[Python-ideas] Python Numbers as Human Concept Decimal System

[Mark Dickinson]

On Sat, Mar 8, 2014 at 12:10 AM, Guido van Rossum <guido at python.org> wrote:

>
> But Decimal(<float>) is relatively new (it was an error in 2.6). I know
> it's annoying to change it again, but I also have the feeling that there's
> not much use in producing a Decimal with 53 (or more?) *decimal digits* of
> precision from a float with 53 *bits* -- at least not by default. Maybe we
> can relent on this guarantee and make the constructor by default use fewer
> digits (e.g. using the same algorithm used by repr(<float>)) and have an
> optional argument to produce the full precision? Or reserve
> Decimal.from_float() for that?
>

Using the same algorithm as used by repr(float) feels like a bad idea to
me:  my gut feeling is that a conversion from float to Decimal is a
fundamental operation that should be easily describable in simple terms,
and should not involve the level of complication and 'magic' involved in
the float repr.  (That level of magic seems fine for the repr, because in
most cases you don't actually care too much what string you get so long as
it evaluates back to the correct float;  you're not doing arithmetic with
the result.)

IEEE 754-2008 requires simply that conversions between numbers in different
formats round correctly.  It specifies a "convertFormat" operation,
described as follows:

"""
If the conversion is to a format in a different radix or to a narrower
precision in the same radix, the result shall be rounded as specified in
Clause 4. Conversion to a format with the same radix but wider precision
and range is always exact. ...
"""

... where clause 4 is the one that outlines the general rounding rules that
apply to almost all IEEE 754 operations.

I see three sane options for float to Decimal conversion:

1. Raise an exception.
2. Round to the nearest Decimal value using the current context for that
round operation.
3. Do what we're currently doing, and do an exact conversion.

Option 2 would seem closest to what IEEE 754 specifies.  To augment option
2, we could also make it easier to create Decimal contexts corresponding to
the IEEE 754 recommended interchange formats (decimal32, decimal64,
decimal128).  This was already proposed in http://bugs.python.org/issue8786.

Mark
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