Re: logarithms on ada

[dewar@merv.cs.nyu.edu (Robert Dewar)]

Robert Duff said

<<> Really?  I would think students shouldn't be exposed to floating-point
> (and therefore logs and whatnot) until fairly late in the game.  I know
> *I* don't understand floating point arithmetic very well>>

I have often introduced floating-point fairly early on. One nice
assignment is the following.

Given a function f, compute its integral using Simpson's rule
using successively smaller intervals to see how smaller intervals
give better accuracy.

be prepared for a lot of infinite loops, this does not cconverge absolutley,
but instead after a while starts to diverge as the error of adding
lots of small numbers becomes more important than the inherent error
in the approximation. The trick is to catch it at the right point, which
means looking at second deriviatives.

Of course students need to know some calculus to do this (and knowing
some calculus is, alas, not the same thing as having got a passing grade
on a calculus class) :-)