En Mon, 21 Dec 2009 17:40:40 -0300, Albert van der Horst
<alb...@spenarnc.xs4all.nl> escribió:
In article <kv0dvx....@spenarnc.xs4all.nl>,
Albert van der Horst <alb...@spenarnc.xs4all.nl> wrote:
In article
<a266b155-02df-4294-8b91-41be4a1e4...@a32g2000yqm.googlegroups.com>,
Mark Dickinson <dicki...@gmail.com> wrote:
After a cup of coffee, it's much clearer: this just comes from the
Taylor series for arcsin(x), applied to x = 1/2 to get asin(1/2) =
pi/6.
Below you see cos which just calculates cosine with a
Taylor series.
Then there is pi2() that uses it to calculate pi, for the
normal fp precision.
pi3() shows the algorithm in its glory and should work for
any floating point package.
pi4() does the same, if precision is given.
And last but not least pi5() that uses the Decimal package
to advantage. It precalculates a starting point in 1/5 of
the precision. Then it does one more iteration in the full precision.
For 1000 digits it is about 5 times faster than pi(), for
a moderate increase in complexity.
You may try Demo/scripts/pi.py in the source distribution; it uses long
integers to compute a continued fraction approximation to pi. I wonder how
does it compare to those other algorithms.
--
Gabriel Genellina
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