@triton.autotune(configs=warps_kernel_configs(), key=['batch_dim', 'feat_dim'])
@triton.heuristics({'BLOCK_SIZE_BATCH': BLOCK_SIZE_BATCH_heuristic,
    'BLOCK_SIZE_FEAT': lambda args: next_power_of_2(args['feat_dim'])})
@triton.jit
def cross_entropy_loss_backward_kernel(output_grad_pointer, target_pointer,
    input_pointer, weight_pointer, sum_weights_pointer, input_grad_pointer,
    batch_dim, feat_dim, input_batch_stride, input_feat_stride,
    input_grad_batch_stride, input_grad_feat_stride, weighted: tl.constexpr,
    BLOCK_SIZE_BATCH: tl.constexpr, BLOCK_SIZE_FEAT: tl.constexpr):
    """
    Calculates the input gradient of cross entropy loss.

    Args:
        output_grad_pointer: Pointer to the loss's output gradients.
            The output gradient must be a scalar.
        target_pointer: Pointer to the target.
            The target must be of shape [batch_dim].
        input_pointer: Pointer to the input.
            The input must be of shape [batch_dim, feat_dim].
        weight_pointer: Pointer to an optional class weight vector.
            The class weight vector, if provided, must be of shape [feat_dim].
        sum_weights_pointer: Pointer to the sum of the class weights if the classes were weighed.
            The sum of weights must be a scalar.
        input_grad_pointer: Pointer to a container the input's gradients are written to.
            The container must be of shape [batch_dim, feat_dim].
        batch_dim: Batch dimension.
        feat_dim: Dimensionality of the features.
        input_batch_stride: Stride necessary to jump one element along the
            input's batch dimension.
        input_feat_stride: Stride necessary to jump one element along the
            input's feature dimension.
        input_grad_batch_stride: Stride necessary to jump one element along the
            input gradient container's batch dimension.
        input_grad_feat_stride: Stride necessary to jump one element along the
            input gradient container's feature dimension.
        weighted: Flag for weighing each class.
        BLOCK_SIZE_BATCH: Block size across the batch dimension.
        BLOCK_SIZE_FEAT: Block size across the feature dimension.
    """
    batch_pid = tl.program_id(axis=0)
    batch_offset = batch_pid * BLOCK_SIZE_BATCH + tl.arange(0, BLOCK_SIZE_BATCH
        )
    feat_offset = tl.arange(0, BLOCK_SIZE_FEAT)
    batch_mask = batch_offset < batch_dim
    feat_mask = feat_offset < feat_dim
    input_pointer += input_batch_stride * batch_offset[:, None
        ] + input_feat_stride * feat_offset[None, :]
    input_grad_pointer += input_grad_batch_stride * batch_offset[:, None
        ] + input_grad_feat_stride * feat_offset[None, :]
    input = tl.load(input_pointer, mask=batch_mask[:, None] & feat_mask[
        None, :], other=-float('inf')).to(tl.float32)
    input -= tl.max(input, axis=1)[:, None]
    numerator = tl.exp(input)
    softmax = numerator / tl.sum(numerator, axis=1)[:, None]
    output_grad = tl.load(output_grad_pointer).to(tl.float32)
    target = tl.load(target_pointer + batch_offset, mask=batch_mask)
    broadcasted_feat_offset = tl.broadcast_to(feat_offset[None, :], (
        BLOCK_SIZE_BATCH, BLOCK_SIZE_FEAT))
    broadcasted_target = tl.broadcast_to(target[:, None], (BLOCK_SIZE_BATCH,
        BLOCK_SIZE_FEAT))
    input_grad = output_grad * (softmax - (broadcasted_feat_offset ==
        broadcasted_target))
    if weighted:
        weight = tl.load(weight_pointer + target, mask=batch_mask).to(tl.
            float32)
        sum_weights = tl.load(sum_weights_pointer)
        input_grad *= weight[:, None] / sum_weights
    else:
        input_grad /= batch_dim
    tl.store(input_grad_pointer, input_grad, mask=batch_mask[:, None] &
        feat_mask[None, :])
