Thom L. wrote:
Hmm…yeah, I figured that must be it, but I just didn’t expect it with
numbers of this scale. Thanks for the insight!
It isn’t about the magnitude of the numbers, it is about the unseen
You could produce examples of numbers with very large or very small
exponents and they are equally likely to have the sort of roundoff error
The only thing you can rely on with floating-point numbers is that the
sequence of operations, on the same platform, will produce numbers that
will agree with each other when compared later.
There are many packages now that use decimal instead of binary internal
storage to avoid this sort of thing, at the expense of execution speed
storage space. But an interesting fact about binary vs. decimal is that
projects that compute Pi to billions of places, now perform the entire
operation in decimal internally, because the time required to convert
result from binary to decimal at the end of the computation turned out
be a substantial percentage of the entire calculation time.