Re: String representations of numeric values

Hi Ed,

I don't understand your arithmetics -- double have 52 bits for the mantissa (53 if you include the hidden bit), that means a dynamics of 2^53 or 10^16. If the largest angle is 360degrees, to get an accuracy of 1 nano-arcsec you need only 51 bits only (360deg = 1.296E+15 nano-arcsec).

243 degrees plus 9.13 microarcsec, with an accuracy of 0.01micro-arcsec, is just 243.00000000254 or 243.000000002536 -- the number 243.00000000025361 you quote is 243 + 0.9130 microarcsec, i.e. expressed with an accuracy of 0.1nano-arcsec ...

>As a representative of the SIM mission I should mention that SIM will be
>regularly be making measurements of positions with precision order 0.1
>microarcsec (although accuracy may be limited by fiducial grid accuracy).
>1 microarcsec = 1E-6/3600 = 2.778E-10.
>So to express, say 243 degrees plus 9.13 microarcsec or
>243.00000000025361 which has 17 digits, is not expressable in double
>precision (where the significand holds a bit over 15 digits).
>Therefore we need to introduce quad precision if VOTable is to be used
>in SIM and GAIA preparatory work.
>
>Although I would prefer to use hh mm ss.ssssssss since quad precision is
>way overkill.
>
>Ed
>
>

Francois Ochsenbein       ------       Observatoire Astronomique de Strasbourg
   11, rue de l'Universite F-67000 STRASBOURG       Phone: +33-(0)390 24 24 29
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