Mean implementation for Fixed-Points

[manel1874]

Hi, I am curious why we have the following implementation for the mean over FP:

mpyc/mpyc/statistics.py

Line 59 in b8d2d5d

return s * (2**e / n) * 2**-e

Is that because it's faster to divide a secret number by a power of two rather than by some general number?

[lschoe]

It's to prevent (unnecessary) loss of precision in the division by the public integer n. If we simply divide by n, which works out as multiplying by 1/n, we get a fixed-point number of the form 0.00001*** say, in binary, with a lot of leading zeros and few significant bits. Therefore, we shift this to the left to make it of the form 0.1*******, which represents 1/n with more significant bits. The product with the sum s is shifted back at the end. Note that e = n.bit_length()-1 to ensure 1/2 < 2**e / n <= 1 as written in the comment on line 58.

[manel1874]

Great, thanks for you fast reply!