Re: Division-Bug in decimal and mpmath

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}")