# -*- coding: utf-8 -*-
"""
Simulate lattice reduction on the rows of::

    ⌜ ξI  A  0 ⌝
    ǀ  0 qI  0 |
    ⌞ 0   c  τ ⌟

where

- ξI ∈ ZZ^{n × n},
- A ∈ ZZ_q^{n × m},
- qI ∈ ZZ^{m × m},
- τ ∈ ZZ and
- d = m + n + 1.

The last row is optional.
"""

from sage.all import RR, log


def CN11(d, n, q, beta, xi=1, tau=1):
    from fpylll import BKZ
    from fpylll.tools.bkz_simulator import simulate

    if tau is not None:
        r = [q ** 2] * (d - n - 1) + [xi ** 2] * n + [tau ** 2]
    else:
        r = [q ** 2] * (d - n) + [xi ** 2] * n

    return simulate(r, BKZ.EasyParam(beta))[0]


def GSA(d, n, q, beta, xi=1, tau=1):

    """Reduced lattice shape fallowing the Geometric Series Assumption [Schnorr03]_

    :param d: Lattice dimension.
    :param n: Number of `q` vectors
    :param q: Modulus `q`
    :param beta: Block size β.
    :param xi: Scaling factor ξ for identity part.
    :param tau: Kannan factor τ.

    """
    from .reduction import delta as deltaf

    if tau is not None:
        log_vol = RR(log(q, 2) * (d - n - 1) + log(xi, 2) * n + log(tau, 2))
    else:
        log_vol = RR(log(q, 2) * (d - n) + log(xi, 2) * n)

    delta = deltaf(beta)
    r_log = [(d - 1 - 2 * i) * RR(log(delta, 2)) + log_vol / d for i in range(d)]
    r = [2 ** (2 * r_) for r_ in r_log]
    return r


def normalize(name):
    if str(name).upper() == "CN11":
        return CN11
    elif str(name).upper() == "GSA":
        return GSA
    else:
        return name


def plot_gso(r, *args, **kwds):
    from sage.all import line

    return line([(i, log(r_, 2) / 2.0) for i, r_ in enumerate(r)], *args, **kwds)