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Symbolic pkg vpa trig speed


From: Colin Macdonald
Subject: Symbolic pkg vpa trig speed
Date: Wed, 6 Jul 2016 00:15:57 -0700
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.1.1

In a bug report Dan asked:
Just curious, from what you know about the arbitrary precision
library, is it slow to compute trig functions out to sixteen digits
compared to the floating point library?

Its currently a bit hard to tell, especially as Symbolic's handling of
large arrays of doubles is non-optimal (pending pytave GSoC work!) but probably hundreds of times slower.

x = rand(10, 10);

% make vpa objects from x in 16, 32, 48 (of course these will not magically have extra precision, its just for timing)
xv16 = vpa(x, 16);
xv32 = vpa(x, 32);
xv48 = vpa(x, 48);

tic; sin(x); toc
Elapsed time is 0.000461817 seconds.
tic; sin(xv16); toc
Elapsed time is 0.156639 seconds.
tic; sin(xv32); toc
Elapsed time is 0.118703 seconds.
tic; sin(xv48); toc
Elapsed time is 0.175145 seconds.

The xv16 = bit seems take longer than I expect..., I filed https://github.com/cbm755/octsympy/issues/499)

best,
Colin



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