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by jacobolus
826 days ago
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> the more operations you perform on a float input, the fuzzier the value is No, any float always precisely represents a specific number. The issue is that only a finite number of numbers are representable. Some algorithms are poorly conditioned and when implemented using floating point arithmetic will lead to a result that is different than what you would get in idealized real number arithmetic. That doesn't make any floating point value "fuzzy". |
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A float always precisely represents a specific number, but that number is not always precisely the equal to the algebraic result of the operations performed (even when ignoring transcendental and irrational functions). This should be obvious since there is no limit to rational numbers, but finite floating point numbers.
If you design your algorithms very carefully, you can end up with the ratio of the output of your algorithm to the ratio of the algebraic result close to unity over a wide domain of inputs.