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    Re: Logarithms by Hand
    From: Peter Monta
    Date: 2014 Jun 6, 19:17 -0700
    Here's a hand-worked four-place sine/cosine (attached).  Takes around 10 minutes, so for a sight reduction with three of these, plus an arcsine and arctangent, plus a few additional multiplies and adds, you're looking at something like an hour.

    If one needs to do a lot of these, it might be better to precompute a small table every 5 degrees or so, then use a lower-order method.

    The angle shown is near the upper end of the 45-degree interval to illustrate the need for all the terms.  Angles outside of 0..45 degrees can be handled by symmetry.

    The check is really essential---I tried several of these and made arithmetic blunders on about half of them.  Also writing out the partial products in full and not propagating carries until the end (unlike the method taught in grade school) seems to give better reliability.  If working to more places, omitting many of the low-order partial products cuts the time in half.

    Cheers,
    Peter

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