"""
This module provides functions for transforming curves to different models.
"""
from public import public

from .coordinates import AffineCoordinateModel
from .curve import EllipticCurve
from .model import ShortWeierstrassModel, MontgomeryModel, TwistedEdwardsModel
from .params import DomainParameters
from .point import InfinityPoint, Point


def __M_map(params, map_parameters, map_point, model):
    A = params.curve.parameters["a"]
    B = params.curve.parameters["b"]
    parameters = map_parameters(A, B)
    aff = AffineCoordinateModel(model)
    if isinstance(params.curve.neutral, InfinityPoint):
        neutral = InfinityPoint(aff)
    else:
        neutral = map_point(A, B, params.curve.neutral, aff)
    curve = EllipticCurve(model, aff, params.curve.prime, neutral, parameters)
    return DomainParameters(curve, map_point(A, B, params.generator, aff), params.order,
                            params.cofactor)


@public
def M2SW(params: DomainParameters) -> DomainParameters:
    """
    Convert a Montgomery curve to ShortWeierstrass.

    :param params: The domain parameters to convert.
    :return: The converted domain parameters.
    """
    if not isinstance(params.curve.model, MontgomeryModel) or not isinstance(
            params.curve.coordinate_model, AffineCoordinateModel):
        raise ValueError

    def map_parameters(A, B):
        a = (3 - A ** 2) / (3 * B ** 2)
        b = (2 * A ** 3 - 9 * A) / (27 * B ** 3)
        return {"a": a, "b": b}

    def map_point(A, B, pt, aff):
        u = pt.x / B + A / (3 * B)
        v = pt.y / B
        return Point(aff, x=u, y=v)

    return __M_map(params, map_parameters, map_point, ShortWeierstrassModel())


@public
def M2TE(params: DomainParameters) -> DomainParameters:
    """
    Convert a Montgomery curve to TwistedEdwards.

    :param params: The domain parameters to convert.
    :return: The converted domain parameters.
    """
    if not isinstance(params.curve.model, MontgomeryModel) or not isinstance(
            params.curve.coordinate_model, AffineCoordinateModel):
        raise ValueError

    def map_parameters(A, B):
        a = (A + 2) / B
        d = (A - 2) / B
        return {"a": a, "d": d}

    def map_point(A, B, pt, aff):
        u = pt.x / pt.y
        v = (pt.x - 1) / (pt.x + 1)
        return Point(aff, x=u, y=v)

    return __M_map(params, map_parameters, map_point, TwistedEdwardsModel())