# Copyright 2022 EleutherAI and the HuggingFace Inc. team. All rights reserved.
#
# This code is based on EleutherAI's GPT-NeoX library and the GPT-NeoX
# and OPT implementations in this library. It has been modified from its
# original forms to accommodate minor architectural differences compared
# to GPT-NeoX and OPT used by the Meta AI team that trained the model.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# NOTE: this implementation is from LLaMA 2:
# https://huggingface.co/togethercomputer/LLaMA-2-7B-32K/blob/08639a72e17836184096ae6a7e2766f2a34c3e36/modeling_flash_llama.py#L114
# Flash attention rotary implementation can be installed like so: `pip install git+https://github.com/HazyResearch/flash-attention.git#subdirectory=csrc/rotary`

from typing import Tuple

import torch
from einops import rearrange, repeat


def rotate_half(x, interleaved=False):
    if not interleaved:
        x1, x2 = x.chunk(2, dim=-1)
        return torch.cat((-x2, x1), dim=-1)
    else:
        x1, x2 = x[..., ::2], x[..., 1::2]
        return rearrange(
            torch.stack((-x2, x1), dim=-1), "... d two -> ... (d two)", two=2
        )


def apply_rotary_emb_torch(x, cos, sin, interleaved=False, _inplace=False):
    """
    x: (batch_size, seqlen, nheads, headdim)
    cos, sin: (seqlen, rotary_dim / 2)
    """
    ro_dim = cos.shape[-1] * 2
    assert ro_dim <= x.shape[-1]
    seqlen = x.size(1)
    cos = cos[:seqlen]
    sin = sin[:seqlen]
    cos = repeat(cos, "s d -> s 1 (2 d)")
    sin = repeat(sin, "s d -> s 1 (2 d)")
    return torch.cat(
        [
            x[..., :ro_dim] * cos + rotate_half(x[..., :ro_dim], interleaved) * sin,
            x[..., ro_dim:],
        ],
        dim=-1,
    )


class RotaryEmbedding(torch.nn.Module):
    """
    The rotary position embeddings from RoFormer_ (Su et. al).
    A crucial insight from the method is that the query and keys are
    transformed by rotation matrices which depend on the relative positions.
    Other implementations are available in the Rotary Transformer repo_ and in
    GPT-NeoX_, GPT-NeoX was an inspiration
    .. _RoFormer: https://arxiv.org/abs/2104.09864
    .. _repo: https://github.com/ZhuiyiTechnology/roformer
    .. _GPT-NeoX: https://github.com/EleutherAI/gpt-neox
    If scale_base is not None, this implements XPos (Sun et al., https://arxiv.org/abs/2212.10554).
    A recommended value for scale_base is 512: https://github.com/HazyResearch/flash-attention/issues/96
    Reference: https://github.com/sunyt32/torchscale/blob/main/torchscale/component/xpos_relative_position.py
    """

    def __init__(
        self,
        dim: int,
        base=10000.0,
        interleaved=False,
        scale_base=None,
        scaling_factor=1.0,
        pos_idx_in_fp32=True,
        device=None,
    ):
        """
        interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead
            of 1st half and 2nd half (GPT-NeoX style).
        pos_idx_in_fp32: if True, the position indices [0.0, ..., seqlen - 1] are in fp32,
            otherwise they might be in lower precision.
            This option was added because previously (before 2023-07-02), when we construct
            the position indices, we use the dtype of self.inv_freq. In most cases this would
            be fp32, but if the model is trained in pure bf16 (not mixed precision), then
            self.inv_freq would be bf16, and the position indices are also in bf16.
            Because of the limited precision of bf16 (e.g. 1995.0 is rounded to 2000.0), the
            embeddings for some positions will coincide.
            To maintain compatibility with models previously trained in pure bf16,
            we add this option.
        scaling_factor: RotaryEmbedding extended with linear scaling.
        """
        super().__init__()
        self.dim = dim
        self.base = float(base)
        self.pos_idx_in_fp32 = pos_idx_in_fp32
        # Generate and save the inverse frequency buffer (non trainable)
        self.interleaved = interleaved
        self.scale_base = scale_base
        self.scaling_factor = scaling_factor
        self.device = device

        self._seq_len_cached = 0
        self._cos_cached = None
        self._sin_cached = None
        self._cos_k_cached = None
        self._sin_k_cached = None
        self.reset_parameters()

    def reset_parameters(self):
        inv_freq = self._compute_inv_freq(self.device)
        self.register_buffer("inv_freq", inv_freq, persistent=False)
        arange = torch.arange(0, self.dim, 2, device=self.device, dtype=torch.float32)
        scale = (
            (arange + 0.4 * self.dim) / (1.4 * self.dim)
            if self.scale_base is not None
            else None
        )
        self.register_buffer("scale", scale)

    def _compute_inv_freq(self, device=None):
        return 1 / (
            self.base
            ** (
                torch.arange(0, self.dim, 2, device=device, dtype=torch.float32)
                / self.dim
            )
        )

    def _update_cos_sin_cache(self, seqlen, device=None, dtype=None):
        # Reset the tables if the sequence length has changed,
        # if we're on a new device (possibly due to tracing for instance),
        # or if we're switching from inference mode to training
        if (
            seqlen > self._seq_len_cached
            or self._cos_cached is None
            or self._cos_cached.device != device
            or self._cos_cached.dtype != dtype
            or (self.training and self._cos_cached.is_inference())
        ):
            self._seq_len_cached = seqlen
            # We want fp32 here, not self.inv_freq.dtype, since the model could be loaded in bf16
            # And the output of arange can be quite large, so bf16 would lose a lot of precision.
            # However, for compatibility reason, we add an option to use the dtype of self.inv_freq.
            if self.pos_idx_in_fp32:
                t = torch.arange(seqlen, device=device, dtype=torch.float32)
                t /= self.scaling_factor
                # We want fp32 here as well since inv_freq will be multiplied with t, and the output
                # will be large. Having it in bf16 will lose a lot of precision and cause the
                # cos & sin output to change significantly.
                # We want to recompute self.inv_freq if it was not loaded in fp32
                if self.inv_freq.dtype != torch.float32:
                    inv_freq = self.inv_freq.to(torch.float32)
                else:
                    inv_freq = self.inv_freq
            else:
                t = torch.arange(seqlen, device=device, dtype=self.inv_freq.dtype)
                t /= self.scaling_factor
                inv_freq = self.inv_freq
            # Don't do einsum, it converts fp32 to fp16 under AMP
            # freqs = torch.einsum("i,j->ij", t, self.inv_freq)
            freqs = torch.outer(t, inv_freq)

            if self.scale is None:
                self._cos_cached = torch.cos(freqs).to(dtype)
                self._sin_cached = torch.sin(freqs).to(dtype)
            else:
                power = (
                    torch.arange(
                        seqlen, dtype=self.scale.dtype, device=self.scale.device
                    )
                    - seqlen // 2
                ) / self.scale_base
                scale = self.scale.to(device=power.device) ** power.unsqueeze(-1)
                # We want the multiplication by scale to happen in fp32
                self._cos_cached = (torch.cos(freqs) * scale).to(dtype)
                self._sin_cached = (torch.sin(freqs) * scale).to(dtype)
                self._cos_k_cached = (torch.cos(freqs) / scale).to(dtype)
                self._sin_k_cached = (torch.sin(freqs) / scale).to(dtype)

    def forward(
        self, q: torch.Tensor, k: torch.Tensor, seqlen_offset: int = 0
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """
        q: (batch, seqlen, nheads, headdim)
        k: (batch, seqlen, nheads, headdim)
        seqlen_offset: can be used in generation where the qkv being passed in is only the last
        token in the batch.
        """
        self._update_cos_sin_cache(
            q.shape[1] + seqlen_offset, device=q.device, dtype=q.dtype
        )
        assert self._cos_cached is not None
        assert self._sin_cached is not None
        if self.scale is None:
            return (
                apply_rotary_emb_torch(
                    q,
                    self._cos_cached[seqlen_offset:],
                    self._sin_cached[seqlen_offset:],
                    self.interleaved,
                    True,  # inplace=True
                ),
                apply_rotary_emb_torch(
                    k,
                    self._cos_cached[seqlen_offset:],
                    self._sin_cached[seqlen_offset:],
                    self.interleaved,
                    True,  # inplace=True
                ),
            )  # type: ignore
        else:
            assert False