Floating-point representation

Marc Glisse marc.glisse at inria.fr
Tue May 18 09:53:32 UTC 2021

On Thu, 13 May 2021, David M. Warme wrote:

> Consider the floating-point representation
>    m * b**e
> where m, b and e are integers and b >= 2 is a fixed constant.
> (The mantissa m could be a GMP integer, and e a fixed-precision
> signed integer.)
> The normalization rule is that the mantissa m is either zero
> or not divisible by b.  (For the usual case of b = 2, the
> mantissa m is either zero or an odd integer.)
> This representation supports add, subtract and multiply with
> no rounding error.
> Q1: Does this representation have a well-defined name (especially
>    for the b = 2 case)?
> Q2: If so, does anyone have a reference in the literature?

No idea about references, but I think that's what I implemented in CGAL as 
CGAL::Mpzf, with b = 2**64, where we already had CGAL::Gmpzf with b=2.

Marc Glisse

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