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Subject: Re: Division-Bug in decimal and mpmath
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On 2024-12-14 at 12:08:29 +0000,
Mark Bourne via Python-list <python-list@python.org> wrote:

> Martin Ruppert wrote:
> > Hi,
> > 
> > the division 0.4/7 provides a wrong result. It should give a periodic
> > decimal fraction with at most six digits, but it doesn't.
> > 
> > Below is the comparison of the result of decimal, mpmath, dc and calc.
> > 
> > 0.0571428571428571460292086417861615440675190516880580357142857 decimal: 0.4/7
> > 0.0571428571428571460292086417861615440675190516880580357142857 mpmath: 0.4/7
> > 0.0571428571428571428571428571428571428571428571428571428571428 dc: 0.4/7
> > 0.0571428571428571428571428571428571428571428571428571428571429 calc: 0.4/7
> > 0.05714285714285715 builtin: 0.4/7
> > 
> > Both decimal and mpmath give an identical result, which is not a
> > periodic decimal fraction with at most six digits.
> > 
> > calc and dc provide as well an identical result, which *is* a periodic
> > decimal fraction with six digits, so I think that's right.
> 
> I looks like you might be running into limitations in floating-point
> numbers.  At least with decimal, calculating 4/70 instead of 0.4/7 appears
> to give the correct result.  As does:
> ```
> from decimal import Decimal as dec
> z2 = dec(4) / dec(10)
> print(z2 / dec(nen))
> ```
> You can also pass a string, and `dec("0.4")/dec(10)` gives the correct
> result as well.
> 
> Your `z` is a float, and therefore limited by the precision of a float. It
> doesn't represent exactly 0.4, since that can't be exactly represented by a
> float.  Anything you do from then on is limited to that precision.
> 
> I can't easily find documentation for dc and calc (links from PyPI are
> either broken or don't exist), but I'm guessing they use some heuristics to
> determine that the float passed in very close to 0.4 so that was probably
> intended, rather than using the exact value represented by that float.

I'm going to guess that since dc is a shell utility and calc is either
another shell utility or the calculator in emacs, and that they both do
their own conversion from a string to an internal representation without
going through an IEEE float.

Why couldn't we have evolved with eight fingers on each hand?  ;-)