doc/helper.html - platform/external/libvorbis - Git at Google

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 <h1>Ogg Vorbis I format specification: helper equations</h1>

 <h1>Overview</h1>

 <p>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 linked in the main documents
 where appropriate.</p>

 <h2><a name="log">ilog</a></h2>

 <p>The "ilog(x)" function returns the position number (1 through n) of the
 highest set bit in the two's complement integer value
 <tt>[x]</tt>. Values of <tt>[x]</tt> less than zero are defined to return zero.</p>

 <pre>
   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
 </pre>

 <p>Examples:</p>

 <ul>
 <li>ilog(0) = 0;</li>
 <li>ilog(1) = 1;</li>
 <li>ilog(2) = 2;</li>
 <li>ilog(3) = 2;</li>
 <li>ilog(4) = 3;</li>
 <li>ilog(7) = 3;</li>
 <li>ilog(negative number) = 0;</li>
 </ul>

 <h2><a name="float32_unpack">float32_unpack</a></h2>

 <p>"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.</p>

 <pre>
   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 ) )
 </pre>

 <h2><a name="lookup1_values">lookup1_values</a></h2>

 <p>"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
 <tt>[codebook_entries]</tt>.</p>

 <p>The return value for this function is defined to be 'the greatest
 integer value for which <tt>[return_value] to the power of
 [codebook_dimensions] is less than or equal to
 [codebook_entries]</tt>'.</p>

 <h2><a name="low_neighbor">low_neighbor</a></h2>

 <p>"low_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
 the greatest value scalar element for which <i>n</i> is less than
 <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is less
 than vector [v] element [x]</tt>.</p>

 <h2><a name="high_neighbor">high_neighbor</a></h2>

 <p>"high_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
 the lowest value scalar element for which <i>n</i> is less than
 <tt>[x]</tt> and <tt>vector [v] element <i>n</i> is greater
 than vector [v] element [x]</tt>.</p>

 <h2><a name="render_point">render_point</a></h2>

 <p>"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.</p>

 <pre>
   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
 </pre>

 <h2><a name="render_line">render_line</a></h2>

 <p>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.</p>

 <pre>
   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] ) {

              15) [err] = [err] - [adx]
              16)   [y] = [y] + [sy]

            } else {

              17) [y] = [y] + [base]

            }

        18) vector [v] element [x] = [y]

      }
 </pre>

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	</div>

	<h1>Ogg Vorbis I format specification: helper equations</h1>

	<h1>Overview</h1>

	<p>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 linked in the main documents
	where appropriate.</p>

	<h2><a name="log">ilog</a></h2>

	<p>The "ilog(x)" function returns the position number (1 through n) of the
	highest set bit in the two's complement integer value
	<tt>[x]</tt>. Values of <tt>[x]</tt> less than zero are defined to return zero.</p>

	<pre>
	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
	</pre>

	<p>Examples:</p>

	<ul>
	<li>ilog(0) = 0;</li>
	<li>ilog(1) = 1;</li>
	<li>ilog(2) = 2;</li>
	<li>ilog(3) = 2;</li>
	<li>ilog(4) = 3;</li>
	<li>ilog(7) = 3;</li>
	<li>ilog(negative number) = 0;</li>
	</ul>

	<h2><a name="float32_unpack">float32_unpack</a></h2>

	<p>"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.</p>

	<pre>
	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 ) )
	</pre>

	<h2><a name="lookup1_values">lookup1_values</a></h2>

	<p>"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
	<tt>[codebook_entries]</tt>.</p>

	<p>The return value for this function is defined to be 'the greatest
	integer value for which <tt>[return_value] to the power of
	[codebook_dimensions] is less than or equal to
	[codebook_entries]</tt>'.</p>

	<h2><a name="low_neighbor">low_neighbor</a></h2>

	<p>"low_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
	the greatest value scalar element for which <i>n</i> is less than
	<tt>[x]</tt> and <tt>vector [v] element <i>n</i> is less
	than vector [v] element [x]</tt>.</p>

	<h2><a name="high_neighbor">high_neighbor</a></h2>

	<p>"high_neighbor(v,x)" finds the position <i>n</i> in vector [v] of
	the lowest value scalar element for which <i>n</i> is less than
	<tt>[x]</tt> and <tt>vector [v] element <i>n</i> is greater
	than vector [v] element [x]</tt>.</p>

	<h2><a name="render_point">render_point</a></h2>

	<p>"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.</p>

	<pre>
	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
	</pre>

	<h2><a name="render_line">render_line</a></h2>

	<p>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.</p>

	<pre>
	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] ) {

	15) [err] = [err] - [adx]
	16) [y] = [y] + [sy]

	} else {

	17) [y] = [y] + [base]

	}

	18) vector [v] element [x] = [y]

	}
	</pre>

	<div id="copyright">
	The Xiph Fish Logo is a
	trademark (™) of Xiph.Org.<br/>

	These pages © 1994 - 2005 Xiph.Org. All rights reserved.
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