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by lifthrasiir
1 hour ago
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The dilemma is hypothetical (because we now know the exact precision requirement for those functions over all 64-bit doubles) but let's assume that we don't know that and also we happen to use decimals instead. What if, some f(x) is known to be, say, 123.4999...9997 with 1,000 fractional digits? You have to calculate at least 1,000 decimal digits of f(x) in order to correctly round, before that we only know it's between 123.4999...999 and 123.5000...001. There seems no mathematical theory that specially prevents this annoying possibility, hence the dilemma. |
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