[Python-ideas] Consider generalizing Decimal to support arbitrary radix

[Terry Reedy]

On 2/7/2018 6:08 PM, Neil Girdhar wrote:
> 
> On Wed, Feb 7, 2018 at 5:52 PM Steven D'Aprano 
> <steve at pearwood.info 
> <mailto:steve at pearwood.info>> wrote:
> 
>     On Wed, Feb 07, 2018 at 10:08:50PM +0000, Neil Girdhar wrote:
> 
>      > Oh, and to answer your specific question, I want to change the way
>      > arithmetic is done.  I want it to be done in a different radix.
> 
>     Why?
> 
>     There are clear advantages to floating point arithmetic done in base 2
>     (speed, minimum possible rounding error, least amount of wobble), and a
>     different advantage to floating point done in base 10 (matches exactly
>     the standard decimal notation used by humans with no conversion error),

This is the specialness of base 10

>     Outside of those two bases, arithmetic done in any other base is going
>     to combine the worst of both:
> 
>     - slower;
>     - larger errors when converting from decimal numbers (in general);
>     - larger rounding errors;
>     - larger wobble;

> I don't see why it would have any of those problems.

Any base other than 2 has decreased speed (on a binary computer) and 
increased computational rounding errors and wobble.

>  Base 10 isn't special in any way.

Except as noted above and the fact that computation with binary coded 
decimal goes back to the early days of electronic computation.

>     with no corresponding advantages unless your data is coming to you in
>     arbitrary bases.

> Right, I was playing with this problem 
> (https://brilliant.org/weekly-problems/2017-10-02/advanced/?problem=no-computer-needed) 
> and wanted to work in base 2.  I realize it's niche, but it's not 
> exactly a significant change to the interface even if it's a big change 
> to the implementation.

In cpython, decimal uses _cdecimal for speed.  I suspect that 10 is not 
only explicitly hard-coded as the base but implicitly hard-coded by 
using algorithm tricks that depend on and only work when the base is 10.

-- 
Terry Jan Reedy