problem with the 'math' module in 2.5?

andy2O at hotmail.com andy2O at hotmail.com
Sun Oct 15 23:10:50 CEST 2006


Chris wrote:
> sin(pi*0.5) is what I expected, but I expected to get 0 for sin(pi).

Computers in general, and Python too, usually use floating point
arithmetic in which all numbers are approximated by rational numbers of
a particular form (see http://en.wikipedia.org/wiki/Floating_point for
details).

1) pi is an irrational number, so it *cannot* be represented exactly in
floating point. Therefore the value of pi in your call to the sin
function is definitely, proveably, *not* exactly equal to the true
value of pi.

2) So, even if the function "sin" could be evaluated exactly, the fact
that you are not evaluating it exactly at the true value of pi, but
instead at a good but imperfect approximation to this value, means that
the sine function *should not* give the result = 0 for your request!

3) The function sin is also evaluated to only a finite degree of
precision - just like everything else in floating point arithmetic.
Therefore you should not expect absolutely precise results. Instead,
you need to understand the limitations of floating point arithmetic,
understand the precision you *can* expect, and work within these
bounds. It's a good system, but you do need to understand its
limitations. The links other people have posted are good resources for
this.

Best wishes,
andy




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