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libs/libvorbis-1.3.7: Re-exporting, hopefully this time everything is there. bugref:10275

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1% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
2%!TEX root = Vorbis_I_spec.tex
3\section{Helper equations} \label{vorbis:spec:helper}
4
5\subsection{Overview}
6
7The equations below are used in multiple places by the Vorbis codec
8specification. Rather than cluttering up the main specification
9documents, they are defined here and referenced where appropriate.
10
11
12\subsection{Functions}
13
14\subsubsection{ilog} \label{vorbis:spec:ilog}
15
16The "ilog(x)" function returns the position number (1 through n) of the highest set bit in the two's complement integer value
17\varname{[x]}. Values of \varname{[x]} less than zero are defined to return zero.
18
19\begin{programlisting}
20 1) [return\_value] = 0;
21 2) if ( [x] is greater than zero ) {
22
23 3) increment [return\_value];
24 4) logical shift [x] one bit to the right, padding the MSb with zero
25 5) repeat at step 2)
26
27 }
28
29 6) done
30\end{programlisting}
31
32Examples:
33
34\begin{itemize}
35 \item ilog(0) = 0;
36 \item ilog(1) = 1;
37 \item ilog(2) = 2;
38 \item ilog(3) = 2;
39 \item ilog(4) = 3;
40 \item ilog(7) = 3;
41 \item ilog(negative number) = 0;
42\end{itemize}
43
44
45
46
47\subsubsection{float32\_unpack} \label{vorbis:spec:float32:unpack}
48
49"float32\_unpack(x)" is intended to translate the packed binary
50representation of a Vorbis codebook float value into the
51representation used by the decoder for floating point numbers. For
52purposes of this example, we will unpack a Vorbis float32 into a
53host-native floating point number.
54
55\begin{programlisting}
56 1) [mantissa] = [x] bitwise AND 0x1fffff (unsigned result)
57 2) [sign] = [x] bitwise AND 0x80000000 (unsigned result)
58 3) [exponent] = ( [x] bitwise AND 0x7fe00000) shifted right 21 bits (unsigned result)
59 4) if ( [sign] is nonzero ) then negate [mantissa]
60 5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) )
61\end{programlisting}
62
63
64
65\subsubsection{lookup1\_values} \label{vorbis:spec:lookup1:values}
66
67"lookup1\_values(codebook\_entries,codebook\_dimensions)" is used to
68compute the correct length of the value index for a codebook VQ lookup
69table of lookup type 1. The values on this list are permuted to
70construct the VQ vector lookup table of size
71\varname{[codebook\_entries]}.
72
73The return value for this function is defined to be 'the greatest
74integer value for which \varname{[return\_value]} to the power of
75\varname{[codebook\_dimensions]} is less than or equal to
76\varname{[codebook\_entries]}'.
77
78
79
80\subsubsection{low\_neighbor} \label{vorbis:spec:low:neighbor}
81
82"low\_neighbor(v,x)" finds the position \varname{n} in vector \varname{[v]} of
83the greatest value scalar element for which \varname{n} is less than
84\varname{[x]} and vector \varname{[v]} element \varname{n} is less
85than vector \varname{[v]} element \varname{[x]}.
86
87\subsubsection{high\_neighbor} \label{vorbis:spec:high:neighbor}
88
89"high\_neighbor(v,x)" finds the position \varname{n} in vector [v] of
90the lowest value scalar element for which \varname{n} is less than
91\varname{[x]} and vector \varname{[v]} element \varname{n} is greater
92than vector \varname{[v]} element \varname{[x]}.
93
94
95
96\subsubsection{render\_point} \label{vorbis:spec:render:point}
97
98"render\_point(x0,y0,x1,y1,X)" is used to find the Y value at point X
99along the line specified by x0, x1, y0 and y1. This function uses an
100integer algorithm to solve for the point directly without calculating
101intervening values along the line.
102
103\begin{programlisting}
104 1) [dy] = [y1] - [y0]
105 2) [adx] = [x1] - [x0]
106 3) [ady] = absolute value of [dy]
107 4) [err] = [ady] * ([X] - [x0])
108 5) [off] = [err] / [adx] using integer division
109 6) if ( [dy] is less than zero ) {
110
111 7) [Y] = [y0] - [off]
112
113 } else {
114
115 8) [Y] = [y0] + [off]
116
117 }
118
119 9) done
120\end{programlisting}
121
122
123
124\subsubsection{render\_line} \label{vorbis:spec:render:line}
125
126Floor decode type one uses the integer line drawing algorithm of
127"render\_line(x0, y0, x1, y1, v)" to construct an integer floor
128curve for contiguous piecewise line segments. Note that it has not
129been relevant elsewhere, but here we must define integer division as
130rounding division of both positive and negative numbers toward zero.
131
132
133\begin{programlisting}
134 1) [dy] = [y1] - [y0]
135 2) [adx] = [x1] - [x0]
136 3) [ady] = absolute value of [dy]
137 4) [base] = [dy] / [adx] using integer division
138 5) [x] = [x0]
139 6) [y] = [y0]
140 7) [err] = 0
141
142 8) if ( [dy] is less than 0 ) {
143
144 9) [sy] = [base] - 1
145
146 } else {
147
148 10) [sy] = [base] + 1
149
150 }
151
152 11) [ady] = [ady] - (absolute value of [base]) * [adx]
153 12) vector [v] element [x] = [y]
154
155 13) iterate [x] over the range [x0]+1 ... [x1]-1 {
156
157 14) [err] = [err] + [ady];
158 15) if ( [err] >= [adx] ) {
159
160 16) [err] = [err] - [adx]
161 17) [y] = [y] + [sy]
162
163 } else {
164
165 18) [y] = [y] + [base]
166
167 }
168
169 19) vector [v] element [x] = [y]
170
171 }
172\end{programlisting}
173
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