Monthly archive of July, 2010

As promised last week I’m going to compare three methods of optimizing 2 ^ x calculation:

• Cache table – described in my previous post
• Polynomial approximation – suggested by Gregory, implemented here celt_exp2(…) and described here
• Compact IEEE-754 – 3 lines of code(!) described here and here

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Signal processing often requires moving between logarithmic & linear domains. In audio area we can talk about Octaves (logarithmic representation) and Frequencies (linear representation). Octave -> Frequency conversion corresponds to transformation x = 2 ^ x.

Most programming languages provide support for such calculation, for example Pow(a, b) in C#.
Those functions however tend to be time consuming. We can take advantage of the fact that in our case a = const = 2 and optimize the calculation.
Let’s start with equation:

a ^ ( b + c ) = a ^ b * a ^ c

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