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1 %$Header: /home/dashley/cvsrep/uculib01/uculib01/doc/manual/c_fpa0/c_fpa0.tex,v 1.4 2010/02/22 15:40:28 dashley Exp $
2
3 \chapter{Fixed-Point Arithmetic Functions}
4
5 \label{cfpa0}
6
7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
9 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10 \section{Introduction and Overview}
11 \label{cfpa0:siov0}
12
13 TBD.
14
15
16 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
19 \section{UCU\_UINT16 [0, 1024] [0,1] Bounded Functions}
20 \label{cfpa0:subf0}
21
22
23 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
24 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
25 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
26 \subsection[\emph{UcuFpUm1024uProjIntoRU16aRxx(\protect\mbox{\protect$\cdot$})}]
27 {\emph{UcuFpUm1024uProjIntoRU16aRxx(\protect\mbox{\protect\boldmath $\cdot$})}}
28 %Subsection tag: faa1
29 \label{cfpa0:subf0:sfaa0}
30
31 \index{UcuFpUm1024uProjIntoRU16aRxx()@\emph{UcuFpUm1024uProjIntoRU16aRxx($\cdot$)}}%
32
33 \noindent\textbf{PROTOTYPE}
34 \begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
35 \item
36 \begin{verbatim}
37 UCU_UINT16 UcuFpUm1024uProjIntoRU16aRxx(
38 UCU_UINT16 x,
39 UCU_UINT16 x_max,
40 )
41 \end{verbatim}
42 \end{list}
43 \vspace{2.8ex}
44
45 \noindent\textbf{SYNOPSIS}
46 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
47 \item Linearly scales from $[0, x_{max}]$ to $[0, 1024]$, rounding the result
48 to the nearest integer with a downward bias. The result calculated is
49 $\displaystyle{\left\lfloor \frac{1024 x + \left\lfloor \displaystyle{\frac{x_{max} - 1}{2}} \right\rfloor}{x_{max}} \right\rfloor}$,
50 with the provision that the function output will never exceed 1024.
51 \end{list}
52 \vspace{2.8ex}
53
54 \noindent\textbf{INPUTS}
55 \begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}}
56 \item \emph{\textbf{x}}\\
57 The input to scale.
58 \item \emph{\textbf{x\_max}}\\
59 The value of $x$ that should correspond to 1024.
60 \end{list}
61 \vspace{2.8ex}
62
63 \noindent\textbf{OUTPUT}
64 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
65 \item $\displaystyle{\left\lfloor \frac{1024 x + \left\lfloor \displaystyle{\frac{x_{max} - 1}{2}} \right\rfloor}{x_{max}} \right\rfloor}$,
66 with a maximum of 1024.
67 \end{list}
68 \vspace{2.8ex}
69
70 \noindent\textbf{EXCEPTION CASES}
71 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
72 \item If $x>x_{max}$, 1024 is returned.
73 \item If $x_{max}=0$, 0 is returned. (In this
74 case, it isn't possible to determine the intent of
75 the caller, so 0 is the safest return value.)
76 \end{list}
77 \vspace{2.8ex}
78
79 \noindent\textbf{INTERRUPT COMPATIBILITY}
80 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
81 \item This function may be used from both non-ISR and ISR software.
82 \item This function is thread-safe.
83 \end{list}
84 \vspace{2.8ex}
85
86 \noindent\textbf{EXECUTION TIME}
87 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
88 \item TBD.
89 \end{list}
90 \vspace{2.8ex}
91
92 \noindent\textbf{FUNCTION NAME MNEMONIC}
93 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
94 \item \emph{Um1024u}: unsigned maximum-1024 unsigned.
95 \emph{Proj}: projection.
96 \emph{Into}: into.
97 \emph{R}: result rounded to nearest integer.
98 \emph{U16a}: the argument is UCU\_UINT16.
99 \end{list}
100
101
102 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
103 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
104 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
105 \subsection[\emph{UcuFpUm1024uMulRRxx(\protect\mbox{\protect$\cdot$})}]
106 {\emph{UcuFpUm1024uMulRRxx(\protect\mbox{\protect\boldmath $\cdot$})}}
107 \label{cfpa0:subf0:sfaa1}
108
109 \index{UcuFpUm1024uMulRRxx()@\emph{UcuFpUm1024uMulRRxx($\cdot$)}}%
110
111 \noindent\textbf{PROTOTYPE}
112 \begin {list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
113 \item
114 \begin{verbatim}
115 UCU_UINT16 UcuFpUm1024uMulRRxx(
116 UCU_UINT16 x_1,
117 UCU_UINT16 x_2,
118 )
119 \end{verbatim}
120 \end{list}
121 \vspace{2.8ex}
122
123 \noindent\textbf{SYNOPSIS}
124 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
125 \item Calculates $x_1 x_2$, treating $x_1$ and $x_2$ as fixed-point numbers with 1024 corresponding
126 to 1, and with $x_1$ and $x_2$ having a maximum of 1. The output is rounded to the nearest
127 integer with a slight downward bias.
128 \item The precise function implemented is
129 \begin{equation}
130 \left\lfloor \frac{min(x_1, 1024) \; min(x_2, 1024) + 511}{1024} \right\rfloor.
131 \end{equation}
132 \item The function output cannot exceed 1024.
133 \end{list}
134 \vspace{2.8ex}
135
136 \noindent\textbf{INPUTS}
137 \begin{list}{}{\setlength{\leftmargin}{0.5in}\setlength{\itemindent}{-0.25in}\setlength{\topsep}{0.0in}\setlength{\partopsep}{0.0in}}
138 \item \emph{\textbf{x\_1}}, \emph{\textbf{x\_2}} \\
139 The inputs to multiply together.
140 \end{list}
141 \vspace{2.8ex}
142
143 \noindent\textbf{OUTPUT}
144 \vspace{0.4ex}
145 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
146 \item $\displaystyle{\left\lfloor \frac{min(x_1, 1024) \; min(x_2, 1024) + 511}{1024} \right\rfloor}$.
147 \end{list}
148 \vspace{2.8ex}
149
150 \noindent\textbf{EXCEPTION CASES}
151 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
152 \item As indicated above, $x_1$ and $x_2$ are clipped at 1024 before being used
153 in the calculation.
154 \end{list}
155 \vspace{2.8ex}
156
157 \noindent\textbf{INTERRUPT COMPATIBILITY}
158 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
159 \item This function may be used from both non-ISR and ISR software.
160 \item This function is thread-safe.
161 \end{list}
162 \vspace{2.8ex}
163
164 \noindent\textbf{EXECUTION TIME}
165 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
166 \item TBD.
167 \end{list}
168 \vspace{2.8ex}
169
170 \noindent\textbf{FUNCTION NAME MNEMONIC}
171 \begin{list}{}{\setlength{\leftmargin}{0.25in}\setlength{\topsep}{0.0in}}
172 \item \emph{Um1024u}: unsigned maximum-1024 unsigned.
173 \emph{Mul}: multiplication.
174 \emph{R}: result is rounded to nearest integer (with slight downward bias).
175 \end{list}
176
177
178 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
179 \noindent\begin{figure}[!b]
180 \noindent\rule[-0.25in]{\textwidth}{1pt}
181 \begin{tiny}
182 \begin{verbatim}
183 $RCSfile: c_fpa0.tex,v $
184 $Source: /home/dashley/cvsrep/uculib01/uculib01/doc/manual/c_fpa0/c_fpa0.tex,v $
185 $Revision: 1.4 $
186 $Author: dashley $
187 $Date: 2010/02/22 15:40:28 $
188 \end{verbatim}
189 \end{tiny}
190 \noindent\rule[0.25in]{\textwidth}{1pt}
191 \end{figure}
192
193 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
194 %$Log: c_fpa0.tex,v $
195 %Revision 1.4 2010/02/22 15:40:28 dashley
196 %Function added.
197 %
198 %Revision 1.3 2010/02/22 00:16:02 dashley
199 %Documentation added.
200 %
201 %Revision 1.2 2010/01/28 21:18:32 dashley
202 %a)Chapter start quotes removed.
203 %b)Aesthetic comment line added at the bottom of most files.
204 %
205 %Revision 1.1 2010/01/24 03:00:41 dashley
206 %Initial checkin.
207 %
208 %End of $RCSfile: c_fpa0.tex,v $.
209 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
210

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