Chris Angelico <ros...@gmail.com> writes: > On Sun, Sep 5, 2021 at 1:04 PM Hope Rouselle <hrouse...@jevedi.com> wrote: >> The same question in other words --- what's a trivial way for the REPL >> to show me such cycles occur? >> >> >>>>>> 7.23.as_integer_ratio() >> >>> (2035064081618043, 281474976710656) >> >> Here's what I did on this case. The REPL is telling me that >> >> 7.23 = 2035064081618043/281474976710656 >> >> If that were true, then 7.23 * 281474976710656 would have to equal >> 2035064081618043. So I typed: >> >> >>> 7.23 * 281474976710656 >> 2035064081618043.0 >> >> That agrees with the falsehood. I'm getting no evidence of the problem. >> >> When take control of my life out of the hands of misleading computers, I >> calculate the sum: >> >> 844424930131968 >> + 5629499534213120 >> 197032483697459200 >> ================== >> 203506408161804288 >> =/= 203506408161804300 >> >> How I can save the energy spent on manual verification? > > What you've stumbled upon here is actually a neat elegance of > floating-point, and an often-forgotten fundamental of it: rounding > occurs exactly the same regardless of the scale. The number 7.23 is > represented with a certain mantissa, and multiplying it by some power > of two doesn't change the mantissa, only the exponent. So the rounding > happens exactly the same, and it comes out looking equal!
That's insightful. Thanks! > The easiest way, in Python, to probe this sort of thing is to use > either fractions.Fraction or decimal.Decimal. I prefer Fraction, since > a float is fundamentally a rational number, and you can easily see > what's happening. You can construct a Fraction from a string, and > it'll do what you would expect; or you can construct one from a float, > and it'll show you what that float truly represents. > > It's often cleanest to print fractions out rather than just dumping > them to the console, since the str() of a fraction looks like a > fraction, but the repr() looks like a constructor call. > >>>> Fraction(0.25) > Fraction(1, 4) >>>> Fraction(0.1) > Fraction(3602879701896397, 36028797018963968) > > If it looks like the number you put in, it was perfectly > representable. If it looks like something of roughly that many digits, > it's probably not the number you started with. That's pretty, pretty nice. It was really what I was looking for. -- You're the best ``little lord of local nonsense'' I've ever met! :-D (Lol. The guy is kinda stressed out! Plonk, plonk, plonk. EOD.) -- https://mail.python.org/mailman/listinfo/python-list
