import torch
import functools
from torch import Tensor
from typing import Any, Callable, Optional, Tuple, Union
import warnings

in_dims_t = Union[int, Tuple[Optional[int], ...]]
out_dims_t = Union[int, Tuple[int, ...]]

# Checks that all args-to-be-batched have the same batch dim size
def _validate_and_get_batch_size(
        in_dims_as_tuple: Tuple[Optional[int], ...],
        args: Tuple) -> int:
    batch_sizes = [arg.size(in_dim) for in_dim, arg in zip(in_dims_as_tuple, args)
                   if in_dim is not None]
    if batch_sizes and any([size != batch_sizes[0] for size in batch_sizes]):
        raise ValueError(
            f'vmap: Expected all tensors to have the same size in the mapped '
            f'dimension, got sizes {batch_sizes} for the mapped dimension')
    return batch_sizes[0]

# Check compatibility of `in_dims` and `args`. More specifically, checks the following:
# Wherever an in_dim is not None, then the corresponding index in args must be
# a Tensor. Furthermore, tensor must have the `in_dim` (0 <= in_dim < tensor.dim())
def _check_args_can_be_mapped_with_in_dims(
        in_dims_as_tuple: Tuple[Optional[int], ...],
        args: Tuple,
        fn_name: str,
        in_dims: in_dims_t) -> None:
    for idx, (in_dim, arg) in enumerate(zip(in_dims_as_tuple, args)):
        if in_dim is None:
            continue
        if not isinstance(in_dim, int):
            raise ValueError(
                f'vmap({fn_name}, in_dims={in_dims}, ...)(<inputs>): in_dims '
                f'must be a flat tuple containing ints and/or Nones. If you were '
                f'trying to vmap over a Tensor inside a Python collection in '
                f'`inputs`, we do not yet support that.')
        if not isinstance(arg, Tensor):
            raise ValueError(
                f'vmap({fn_name}, in_dims={in_dims}, ...)(<inputs>): Got '
                f'in_dim={in_dim} for input {idx}, but input {idx} is not a '
                f'Tensor (got {type(arg)}) so it cannot be vmap\'ed over. '
                f'If you were trying to vmap over a Tensor inside a Python '
                f'collection in `inputs`, we do not yet support that; otherwise, '
                f'use None as the respective in_dim for input {idx}.')
        # NB: We don't do dimension wrapping here. Consider allowing it in the
        # future if there is demand.
        if in_dim >= 0 and in_dim < arg.dim():
            continue
        raise ValueError(
            f'vmap({fn_name}, in_dims={in_dims}, ...)(<inputs>): Got in_dim={in_dim} '
            f'for input {idx}, but input {idx} is a Tensor of dimensionality '
            f'{arg.dim()} so expected in_dim to satisfy 0 <= in_dim < {arg.dim()}.')

def _num_outputs(batched_outputs: Union[Tensor, Tuple[Tensor, ...]]) -> int:
    if isinstance(batched_outputs, tuple):
        return len(batched_outputs)
    return 1

# If value is a tuple, check it has length `num_elements`.
# If value is not a tuple, make a tuple with `value` repeated `num_elements` times
def _as_tuple(value: Any, num_elements: int, error_message_lambda: Callable[[], str]) -> Tuple:
    if not isinstance(value, tuple):
        return (value,) * num_elements
    if len(value) != num_elements:
        raise ValueError(error_message_lambda())
    return value

# Creates BatchedTensors for every Tensor in arg that should be batched.
# Returns the (potentially) batched arguments and the batch_size.
def _create_batched_inputs(
        in_dims: in_dims_t, args: Tuple, vmap_level: int, fn_name: str) -> Tuple[Tuple, int]:
    if not isinstance(in_dims, int) and not isinstance(in_dims, tuple):
        raise ValueError(
            f'vmap({fn_name}, in_dims={in_dims}, ...): expected `in_dims` to '
            f'be int or tuple, got: {type(in_dims)}.')

    # NB: Checks that len(in_dims) == len(args) (if in_dims is a tuple).
    in_dims_as_tuple = _as_tuple(
        in_dims, len(args),
        lambda: f'vmap({fn_name}, in_dims={in_dims}, ...)(<inputs>): expected '
                f'one `in_dim` per input (got {len(args)} inputs) of {fn_name}')

    if len(args) == 0:
        raise ValueError(
            f'vmap({fn_name})(<inputs>): got no inputs. Maybe you forgot to add '
            f'inputs, or you are trying to vmap over a function with no inputs. '
            f'The latter is unsupported.')

    _check_args_can_be_mapped_with_in_dims(in_dims_as_tuple, args, fn_name, in_dims)
    batch_size = _validate_and_get_batch_size(in_dims_as_tuple, args)
    # See NOTE [Ignored _remove_batch_dim, _add_batch_dim]
    batched_inputs = tuple(arg if in_dim is None else
                           torch._add_batch_dim(arg, in_dim, vmap_level)  # type: ignore
                           for in_dim, arg in zip(in_dims_as_tuple, args))
    return batched_inputs, batch_size

# Undos the batching (and any batch dimensions) associated with the `vmap_level`.
def _unwrap_batched(
        batched_outputs: Union[Tensor, Tuple[Tensor, ...]],
        out_dims: out_dims_t,
        vmap_level: int, batch_size: int, fn_name: str) -> Tuple:
    num_outputs = _num_outputs(batched_outputs)
    out_dims_as_tuple = _as_tuple(
        out_dims, num_outputs,
        lambda: f'vmap({fn_name}, ..., out_dims={out_dims}): `out_dims` must '
                f'have one dim per output (got {num_outputs} outputs) of {fn_name}.')

    # NOTE [Ignored _remove_batch_dim, _add_batch_dim]
    # There is something wrong with our type bindings for functions that begin
    # with '_', see #40397.
    if isinstance(batched_outputs, Tensor):
        out_dim = out_dims_as_tuple[0]
        return torch._remove_batch_dim(batched_outputs, vmap_level, batch_size, out_dim)  # type: ignore
    return tuple(torch._remove_batch_dim(out, vmap_level, batch_size, out_dim)  # type: ignore
                 for out, out_dim in zip(batched_outputs, out_dims_as_tuple))

# Checks that `fn` returned one or more Tensors and nothing else.
# NB: A python function that return multiple arguments returns a single tuple,
# so we are effectively checking that `outputs` is a single Tensor or a tuple of
# Tensors.
def _validate_outputs(outputs: Any, fn_name: str) -> None:
    if isinstance(outputs, Tensor):
        return
    if not isinstance(outputs, tuple):
        raise ValueError(f'vmap({fn_name}, ...): `{fn_name}` must only return '
                         f'Tensors, got type {type(outputs)} as the return.')
    for idx, output in enumerate(outputs):
        if isinstance(output, Tensor):
            continue
        raise ValueError(f'vmap({fn_name}, ...): `{fn_name}` must only return '
                         f'Tensors, got type {type(output)} for return {idx}.')

def _check_out_dims_is_int_or_int_tuple(out_dims: out_dims_t, fn_name: str) -> None:
    if isinstance(out_dims, int):
        return
    if not isinstance(out_dims, tuple) or \
            not all([isinstance(out_dim, int) for out_dim in out_dims]):
        raise ValueError(
            f'vmap({fn_name}, ..., out_dims={out_dims}): `out_dims` must be '
            f'an int or a tuple of int representing where in the outputs the '
            f'vmapped dimension should appear.')

# This is the global tracker for how many nested vmaps we are currently inside.
VMAP_LEVEL: int = 0

# vmap(func)(inputs) wraps all Tensor inputs to be batched in BatchedTensors,
# sends those into func, and then unwraps the output BatchedTensors. Operations
# on BatchedTensors perform the batched operations that the user is asking for.
def vmap(func: Callable, in_dims: in_dims_t = 0, out_dims: out_dims_t = 0) -> Callable:
    """
    vmap is the vectorizing map. Returns a new function that maps `func` over some
    dimension of the inputs. Semantically, vmap pushes the map into PyTorch
    operations called by `func`, effectively vectorizing those operations.

    vmap is useful for handling batch dimensions: one can write a function `func`
    that runs on examples and the lift it to a function that can take batches of
    examples with `vmap(func)`. Furthermore, it is possible to use vmap to obtain
    batched gradients when composed with autograd.

    Args:
        func (function): A Python function that takes one or more arguments.
            Must return one or more Tensors.
        in_dims (int or Tuple[Optional[int]]): Specifies which dimension of the
            inputs should be mapped over. If `in_dims` is a Tuple, then it should have
            one element per input. If the `in_dim` for a particular input is
            None, then that indicates there is no map dimension. Default: 0.
        out_dims (int or Tuple[int]): Specifies where the mapped dimension
            should appear in the outputs. If `out_dims` is a Tuple, then it should
            have one element per output. Default: 0.

    Returns:
        Returns a new "batched" function. It takes the same inputs as `func`,
        except each input has an extra dimension at the index specified by `in_dims`.
        It takes returns the same outputs as `func`, except each output has
        an extra dimension at the index specified by `out_dims`.

    .. warning:
        vmap works best with functional-style code. Please do not perform any
        side-effects in `func`, with the exception of in-place PyTorch operations.
        Examples of side-effects include mutating Python data structures and
        assigning values to variables not captured in `func`.

    .. warning::
        torch.vmap is an experimental prototype that is subject to
        change and/or deletion. Please use at your own risk.
    """
    warnings.warn(
        'torch.vmap is an experimental prototype that is subject to '
        'change and/or deletion. Please use at your own risk.')

    @functools.wraps(func)
    def wrapped(*args):
        fn_name = func.__name__
        _check_out_dims_is_int_or_int_tuple(out_dims, fn_name)
        global VMAP_LEVEL
        VMAP_LEVEL += 1
        try:
            batched_inputs, batch_size = _create_batched_inputs(in_dims, args, VMAP_LEVEL, fn_name)
            batched_outputs = func(*batched_inputs)
            _validate_outputs(batched_outputs, fn_name)
            return _unwrap_batched(batched_outputs, out_dims, VMAP_LEVEL, batch_size, fn_name)
        finally:
            VMAP_LEVEL -= 1
    return wrapped
