Date: Thu, 30 Nov 2017 13:16:01 -0800 From: John Reiser <jreiser@...wagon.com> To: musl@...ts.openwall.com Subject: Re: remquo - underlying logic > I was asking the question in case anybody had done it before and found it useless, > could think of major pitfalls, or had any pearls of wisdom before we started. The range of a floating-point exponent will limit the applicability. Packing and unpacking floating-point format (logb, scalb, etc.) are non-trivial costs, as are mucking around with NaN, +inf, -inf, denormals, etc. The "big-O" efficiency is the same: find the difference in exponents, scale both operands to have the same exponent, perform "ordinary long division" with the number of steps equal to the difference in exponents; take care to preserve enough precision. Floating-point division of the scaled operands (perhaps using a narrower precision) can be a contender, especially because mis-predicted branches in long division are VERY expensive (typically: 70% of CPU pipeline depth [==> a dozen or more cycles].) Newton-Raphson iteration can be a contender for some range of difference in exponents. --
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