Method and apparatus for providing a base-2 logarithm approximation to a binary number

An apparatus for approximating a base-2 logarithm of a binary number, said apparatus comprising:

• means for determining a position k within said binary number at which a “1” is first occurred;
• means for assigning all bits to the right of said position k within said binary number as a fractional portion of a base-2 logarithm approximation of said binary number;
• means for utilizing a subset of said fractional portion to generate an adjustment value βm for said fractional portion;
• wherein said means for utilizing further includes means for utilizing said subset of said fractional portion to generate said adjustment value βm by
• β
• m
• =
• 1
• 2
• ⁢
• ⁢
• log
• 2
• ⁡
• [
• (
• 1
• +
• m
• M
• )
• ⁢
• ⁢
• (
• 1
• +
• m
• +
• 1
• M
• )
• ]
• -
• m
• +
• 1
• 2
• M
• where m is said subset of said fractional portion;
• and
• means for adding said fractional portion along with said adjustment value βm for said fractional portion to said k as a binary number representing an integer portion of said base-2 logarithm approximation of said binary number to form said base-2 logarithm approximation of said binary number.

A recordable type signal bearing media having a computer program product for approximating a base-2 logarithm of a binary number comprising:

• computer program code for determining a position k within said binary number at which a “1” is first occurred;
• computer program code for assigning all bits to the right of said position k within said binary number as a fractional portion of a base-2 logarithm approximation of said binary number;
• computer program code for utilizing a subset of said fractional portion to generate an adjustment value βm for said fractional portion;
• wherein said computer program code for utilizing further includes computer program code for utilizing said subset of said fractional portion to generate said adjustment value βm by
• β
• m
• =
• 1
• 2
• ⁢
• ⁢
• log
• 2
• ⁡
• [
• (
• 1
• +
• m
• M
• )
• ⁢
• ⁢
• (
• 1
• +
• m
• +
• 1
• M
• )
• ]
• -
• m
• +
• 1
• 2
• M
• where m is said subset of said fractional portion;
• and
• computer program code for adding said fractional portion along with said adjustment value βm for said fractional portion to said k as a binary number representing an integer portion of said base-2 logarithm approximation of said binary number to form said base-2 logarithm approximation of said binary number.