Re: "Numeric overflow"?
Re: "Numeric overflow"?
- Subject: Re: "Numeric overflow"?
- From: Jon Pugh <email@hidden>
- Date: Thu, 15 Sep 2005 08:14:46 -0700
At 6:31 PM +0200 9/13/05, Emmanuel wrote:
>Pardon my stubbornness, Jon, but do you have an example of an unreasonably small number, Jon?
My flippant response is Plank's Constant:
http://en.wikipedia.org/wiki/Plank's_constant
This is the size of a "quanta" which is the basic unit of quantum mechanics. This constant is also used in the Heisenberg Uncertainty Principle. It is approximately the smallest amount of energy one can measure in a given unit of time.
In practice, any number "sufficiently close to zero" can be unreasonable in a problem domain. The determination of "unreasonable" is left to the implementor of the algorithm.
set N to 10000
set s1 to 0
repeat with i from 1 to N
set s1 to s1 + i / N
end repeat
set s2 to 0
repeat with i from N to 1 by -1
set s2 to s2 + i / N
end repeat
set diff to s2 - s1
set inv to 1 / diff
{s1, s2, diff, inv}
Results in:
{5000.499999999991, 5000.500000000002, 1.09139364212751E-11, 9.16259689813333E+10}
In this example, diff is the difference between summing from small to large and from large to small. It is unreasonably small and functionally equivalent to zero. The inverse of it, inv, is unreasonably large, given this program's purpose (which is largely to show how round off accumulates).
Jon
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