import torch
import torch.distributed as dist
from torch.distributed import ProcessGroup


def build_bloom_alibi_tensor_fn(process_group: ProcessGroup) -> torch.Tensor:

    def build_bloom_alibi_tensor(self, attention_mask: torch.Tensor, num_heads: int,
                                 dtype: torch.dtype) -> torch.Tensor:
        """
        Link to paper: https://arxiv.org/abs/2108.12409 Alibi tensor is not causal as the original paper mentions, it
        relies on a translation invariance of softmax for quick implementation: with l being a tensor, and a fixed value
        `softmax(l+a) = softmax(l)`. Based on
        https://github.com/ofirpress/attention_with_linear_biases/blob/a35aaca144e0eb6b789dfcb46784c4b8e31b7983/fairseq/models/transformer.py#L742
        TODO @thomasw21 this doesn't work as nicely due to the masking strategy, and so masking varies slightly.

        Args:
        Returns tensor shaped (batch_size * num_heads, 1, max_seq_len)
            attention_mask (`torch.Tensor`):
                Token-wise attention mask, this should be of shape (batch_size, max_seq_len).
            num_heads (`int`, *required*):
                number of heads
            dtype (`torch.dtype`, *optional*, default=`torch.bfloat16`):
                dtype of the output tensor
        """
        import math

        if dist.is_initialized():
            world_size = dist.get_world_size(process_group)
            num_heads = num_heads * world_size

        batch_size, seq_length = attention_mask.shape
        closest_power_of_2 = 2**math.floor(math.log2(num_heads))
        base = torch.tensor(2**(-(2**-(math.log2(closest_power_of_2) - 3))),
                            device=attention_mask.device,
                            dtype=torch.float32)
        powers = torch.arange(1, 1 + closest_power_of_2, device=attention_mask.device, dtype=torch.int32)
        slopes = torch.pow(base, powers)

        if closest_power_of_2 != num_heads:
            extra_base = torch.tensor(2**(-(2**-(math.log2(2 * closest_power_of_2) - 3))),
                                      device=attention_mask.device,
                                      dtype=torch.float32)
            num_remaining_heads = min(closest_power_of_2, num_heads - closest_power_of_2)
            extra_powers = torch.arange(1,
                                        1 + 2 * num_remaining_heads,
                                        2,
                                        device=attention_mask.device,
                                        dtype=torch.int32)
            slopes = torch.cat([slopes, torch.pow(extra_base, extra_powers)], dim=0)

        # Note: alibi will added to the attention bias that will be applied to the query, key product of attention
        # => therefore alibi will have to be of shape (batch_size, num_heads, query_length, key_length)
        # => here we set (batch_size=1, num_heads=num_heads, query_length=1, key_length=max_length)
        # => the query_length dimension will then be broadcasted correctly
        # This is more or less identical to T5's relative position bias:
        # https://github.com/huggingface/transformers/blob/f681437203baa7671de3174b0fa583c349d9d5e1/src/transformers/models/t5/modeling_t5.py#L527
        arange_tensor = ((attention_mask.cumsum(dim=-1) - 1) * attention_mask)[:, None, :]
        alibi = slopes[..., None] * arange_tensor
        if dist.is_initialized():
            num_heads_per_rank = int(num_heads / dist.get_world_size(process_group))
            offset = dist.get_rank(process_group) * num_heads_per_rank
            alibi = alibi.view(batch_size, num_heads, 1, seq_length)
            alibi = alibi[:, offset:num_heads_per_rank + offset, :, :]
            return alibi.reshape(batch_size * num_heads_per_rank, 1, seq_length).to(dtype)
        else:
            return alibi.reshape(batch_size * num_heads, 1, seq_length).to(dtype)

    return build_bloom_alibi_tensor