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Today I used atand(x) and atan(x). To my great surprise atand(x) was not just a little bit slower than atan(x) but is incredibly slow compared to atan(x)?
I tried to verify this by using the code below. First a time measurement for atan(x), than for atan(x) multiplied with 360/2/pi to go to degrees and finally one loop for atand(x). The results I found were:
Elapsed time is 0.047019 seconds. -> atan(x)
Elapsed time is 0.062016 seconds. -> atan(x)*360/2/pi
Elapsed time is 4.166911 seconds. -> atand(x)
And finally a test to check if atand(x) yielded identical results to atan(x) which was 'true' for all arguments tested.
This would mean that one should never use atan2d because atan2(x)*360/2/pi is much and much quicker? Why is there even a atan2d(x) function or why is it so slow?
Ernst Jan Grift
clear all n=1000000; x_rad=zeros(1,n); x_rad_to_d=zeros(1,n); x_d=zeros(1,n); arg=rand(1,n);
tic for i=1:n x_rad(i)=atan(arg(n)); end toc
tic for i=1:n x_rad_to_d(i)=atan(arg(n))*360/2/pi; end toc
tic for i=1:n x_d(i)=atand(arg(n)); end toc
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I don't see any record of this; please file an enhancement request.
Your observation is interesting, but I don't think the conclusion is that you should never use ATAND, but only that it hasn't been well-optimized for the JIT yet, and shouldn't be used in for-loops. When vectorized, its performance is fine,
x_rad=atan(arg); toc %Elapsed time is 0.106370 seconds.
x_rad_to_d=atan(arg)*180/pi; toc %Elapsed time is 0.111417 seconds.
x_d=atand(arg); toc %Elapsed time is 0.115595 seconds.