Re: Increasing precision in octave

[Przemek Klosowski]

   1/ Why is it 16, not 32?

Because the internal representation of a double precision floating
point number is a 64-bit unit, which is divided between a 11-bit
exponent and a 52-bit mantissa. Now, 2^52 is about 5*10^15, i.e. tbe
52-bit binary number is equivalent to a 16-bit decimal number. Check:

        http://en.wikipedia.org/wiki/Double_precision


   2/ Any way I sometimes see p-values of order e-50, e-70 (for example,
   when calculating p-values with BLAST - best local alignment search tool,
   ncbi.hlm.nih.gov/BLAST). How are they calculated considering that they
   are very unlikely to use 128 processors?

The processors don't enter into it---we are talking about the precision
limits in any numerical calculation.

Maybe the confusion is because a number like e-50 doesn't mean that
you have 50 significant digits---the exponent is -50, and the mantissa
has the usual 16 significant digits. By the way, those 64-bit double
precision numbers have an exponent range between plus and minus 308 or
so. All this is actually available in Octave; check the values of
built-in Octave variables realmin, realmax and eps.

octave:5> realmin
realmin =  2.2251e-308
octave:6> realmax
realmax =  1.7977e+308
octave:7> eps
eps =  2.2204e-16