4 ms·
> Decimal calculations getting rounded off is a problem that is a lot easier to see and understand. If you carefully, tediously work by hand some calculations
by moonchild 3y ago
> Decimal calculations getting rounded off is a problem that is a lot easier to see and understand.
If you carefully, tediously work by hand some calculations such as addition, multiplication, or division (but not, say, square roots, exponentials, or sines, since there are no generally known methods for computing those by hand), you may be able to replicate some specific results of the computer without needing to learn anything new. I don't really see what the point of doing that would be. Oh, and you must use banker's rounding, which is also not generally done. Otherwise, the results will appear to manifest as just some inaccuracy incurred after every operation, just the same as with binary floating point. The full complexity of error analysis remains.
(Note also in particular that addition, multiplication, and division are closed over the rationals, which can be readily represented exactly by computer—I did mention I think rationals are a good thing.)
- lmm 3y ago> If you carefully, tediously work by hand some calculations such as addition, multiplication, or division (but not, say, square roots, exponentials, or sines, since there are no generally known methods for computing those by hand), you may be able to replicate some specific results of the computer without needing to learn anything new. Adding 0.1 and 0.2 to get 0.3 is hardly advanced mathematics. > Otherwise, the results will appear to manifest as just some inaccuracy incurred after every operation, just the same as with binary floating point. Perhaps, but it will be a comprehensible inaccuracy. Running out of decimal places is a well-known and understood phenomenon, and something already experienced with regular calculators.