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