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author | Aki <please@ignore.pl> | 2021-10-01 23:46:47 +0200 |
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committer | Aki <please@ignore.pl> | 2021-10-01 23:46:47 +0200 |
commit | ddd76aa4e1571c8d5965709db5c3cd47a89c9a38 (patch) | |
tree | 4e07bfaebede6531a70984fdebc855bca52f394a /vorbis/doc/09-helper.tex | |
parent | 3a507e08b1d4e5970b27401a7e6517570d529400 (diff) | |
parent | c2d2c3551501110fddd78674d5435bfaa70382a3 (diff) | |
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diff --git a/vorbis/doc/09-helper.tex b/vorbis/doc/09-helper.tex new file mode 100644 index 0000000..0a13795 --- /dev/null +++ b/vorbis/doc/09-helper.tex @@ -0,0 +1,180 @@ +% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*- +%!TEX root = Vorbis_I_spec.tex +\section{Helper equations} \label{vorbis:spec:helper} + +\subsection{Overview} + +The equations below are used in multiple places by the Vorbis codec +specification. Rather than cluttering up the main specification +documents, they are defined here and referenced where appropriate. + + +\subsection{Functions} + +\subsubsection{ilog} \label{vorbis:spec:ilog} + +The "ilog(x)" function returns the position number (1 through n) of the highest set bit in the two's complement integer value +\varname{[x]}. Values of \varname{[x]} less than zero are defined to return zero. + +\begin{programlisting} + 1) [return\_value] = 0; + 2) if ( [x] is greater than zero ) { + + 3) increment [return\_value]; + 4) logical shift [x] one bit to the right, padding the MSb with zero + 5) repeat at step 2) + + } + + 6) done +\end{programlisting} + +Examples: + +\begin{itemize} + \item ilog(0) = 0; + \item ilog(1) = 1; + \item ilog(2) = 2; + \item ilog(3) = 2; + \item ilog(4) = 3; + \item ilog(7) = 3; + \item ilog(negative number) = 0; +\end{itemize} + + + + +\subsubsection{float32\_unpack} \label{vorbis:spec:float32:unpack} + +"float32\_unpack(x)" is intended to translate the packed binary +representation of a Vorbis codebook float value into the +representation used by the decoder for floating point numbers. For +purposes of this example, we will unpack a Vorbis float32 into a +host-native floating point number. + +\begin{programlisting} + 1) [mantissa] = [x] bitwise AND 0x1fffff (unsigned result) + 2) [sign] = [x] bitwise AND 0x80000000 (unsigned result) + 3) [exponent] = ( [x] bitwise AND 0x7fe00000) shifted right 21 bits (unsigned result) + 4) if ( [sign] is nonzero ) then negate [mantissa] + 5) return [mantissa] * ( 2 ^ ( [exponent] - 788 ) ) +\end{programlisting} + + + +\subsubsection{lookup1\_values} \label{vorbis:spec:lookup1:values} + +"lookup1\_values(codebook\_entries,codebook\_dimensions)" is used to +compute the correct length of the value index for a codebook VQ lookup +table of lookup type 1. The values on this list are permuted to +construct the VQ vector lookup table of size +\varname{[codebook\_entries]}. + +The return value for this function is defined to be 'the greatest +integer value for which \varname{[return\_value]} to the power of +\varname{[codebook\_dimensions]} is less than or equal to +\varname{[codebook\_entries]}'. + + + +\subsubsection{low\_neighbor} \label{vorbis:spec:low:neighbor} + +"low\_neighbor(v,x)" finds the position \varname{n} in vector \varname{[v]} of +the greatest value scalar element for which \varname{n} is less than +\varname{[x]} and vector \varname{[v]} element \varname{n} is less +than vector \varname{[v]} element \varname{[x]}. + +\subsubsection{high\_neighbor} \label{vorbis:spec:high:neighbor} + +"high\_neighbor(v,x)" finds the position \varname{n} in vector [v] of +the lowest value scalar element for which \varname{n} is less than +\varname{[x]} and vector \varname{[v]} element \varname{n} is greater +than vector \varname{[v]} element \varname{[x]}. + + + +\subsubsection{render\_point} \label{vorbis:spec:render:point} + +"render\_point(x0,y0,x1,y1,X)" is used to find the Y value at point X +along the line specified by x0, x1, y0 and y1. This function uses an +integer algorithm to solve for the point directly without calculating +intervening values along the line. + +\begin{programlisting} + 1) [dy] = [y1] - [y0] + 2) [adx] = [x1] - [x0] + 3) [ady] = absolute value of [dy] + 4) [err] = [ady] * ([X] - [x0]) + 5) [off] = [err] / [adx] using integer division + 6) if ( [dy] is less than zero ) { + + 7) [Y] = [y0] - [off] + + } else { + + 8) [Y] = [y0] + [off] + + } + + 9) done +\end{programlisting} + + + +\subsubsection{render\_line} \label{vorbis:spec:render:line} + +Floor decode type one uses the integer line drawing algorithm of +"render\_line(x0, y0, x1, y1, v)" to construct an integer floor +curve for contiguous piecewise line segments. Note that it has not +been relevant elsewhere, but here we must define integer division as +rounding division of both positive and negative numbers toward zero. + + +\begin{programlisting} + 1) [dy] = [y1] - [y0] + 2) [adx] = [x1] - [x0] + 3) [ady] = absolute value of [dy] + 4) [base] = [dy] / [adx] using integer division + 5) [x] = [x0] + 6) [y] = [y0] + 7) [err] = 0 + + 8) if ( [dy] is less than 0 ) { + + 9) [sy] = [base] - 1 + + } else { + + 10) [sy] = [base] + 1 + + } + + 11) [ady] = [ady] - (absolute value of [base]) * [adx] + 12) vector [v] element [x] = [y] + + 13) iterate [x] over the range [x0]+1 ... [x1]-1 { + + 14) [err] = [err] + [ady]; + 15) if ( [err] >= [adx] ) { + + 16) [err] = [err] - [adx] + 17) [y] = [y] + [sy] + + } else { + + 18) [y] = [y] + [base] + + } + + 19) vector [v] element [x] = [y] + + } +\end{programlisting} + + + + + + + + |