Question

I am trying to build a deterministic simulation, where the floating point numbers are truncated off via the following function:
(I found it here: http://joshblog.net/2007/01/30/flash-floating-point-number-errors )

return Math.round(10000 * float) / 10000;

My question is: wouldn’t the fact that I am dividing it by 10000, be in itself a source of floatpoint errors?
IE every time a dividision takes place, it will result in a new float with further possible nondeterministic results.

EDIT:
how about this? using only powers of 2

return Math.round(float* 1024) / 1024;

Answer 1

My goal was to achieve greater consistency across platforms(C# / AS3 and 32/64 bits), while I accept that 100% consistency is not possible.
(due to AS3 not capable of real integer math, as all internal operations are performed via floats)

What I have gathered so far( Thanks to Eric Postpischil and Jeffrey Sax):

Math.round(1024 * float) / 1024;

Out of the above, the “Math.round(1024 * float)” operation may NOT produce identical results on all platforms, if the “errors have accumulated to more than half of the quantum” which is possible even “within a single operation“.

• While this is mathematically possible, it is likely to be very rare, so overall this operation will still eliminate more inconsistencies than it would generate, so it is worthwhile to perform it as it will reduce inconsistency across platforms (though cannot eliminate them)

.

Where as for the “/ 1024” part, as 1024 is a power of 2, that is a straight bit shift, it will NOT introduce extra errors, where as if I divided by 1000 that would introduce a small chance of an extra error, as 1000 cannot be perfectly represented. So a division with 1000 could introduce another error after the rounding which the division by 1024 could not.

.

CONCLUSION: Math.round(1024 * float) / 1024; is better than Math.round(1000 * float) / 1000; although neither of them is perfect.

Is this an accurate statement?