import torch
import torch.nn as nn
from torchdiffeq import  odeint



import math

class ODELinear(nn.Module):
    def __init__(
        self, 
        dim: int, 
        factor,
        **kwargs
    ):
        super().__init__()
        self.ode_up_proj = nn.Parameter(torch.empty(dim//2, factor*dim).to(torch.float32))
        self.ode_down_proj = nn.Parameter(torch.empty(factor*dim, dim//2).to(torch.float32))
        self.dim = dim
        self.act = torch.nn.SiLU()
        self.reset_parameters()

    def reset_parameters(self):
        nn.init.kaiming_uniform_(self.ode_up_proj, a=math.sqrt(5))
        nn.init.zeros_(self.ode_down_proj)

    def get_time_embedding(self, t, base=10000, device='cuda', dtype=torch.float32):
        if t < 1:
            alpha = 1
        else:
            alpha = 2*t-1
        ntk_base = base * alpha ** (self.dim / (self.dim-2))
        ntk_inv_freq = 1.0 / (ntk_base ** (torch.arange(0, self.dim, 2, dtype=torch.float32).to(device) / self.dim))
        index = torch.arange(0, self.dim, 2, dtype=torch.float32).to(device)
        delta_ntk_freq = -2*index/(self.dim-2) * 1 / (base ** (index/self.dim) * (alpha ** (index/(self.dim-2) + 1)))
        return delta_ntk_freq.to(device, dtype=dtype), ntk_inv_freq.to(device, dtype=dtype)

    def forward(self, t, x: torch.Tensor):
        delta_time, time = self.get_time_embedding(t, device=x.device, dtype=x.dtype)
        x = x + torch.log(time)
        time_embed = delta_time / time
        delta_inv_freq = self.act(x @ self.ode_up_proj.float()) @ self.ode_down_proj.float() + time_embed
        return delta_inv_freq



class LlamaCLEXScalingRotaryEmbedding(nn.Module):

    def __init__(self, dim, max_position_embeddings=2048, rope_scaling=None, base=10000, device=None) -> None:
        super().__init__()

        self.max_t = rope_scaling["max_factor"]
        self.dim = dim
        self.max_position_embeddings = max_position_embeddings
        self.base = base
        inv_freq = 1.0 / (self.base ** (torch.arange(0, self.dim, 2).float().to(device) / self.dim))
        self.register_buffer("inv_freq", inv_freq)

        self.proj_func = ODELinear(dim, rope_scaling["param_factor"])
        self.rope_cached = None
        self.max_t_cached = 0
        self.freq_cached = None
        self.time_dt = 0.01
        self.ode_args = {
            "method": "rk4",
            "options": {"step_size": self.time_dt},
        }

    def sample_random_times(self, max_t, device):
        return torch.randint(2, max_t, (1,), dtype = torch.long, device=device)

    def get_random_position_ids(self, n=2048, max=8192):
        positions = torch.randperm(max)[:n].sort().values
        # positions = positions.to(device=device)
        return positions
    

    def get_continuous_freq(self, time_grid, ex_positions, device):
        solution = odeint(
            self.proj_func, torch.log(self.inv_freq.to(device, dtype=torch.float32)), time_grid, **self.ode_args
        )
        if time_grid.size(0) == 2:
            training
            scale_inv_freq = torch.exp(solution[1])
            # print(time_grid[1].tolist(), torch.sum(scale_inv_freq).tolist(), torch.sum(self.proj_func.ode_down_proj).tolist())
            freqs = torch.outer(ex_positions.float().squeeze(), scale_inv_freq)
        else:
            scale_inv_freq = torch.exp(solution)
            freqs = torch.einsum('i, kl -> kil', ex_positions, scale_inv_freq)
        embed = torch.cat((freqs,freqs), dim=-1)
        return embed



    def forward(self, device, dtype, seq_len, do_train=False):
        device = self.proj_func.ode_up_proj.device
        scale_factor = seq_len // self.max_position_embeddings
        if do_train:
            t_val = self.sample_random_times(self.max_t+1, device)[0]
            import math
            sampled_position_ids = self.get_random_position_ids(n=seq_len-2, max=seq_len*t_val-2).float()
            ex_positions = torch.cat([
                torch.tensor([0]), 
                (sampled_position_ids + 1) / scale_factor,
                torch.tensor([seq_len*t_val//scale_factor-1])]
            ).to(device, dtype=torch.float32)
        else:
            t_val = scale_factor if seq_len%self.max_position_embeddings == 0.0 else scale_factor + 1
            t_val = t_val if t_val <= self.max_t else self.max_t
            ex_positions = torch.arange(0, self.max_position_embeddings * t_val, dtype=torch.float32).to(device)


        
        if t_val == 1.0:
            scale_inv_freq = self.inv_freq.to(device)
            freqs = torch.outer(ex_positions.float().squeeze(), scale_inv_freq)
            embed = torch.cat((freqs,freqs), dim=-1)
            cos, sin = embed.cos()[None, None, :, :], embed.sin()[None, None, :, :]
        elif do_train:
            time_grid = torch.tensor([1.0, t_val]).float().to(device)
            embed = self.get_continuous_freq(time_grid, ex_positions, device)
            cos, sin = embed.cos()[None, None, :, :], embed.sin()[None, None, :, :]
        else:
            if t_val > self.max_t_cached:
                time_grid = torch.arange(1.0, self.max_t + 1.0, dtype=torch.float32).to(device)
                if self.freq_cached is None:
                    self.freq_cached = self.get_continuous_freq(time_grid, ex_positions, device)
                embed = self.freq_cached[int(t_val)-1.0]
                self.rope_cached = torch.cat((embed.cos()[None, None, None, :, :], embed.sin()[None, None, None, :, :]), dim=0)
                self.max_t_cached = t_val
            cos, sin = self.rope_cached
        
        return torch.cat(
            (cos[None, :, :, :seq_len, ...].to(dtype=dtype),
            sin[None, :, :, :seq_len, ...].to(dtype=dtype)),
            dim=0
        )