NavList:

Rafal, looking at your example to find the SHA and Dec of Rigel:

Sight time: 1855/01/15 18:31:34
Star: Rigel

GHA Aries:
(a) correction for year 1855:
    113:45:48 + 00:07:00 = 113:52:48
(b) increment for hours:
    113:52:48 + 270:44:21 = 384:37:09 = 24:37:09
(b) increment for minutes:
    24:37:09 + 7:46:16 = 32:23:25
(c) increment for seconds:
    32:23:25 + 0:08:31 = 32:31:56

Rigel's SHA:
(a) correction for years (y=-145):
    -(10 * 10 + 10 * 4 + 5) = -(-4329 - 1732 - 216) = -6277 = -(3600 + 2677) = -(-1deg 44min 37sec) = 1:44:37
(b) non-linear correction for 1855:
    +9"
(c) total correction: 1:44:37 + 0:00:09 = 1:44:46
(d) 281:21:32 + 1:44:37 = 283:06:09

Rigel's dec:
(a) correction for years (y=-145):
    -(10 * 10 + 10 * 4 + 5) = -(395 + 158 + 20) = -573
(b) non-linear correction for 1855:
    -11
(c) total correction: -573 - 11 = -584 = -0:09:44
(d) -8:12:39 - 0:09:44 = -8:22:23 = 8:22:23 S

This is all good, and it's great that you've included all the bits and pieces including aberration. Your coordinates here are good enough for celestial navigation. But this is what we might refer to as a non-trivial amount of work just to get the SHA and Dec of one star. 

What are you imagining as a "use case" for this long procedure? Who would benefit from this? If you're just experimenting to see what can be achieved, no problem, of course. But if you're trying to develop a practical solution for a practical problem, I think you'll need to do something differently. This is too much work for too little benefit, and I just can't imagine more than a handful of end users who would ever do this in the twenty-first century... Is that worth your effort?

Frank Reed