Re: [boost] Is there interest in Computable Calculus?

Subject: Re: [boost] Is there interest in Computable Calculus?
From: Phil Endecott (spam_from_boost_dev_at_[hidden])
Date: 2016-01-13 13:15:02

Damian Vicino wrote:
> I'm interested in developing basic support of "real numbers" 
> for computable calculus applications.
>
> In computable calculus, reals have infinite precision (certain 
> restrictions may apply).
> The usual approach is representing numbers as functions producing 
> digits. 

Considering, for example, the Delaunay condition:

bool delaunay(T ax, T ay, T bx, T by, T cx, T cy, T dx, T dy)
{
  T cos_abc = (ax-bx)*(cx-bx) + (ay-by)*(cy-by);
  T cos_cda = (cx-dx)*(ax-dx) + (cy-dy)*(ay-dy);
  if (cos_abc >= 0 && cos_cda >= 0) return false;
  if (cos_abc < 0 && cos_cda < 0) return true;

  T sin_abc = (ax-bx)*(cy-by) - (cx-bx)*(ay-by);
  T sin_cda = (cx-dx)*(ay-dy) - (ax-dx)*(cy-dy);

  T sin_sum = sin_abc * cos_cda + cos_abc * sin_cda;
  return sin_sum < 0;
}

I'd be interested to know how this approach of effectively "lazy 
evaluation" compares to using eagerly-evaluated arbitrary-precision 
types (e.g. Boost.Multiprecision's floating point types).  I.e. in 
terms of performance and any complexity introduced to the code.  
For what sorts of problems is it better?  How much work is actually 
saved by laziness in practice?

Regards,  Phil.