[Numpy-discussion] Log Arrays
Thu May 8 12:06:57 CDT 2008
Is the 80 bits float (float96 on IA32, float128 on AMD64) isn't enough? It has a 64 bits mantissa and can represent numbers up to nearly 1E(+-)5000.
מאת: firstname.lastname@example.org בשם Charles R Harris
נשלח: ה 08-מאי-08 19:25
אל: Discussion of Numerical Python
נושא: Re: [Numpy-discussion] Log Arrays
On Thu, May 8, 2008 at 10:11 AM, Anne Archibald <email@example.com>
> 2008/5/8 Charles R Harris <firstname.lastname@example.org>:
> > What realistic probability is in the range exp(-1000) ?
> Well, I ran into it while doing a maximum-likelihood fit - my early
> guesses had exceedingly low probabilities, but I needed to know which
> way the probabilities were increasing.
The number of bosons in the universe is only on the order of 1e-42.
Exp(-1000) may be convenient, but as a probability it is a delusion. The
hypothesis "none of the above" would have a much larger prior.
But to expand on David's computation... If the numbers are stored without
using logs, i.e., as the exponentials, then the sum is of the form:
x_1*2**y_1 + ... + x_i*2**y_i
Where 1<= x_j < 2 and both x_i and y_i are available. When the numbers are
all of the same general magnitude you get essentially the same result as
David's formula by simply by dividing out the first value.
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