On 25 August 2016 at 00:51, MarLinn via Haskell-Cafe
Hi,
I discovered that in base logBase, the functions representing arbitrary logarithms, are defined in terms of two applications of log. log, the functions representing the natural logarithm, just pass responsibility on to some primitives. That is fine, mathematically speaking. But from an implementation standpoint, I wonder why one would do that.
The logarithm that should be the fastest and the most precise one to approximate by a cpu should be the one to base two. In fact if one already has a floating point representation, it should be almost ridiculously easy to compute from the exponent.
Speaking of precision. log in any base is a transcendental function so best we can do is to ensure that approximation differs from true answer no more that 0.5 ULPs. Also I don't think log in base 2 would be any more performant than natural logarithm. Yes calculations for exponent is easy but you still need to calculate it for mantissa and it's not easier task. And most of the time natural logarithm is used.