Handling of floats in sympy

[Oscar Benjamin]

I find sympy's handling of Python floats strange and unintuitive.

In [3]: sympify(0.1)
Out[3]: 0.100000000000000

In [4]: sympify(0.1) == S(1)/S(10)
Out[4]: True

In [5]: 0.1 == S(1)/S(10)
Out[5]: True

In [6]: from decimal import Decimal

In [7]: 0.1 == Decimal('0.1')
Out[7]: False

In [8]: 1.0 == Decimal('1.0')
Out[8]: True

In [9]: a = Decimal('0.1')

In [10]: a
Out[10]: Decimal('0.1')

In [11]: b = sympify(0.1)

In [12]: c = 0.1

In [13]: a == b == c
Out[13]: True

In [14]: a == c
Out[14]: False

The true value of c is:

In [18]: Decimal(c)
Out[18]: Decimal('0.1000000000000000055511151231257827021181583404541015625')

In [19]: from fractions import Fraction

In [20]: Fraction(c)
Out[20]: Fraction(3602879701896397, 36028797018963968)

But sympy seems to just convert it to 15 decimal digits without any
indication that the conversion was inexact.

What's the rationale for the inexactness here? How do I convert a
float to a sympy object with the exact same value?

It looks as if sympy converts Python Decimals using __float__ e.g.:

In [31]: a = Decimal(0.1)

In [32]: a
Out[32]: Decimal('0.1000000000000000055511151231257827021181583404541015625')

In [33]: S(a)
Out[33]: 0.100000000000000

OTOH Fraction can do it:

In [34]: Fraction(0.1)
Out[34]: Fraction(3602879701896397, 36028797018963968)

In [35]: S(Fraction(0.1))
Out[35]:
3602879701896397
─────────────────
36028797018963968


--
Oscar