Answer 7
Yes. One more multiplication operation gives a result that has less than 4% error:

Magnitude = 0.960433 × maximum (|x|, |y|) + 0.397826 × minimum (|x|, |y|)

This function is most negative at 0° and 45°, and most positive at 22.5°. The error is ± 3.96%. This form is well-suited to DSPs that have multiply-accumulate units. The two constants can be expressed as 62,943/65,536 and 26,072/65,536, respectively.

Contributor: Dave Tweed

Published April 2003