Richard A. O'Keefe wrote:
On 12 Feb 2008, at 5:14 pm, jerzy.karczmarczuk@info.unicaen.fr wrote:
Would you say that *no* typical floating-point software is reliable?
With lots of hedging and clutching of protective amulets around the word "reliable", of course not. What I *am* saying is that (a) it's exceptionally HARD to make reliable because although the operations are well defined and arguably reasonable they do NOT obey the laws that school and university mathematics teach us to expect them to obey
Ints do not obey those laws, either. It is not exceptionally hard to write reliable software using ints. You just have to check for exceptional conditions. That's also the case for floating point. That said, I suspect that 90% of programs that use float and double would be much better off using something else. The only reason to use floating point is performance.
This is leaving aside all sorts of machine strangeness, like the student whose neural net program started running hundreds of times slower than he expected. I advised him to replace s = 0; for (i = 0; i < n; i++) s += x[i]*x[i]; by s = 0; for (i = 0; i < n; i++) if (fabs(x[i]) > 1e-19) s += x[i]*x[i]; and the problem went away. Dear reader: do you know why I expected this problem, what it was, and why this is NOT a general solution?
I guess it trapped on creating denormals. But again, presumably the reason the student used doubles here was because he wanted his program to be fast. Had he read just a little bit about floating point, he would have known that it is *not* fast under certain conditions. As it were, he seems to have applied what he though was an optimisation (using floating point) without knowing anything about it. A professional programmer would get (almost) no sympathy in such a situation. Roman