From 373dc625f82b47096893add42c4472e4a57ab7eb Mon Sep 17 00:00:00 2001 From: Aki Date: Wed, 9 Feb 2022 22:23:03 +0100 Subject: Moved third-party libraries to a separate subdirectory --- vorbis/doc/09-helper.tex | 180 ----------------------------------------------- 1 file changed, 180 deletions(-) delete mode 100644 vorbis/doc/09-helper.tex (limited to 'vorbis/doc/09-helper.tex') diff --git a/vorbis/doc/09-helper.tex b/vorbis/doc/09-helper.tex deleted file mode 100644 index 0a13795..0000000 --- a/vorbis/doc/09-helper.tex +++ /dev/null @@ -1,180 +0,0 @@ -% -*- 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} - - - - - - - - -- cgit v1.1