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From: Mark Bourne <nntp.mbourne@spamgourmet.com>
Newsgroups: comp.lang.python
Subject: Re: Division-Bug in decimal and mpmath
Date: Sat, 14 Dec 2024 12:08:29 +0000
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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.

> Below ist the python-script, with which the computation was done.
> 
> Best regards
> Martin Ruppert
> 
> #!/usr/bin/env python3
> from decimal import Decimal as dec
> from mpmath import *
> from os import popen
> import decimal
> 
> z=.4
> nen=7
> 
> decimal.getcontext().prec=60
> print(dec(z)/dec(nen),end=' ');print(f"decimal: {z}/{nen}")
> 
> mp.dps=60
> a=fdiv(z,nen);print(a,end=' ');print(f"mpmath: {z}/{nen}")
> 
> f=popen(f"dc -e'61k{z} {nen}/f'")
> for i in f:i=i.rstrip()
> f.close()
> print(f"0{i}",end=' ');print(f"dc: {z}/{nen}")
> 
> f=popen(f"calc 'config(\"display\",61);{z}/{nen}'")
> j=0
> for i in f:
>      if j>0:i=i.rstrip();print(i,end=' ');print(f"calc: {z}/{nen}")
>      j+=1
> f.close()
> 
> print(f"{z/nen}",end=' ');print(f"builtin: {z}/{nen}")
>