Quote:
Originally Posted by Khanattila
Agree, but the input can have infinite precision like natural logarithm. Euler's number is not a ratio of integers and it is not a root of any non-zero polynomial with rational coefficients. Like log (param).
EDIT. Forget it... you always think that the input is only 'param'.
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No, in computers it cannot. Computers don't do infinite precision. The input will always have finite precision.
Quote:
Originally Posted by feisty2
@vivan
you and I have different perceptions of "lossless", I can live with that
but please don't drag physics stuff here, computers do mathematical calculations, not physical experiments
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Vivan's point was a mathematical one, not a physical one.
If you can only output integers there is a point where keeping track of extra precision cannot change the result at all. This point depends on the equation(s), of course, but it can be calculated with certainty. In physics/chemistry it is based on the precision of your measurements while in computers it is based on the precision of your input and output.