Which is the "correct" way to implement equal power panning, using square roots or cosines? After doing some googling, I found posts recommending both methods. And which would be more efficient, if they're both "correct"? I've tried both and they both sound the same to me, and seem to give the same results, as far as I can tell. I compared the output from [env~] of the input signal with the summed output signals (left and right), and didn't see any difference. When panned near the middle, the RMS of the output signal is a little higher than the input signal, using either method (see screen prints below). But that may be due to the way [env~] calculates RMS, I don't know.
Here are my two implementations, [pan~] using the square root method and [pan2~] using the cosine method.