[Python-Dev] Expert floats

[Shane Hathaway]

Tim Peters wrote:
> Suppose you had a binary float format with 3 bits of precision, and the
> result of a computation on that box is .001 binary = 1/8 = 0.125 decimal.
> The "shortest-possible reproducing decimal representation" on that box is
> 0.1.  Is it more accurate to move that result to a wider machine via the
> string "0.1" or via the string "0.125"?  The former is off by 25%, but the
> latter is exactly right.  repr() on the former machine has no way to guess
> whether the 1/8 it's fed is the result of the user typing in "0.1" or the
> result of dividing 1.0 by 8.0.  By taking the bits at face value, and
> striving to communicate that as faithfully as possible, it's explainable,
> predictable, and indeed as faithful as possible.  "Looks pretty too" isn't a
> requirement for serious floating-point work.

It seems like most people who write '1.1' don't really want to dive into 
serious floating-point work.  I wonder if literals like 1.1 should 
generate decimal objects as described by PEP 327, rather than floats. 
Operations on decimals that have no finite decimal representation (like 
1.1 / 3) should use floating-point arithmetic internally, but they 
should store in decimal rather than floating-point format.

Shane