On Thu, 30 May 2013 13:45:13 +1000, Chris Angelico wrote: > Let's suppose someone is told to compare floating point numbers by > seeing if the absolute value of the difference is less than some > epsilon.
Which is usually the wrong way to do it! Normally one would prefer *relative* error, not absolute: # absolute error: abs(a - b) < epsilon # relative error: abs(a - b)/a < epsilon One problem with absolute error is that it can give an entirely spurious image of "fuzziness", when in reality it is actually performing the same exact equality as == only slower and more verbosely. If a and b are sufficiently large, the smallest possible difference between a and b may be greater than epsilon (for whichever epsilon you pick). When that happens, you might as well just use == and be done with it. But using relative error also raises questions: - what if a is negative? - why relative to a instead of relative to b? - what if a is zero? The first, at least, is easy to solve: take the absolute value of a. But strangely, you rarely see programming books mention that, so I expect that there is a lot of code in the real world that assumes a is positive and does the wrong thing when it isn't. Here's another way, mathematically equivalent (although not necessarily equivalent using floating point computations!) which avoids the divide-by- zero problem: abs(a - b) < epsilon*a Whichever method you choose, there are gotchas to watch out for. > http://xkcd.com/1047/ Nice! -- Steven -- http://mail.python.org/mailman/listinfo/python-list
