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

### Ernst Jan (view profile)

on 28 Mar 2013
Accepted Answer by Sean de Wolski

### Sean de Wolski (view profile)

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_d=zeros(1,n);
arg=rand(1,n);
```
```tic
for i=1:n
end
toc
```
```tic
for i=1:n
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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### Sean de Wolski (view profile)

on 28 Mar 2013

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

Ernst Jan

### Ernst Jan (view profile)

on 28 Mar 2013

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

on 28 Mar 2013
Edited by Matt J

### Matt J (view profile)

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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