Trialog: Roman Leshchinskiy writes:
Richard A. O'Keefe wrote:
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.
I have a bit different perspective... First, when I see the advice "use something else", I always ask "what", and I get an answer very, very rarely... Well? What do you propose? Then, the problem is not always pathological, in the sense of "exceptional conditions". There are touchy points related to the stability of the algorithms for the solution of differential equations. There are doubtful random number generators in Monte-Carlo business. There are ill-conditioned matrices and screwed-up iterative definitions. Algorithms work, work, and ultimately explode or produce rubbish. The "laws" which get broken are "almost" respected for a long time, and then we have the Bald Man (Sorites) paradox... RAO'K very wisely says that people should avoid reinventing wheels, and they should use established packages, written by people who know. The problem *here* is that we would like to have something fabulous in Haskell - for example... And there aren't too many experts, who would convert to the Functional Religion just for fun. What is *much worse*, some potential users who could encourage building such packages in the numerical domain, typically don't believe that FP gives anything interesting. At least, this is the opinion of physicists I spoke to recently. Never mind. We shall dance over their cadavers, unless they dance over ours. In both cases we shall be happy. Jerzy Karczmarczuk