from typing import Optional, Tuple

import torch


def precompute_freqs_cis(
    dim: int, end: int, theta: float, device: Optional[torch.device] = None
) -> torch.Tensor:
    freqs = 1.0 / (
        theta ** (torch.arange(0, dim, 2, device=device)[: (dim // 2)].float() / dim)
    )
    t = torch.arange(end, device=freqs.device)  # type: ignore
    freqs = torch.outer(t, freqs).float()  # type: ignore
    return torch.polar(torch.ones_like(freqs), freqs)  # complex64


def apply_rotary_emb(
    xq: torch.Tensor,
    xk: torch.Tensor,
    freqs_cis: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor]:
    xq_ = torch.view_as_complex(xq.float().reshape(*xq.shape[:-1], -1, 2))
    xk_ = torch.view_as_complex(xk.float().reshape(*xk.shape[:-1], -1, 2))
    freqs_cis = freqs_cis[:, None, :]
    xq_out = torch.view_as_real(xq_ * freqs_cis).flatten(2)
    xk_out = torch.view_as_real(xk_ * freqs_cis).flatten(2)
    return xq_out.type_as(xq), xk_out.type_as(xk)