Multiplication of matrix in C and OCaml
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Date:   (:) 
From:  Brian Hurt <bhurt@s...> 
Subject:  Re: [Camllist] Multiplication of matrix in C and OCaml 
On Fri, 9 Feb 2007, Andrej Bauer wrote: > I hate to add to this long discussion, but since when is floating point > multiplication associative? > > # 1.3 *. (0.7 *. 2.1) = (1.3 *. 0.7) *. 2.1 ;; >  : bool = false Round off error. You can't represent numbers like 7/10 or 13/10 in binary precisely in a finite number of digits, any more than you can represent the numbers 1/3 or 4/7 precisely in base10 in a finite number of digits. This is a fundamental problem with floating point numbers, and shows up in every language that has them. But this means reordering the calculations will result in slightly different answers. And no, most of the "obvious" solutions don't work. Using rational arithmetic doesn't help if I ask you to calculate the euclidean length of the vector (1, 1) for example (hint: sqrt (1.*.1. +. 1.*.1.)). Interval arithmetic fails miserably on simple algorithms like Newton's method. And so on. On the other hand, the precision given by double precision floating point numbers is generally more than enough they're precise enough to hold the distance from here to the moon in microns, for example. My advice: if you're doing much of anything with floating point numbers, get a book on numerical analysis and follow the algorithms and recommendations it gives you (any book except "Numerical Recipies", which suck). And don't use floating point for money. Brian