$ ./ana_2.pl 24 2 1000000
N=16777216, V=2, X=1000000 integral(1000000)=25166956.740071, integral(0)=25165824
Expected collisions: 1132.74007095024

$ ./ana_2.pl 26 2 1000000
N=67108864, V=2, X=1000000 integral(1000000)=100663369.193409, integral(0)=100663296
Expected collisions: 73.1934093236923

$ ./ana_2.pl 28 2 1000000
N=268435456, V=2, X=1000000 integral(1000000)=402653188.613027, integral(0)=402653184
Expected collisions: 4.61302703619003

$ ./ana_2.pl 30 2 1000000
N=1073741824, V=2, X=1000000 integral(1000000)=1610612736.28892, integral(0)=1610612736
Expected collisions: 0.288918733596802

$ ./ana_2.pl 31 2 1000000
N=2147483648, V=2, X=1000000 integral(1000000)=3221225472.07225, integral(0)=3221225472
Expected collisions: 0.0722546577453613