* quad <quadricode@gmail.com> [Apr 08. 2011 08:20]:
Hello all!
Many months ago, maybe even a couple years ago (I lost count), I wrote a high precision floating point arithmetic library in C. Here's a sample demo of it:
[...]
Anyway, you don't need to run it, and it's not the point of this email. The algorithms I use are here:
http://www.symbo1ics.com/files/algs.pdf [Section 3]
Any corrections would be helpful.
The iterations for reciprocal and a-th roots on page 8 should be written in a form that keeps the term (1-x*y^a) intact. For example, your iteration for the reciprocal y --> y*(2-x*y) should be y --> y + y*(1-x*y) See p.567ff of the fxtbook.
Anyway, I'm looking:
1. to include more algorithms that are known to work well for computing special functions and whatever to high precision. 2. to include improvements to what I have at the moment, algorithmically. Is the way I compute sine slow? Are there faster ways?
The "rectangular method" (p.658ff) might be something to check out: while its asymptotics isn't that fantastic it works surprisingly good (fast!) in practice. Binary splitting (p.651ff) can be an option if you are able to work with integers.
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Thanks all!
Robert
regards, jj