import torch
from torch.cuda.amp import custom_bwd, custom_fwd


class _VocabCrossEntropy(torch.autograd.Function):
    @staticmethod
    @custom_fwd
    def forward(ctx, vocab_parallel_logits, target):
        # Maximum value along vocab dimension across all GPUs.
        logits_max = torch.max(vocab_parallel_logits, dim=-1)[0]

        # Subtract the maximum value.
        vocab_parallel_logits.sub_(logits_max.unsqueeze(dim=-1))

        # Create a mask of valid vocab ids (1 means it needs to be masked).
        target_mask = target < 0
        masked_target = target.clone()
        masked_target[target_mask] = 0

        # Get predicted-logits = logits[target].
        # For Simplicity, we convert logits to a 2-D tensor with size
        # [*, partition-vocab-size] and target to a 1-D tensor of size [*].
        logits_2d = vocab_parallel_logits.view(-1, vocab_parallel_logits.size(-1))
        masked_target_1d = masked_target.view(-1)
        arange_1d = torch.arange(start=0, end=logits_2d.size()[0], device=logits_2d.device)
        predicted_logits_1d = logits_2d[arange_1d, masked_target_1d]
        predicted_logits_1d = predicted_logits_1d.clone().contiguous()
        predicted_logits = predicted_logits_1d.view_as(target)
        predicted_logits[target_mask] = 0.0

        # Sum of exponential of logits along vocab dimension across all GPUs.
        exp_logits = vocab_parallel_logits
        torch.exp(vocab_parallel_logits, out=exp_logits)
        sum_exp_logits = exp_logits.sum(dim=-1)

        # Loss = log(sum(exp(logits))) - predicted-logit.
        loss = torch.log(sum_exp_logits) - predicted_logits

        # Store softmax, target-mask and masked-target for backward pass.
        exp_logits.div_(sum_exp_logits.unsqueeze(dim=-1))
        ctx.save_for_backward(exp_logits, target_mask, masked_target_1d)

        return loss

    @staticmethod
    @custom_bwd
    def backward(ctx, grad_output):
        # Retreive tensors from the forward path.
        softmax, target_mask, masked_target_1d = ctx.saved_tensors

        # All the inputs have softmax as their gradient.
        grad_input = softmax
        # For simplicity, work with the 2D gradient.
        partition_vocab_size = softmax.size()[-1]
        grad_2d = grad_input.view(-1, partition_vocab_size)

        # Add the gradient from matching classes.
        arange_1d = torch.arange(start=0, end=grad_2d.size()[0], device=grad_2d.device)
        grad_2d[arange_1d, masked_target_1d] -= 1.0 - target_mask.view(-1).float()

        # Finally elementwise multiplication with the output gradients.
        grad_input.mul_(grad_output.unsqueeze(dim=-1))

        return grad_input, None


def vocab_cross_entropy(vocab_logits, target):
    """helper function for the cross entropy."""

    return _VocabCrossEntropy.apply(vocab_logits, target)