Dodd: No one will know until this is actually in place how it works

The Washington Post ^ | June 25, 2010

[grey_whiskers]

It is an inherent precision of floating-point representations using binary arithmetic: but with enough bits for each floating point number, you can go to more and more precision before running into problems, e.g. IIRC, according to IEEE754 64-bit precision allowed floating point decimals from 10³⁰⁸ to 10^-308, much better than the range allowed by 32-bit precision.

That being said, you are right, there are some numbers which cannot be represented exactly using floating-opoint arithmetic, including (I think) the square root of two (or was it three?).

I recall working on optimizing an engineering simulation program where we had to turn off compiler options in order to get the answers to come out right: the compiler was taking a group of operands and rearranging the order they were being added in -- with the side effect that some of the smaller numbers were "dropped" as rounding errors. We had to change the code by hand so that it sorted the numbers first, and then began adding from smallest to largest...

Cheers!

[OneWingedShark]

I’ll take “D:” Adolf the above.

[RWB Patriot]

America’s Directive 10-289.