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If you mean arithmetic on floating point numbers that only store integers, then no equivalence is not ok, because there are examples where bit equivalence fails. One example is repeatedly adding 1.0 to a float something like 1 trillion times versus multiplying 1000000.0 by 1000000.0

What do you mean by

    algorithms that are more reliably written not to contain any empty intervals are two examples.



Obviously I'm referring to integer operations within a 52-bit or 23-bit range, not outside the ability of floating point representations to represent integers!

> What do you mean by

I mean exactly that sort of thing. Algorithms that, for example, divide a line into intervals, where empty intervals are not needed, or desired, and are generally risky with respect to the probability of having a correct implementation. An example of this would be computations of the area of a union of rectangles. You might make a segment tree -- and avoid having degenerate rectangles in your segment tree.




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