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    Re: Longhand Sight Reduction
    From: Peter Monta
    Date: 2014 Jun 12, 12:18 -0700
    Hi Hanno,

    The multiplications show each partial product separately in the array.  It's less compact than the usual method, but somehow I find it more reliable to add up everything at the end.  It's essentially the lattice method:


    but turned on its side and with the low-order terms dropped.  The aim was to calculate one or two places beyond the least-significant digit of the inputs, then round.  Almost always this will give the same result as rounding the full-precision product (and for even lower expected error at very small additional cost, one can add a bias term before rounding to represent the dropped terms).  Computer arithmetic people worry about this sort of thing because the factor-of-2 savings is very attractive; I'm sure there was historical precedent too, before log tables took over the medium-precision market.

    Perhaps it's better just to do the full-precision multiplies.  The aim was to have a very robust, simple, desert-island-derivable method with no complications.  Your polynomial approximations sound fine, but our desert-island resident would have to devote time to reproduce them without high-tech aids (of course, if you're on a desert island, you have plenty of time).

    So no-table sight reduction seems tractable.  The other part of this is the almanac, and here we really have to memorize a few numbers.  The minimal set might be something like (ra,dec)@J2000 of half a dozen bright stars plus the expression for sidereal time at Greenwich (including an estimate of the current delta-T).  The Sun seems a bit too complicated to memorize to any usable accuracy, let alone the Moon and planets; but any of these bodies could be used as "transfer standards" by measuring them against the stars.

    Here are my assumptions, which are of course pretty absurd:

    - available: sextant; chronometer showing UTC; pencil and paper
    - not available: tables or any other computational aid; almanac
    - known: micro-almanac of a few stars; sight reduction algorithm

    Hanno, just read your reply:  yes, exactly, Napier's bones.  The desert-island guy might well want to make a set.


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