On Wednesday, July 20, 2016 at 8:29:25 PM UTC+5:30, Marko Rauhamaa wrote: > Chris Angelico : > > > On Wed, Jul 20, 2016 at 11:54 PM, Marko Rauhamaa wrote: > >> 2. Floating-point numbers are *imperfect approximations* of real > >> numbers. Even when real numbers are derived exactly, > >> floating-point operations may introduce "lossy compression > >> artifacts" that have to be compensated for in application > >> programs. > > > > This is the kind of black FUD that has to be fought off. What > > "compression artifacts" are introduced? The *only* lossiness in IEEE > > binary floating-point arithmetic is rounding. > > You are joining me in spreading the FUD. Yes, the immediate lossiness is > rounding, but the effects of that rounding can result in atrocious > accumulative errors in numeric calculations. > > > Unless you are working with numbers that require more precision than > > you have available, the result should be perfectly accurate. > > Whoa, hold it there! Catastrophic cancellation (<URL: > https://en.wikipedia.org/wiki/Loss_of_significance>) is not a myth:
Whose lead para starts: | Catastrophic cancellation… The effect is that the number of accurate | (significant) digits in the result is reduced unacceptably. Ways to avoid this | effect are studied in numerical analysis. I would go a step further: The field of numerical analysis came into existence only because this fact multiplied by the fact that computers do their (inaccurate ≠inexact) computations billions of times faster than we do makes significance a very significant problem! -- https://mail.python.org/mailman/listinfo/python-list
