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Ogg Vorbis I format specification: helper equations

Overview

ilog

  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

• ilog(0) = 0;
• ilog(1) = 1;
• ilog(2) = 2;
• ilog(3) = 2;
• ilog(4) = 3;
• ilog(7) = 3;
• ilog(negative number) = 0;

  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 ) )

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

low_neighbor

  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

  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]

     }