def exclusive_cumprod(tensor, dim: int, eps: float = 1e-10):
    """
    Implementing exclusive cumprod.
    There is cumprod in pytorch, however there is no exclusive mode.
    cumprod(x) = [x1, x1x2, x2x3x4, ..., prod_{i=1}^n x_i]
    exclusive means
    cumprod(x) = [1, x1, x1x2, x1x2x3, ..., prod_{i=1}^{n-1} x_i]
    """
    tensor_size = list(tensor.size())
    tensor_size[dim] = 1
    return_tensor = safe_cumprod(
        torch.cat([torch.ones(tensor_size).type_as(tensor), tensor], dim=dim),
        dim=dim,
        eps=eps,
    )

    if dim == 0:
        return return_tensor[:-1]
    elif dim == 1:
        return return_tensor[:, :-1]
    elif dim == 2:
        return return_tensor[:, :, :-1]
    else:
        raise RuntimeError(
            "Cumprod on dimension 3 and more is not implemented"
        )
Implementing exclusive cumprod.
There is cumprod in pytorch, however there is no exclusive mode.
cumprod(x) = [x1, x1x2, x2x3x4, ..., prod_{i=1}^n x_i]
exclusive means
cumprod(x) = [1, x1, x1x2, x1x2x3, ..., prod_{i=1}^{n-1} x_i]
examples/simultaneous_translation/utils/functions.py