[Skip Montanaro] > ... > Is there a middle ground where you can say, in effect, "give me rational > numbers which are truncated to provide precision no worse than N-bit > floating point numbers"? Yes, so-called "fixed slash" and "floating slash" arithmetics do exactly that. BTW, they tend to give exactly the right results despite intermediate roundoff errors when the *problem* domain is such that the correct results are simple fractions. But this is just another thing that gets mentioned every time this discussion resurrects, so that's all I'm going to say about it this time around. There are literally hundreds of schemes for computer arithmetics that have been tried and found genuinely useful for *some* things. The only ones on the table with any claim to broad usefulness are rationals and decimal fp.
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