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Floating point numbers can be justified by two criteria: 1) The distribution of typical numbers 2) The desired precision across a distribution 1: Floating po
by darkmighty 12y ago
Floating point numbers can be justified by two criteria:
1) The distribution of typical numbers
2) The desired precision across a distribution
1: Floating point numbers suggest an exponential distribution, which comes up very often in science, engineering, etc. Very rarely we have real data neatly packet in a small [-a,a] range.
2: Floating point satisfy the following error metric approximately uniformly: for any -max < x < max, Error = float(x)/x; that is, the relative error is small. This again agrees with real world requirements for data, where we tolerate larger errors for larger numbers.