Generate set of 64-bit FPs with fully unique pairwise Tanimotos

fps.txt

0x831A122F5DED0F74
0xF1E6F872274DB4B4
0x8940578CC91025A7
0x5DFE2CABD588AB8A
0xF17DA5DF5A7438AB
0x8F97D17115314C0D
0xAFCF937513811F3B
0xDE69E942303BA44D
0x64D37E0B37C3B362
0x09171FE07590059D
0x721B780423404B05
0xD9EDEBF5C845228D
0x1FF6DFEA53D3D91D
0x01105E18B5017860
0x00414301D8203AC1
0x66DE9C6AF591BD0D
0xFD6FF4DF2FFF3EFB

make_tanimoto_set.py

# Uses int.bit_count from Python 3.10rc1

from fractions import Fraction
from random import randint, seed
from sys import stdout
from time import time

def rand64():
    return randint(0,0xFFFFFFFFFFFFFFFF)

def tanimoto(a,b):
    return Fraction((a&b).bit_count(), (a|b).bit_count())

if __name__ == '__main__':
    start = time()
    seed()
    fps = [rand64(), rand64()]
    all_tans = {tanimoto(fps[0], fps[1])}

    tried_since_pass = 0
    while True:
        new = rand64()
        new_tans = {tanimoto(new, x) for x in fps}
        # If all Tanimotos in this row are unique and do not overlap with
        # previously calculated Tanimotos, then the full matrix will continue
        # to be unique
        if (len(new_tans) == len(fps)) and len(new_tans & all_tans) == 0:
            fps.append(new)
            all_tans = all_tans | new_tans
            print('\nTook %d tries to add, now at %d, %d tans, et %.1fs' %
                    (tried_since_pass, len(fps), len(all_tans), time() - start))
            for fp in fps:
                print('0x%016X' % fp)
            assert(len(all_tans) == (len(fps) * (len(fps)-1))/2)
            tried_since_pass = 0
        else:
            tried_since_pass += 1
            if tried_since_pass % 10000 == 0:
                stdout.write('.')
                stdout.flush()

test_fps.py

import sys
from fractions import Fraction

fps = []
tans = set()

def tanimoto(a,b):
    return Fraction((a & b).bit_count() , (a | b).bit_count())

for line in sys.stdin:
    num = int(line.rstrip(),16)
    print('0x%016X' % num)
    assert num not in fps
    fps.append(num)

for i in fps:
    for j in fps:
        if i == j:
            continue
    tan = tanimoto(i,j)
    assert tan not in tans
    tans.add(tan)
print('Pass! %d Tanimotos, %d FPs' % (len(tans), len(fps)))