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atand(x) very much slower than atan(x)!?

Asked by Ernst Jan on 28 Mar 2013

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?

Kind regards,

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
same=x_rad_to_d==x_d;
all(same)

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Ernst Jan

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2 Answers

Answer by Sean de Wolski on 28 Mar 2013
Accepted answer

I don't see any record of this; please file an enhancement request.

1 Comment

Ernst Jan on 28 Mar 2013

A service request has been submitted. Both atand(x) and atan2d(x) show this slow behaviour.

Sean de Wolski
Answer by Matt J on 28 Mar 2013
Edited by Matt J on 28 Mar 2013

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,

    n=1e7;
    arg=rand(1,n);
    tic
        x_rad=atan(arg);
    toc
    %Elapsed time is 0.106370 seconds.    
    tic
        x_rad_to_d=atan(arg)*180/pi;
    toc
    %Elapsed time is 0.111417 seconds.    
    tic
        x_d=atand(arg);
    toc
    %Elapsed time is 0.115595 seconds.

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Matt J

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