import torch


def fixed_positional_encoding(
    sentence_dimension: int,
    embedding_dimension: int,
) -> torch.Tensor:

    BIG_CONST = int(1e4)
    INITIAL_ENCODING = torch.tensor([i for i in range(0, sentence_dimension)])

    ENCODINGS: list[torch.Tensor] = []

    for i in range(0, embedding_dimension):
        EMBEDDING_POSITION = i

        # Note: The original paper did not specify
        #   to compute: pos mod 2!!
        DIVISOR = BIG_CONST ** ((2 * (EMBEDDING_POSITION // 2)) / embedding_dimension)
        INTERMEDIATE_ENCODING = INITIAL_ENCODING / DIVISOR

        if EMBEDDING_POSITION % 2 == 0:
            ENCODINGS.append(torch.sin(INTERMEDIATE_ENCODING))
            continue

        ENCODINGS.append(torch.cos(INTERMEDIATE_ENCODING))

    return torch.stack(ENCODINGS).transpose(0, 1)