3 ms·
Well, every base has issues with non-termination. In base 10, we have problems like 1/3 = 0.33333... . Base 2 has its own set of non-terminating decimal expansi
by krzysz00 12y ago
Well, every base has issues with non-termination. In base 10, we have problems like 1/3 = 0.33333... . Base 2 has its own set of non-terminating decimal expansions, including 1 / 3 = 0.01010101... and 1 / 10 = 0.0001100110011... . Since we only have finite storage space, we have to cut the repeating string of digits off somewhere, no matter what base we're in. This can cause rounding issues.
You can't dodge all your rounding problems by changing base. There are binary-coded decimal (BCD) systems that store numbers as strings of decimal digits. You can generally find these in calculators (ever notice that a TI-84 overflows after 9.(9)e99) or some financial software. However, you'll still have problems like the 0.1 * 0.2 issue in binary floating-point. For example (assuming shorter-than-usual numbers):
2/3 = 0.66... ~ 0.66667
2/3 + 2/3 ~ 0.66667 + 0.66667 = 1.33334
However, 4/3 = 1.33333... ~ 1.33333, which isn't the same result.
Basically, you can't get away from this problem, you can only push it around to cases you care less about.
(You probably can't find an API for binary-coded decimal in $LANGUAGE unless $LANGUAGE is often used for tasks where you really really don't want any float-related gotchas since most everyone else doesn't care too much).
- edwintorok 12y agoYou could represent your numbers as fractions of integers and do all operations on them as fractions of integers: https://gmplib.org/manual/Rational-Number-Functions.html#Rational-Number-Functions https://gmplib.org/manual/Rational-Number-Functions.html#Rat... And only converting them to floating point for display purposes: http://www.mpfr.org/mpfr-current/mpfr.html#index-mpfr_005fset_005fq-50 http://www.mpfr.org/mpfr-current/mpfr.html#index-mpfr_005fse...
- shortstuffsushi 12y agoHmm, so BCD seems closer to what I was roughly imagining (though, I haven't really thought this issue through deeply or anything), but you mention it has shortcomings as well. I guess I'll just have to trust that other people have thought about this, and have determined this to be the best solution, even with its flaws.