Round() bug or limit?

[goMiddleton]

Take the number 153.49 and divide by the integer 2000. The result in Panorama X is 0.07674500000000001.

Here are the results of the following round functions.
round(153.49 / 2000,.01) = 0.08
round(153.49 / 2000,.001) = 0.077
round(153.49 / 2000,.0001) = 0.0767
round(153.49 / 2000,.00001) = 0.07675000000000001

Is .0001 the limit of Round() or is this a bug?

[admin]

This is caused by the fact that floating point arithmetic is performed using base 2 rather than base 10 arithmetic. Many decimal numbers are not expressible using base 2, so this type of discrepancy occurs. Panorama is using the C compiler to perform arithmetic, which presumably is using the floating point operations available on the Intel CPU chip.

If you do a google search for floating point accuracy you'll find lots of information about this topic. A couple of post that jump out at me are:

What range of numbers can be represented in a 16-, 32- and 64-bit IEEE-754 systems?

especially this quote about half way down the page:

The fact that the "point" in "floating point" is a binary point and not decimal point has a way of defeating our intuitions. The classic example is 0.1, which needs a precision of only one digit in decimal but isn't representable exactly in binary at all.

and also this post:

Floating point inaccuracy examples

But there are plenty more if you have some time to kill.