Re: [boost] [Review Request] Multiprecision Arithmetic Library

Subject: Re: [boost] [Review Request] Multiprecision Arithmetic Library
From: Topher Cooper (topher_at_[hidden])
Date: 2012-04-03 00:37:51

On 4/2/2012 6:29 PM, Andrii Sydorchuk wrote:
> Yes, those are very large numbers:-). I would say that int32 exponent
> should be good enough (I don't mean that it should be used). I am eager to
> see applications of int64 exponent range.
>
> Andrii
>    
Yeah -- the diameter of the observable universe (not the observed 
universe -- the physically observable universe) in Plank units (the 
smallest physically meaningful length according to QM) is about 
1.5*2^204, so 9 bits (positive and negative exponents) is all that is 
required to express the exponent for any physical distance in any 
physically meaningful units.  Volumes would reach binary exponent of 613 
so 11 bits covers this with generous room to spare.  I doubt you will 
find any physical quantities that will be much larger.  Combinatorics 
can easily generate very large quantities, of course, but if you are 
getting into those ranges you probably will be using logarithms.  So 16 
bits is probably as much as you can reasonably expect to need (lots of 
bits in the mantissa is, of course, justifiable to preserve precision in 
intermediate results), and 32 would be as much as you can *un*reasonably 
expect to need -- and more.

I'm not actually arguing against the choice of int64 representation for 
the exponents either.  There are other issues then utility in efficient 
design and a few unused bits are worth it for performance or even just 
code simplicity.  Just thought I would put things in perspective.   (I'm 
partially responding with amusment here, because I remember when we 
wondered whether there really was any point to the 15 bit exponents when 
the HFloat (H = Huge) format was introduced the the VAX architecture on 
request/recommendation of some members of the scientific community, the 
GFloat format (G=Grand) introduced at the same time for the same reason 
had 11 bit exponents).

Topher