Diva2}: divided by the second argument (the second vector). |
| 656 |
\emph{F}: the result is floor'd. |
| 657 |
\end{list} |
| 658 |
|
| 659 |
|
| 660 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 661 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 662 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 663 |
%\subsection[\emph{UcuAtS32S16v2CpDiva2FRxx(\protect\mbox{\protect$\cdot$})}] |
| 664 |
% {\emph{UcuAtS32S16v2CpDiva2FRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 665 |
%\label{cafn0:svft0:scpt2} |
| 666 |
% |
| 667 |
%\index{UcuAtS32S16v2CpDiva2FRxx()@\emph{UcuAtS32S16v2CpDiva2FRxx($\cdot$)}}% |
| 668 |
% |
| 669 |
%\noindent\textbf{PROTOTYPE} |
| 670 |
%\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 671 |
%\item |
| 672 |
%\begin{verbatim} |
| 673 |
%UCU_SINT32 UcuAtS32S16v2CpDiva2FRxx( |
| 674 |
% UCU_SINT16 a_x, |
| 675 |
% UCU_SINT16 a_y, |
| 676 |
% UCU_SINT16 b_x, |
| 677 |
% UCU_SINT16 b_y |
| 678 |
% ) |
| 679 |
%\end{verbatim} |
| 680 |
%\end{list} |
| 681 |
%\vspace{2.8ex} |
| 682 |
% |
| 683 |
%\noindent\textbf{SYNOPSIS} |
| 684 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 685 |
%\item Calculates |
| 686 |
% |
| 687 |
% \begin{equation} |
| 688 |
% \label{eq:cafn0:svft0:scpt2:01} |
| 689 |
% \left\lfloor \frac{\vec{a} \times \vec{b}}{| \vec{b} | \hat{k}} \right\rfloor , |
| 690 |
% \end{equation} |
| 691 |
% |
| 692 |
% where the floor function rounds negative values towards zero. It should be noted that by definition |
| 693 |
% |
| 694 |
% \begin{equation} |
| 695 |
% \label{eq:cafn0:svft0:scpt2:02} |
| 696 |
% \left\lfloor \left| \frac{\vec{a} \times \vec{b}}{| \vec{b} | \hat{k}} \right| \right\rfloor |
| 697 |
% = |
| 698 |
% \lfloor |\vec{a}| \sin \theta \rfloor , |
| 699 |
% \end{equation} |
| 700 |
% |
| 701 |
% where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$, $0 \leq \theta \leq \pi$, |
| 702 |
% so that this function provides an excellent approximation to |
| 703 |
% $\lfloor |\vec{a}| \sin \theta \rfloor$. |
| 704 |
%\item For two vectors $\vec{a}$ and $\vec{b}$ that both begin at the origin, |
| 705 |
% the absolute value of this function's return value is |
| 706 |
% the floor of the shortest distance between the tip of $\vec{a}$ and the line coincident with |
| 707 |
% $\vec{b}$. |
| 708 |
%\item The precise calculation method used by this function is described in |
| 709 |
% \S{}\ref{ctbg0:svec2} (p. \pageref{ctbg0:svec2}). |
| 710 |
%\end{list} |
| 711 |
%\vspace{2.8ex} |
| 712 |
% |
| 713 |
%\noindent\textbf{INPUTS} |
| 714 |
%\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 715 |
%\item \emph{\textbf{a\_x, a\_y, b\_x, b\_y}}\\ |
| 716 |
% The $x$ and $y$ components of the two vectors. All components are signed, and this function |
| 717 |
% will return correct results over the entire input domain. |
| 718 |
%\end{list} |
| 719 |
%\vspace{2.8ex} |
| 720 |
% |
| 721 |
%\noindent\textbf{OUTPUT} |
| 722 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 723 |
%\item $\displaystyle{\left\lfloor \frac{\vec{a} \times \vec{b}}{| \vec{b} | \hat{k}} \right\rfloor}$, |
| 724 |
% where the floor function rounds negative values towards zero. |
| 725 |
%\end{list} |
| 726 |
%\vspace{2.8ex} |
| 727 |
% |
| 728 |
%\noindent\textbf{EXCEPTION CASES} |
| 729 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 730 |
%\item None. |
| 731 |
%\end{list} |
| 732 |
%\vspace{2.8ex} |
| 733 |
% |
| 734 |
%\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 735 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 736 |
%\item This function may be used from both non-ISR and ISR software. |
| 737 |
%\item This function is thread-safe. |
| 738 |
%\end{list} |
| 739 |
%\vspace{2.8ex} |
| 740 |
% |
| 741 |
%\noindent\textbf{EXECUTION TIME} |
| 742 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 743 |
%\item TBD. |
| 744 |
%\end{list} |
| 745 |
%\vspace{2.8ex} |
| 746 |
% |
| 747 |
%\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 748 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 749 |
%\item \emph{S32}: the return value is UCU\_SINT32. |
| 750 |
% \emph{S16v2}: operates on 2-dimensional vectors with UCU\_SINT16 components. |
| 751 |
% \emph{Cp}: cross-product. |
| 752 |
% \emph{Diva2}: divided by the second argument (the second vector). |
| 753 |
% \emph{F}: the result is floor'd. |
| 754 |
%\end{list} |
| 755 |
% |
| 756 |
% |
| 757 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 758 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 759 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 760 |
%\subsection[\emph{UcuAtU32S16v2MagSquaredRxx(\protect\mbox{\protect$\cdot$})}] |
| 761 |
% {\emph{UcuAtU32S16v2MagSquaredRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 762 |
%\label{cafn0:svft0:svmf0} |
| 763 |
% |
| 764 |
%\index{UcuAtU32S16v2MagSquaredRxx()@\emph{UcuAtU32S16v2MagSquaredRxx($\cdot$)}}% |
| 765 |
% |
| 766 |
%\noindent\textbf{PROTOTYPE} |
| 767 |
%\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 768 |
%\item |
| 769 |
%\begin{verbatim} |
| 770 |
%UCU_UINT32 UcuAtU32S16v2MagSquaredRxx( |
| 771 |
% UCU_SINT16 a_x, |
| 772 |
% UCU_SINT16 a_y |
| 773 |
% ) |
| 774 |
%\end{verbatim} |
| 775 |
%\end{list} |
| 776 |
%\vspace{2.8ex} |
| 777 |
% |
| 778 |
%\noindent\textbf{SYNOPSIS} |
| 779 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 780 |
%\item Calculates $a_x^2 + a_y^2$. |
| 781 |
%\item The maximum value of $a_x^2 + a_y^2$ is $2(2^{15})^2$ = $2^{31}$, |
| 782 |
% so the return value of this function may exceed the maximum value |
| 783 |
% of an UCU\_SINT32, hence the return type UCU\_UINT32 is necessary, |
| 784 |
% and the result of this function may not be safely cast to |
| 785 |
% UCU\_SINT32. |
| 786 |
%\end{list} |
| 787 |
%\vspace{2.8ex} |
| 788 |
% |
| 789 |
%\noindent\textbf{INPUTS} |
| 790 |
%\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 791 |
%\item \emph{\textbf{a\_x, a\_y}}\\ |
| 792 |
% The $x$ and $y$ components of a vector. The components are signed, and this function |
| 793 |
% will return correct results over the entire input domain. |
| 794 |
%\end{list} |
| 795 |
%\vspace{2.8ex} |
| 796 |
% |
| 797 |
%\noindent\textbf{OUTPUT} |
| 798 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 799 |
%\item $a_x^2 + a_y^2$. |
| 800 |
%\end{list} |
| 801 |
%\vspace{2.8ex} |
| 802 |
% |
| 803 |
%\noindent\textbf{EXCEPTION CASES} |
| 804 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 805 |
%\item None. |
| 806 |
%\end{list} |
| 807 |
%\vspace{2.8ex} |
| 808 |
% |
| 809 |
%\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 810 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 811 |
%\item This function may be used from both non-ISR and ISR software. |
| 812 |
%\item This function is thread-safe. |
| 813 |
%\end{list} |
| 814 |
%\vspace{2.8ex} |
| 815 |
% |
| 816 |
%\noindent\textbf{EXECUTION TIME} |
| 817 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 818 |
%\item TBD. |
| 819 |
%\end{list} |
| 820 |
%\vspace{2.8ex} |
| 821 |
% |
| 822 |
%\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 823 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 824 |
%\item \emph{U32}: the return value is UCU\_UINT32. |
| 825 |
% \emph{S16v2}: operates on 2-dimensional vectors with UCU\_SINT16 components. |
| 826 |
% \emph{MagSquared}: returns the vector magnitude squared. |
| 827 |
%\end{list} |
| 828 |
% |
| 829 |
% |
| 830 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 831 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 832 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 833 |
\section{Square Root Extraction Functions} |
| 834 |
%Section tag: sre0 |
| 835 |
\label{cafn0:ssre0} |
| 836 |
|
| 837 |
|
| 838 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 839 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 840 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 841 |
\subsection[\emph{UcuAtU8SqrtFRxx(\protect\mbox{\protect$\cdot$})}] |
| 842 |
{\emph{UcuAtU8SqrtFRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 843 |
%Subsection tag: lcp0 |
| 844 |
\label{cafn0:ssre0:suee0} |
| 845 |
|
| 846 |
\index{UcuAtU8SqrtFRxx()@\emph{UcuAtU8SqrtFRxx($\cdot$)}}% |
| 847 |
|
| 848 |
\noindent\textbf{PROTOTYPE} |
| 849 |
\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 850 |
\item |
| 851 |
\begin{verbatim} |
| 852 |
UCU_UINT8 UcuAtU8SqrtFRxx( UCU_UINT8 x ) |
| 853 |
\end{verbatim} |
| 854 |
\end{list} |
| 855 |
\vspace{2.8ex} |
| 856 |
|
| 857 |
\noindent\textbf{SYNOPSIS} |
| 858 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 859 |
\item |
| 860 |
Calculates $\lfloor \sqrt{x} \rfloor$ using a 4-iteration |
| 861 |
trial squaring algorithm. |
| 862 |
\end{list} |
| 863 |
\vspace{2.8ex} |
| 864 |
|
| 865 |
\noindent\textbf{INPUT} |
| 866 |
\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 867 |
\item \emph{\textbf{x}}\\ |
| 868 |
The unsigned 8-bit integer whose square root is to be calculated. |
| 869 |
\end{list} |
| 870 |
\vspace{2.8ex} |
| 871 |
|
| 872 |
\noindent\textbf{OUTPUT} |
| 873 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 874 |
\item $\lfloor \sqrt{x} \rfloor$. |
| 875 |
\end{list} |
| 876 |
\vspace{2.8ex} |
| 877 |
|
| 878 |
\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 879 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 880 |
\item This function may be used from both non-ISR and ISR software. |
| 881 |
\item This function is thread-safe. |
| 882 |
\end{list} |
| 883 |
\vspace{2.8ex} |
| 884 |
|
| 885 |
\noindent\textbf{EXECUTION TIME} |
| 886 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 887 |
\item TBD. |
| 888 |
\end{list} |
| 889 |
\vspace{2.8ex} |
| 890 |
|
| 891 |
\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 892 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 893 |
\item \emph{U8}: operates on UCU\_UINT8 operands. |
| 894 |
\emph{Sqrt}: square root. |
| 895 |
\emph{F}: result is floor'd. |
| 896 |
\end{list} |
| 897 |
|
| 898 |
|
| 899 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 900 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 901 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 902 |
\subsection[\emph{UcuAtU16SqrtFRxx(\protect\mbox{\protect$\cdot$})}] |
| 903 |
{\emph{UcuAtU16SqrtFRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 904 |
\label{cafn0:ssre0:suee1} |
| 905 |
|
| 906 |
\index{UcuAtU16SqrtFRxx()@\emph{UcuAtU16SqrtFRxx($\cdot$)}}% |
| 907 |
|
| 908 |
\noindent\textbf{PROTOTYPE} |
| 909 |
\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 910 |
\item |
| 911 |
\begin{verbatim} |
| 912 |
UCU_UINT8 UcuAtU16SqrtFRxx( UCU_UINT16 x ) |
| 913 |
\end{verbatim} |
| 914 |
\end{list} |
| 915 |
\vspace{2.8ex} |
| 916 |
|
| 917 |
\noindent\textbf{SYNOPSIS} |
| 918 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 919 |
\item |
| 920 |
Calculates $\lfloor \sqrt{x} \rfloor$ using an 8-iteration |
| 921 |
trial squaring algorithm. |
| 922 |
\end{list} |
| 923 |
\vspace{2.8ex} |
| 924 |
|
| 925 |
\noindent\textbf{INPUT} |
| 926 |
\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 927 |
\item \emph{\textbf{x}}\\ |
| 928 |
The unsigned 16-bit integer whose square root is to be calculated. |
| 929 |
\end{list} |
| 930 |
\vspace{2.8ex} |
| 931 |
|
| 932 |
\noindent\textbf{OUTPUT} |
| 933 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 934 |
\item $\lfloor \sqrt{x} \rfloor$. |
| 935 |
\end{list} |
| 936 |
\vspace{2.8ex} |
| 937 |
|
| 938 |
\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 939 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 940 |
\item This function may be used from both non-ISR and ISR software. |
| 941 |
\item This function is thread-safe. |
| 942 |
\end{list} |
| 943 |
\vspace{2.8ex} |
| 944 |
|
| 945 |
\noindent\textbf{EXECUTION TIME} |
| 946 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 947 |
\item TBD. |
| 948 |
\end{list} |
| 949 |
\vspace{2.8ex} |
| 950 |
|
| 951 |
\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 952 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 953 |
\item \emph{U16}: operates on UCU\_UINT16 operands. |
| 954 |
\emph{Sqrt}: square root. |
| 955 |
\emph{F}: result is floor'd. |
| 956 |
\end{list} |
| 957 |
|
| 958 |
|
| 959 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 960 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 961 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 962 |
\subsection[\emph{UcuAtU16SqrtX10FRxx(\protect\mbox{\protect$\cdot$})}] |
| 963 |
{\emph{UcuAtU16SqrtX10FRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 964 |
\label{cafn0:ssre0:suee2} |
| 965 |
|
| 966 |
\index{UcuAtU16SqrtX10FRxx()@\emph{UcuAtU16SqrtX10FRxx($\cdot$)}}% |
| 967 |
|
| 968 |
\noindent\textbf{PROTOTYPE} |
| 969 |
\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 970 |
\item |
| 971 |
\begin{verbatim} |
| 972 |
UCU_UINT16 UcuAtU16SqrtX10FRxx( UCU_UINT16 val ) |
| 973 |
\end{verbatim} |
| 974 |
\end{list} |
| 975 |
\vspace{2.8ex} |
| 976 |
|
| 977 |
\noindent\textbf{SYNOPSIS} |
| 978 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 979 |
\item |
| 980 |
Calculates an approximation to $10 \sqrt{x}$ using the Babylonian method. |
| 981 |
The value returned will be either $\lfloor 10 \sqrt{x} \rfloor$ |
| 982 |
or $\lfloor 10 \sqrt{x} \rfloor + 1$. |
| 983 |
\end{list} |
| 984 |
\vspace{2.8ex} |
| 985 |
|
| 986 |
\noindent\textbf{INPUT} |
| 987 |
\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 988 |
\item \emph{\textbf{x}}\\ |
| 989 |
The unsigned 16-bit integer whose square root is to be calculated. |
| 990 |
\end{list} |
| 991 |
\vspace{2.8ex} |
| 992 |
|
| 993 |
\noindent\textbf{OUTPUT} |
| 994 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 995 |
\item $\lfloor 10 \sqrt{x} \rfloor$ or $\lfloor 10 \sqrt{x} \rfloor + 1$. There is |
| 996 |
no rule as to which will be returned (i.e. the value returned does not |
| 997 |
represent rounding). The possibility of returning either value is tied |
| 998 |
to the algorithm used.\footnote{This is a to-do item for this function. |
| 999 |
It should be modified to return $\lfloor 10 \sqrt{x} \rfloor$ in |
| 1000 |
all cases. Alternate algorithms should also be explored (for speed).} |
| 1001 |
\item This function is known to return a maximum of 2,559, |
| 1002 |
corresponding to $x = 65535$. |
| 1003 |
\end{list} |
| 1004 |
\vspace{2.8ex} |
| 1005 |
|
| 1006 |
\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 1007 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1008 |
\item This function may be used from both non-ISR and ISR software. |
| 1009 |
\item This function is thread-safe. |
| 1010 |
\end{list} |
| 1011 |
\vspace{2.8ex} |
| 1012 |
|
| 1013 |
\noindent\textbf{EXECUTION TIME} |
| 1014 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1015 |
\item TBD. |
| 1016 |
\end{list} |
| 1017 |
\vspace{2.8ex} |
| 1018 |
|
| 1019 |
\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 1020 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1021 |
\item \emph{U16}: operates on UCU\_UINT16 operands. |
| 1022 |
\emph{Sqrt}: square root. |
| 1023 |
\emph{X10}: result is multiplied by 10. |
| 1024 |
\emph{F}: result is floor'd. |
| 1025 |
\end{list} |
| 1026 |
|
| 1027 |
|
| 1028 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1029 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1030 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1031 |
%\subsection[\emph{UcuAtU32SqrtFRxx(\protect\mbox{\protect$\cdot$})}] |
| 1032 |
% {\emph{UcuAtU32SqrtFRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 1033 |
%\label{cafn0:ssre0:suee5} |
| 1034 |
% |
| 1035 |
%\index{UcuAtU32SqrtFRxx()@\emph{UcuAtU32SqrtFRxx($\cdot$)}}% |
| 1036 |
% |
| 1037 |
%\noindent\textbf{PROTOTYPE} |
| 1038 |
%\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1039 |
%\item |
| 1040 |
%\begin{verbatim} |
| 1041 |
%UCU_UINT16 UcuAtU32SqrtFRxx( UCU_UINT32 x ) |
| 1042 |
%\end{verbatim} |
| 1043 |
%\end{list} |
| 1044 |
%\vspace{2.8ex} |
| 1045 |
% |
| 1046 |
%\noindent\textbf{SYNOPSIS} |
| 1047 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1048 |
%\item |
| 1049 |
%Calculates $\lfloor \sqrt{x} \rfloor$ using a 16-iteration |
| 1050 |
%trial squaring algorithm. |
| 1051 |
%\end{list} |
| 1052 |
%\vspace{2.8ex} |
| 1053 |
% |
| 1054 |
%\noindent\textbf{INPUT} |
| 1055 |
%\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 1056 |
%\item \emph{\textbf{x}}\\ |
| 1057 |
% The unsigned 32-bit integer whose square root is to be calculated. |
| 1058 |
%\end{list} |
| 1059 |
%\vspace{2.8ex} |
| 1060 |
% |
| 1061 |
%\noindent\textbf{OUTPUT} |
| 1062 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1063 |
%\item $\lfloor \sqrt{x} \rfloor$. |
| 1064 |
%\end{list} |
| 1065 |
%\vspace{2.8ex} |
| 1066 |
% |
| 1067 |
%\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 1068 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1069 |
%\item This function may be used from both non-ISR and ISR software. |
| 1070 |
%\item This function is thread-safe. |
| 1071 |
%\end{list} |
| 1072 |
%\vspace{2.8ex} |
| 1073 |
% |
| 1074 |
%\noindent\textbf{EXECUTION TIME} |
| 1075 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1076 |
%\item TBD. |
| 1077 |
%\end{list} |
| 1078 |
%\vspace{2.8ex} |
| 1079 |
% |
| 1080 |
%\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 1081 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1082 |
%\item \emph{U32}: operates on UCU\_UINT32 operands. |
| 1083 |
% \emph{Sqrt}: square root. |
| 1084 |
% \emph{F}: result is floor'd. |
| 1085 |
%\end{list} |
| 1086 |
% |
| 1087 |
% |
| 1088 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1089 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1090 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1091 |
%\section{Sign Determination Functions} |
| 1092 |
%\label{cafn0:ssdf0} |
| 1093 |
% |
| 1094 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1095 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1096 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1097 |
%\subsection[\emph{UcuAtS32IsNegRxx(\protect\mbox{\protect$\cdot$})}] |
| 1098 |
% {\emph{UcuAtS32IsNegRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 1099 |
%\label{cafn0:ssdf0:sisn0} |
| 1100 |
% |
| 1101 |
%\index{UcuAtS32IsNegRxx()@\emph{UcuAtS32IsNegRxx($\cdot$)}}% |
| 1102 |
% |
| 1103 |
%\noindent\textbf{PROTOTYPE} |
| 1104 |
%\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1105 |
%\item |
| 1106 |
%\begin{verbatim} |
| 1107 |
%UCU_BOOLEAN UcuAtS32IsNegRxx( UCU_SINT32 x ) |
| 1108 |
%\end{verbatim} |
| 1109 |
%\end{list} |
| 1110 |
%\vspace{2.8ex} |
| 1111 |
% |
| 1112 |
%\noindent\textbf{SYNOPSIS} |
| 1113 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1114 |
%\item |
| 1115 |
%Returns UCU\_TRUE if $x<0$ or UCU\_FALSE otherwise. |
| 1116 |
%\end{list} |
| 1117 |
%\vspace{2.8ex} |
| 1118 |
% |
| 1119 |
%\noindent\textbf{INPUT} |
| 1120 |
%\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 1121 |
%\item \emph{\textbf{x}}\\ |
| 1122 |
% The signed 32-bit integer to be tested for negativity. |
| 1123 |
%\end{list} |
| 1124 |
%\vspace{2.8ex} |
| 1125 |
% |
| 1126 |
%\noindent\textbf{OUTPUT} |
| 1127 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1128 |
%\item UCU\_TRUE if $x<0$ or UCU\_FALSE otherwise. |
| 1129 |
%\end{list} |
| 1130 |
%\vspace{2.8ex} |
| 1131 |
% |
| 1132 |
%\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 1133 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1134 |
%\item This function may be used from both non-ISR and ISR software. |
| 1135 |
%\item This function is thread-safe. |
| 1136 |
%\end{list} |
| 1137 |
%\vspace{2.8ex} |
| 1138 |
% |
| 1139 |
%\noindent\textbf{EXECUTION TIME} |
| 1140 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1141 |
%\item TBD. |
| 1142 |
%\end{list} |
| 1143 |
%\vspace{2.8ex} |
| 1144 |
% |
| 1145 |
%\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 1146 |
%\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1147 |
%\item \emph{S32}: operates on UCU\_SINT32 operands. |
| 1148 |
% \emph{IsNeg}: tests if the argument \emph{is} \emph{neg}ative. |
| 1149 |
%\end{list} |
| 1150 |
% |
| 1151 |
% |
| 1152 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1153 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1154 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1155 |
\section{Trigonometric Functions} |
| 1156 |
\label{cafn0:strf0} |
| 1157 |
|
| 1158 |
|
| 1159 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1160 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1161 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1162 |
\subsection[\emph{UcuAtAtanIx100Odegx1RRxx(\protect\mbox{\protect$\cdot$})}] |
| 1163 |
{\emph{UcuAtAtanIx100Odegx1RRxx(\protect\mbox{\protect\boldmath $\cdot$})}} |
| 1164 |
\label{cafn0:strf0:sata0} |
| 1165 |
|
| 1166 |
\index{UcuAtAtanIx100Odegx1RRxx()@\emph{UcuAtAtanIx100Odegx1RRxx($\cdot$)}}% |
| 1167 |
|
| 1168 |
\noindent\textbf{PROTOTYPE} |
| 1169 |
\begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1170 |
\item |
| 1171 |
\begin{verbatim} |
| 1172 |
UCU_UINT8 UcuAtAtanIx100Odegx1RRxx( UCU_UINT16 x ) |
| 1173 |
\end{verbatim} |
| 1174 |
\end{list} |
| 1175 |
\vspace{2.8ex} |
| 1176 |
|
| 1177 |
\noindent\textbf{SYNOPSIS} |
| 1178 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1179 |
\item Calculates $\tan{}^{-1}x$ to 1-degree precision in the first quadrant |
| 1180 |
only using a binary search on an internal 90-element lookup table. |
| 1181 |
\end{list} |
| 1182 |
\vspace{2.8ex} |
| 1183 |
|
| 1184 |
\noindent\textbf{INPUT} |
| 1185 |
\begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}} |
| 1186 |
\item \emph{\textbf{x}}\\ |
| 1187 |
100 times the tangent whose arctangent is to be calculated. |
| 1188 |
For example, 0.58 would be supplied to this function |
| 1189 |
as $x=58$. |
| 1190 |
\end{list} |
| 1191 |
\vspace{2.8ex} |
| 1192 |
|
| 1193 |
\noindent\textbf{OUTPUT} |
| 1194 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1195 |
\item $\tan{}^{-1}x$, in the first quadrant, rounded approximately to the |
| 1196 |
nearest degree. |
| 1197 |
\end{list} |
| 1198 |
\vspace{2.8ex} |
| 1199 |
|
| 1200 |
\noindent\textbf{EXCEPTION CASES} |
| 1201 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1202 |
\item This function returns the expected value for all input arguments, |
| 1203 |
so there are no exception cases. |
| 1204 |
Input arguments from 11459 through $2^{16}-1$ will result |
| 1205 |
in a returned value of 90.\footnote{The tangent of 89.5 degrees is approximately 114.5887, |
| 1206 |
so an input argument of 11458 will result in a return value of 89, while an |
| 1207 |
input argument of 11459 will result in a return value of 90.} |
| 1208 |
\end{list} |
| 1209 |
\vspace{2.8ex} |
| 1210 |
|
| 1211 |
\noindent\textbf{INTERRUPT COMPATIBILITY} |
| 1212 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1213 |
\item This function may be used from both non-ISR and ISR software. |
| 1214 |
\item This function is thread-safe. |
| 1215 |
\end{list} |
| 1216 |
\vspace{2.8ex} |
| 1217 |
|
| 1218 |
\noindent\textbf{EXECUTION TIME} |
| 1219 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1220 |
\item TBD. |
| 1221 |
\end{list} |
| 1222 |
\vspace{2.8ex} |
| 1223 |
|
| 1224 |
\noindent\textbf{FUNCTION NAME MNEMONIC} |
| 1225 |
\begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}} |
| 1226 |
\item \emph{Atan}: arctangent. |
| 1227 |
\emph{Ix100}: input $\times$ 100. |
| 1228 |
\emph{Odegx1}: output in degrees $\times$ 1. |
| 1229 |
\emph{R}: rounded (to nearest degree). |
| 1230 |
\end{list} |
| 1231 |
|
| 1232 |
|
| 1233 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1234 |
\noindent\begin{figure}[!b] |
| 1235 |
\noindent\rule[-0.25in]{\textwidth}{1pt} |
| 1236 |
\begin{tiny} |
| 1237 |
\begin{verbatim} |
| 1238 |
$RCSfile: c_afn0.tex,v $ |
| 1239 |
$Source: /home/dashley/cvsrep/uculib01/uculib01/doc/manual/c_afn0/c_afn0.tex,v $ |
| 1240 |
$Revision: 1.37 $ |
| 1241 |
$Author: dashley $ |
| 1242 |
$Date: 2010/05/12 18:35:49 $ |
| 1243 |
\end{verbatim} |
| 1244 |
\end{tiny} |
| 1245 |
\noindent\rule[0.25in]{\textwidth}{1pt} |
| 1246 |
\end{figure} |
| 1247 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1248 |
%$Log: c_afn0.tex,v $ |
| 1249 |
%Revision 1.37 2010/05/12 18:35:49 dashley |
| 1250 |
%Removal of UcuAtS32S16v2CpDiva2FRxx() function. |
| 1251 |
% |
| 1252 |
%Revision 1.36 2010/05/12 18:29:49 dashley |
| 1253 |
%Removal of UcuAtS32S16v2CpRxx() function. |
| 1254 |
% |
| 1255 |
%Revision 1.35 2010/05/12 17:20:51 dashley |
| 1256 |
%Removal of UcuAtS32NegationRxx() function. |
| 1257 |
% |
| 1258 |
%Revision 1.34 2010/05/12 17:16:47 dashley |
| 1259 |
%Removal of UcuAtU32S16v2MagSquaredRxx() function. |
| 1260 |
% |
| 1261 |
%Revision 1.33 2010/05/12 17:09:42 dashley |
| 1262 |
%UcuAtS32IsNegRxx() function backed out. |
| 1263 |
% |
| 1264 |
%Revision 1.32 2010/05/12 17:04:17 dashley |
| 1265 |
%UcuAtU32SqrtFRxx() function backed out. This function is not yet |
| 1266 |
%implemented. |
| 1267 |
% |
| 1268 |
%Revision 1.31 2010/04/16 19:35:41 dashley |
| 1269 |
%Missing word added. |
| 1270 |
% |
| 1271 |
%Revision 1.30 2010/04/16 19:33:37 dashley |
| 1272 |
%Addition of UcuAtS32NegationRxx() function. |
| 1273 |
% |
| 1274 |
%Revision 1.29 2010/04/15 20:21:07 dashley |
| 1275 |
%Typo corrected. |
| 1276 |
% |
| 1277 |
%Revision 1.28 2010/04/15 19:34:39 dashley |
| 1278 |
%Addition of UcuAtU32S16v2MagSquaredRxx() function. |
| 1279 |
% |
| 1280 |
%Revision 1.27 2010/04/15 17:34:52 dashley |
| 1281 |
%Addition of UcuAtS32IsNegRxx() function. |
| 1282 |
% |
| 1283 |
%Revision 1.26 2010/04/15 14:56:28 dashley |
| 1284 |
%Addition of UcuAtU32SqrtFRxx() function. |
| 1285 |
% |
| 1286 |
%Revision 1.25 2010/04/14 14:29:47 dashley |
| 1287 |
%Incorrect equation labels changed. |
| 1288 |
% |
| 1289 |
%Revision 1.24 2010/04/05 15:13:50 dashley |
| 1290 |
%Edits. |
| 1291 |
% |
| 1292 |
%Revision 1.23 2010/04/05 13:22:09 dashley |
| 1293 |
%Function documentation updated. |
| 1294 |
% |
| 1295 |
%Revision 1.22 2010/04/01 20:21:50 dashley |
| 1296 |
%Edits. |
| 1297 |
% |
| 1298 |
%Revision 1.21 2010/04/01 14:49:25 dashley |
| 1299 |
%Addition of UcuAtS32S16v2CpRxx() function. |
| 1300 |
% |
| 1301 |
%Revision 1.20 2010/02/20 16:55:52 dashley |
| 1302 |
%Function added. |
| 1303 |
% |
| 1304 |
%Revision 1.19 2010/02/19 17:12:55 dashley |
| 1305 |
%Function added. |
| 1306 |
% |
| 1307 |
%Revision 1.18 2010/02/18 17:05:57 dashley |
| 1308 |
%Edits. |
| 1309 |
% |
| 1310 |
%Revision 1.17 2010/02/17 19:07:34 dashley |
| 1311 |
%Documentation added. |
| 1312 |
% |
| 1313 |
%Revision 1.16 2010/02/16 23:38:42 dashley |
| 1314 |
%Description of Sqrtx10 function corrected. |
| 1315 |
% |
| 1316 |
%Revision 1.15 2010/02/15 20:33:56 dashley |
| 1317 |
%Minor typo corrected. |
| 1318 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 1319 |
|
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