Implement the "unum" representation in D ?

[Anthony Di Franco via Digitalmars-d]

On Wednesday, 22 July 2015 at 20:41:42 UTC, jmh530 wrote:
> On Wednesday, 22 July 2015 at 19:28:41 UTC, Andrei Alexandrescu 
> wrote:
>> On 7/13/15 1:20 AM, Nick B wrote:
>>
>> All we can do now, with our limited resources, is to keep an 
>> eye on developments and express cautious interest. If someone 
>> able and willing comes along with a unum library for D, that 
>> would be great.
>>
>
> The book has quite a bit of Mathematica code at the end. A 
> first pass at a unum library could probably just involve 
> porting that to D.

Here is a Python port of the Mathematica code which is that much 
closer to D:
https://github.com/jrmuizel/pyunum

Regardless of whether the representation used follows the unum 
bitwise format proposed in the book, having the semantics of 
interval arithmetic that keeps proper account of amount of 
precision, and exact values vs. open/closed ended intervals on 
the extended real line would be quite valuable for verified 
computation and for how it enables simple root finding / 
optimization / differential equation solving via search, and 
could build on hard float directly andor an extended precision 
float library such as MPFR to keep performance close to raw 
floats.

The bitwise format is intended to fit as much data as possible 
through the time-energy bottleneck between main memory and the 
processor. This would clearly be of great value if the format 
were supported in hardware but of less clear value otherwise. The 
semantic improvements would be quite welcome regardless. They go 
much further than best practices with floats to put error bounds 
on computations, handle over/underflow and infinity correctly, 
and keep algorithms correct by default. We might also consider 
small semantic improvements if not rigidly bound by the proposed 
formats and the need to implement in hardware, such as having 
division by an interval including zero return the union of the 
results from the intervals on either side of the zero as well as 
NaN (1-D intervals are strictly represented as the convex hull of 
at most two points in the proposed format, so an interval such as 
this made of a sentinel value unified with two disjoint 
intervals, though it has better semantics, is not supported).

Anthony