#!/usr/bin/env python3
"""Process calc kernel. Copy this file. Stdlib only."""
from __future__ import annotations

from fractions import Fraction as F


def as_exact(x):
    if isinstance(x, bool):
        raise TypeError("theta bool")
    if isinstance(x, int):
        return F(x)
    if isinstance(x, F):
        return F(x)
    raise TypeError("theta not Q: %s" % type(x).__name__)


def isolate(v, seed):
    v, seed = as_exact(v), as_exact(seed)
    if seed == 0:
        raise ValueError("theta seed 0")
    return (v, seed)


def mix(a, b):
    (v, r), (w, s) = a, b
    return (v * w, r * w + v * s)


def add(a, b):
    (v, r), (w, s) = a, b
    return (v + w, r + s)


def rate(top, bot):
    if bot[1] == 0:
        raise ValueError("theta dead isolator")
    return top[1] / bot[1]


def certify(fn, values, seeds):
    if not values or not seeds:
        raise ValueError("theta empty grid")
    rows = []
    for v in values:
        got = []
        for s in seeds:
            x = isolate(v, s)
            got.append(rate(fn(x), x))
        if any(g != got[0] for g in got):
            raise ValueError("gauge split at %s %s" % (v, got))
        rows.append((v, got[0]))
    return rows


if __name__ == "__main__":
    x = isolate(3, 1)
    print(rate(mix(x, x), x))
    print(certify(lambda z: mix(z, z), (2, 3, -1), (1, 2, F(1, 2), -1)))