#!/usr/bin/env python3
"""Independent exact check of (max distance / min distance)^2 for a point set (stdlib only, integers).

python3 verify_minratio.py FILE DIM [--record VALUE]     (lower is better; exit 0 iff below the record)
"""
import decimal
import sys
from fractions import Fraction


def main():
    f, dim = sys.argv[1], int(sys.argv[2])
    rec = sys.argv[sys.argv.index("--record") + 1] if "--record" in sys.argv else None
    toks = []
    for line in open(f):
        line = line.split("#", 1)[0]
        toks += [decimal.Decimal(t) for t in line.replace(",", " ").split()]
    E = max(-t.as_tuple().exponent for t in toks)
    V = [int(t.scaleb(E)) for t in toks]
    P = [V[i:i + dim] for i in range(0, len(V), dim)]
    n = len(P)
    D = [sum((a - b) ** 2 for a, b in zip(P[i], P[j])) for i in range(n) for j in range(i + 1, n)]
    lo, hi = min(D), max(D)
    if lo == 0:
        print("coincident points")
        return 1
    q = Fraction(hi, lo)
    s = decimal.Decimal(q.numerator) / decimal.Decimal(q.denominator)
    with decimal.localcontext() as c:
        c.prec = 40
        s = decimal.Decimal(q.numerator) / decimal.Decimal(q.denominator)
        print(f"points {n} dim {dim}  ratio^2 = {s}  (exact fraction {q.numerator.bit_length()}-bit / "
              f"{q.denominator.bit_length()}-bit)")
        if rec:
            r = decimal.Decimal(rec)
            print(f"record {rec}  margin (record - ours) = {r - s}")
            return 0 if q < Fraction(rec) else 1
    return 0


if __name__ == "__main__":
    sys.exit(main())