Some of these situations might be avoided by intelligent rounding: in particular, detection of the number of sig figs lost by cancellation (a small output resulting from subtraction of two large inputs). When graphing outputs from circle geometry computations, even in the absence of numerical ill-conditioning, circles with very large or very small radii are difficult to plot accurately. It therefore becomes necessary for the plotting algorithm to decide when such an object should be treated as an approximation to a line or point, then round its coordinate vector to that of the appropriate limit. In practice and in this limited context, the problem seems to be feasible, though slightly tricky. It does depend however on the programmer taking more trouble to tailor the output to the user's application, rather than just disgorging raw hardware results willy-nilly. "Calculator" programs are evidently designed merely to imitate historical desktop calculators, to the extent even of mimicing painstakingly their physical appearance, rather than engineered to meet the practical requirements of a mathematically unsophisticated user. Fred Lunnon On 10/31/09, Simon Plouffe <simon.plouffe@gmail.com> wrote:

Dear all,

here is an interesting article :

http://www.techradar.com/news/computing/why-computers-suck-at-maths-644771

what makes a problem is the conversion of decimal numbers into binary numbers.

have a nice 0.99999... day.

Simon Plouffe

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