Problem 44690. Comparison of floatingpoint numbers (doubles)
Floatingpoint numbers cannot generally be represented exactly, so it is usually inappropriate to test for 'equality' between two floatingpoint numbers. Rather, it is generally appropriate to check whether the difference between the two numbers is sufficiently small that they can be considered practically equal. (In other words, so close in value that any differences could be explained by inherent limitations of computations using floatingpoint numbers.)
Based on two scalar inputs of type double, namely A and B, you must return a scalar logical output set to true if the difference in magnitude between A and B is 'small', or otherwise set to false.
For this problem "small" shall be defined as no more than ten times ε, in which ε is the larger of ε₁ & ε₂, and ε₁ is the floatingpoint precision with which A is represented, and ε₂ is the precision with which B is represented.
EXAMPLE:
% Input A = 0 B = 1E50
% Output practicallyEqual = false
Explanation: A is represented with a precision of ε₁ = 2⁻¹⁰⁷⁴, whereas B is represented with a precision of ε₂ = 2⁻²¹⁹. Thus ε = 2⁻²¹⁹, and the threshold is 10×2⁻²¹⁹. The difference between A and B is 1×10⁻⁵⁰, and this difference exceeds the threshold. Thus A and B are not practically equal in this example.
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2 Comments
Again, good problem, but it would be better if base10 or base2 was adopted as a standard at the description
Hello, Rafael. Thankyou for the feedback. Each approach has pros and cons.
Using the same base for all numbers in the problem statement would make comparison easy at a glance, but the values would not all be exact.
The mixture of bases used in the problem statement means that exact values are used for all numbers; although the reader has some inconvenience to perform a conversion in order to compare magnitudes, there may be some more educational value in that, IMHO.
—DIV
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