Another amazing work by Hans Boehm back in 1999: a constructive real number calculator, https://www.hboehm.info/crcalc/ . In a sense, this is "as far as a computer can go" in the hierarchy of accuracy that includes floating-point, exact rational numbers, and then constructive reals.
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That's old news for computer algebra systems since the 80s, yea? I just opened Mathematica and printed their example to a million digits in about a second with N[E^(Pi*Sqrt[163]), 1000000]. And it can definitely simplfiy Sqrt[2]*Sqrt[2]==2 to True as well.
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True. The neat thing about Boehm's approach is that it's just a normal data type in a normal programming language.
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Except for constructive numbers you can find this in places, eg. Common Lisp.
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Another idea might be using something like this to do what the AIR model does for integers but for reals. Intermediates could be semantically infinite precision, and you use the types of values at the endpoints to work out the needed precision
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Have you looked at "universal numbers" aka posits? https://github.com/libcg/bfp It's not "arbitrary" precision but gets us a good way there. It breaks the excessive NaN degeneracy as well as the signed zero degeneracy.
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As long as you don't ask for anything 128-bit ... *cough* rust 128-bit ints...
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Here is a bit of numerical heresy for you: xGuess = double(floor(50400.0*x + 0.5)/50400.0); if (fabs(xGuess - x) < 8.0*fabs(x)*D_MACHINE_EPS) return xGuess; else return x;
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Didn’t Smalltalk have them all back in 1972-1976?
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I mean, but the CRs
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