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copied!<p>Depending on how much accuracy you need you may be able to avoid the squares and the square root operation. There is a section on this topic in <a href="http://rads.stackoverflow.com/amzn/click/0131089897" rel="nofollow">Understanding Digital Signal Processing by Rick Lyons</a> (section 10.2, <em>"High-Speed Vector-Magnitude Approximation"</em>, starting at page 400 in my edition).</p> <p>The approximation is essentially:</p> <pre><code>magnitude = alpha * min + beta * max </code></pre> <p>where max and min are the maximum and minimum absolute values of the real and imaginary components, and alpha and beta are two constants which are chosen to give a reasonable error distribution over the range of interest. These constants can be represented as fractions with power of 2 divisors to keep the arithemtic simple/efficient. In the book he suggests alpha = 15/16, beta = 15/32, and you can then simplify the formula to:</p> <pre><code>magnitude = (15 / 16) * (max + min / 2) </code></pre> <p>which might be implemented as follows using integer operations:</p> <pre><code>magnitude = 15 * (max + min / 2) / 16 </code></pre> <p>and of course we can use shifts for the divides:</p> <pre><code>magnitude = (15 * (max + (min >> 1))) >> 4 </code></pre> <p>Error is +/- 5% over a quadrant.</p> <p>More information on this technique here: <a href="http://www.dspguru.com/dsp/tricks/magnitude-estimator" rel="nofollow">http://www.dspguru.com/dsp/tricks/magnitude-estimator</a></p>

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