from typing import Callable, Optional
import math

import torch
from torch.optim.optimizer import Optimizer


class RAdam(Optimizer):
    """Implements RAdam algorithm.

    It has been proposed in `On the Variance of the Adaptive Learning Rate
    and Beyond`_.

    @TODO: Docs (add `Example`). Contribution is welcome

    Main origins of inspiration:
        https://github.com/LiyuanLucasLiu/RAdam (Apache-2.0 License)

    .. _On the Variance of the Adaptive Learning Rate and Beyond:
        https://arxiv.org/abs/1908.03265
    """

    def __init__(
        self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0
    ):
        """@TODO: Docs. Contribution is welcome."""
        defaults = {
            "lr": lr,
            "betas": betas,
            "eps": eps,
            "weight_decay": weight_decay,
        }
        self.buffer = [[None, None, None] for _ in range(10)]
        super(RAdam, self).__init__(params, defaults)

    def __setstate__(self, state):
        """@TODO: Docs. Contribution is welcome."""
        super(RAdam, self).__setstate__(state)

    def step(self, closure: Optional[Callable] = None):
        """Makes optimizer step.

        Args:
            closure (callable, optional): A closure that reevaluates
                the model and returns the loss.
        """
        loss = None
        if closure is not None:
            loss = closure()

        for group in self.param_groups:

            for p in group["params"]:
                if p.grad is None:
                    continue
                grad = p.grad.data.float()
                if grad.is_sparse:
                    raise RuntimeError(
                        "RAdam does not support sparse gradients"
                    )

                p_data_fp32 = p.data.float()

                state = self.state[p]

                if len(state) == 0:
                    state["step"] = 0
                    state["exp_avg"] = torch.zeros_like(p_data_fp32)
                    state["exp_avg_sq"] = torch.zeros_like(p_data_fp32)
                else:
                    state["exp_avg"] = state["exp_avg"].type_as(p_data_fp32)
                    state["exp_avg_sq"] = state["exp_avg_sq"].type_as(
                        p_data_fp32
                    )

                exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]
                beta1, beta2 = group["betas"]

                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
                exp_avg.mul_(beta1).add_(1 - beta1, grad)

                state["step"] += 1
                buffered = self.buffer[int(state["step"] % 10)]
                if state["step"] == buffered[0]:
                    N_sma, step_size = buffered[1], buffered[2]
                else:
                    buffered[0] = state["step"]
                    beta2_t = beta2 ** state["step"]
                    N_sma_max = 2 / (1 - beta2) - 1
                    N_sma = N_sma_max - 2 * state["step"] * beta2_t / (
                        1 - beta2_t
                    )
                    buffered[1] = N_sma

                    # more conservative since it's an approximated value
                    if N_sma >= 5:
                        step_size = (
                            group["lr"]
                            * math.sqrt(
                                (1 - beta2_t)
                                * (N_sma - 4)
                                / (N_sma_max - 4)
                                * (N_sma - 2)
                                / N_sma
                                * N_sma_max
                                / (N_sma_max - 2)
                            )
                            / (1 - beta1 ** state["step"])
                        )
                    else:
                        step_size = group["lr"] / (1 - beta1 ** state["step"])
                    buffered[2] = step_size

                if group["weight_decay"] != 0:
                    p_data_fp32.add_(
                        -group["weight_decay"] * group["lr"], p_data_fp32
                    )

                # more conservative since it's an approximated value
                if N_sma >= 5:
                    denom = exp_avg_sq.sqrt().add_(group["eps"])
                    p_data_fp32.addcdiv_(-step_size, exp_avg, denom)
                else:
                    p_data_fp32.add_(-step_size, exp_avg)

                p.data.copy_(p_data_fp32)

        return loss
