mathlogarithmapproximation
Approximate logarithm uses inaccurate approximation for log_2(1+x)-x but it still works
In this article a rational approximation f(z) for g(z) = log_2(1 + x) - x is used for fastlog2 but when plotting f(z) and g(z) they look very different.
Oddly enough the results of fastlog2 are very accurate. If I adjust f(z) to resemble g(z) more closely (parabola) the results turn out to be very inaccurate.
My question is:
Why are the results for fastlog2 very accurate for a f(z) that looks very different from g(z) and how would you find f(z) for better accuracy?
Solution
With some help from the comments I realized what my mistake was and adjusted the formula accordingly which leads to the expected result:
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