# inspired by https://github.com/karpathy/micrograd/blob/master/micrograd/engine.py
from __future__ import annotations
import time, math, itertools, functools, struct, sys, inspect, pathlib, string, hashlib, weakref
from contextlib import ContextDecorator
from typing import Any, Callable, ClassVar, Sequence, cast, get_args, Literal, SupportsIndex, ParamSpec, TypeVar, Generic, TYPE_CHECKING
if TYPE_CHECKING: import numpy
from tinygrad.dtype import DType, DTypeLike, dtypes, ConstType, least_upper_float, least_upper_dtype, to_dtype, truncate
from tinygrad.dtype import _from_np_dtype, _to_np_dtype, PyConst, Invalid, InvalidType
from tinygrad.helpers import argfix, make_tuple, flatten, prod, all_int, round_up, merge_dicts, argsort, getenv, all_same, fully_flatten
from tinygrad.helpers import IMAGE, FLOAT16, WINO, Metadata, TRACEMETA, ceildiv, fetch, is_numpy_ndarray, TracingKey, cpu_profile
from tinygrad.helpers import suppress_finalizing, disable_gc
from tinygrad.gradient import compute_gradient
from tinygrad.mixin import OpMixin
from tinygrad.uop.ops import smax, smin, resolve, UOp, Ops, sint, identity_element, all_metadata, _index_to_concrete_int, sint_to_uop, Variable
from tinygrad.uop.ops import _broadcast_shape
from tinygrad.engine.schedule import ExecItem, complete_create_schedule_with_vars
from tinygrad.device import Buffer
from tinygrad.engine.realize import run_schedule
from tinygrad.engine.allocations import transform_to_call

def canonicalize_device(device:str|tuple|list|None) -> str|tuple[str, ...]:
  from tinygrad.device import Device
  if not isinstance(device, (tuple, list)): return Device.canonicalize(device)
  return canonical[0] if len(canonical:=tuple(Device.canonicalize(d) for d in device)) == 1 else canonical

# *** all in scope Tensors are here. this gets relevant UOps ***

all_tensors: dict[weakref.ref[Tensor], None] = {}
def _apply_map_to_tensors(applied_map:dict[UOp, UOp], name:str, walk:bool=False) -> None:
  with cpu_profile(TracingKey(name), "TINY"):
    # get tensors in scope
    in_scope: dict[UOp, bool] = {}
    def visitor(node: UOp) -> bool: return True if node in applied_map else any(in_scope.get(s, False) for s in node.src)
    scope_tensors: list[Tensor] = [t for tref in list(all_tensors) if (t:=tref()) is not None and t.uop.topovisit(visitor, in_scope)]

    # get all Tensors and apply the map
    sink = UOp.sink(*[t.uop for t in scope_tensors])
    new_sink = sink.substitute(applied_map, name=f"substitute {name}", walk=walk)

    # set the relevant uop to the realized UOps
    for t,s,ns in zip(scope_tensors, sink.src, new_sink.src):
      if s is ns: continue
      t.uop = ns

# **** Tensor helper functions ****

def _fromnp(x: 'numpy.ndarray') -> UOp:
  ret = UOp.new_buffer("NPY", x.size, _from_np_dtype(x.dtype))
  # fake realize
  ret.buffer.allocate(x)
  return ret.reshape(x.shape)

def get_shape(x) -> tuple[int, ...]:
  # NOTE: str is special because __getitem__ on a str is still a str
  if not hasattr(x, "__len__") or not hasattr(x, "__getitem__") or isinstance(x, str) or (hasattr(x, "shape") and x.shape == ()): return ()
  if not all_same(subs:=[get_shape(xi) for xi in x]): raise ValueError(f"inhomogeneous shape from {x}")
  return (len(subs),) + (subs[0] if subs else ())

def _frompy(x:list|tuple|bytes, dtype:DType, device:str|tuple[str,...]) -> UOp:
  if isinstance(x, bytes): ret, data = UOp.new_buffer("PYTHON", len(x)//dtype.itemsize, dtype), x
  else:
    ret = UOp.new_buffer("PYTHON", prod(shape:=get_shape(x)), dtype).reshape(shape)
    assert dtype.fmt is not None, f"{dtype=} has None fmt"
    truncate_function = truncate[dtype]
    data = struct.pack(f"{ret.size}{dtype.fmt}", *[truncate_function(dtype.const(xi)) for xi in fully_flatten(x)])
  # fake realize. if target device is PYTHON it needs bytearray to be writable
  ret.buffer.allocate(memoryview(data if device != "PYTHON" else bytearray(data)))
  return ret

def _get_winograd_matcols(mat, dims:int, shp:tuple[sint, ...], device:str|tuple[str, ...], dtype:DType) -> list[list[Tensor]]:
  return [[Tensor.cat(*[Tensor.full(shp[:dim] + (1,) + shp[dim+1:], float(m[k]), device=device, dtype=dtype) for m in mat], dim=dim)
           for k in range(len(mat[0]))] for dim in range(dims)]

# winograd conv 3 kernel f(4x4,3x3) see: http://arxiv.org/abs/1509.09308
def _apply_winograd_matrix(mat, t:Tensor, dims:int) -> Tensor:
  # multiply mat_1 @ mat_2 @ t with foldable constants, where mat_i acts on vector t along dimension i; roughly kron(mat, mat) @ t
  # due to realize-before-expand rule in lazy.py, we must operate in this order: reshape -> expand -> arithmetic
  t_ = t.reshape(t.shape[:dims] + (1,) * dims + t.shape[dims:]).expand(t.shape[:dims] + (len(mat),) * dims + t.shape[dims:])  # add output dims
  # precalculate mat columns for each dim; prod(itertools.product(matcols)) gives the columns of kron(mat, mat, ...)
  matcols = _get_winograd_matcols(mat, dims, t_.shape[dims:], t_.device, t_.dtype)
  # multiply each element of t_ by the corresponding stacked column of kron(mat, mat), producing only one view for each element of t
  ret = sum(prod(col[idx] for col, idx in zip(matcols, mat_is)) * t_[mat_is] for mat_is in itertools.product(range(len(mat[0])), repeat=dims))
  assert isinstance(ret, Tensor), "sum didn't return a Tensor"
  return ret

def _masked_setitem(target:Tensor, values:Tensor, mask:Tensor, axes:tuple[int, ...]) -> Tensor:
  # reduce such that if mask contains repeated indices the last one remains
  for dim in reversed(axes):
    mask, values = functools.reduce(lambda x,y: (x[0]|y[0], y[0].where(y[1], x[1])), zip(mask.split(1, dim), values.split(1, dim)))
  # remove extra dims from reduce
  for dim in reversed(axes): mask, values = mask.squeeze(dim), values.squeeze(dim)
  # select from values for each True element in mask else select from target
  return mask.where(values, target)

#  `(padding_left, padding_right, padding_top, padding_bottom, ...)` ->  `(..., (padding_top, padding_bottom), (padding_left, padding_right))`
def _flat_to_grouped(padding:Sequence[sint]) -> tuple[tuple[sint, sint], ...]: return tuple(zip(padding[-2::-2], padding[::-2]))

ReductionStr = Literal["mean", "sum", "none"]

class Tensor(OpMixin):
  """
  A `Tensor` is a multi-dimensional matrix containing elements of a single data type.

  ```python exec="true" session="tensor"
  from tinygrad import Tensor, dtypes, nn
  import numpy as np
  import math
  np.set_printoptions(precision=4)
  ```
  """
  __slots__ = "uop", "requires_grad", "grad"
  training: ClassVar[bool] = False

  def __init__(self, data:ConstType|bytes|list|tuple|UOp|'numpy.ndarray'|pathlib.Path|None,
               device:str|tuple|list|None=None, dtype:DTypeLike|None=None, requires_grad:bool|None=None, _force_unique:bool=False):
    if device is None:
      if isinstance(data, pathlib.Path): device = f"DISK:{data.resolve()}"  # keep it on the disk if device is None
      elif isinstance(data, UOp): device = data._device
    _dtype:DType|None = to_dtype(dtype) if dtype is not None else None
    _device:str|tuple[str, ...] = canonicalize_device(device)
    del device, dtype

    # tensors can have gradients if you have called .backward
    self.grad:Tensor|None = None

    # NOTE: this can be in three states. False and None: no gradient, True: gradient
    # None (the default) will be updated to True if it's put in an optimizer
    self.requires_grad:bool|None = requires_grad

    # create a UOp from the different types of inputs
    if isinstance(data, UOp):
      assert _dtype is None or _dtype==data.dtype or data.dtype==dtypes.weakint, f"dtype mismatch: {_dtype} vs {data.dtype}"
      # if data is dtype.weakint that means that this is a symbolic int and we need to lower it to something we can make a Tensor out of
      if data.dtype == dtypes.weakint: data = Tensor.from_uop(data, device=_device).uop
    elif data is None:
      data = UOp.const(_dtype or dtypes.default_float, 0, _device)
    elif isinstance(data, get_args(ConstType)):
      data = (UOp.unique_const if _force_unique or requires_grad else UOp.const)(_dtype or dtypes.from_py(data), data, _device)
    elif isinstance(data, bytes): data = _frompy(data, _dtype or dtypes.uint8, _device)
    elif isinstance(data, (list, tuple)):
      if _dtype is None:
        if (d := fully_flatten(data)) and all(isinstance(s, bool) for s in d): _dtype = dtypes.bool
        else: _dtype = dtypes.default_int if d and all_int(d) else dtypes.default_float  # NOTE: this works because all_int([True, False]) is True
      if _dtype in [dtypes.bfloat16, *dtypes.fp8s]: data = _frompy(data, dtypes.float32, _device).cast(_dtype)
      else: data = _frompy(data, _dtype, _device)
    elif is_numpy_ndarray(data):
      import numpy as np
      assert isinstance(data, np.ndarray), f"expected np.ndarray, got {data}"
      if data.shape == ():
        data = UOp.const(_dtype or _from_np_dtype(data.dtype), data.item(), _device)
      else:
        data = _fromnp(data.astype(npdtype) if _dtype is not None and (npdtype:=_to_np_dtype(_dtype)) is not None else data)
    elif isinstance(data, pathlib.Path):
      _dtype = _dtype or dtypes.uint8
      data = UOp.new_buffer(f"DISK:{data.resolve()}", data.stat().st_size // _dtype.itemsize, _dtype)

    # by this point, it has to be a UOp
    if not isinstance(data, UOp): raise RuntimeError(f"can't create Tensor from {data!r} with type {type(data)}")

    # data might be on a different device
    self.uop:UOp = data if data.device == _device else data.copy_to_device(_device)

    # add to all_tensors after construction succeeds
    all_tensors[weakref.ref(self)] = None

  @suppress_finalizing
  def __del__(self): all_tensors.pop(weakref.ref(self), None)

  def _apply_uop(self, fxn:Callable[..., UOp], *x:Tensor, extra_args=(), **kwargs) -> Tensor:
    srcs = (self,)+x
    new_uop: UOp = fxn(*[t.uop for t in srcs], *extra_args, **kwargs)
    if TRACEMETA >= 1 and (metadata:=_METADATA.get()) is not None: all_metadata[new_uop] = (metadata,)
    needs_input_grad = [t.requires_grad for t in srcs]
    # directly create the Tensor
    ret = Tensor.__new__(Tensor)
    ret.uop, ret.grad = new_uop, None
    ret.requires_grad = True if any(needs_input_grad) else None if None in needs_input_grad else False
    # add to all_tensors after construction succeeds
    all_tensors[weakref.ref(ret)] = None
    return ret

  # _binop, alu, and const_like are used by the mixins
  def _binop(self, op, x, reverse):
    lhs,rhs = self._broadcasted(x, reverse)
    return lhs._apply_uop(lambda *u: u[0].alu(op, *u[1:]), rhs)
  def alu(self, op: Ops, *src: Tensor) -> Tensor: return self._apply_uop(lambda *u: u[0].alu(op, *u[1:]), *src)
  def const_like(self, b:ConstType) -> Tensor: return Tensor(self.uop.const_like(b), requires_grad=False)

  def requires_grad_(self, requires_grad=True) -> Tensor:
    # make the UOp unique if it's a CONST to prevent gradient accumulation bugs with cached const UOps
    if requires_grad and self.uop.op is Ops.CONST: self.replace(Tensor(self.uop.arg, device=self.device, dtype=self.dtype, requires_grad=True))
    self.requires_grad = requires_grad
    return self

  class train(ContextDecorator):
    def __init__(self, mode:bool = True): self.mode = mode
    def __enter__(self): self.prev, Tensor.training = Tensor.training, self.mode
    def __exit__(self, exc_type, exc_value, traceback): Tensor.training = self.prev

  def __repr__(self):
    ld = self.uop
    ld_repr = f"<UOp {ld.device} {ld.shape} {str(ld.dtype)[7:]}>"
    return f"<Tensor {ld_repr} on {self.device} with grad {(self.grad.uop if self.grad is not None else None)!r}>"

  # Python has a non moving GC, so this should be okay
  def __hash__(self): return id(self)

  def __bool__(self): raise TypeError("__bool__ on Tensor is not defined")

  def __len__(self):
    if not self.shape: raise TypeError("len() of a 0-d tensor")
    return self.shape[0]

  @property
  def device(self) -> str|tuple[str, ...]: return self.uop.device

  @property
  def shape(self) -> tuple[sint, ...]: return self.uop.shape

  @property
  def dtype(self) -> DType: return self.uop.dtype

  # ***** data handlers ****

  def as_param(self, slot:int):
    if self.uop.axis is not None:
      param = UOp.param(slot, self.dtype, self.uop.shard_shape, self.device).multi(self.uop.axis)
    else:
      param = UOp.param(slot, self.dtype, self.shape, self.device)
    return Tensor(param)
  def call(self, *lst:Tensor, fxn:Tensor|UOp, grad_fxn:Callable|None=None) -> Tensor:
    fret = (fxn.uop if isinstance(fxn, Tensor) else fxn).call(*[t.uop for t in (self,)+lst], grad_fxn=grad_fxn)
    return Tensor(fret.gettuple(0))

  def custom_kernel(self, *lst:Tensor, fxn:Callable, grad_fxn:Callable|None=None) -> list[Tensor]:
    """
    Call into a custom kernel written in UOps. Returns the Tensors after the Kernel has been applied.

    This API is alpha and may change.
    """
    return [Tensor(u) for u in UOp.custom_kernel(*[t.uop for t in (self,)+lst], fxn=fxn, grad_fxn=grad_fxn)]

  def callify(self, *lst:Tensor) -> Tensor:
    big_sink = UOp.sink(*[x.uop for x in (self,)+lst])
    big_sink, buffer_map = transform_to_call(big_sink)
    _apply_map_to_tensors({x:y.after(big_sink) for x,y in buffer_map.items()}, name="callify")
    return self

  def schedule_with_vars(self, *lst:Tensor) -> tuple[list[ExecItem], dict[str, int]]:
    """
    Creates the schedule needed to realize these Tensor(s), with Variables.

    NOTE: A Tensor can only be scheduled once.
    """
    big_sink, becomes_map = transform_to_call(UOp.sink(*[x.uop for x in (self,)+lst]))
    _apply_map_to_tensors(becomes_map, name="buffers")

    # this is where the schedule cache should go
    schedule, var_vals = complete_create_schedule_with_vars(big_sink)
    return schedule, var_vals

  def schedule(self, *lst:Tensor) -> list[ExecItem]:
    """Creates the schedule needed to realize these Tensor(s)."""
    schedule, var_vals = self.schedule_with_vars(*lst)
    assert len(var_vals) == 0
    return schedule

  @disable_gc()
  def realize(self, *lst:Tensor, do_update_stats=True) -> Tensor:
    """Triggers the computation needed to create these Tensor(s)."""
    if len(to_realize:=[x for x in (self,)+lst if not x.uop.has_buffer_identity()]):
      run_schedule(*Tensor.schedule_with_vars(*to_realize), do_update_stats=do_update_stats)
    return self

  def replace(self, x:Tensor) -> Tensor:
    """
    Replaces the data of this tensor with the data of another tensor. Only the shape of the tensors must match.
    """
    # used for replacing a Tensor with a new version of it (potentially with a different device and dtype)
    assert self.shape == x.shape, f"replace shape mismatch {self.shape} != {x.shape}"
    self.uop = x.uop
    return self

  def assign(self, x:Tensor|PyConst|list|tuple) -> Tensor:
    is_disk = isinstance(self.device, str) and self.device.startswith("DISK")
    if not isinstance(x, Tensor): x = Tensor(x, device="CPU" if is_disk else self.device, dtype=self.dtype)
    if self.uop is x.uop: return self  # a self assign is a NOOP
    # broadcast x (shape only, dtype must match)
    if self.shape != x.shape: x = x._broadcast_to(self.shape)
    if self.shape != x.shape: raise RuntimeError(f"assign shape mismatch {self.shape} != {x.shape}")
    if not is_disk and self.device != x.device: raise RuntimeError(f"assign device mismatch {self.device} != {x.device}")
    if not is_disk and self.dtype != x.dtype: raise RuntimeError(f"assign dtype mismatch {self.dtype} != {x.dtype}")
    if isinstance(self.device, tuple) and self.uop.axis != x.uop.axis: raise RuntimeError(f"multi axis mismatch {self.uop.axis} != {x.uop.axis}")

    # TODO: this is a hack for writing to DISK. remove with working assign
    if is_disk:
      self._buffer().copyin(x._data())
      return self
    # STORE+AFTER: STORE is the write effect (void), AFTER wraps the view for correct shape/ranging
    assign = self.uop.after(self.uop.store(x.uop))
    if (base := self.uop.base).op in {Ops.BUFFER, Ops.AFTER} and self.uop is not base and not self.uop.has_buffer_identity():
      # view assign: replace at the buffer-identity level (e.g. RESHAPE(BUFFER)) so @function's substitution catches it
      ib = self.uop
      while not ib.has_buffer_identity() and ib is not base: ib = ib.src[0]
      assigned_ib = ib.after(assign)
      _apply_map_to_tensors({ib: assigned_ib}, name="Embed View Assign", walk=True)
    else:
      # simple assign
      self.uop = assign
    return self

  def detach(self) -> Tensor:
    """
    Returns a new tensor with the same data as this tensor, but detached from the autograd graph.
    """
    return Tensor(self.uop.detach(), requires_grad=False)

  def _buffer(self) -> Buffer:
    from tinygrad.engine.realize import capturing
    if capturing and not getenv("UNSAFE_ALLOW_JIT_BUFFER"):
      from tinygrad.engine.jit import JitError
      raise JitError("cannot access tensor data during JIT capture, the value will be baked in")
    x = self.cast(self.dtype.base).contiguous()
    if isinstance(self.device, tuple): x = x.to("CPU")
    return cast(Buffer, x.realize().uop.buffer).ensure_allocated()
  def _data(self) -> memoryview: return self._buffer().as_memoryview()

  def data(self) -> memoryview:
    """
    Returns the data of this tensor as a memoryview.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 2, 3, 4])
    print(np.frombuffer(t.data(), dtype=np.int32))
    ```
    """
    if 0 in self.shape: return memoryview(bytearray(0)).cast(self.dtype.base.fmt)
    assert all_int(self.shape), f"no data if shape is symbolic, {self.shape=}"
    assert self.dtype.base.fmt is not None, f"no fmt dtype for {self.dtype.base}"
    assert self.dtype.base.fmt != "e" or sys.version_info >= (3, 12)
    return self._buffer().as_memoryview().cast(self.dtype.base.fmt, self.shape)

  def item(self) -> PyConst:
    """
    Returns the value of this tensor as a standard Python number.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor(42)
    print(t.item())
    ```
    """
    assert self.numel() == 1, "must have one element for item"
    return self.data()[(0,) * len(self.shape)]

  # NOTE: list[Any] because return type is recursive (list[list[...]] for higher dimensions)
  def tolist(self) -> PyConst|list[Any]:
    """
    Returns the value of this tensor as a nested list.
    Returns single value for const tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 2, 3, 4])
    print(t.tolist())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor(5)
    print(t.tolist())
    ```
    """
    # TODO: remove half once minimum python supports it
    if self.dtype in (dtypes.half, dtypes.bfloat16, *dtypes.fp8s): return self.cast(dtypes.float32).tolist()
    return self.data().tolist()

  def numpy(self) -> 'numpy.ndarray':
    """
    Returns the value of this tensor as a `numpy.ndarray`.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 2, 3, 4])
    print(repr(t.numpy()))
    ```
    """
    assert all_int(self.shape), f"no data if shape is symbolic, {self.shape=}"
    import numpy as np
    if self.dtype.base in { dtypes.bfloat16, *dtypes.fp8s }: return self.float().numpy()
    if 0 in self.shape: return np.empty(self.shape, dtype=_to_np_dtype(self.dtype.base))
    return self._buffer().numpy().reshape(self.shape)

  def clone(self) -> Tensor:
    """
    Creates a clone of this tensor allocating a separate buffer for the data.
    """
    ret = self.empty_like()
    if self.grad is not None: ret.grad = self.grad.clone()
    return ret.assign(self)

  def to(self, device:str|tuple[str, ...]|None) -> Tensor:
    """
    Moves the tensor to the given device.
    """
    if (device:=canonicalize_device(device)) == self.device: return self
    ret = Tensor(self.uop.copy_to_device(device), requires_grad=self.requires_grad)
    if self.grad is not None: ret.grad = self.grad.to(device)
    return ret

  def to_(self, device:str|tuple[str, ...]|None) -> Tensor:
    """
    Moves the tensor to the given device in place.
    """
    real = self.to(device)
    if self.grad is not None and real.grad is not None: self.grad.replace(real.grad)
    return self.replace(real)

  def shard(self, devices:tuple[str, ...], axis:int|None=None) -> Tensor:
    """
    Shards the tensor across the given devices. Optionally specify which axis to shard on.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.empty(2, 4)
    print(t.shard((t.device, t.device), axis=1).uop)
    ```
    """
    if not isinstance(self.device, str): raise RuntimeError("can't shard a multi-device tensor")
    if len(devices) == 1: return self.to(devices[0])
    devices = cast(tuple[str, ...], canonicalize_device(devices))
    uop = self.uop.shard(devices, self._resolve_dim(axis)) if axis is not None else self.uop.copy_to_device(devices)
    return Tensor(uop, requires_grad=self.requires_grad)

  def shard_(self, devices:tuple[str, ...], axis:int|None=None) -> Tensor:
    """
    Shards the tensor across the given devices in place.
    """
    return self.replace(self.shard(devices, axis))

  def shard_like(self, y:Tensor) -> Tensor:
    """
    Shards the tensor the same way as `y` (same devices and axis).
    """
    if isinstance(y.device, str): return self.to(y.device)
    return self if isinstance(self.device, tuple) and (y.device, y.uop.axis) == (self.device, self.uop.axis) else self.shard(y.device, y.uop.axis)

  CHUNK_SIZE = 2**20
  def fs_load(self, size:int) -> Tensor:
    """
    Load a tensor from storage.

    self should be a tensor of the hash to load
    """
    # TODO: this should work locally as well
    assert self.dtype == dtypes.uint8, "hash is expected to be uint8"
    h = self.contiguous().flatten()
    assert h.shape[0] == 16, "expected hash"

    base_chunks = math.ceil(size / Tensor.CHUNK_SIZE)
    tree_depth = math.ceil(math.log(base_chunks, Tensor.CHUNK_SIZE // 16))
    data, level_chunks = h, 0
    for i in reversed(range(tree_depth + 1)):
      data = data.to("tinyfs:load")

      # if not last level, its still hashes
      if i > 0 or tree_depth == 0:
        level_chunks = max(1, math.ceil(base_chunks / (Tensor.CHUNK_SIZE // 16)**(i-1)))
        pad_amt = 16 * level_chunks
      else: pad_amt = Tensor.CHUNK_SIZE * level_chunks
      if (tsize := data.shape[0]) < pad_amt: data = data.pad((0, pad_amt - tsize))
      data = data[:pad_amt].contiguous()
      if i != 0: data = data.to(self.device)

    return data[:size]

  def fs_store(self) -> Tensor:
    """
    Store a tensor to storage.
    """
    # TODO: this should work locally as well
    data = self.contiguous().flatten().bitcast(dtypes.uint8)

    # pad to a multiple of 1mb
    if (tsize := data.shape[0]) % Tensor.CHUNK_SIZE != 0: data = data.pad((0, Tensor.CHUNK_SIZE - tsize % Tensor.CHUNK_SIZE))
    size = data.shape[0]

    base_chunks = math.ceil(size / Tensor.CHUNK_SIZE)
    tree_depth = math.ceil(math.log(base_chunks, Tensor.CHUNK_SIZE // 16))

    to_device = "CPU" if isinstance(self.device, str) and self.device.startswith("DISK") else self.device

    level_chunks = base_chunks
    for _ in range(tree_depth + 1):
      data = data.to("tinyfs:store")[:level_chunks * 16].contiguous().to(to_device)
      if (tsize := data.shape[0]) % Tensor.CHUNK_SIZE != 0: data = data.pad((0, Tensor.CHUNK_SIZE - tsize % Tensor.CHUNK_SIZE))
      level_chunks = math.ceil(data.shape[0] / Tensor.CHUNK_SIZE)

    return data[:16].contiguous()

  @staticmethod
  def from_uop(y:UOp, **kwargs) -> Tensor:
    # TODO: remove this and stay in weakint
    if y.dtype == dtypes.weakint: y = _index_to_concrete_int(y)
    if y.op is Ops.BIND:
      var, val = y.unbind()
      _device = canonicalize_device(kwargs.get("device"))
      const = UOp.const(var.dtype, val, _device, ())
      return Tensor(y.replace(src=(var.replace(src=const.src), const)), **kwargs, requires_grad=False)
    if y.op is Ops.CONST: return Tensor(y.arg, **kwargs, requires_grad=False)
    if y.op is Ops.MUL: return Tensor.from_uop(y.src[0]) * Tensor.from_uop(y.src[1])
    if y.op is Ops.ADD: return Tensor.from_uop(y.src[0]) + Tensor.from_uop(y.src[1])
    raise RuntimeError(f"unhandled UOp {y}")

  # ***** creation entrypoint *****

  @staticmethod
  def empty(*shape, device:str|tuple[str, ...]|None=None, dtype:DTypeLike|None=None, **kwargs) -> Tensor:
    """
    Creates an empty tensor with the given shape.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.empty(2, 3)
    print(t.shape)
    ```
    """
    dtype, shape = to_dtype(dtype) if dtype is not None else dtypes.default_float, argfix(*shape)
    if not isinstance(size:=prod([x.vmax if isinstance(x, UOp) else x for x in shape]), int): raise ValueError(f"size must be int {size}")
    # TODO: add test for multidevice tensor
    device = canonicalize_device(device)
    return Tensor(UOp.new_buffer(device, size, dtype), **kwargs).shrink(((0,prod(shape)),)).reshape(shape)

  def empty_like(self, dtype:DTypeLike|None=None, device:str|tuple[str, ...]|None=None, **kwargs) -> Tensor:
    """
    Creates an empty tensor with the same shape as `self`.
    If `dtype` is not specified, the dtype of `self` is used.
    """
    dtype, device = self.dtype if dtype is None else dtype, self.device if device is None else device
    if isinstance(device, tuple) and (axis := self.uop.axis) is not None:
      return Tensor(Tensor.empty(self.uop.max_shard_shape, dtype=dtype, device=device, **kwargs).uop.multi(axis))
    return Tensor.empty(self.shape, dtype=dtype, device=device, **kwargs)

  @staticmethod
  def from_blob(ptr:int, shape:tuple[int, ...], **kwargs) -> Tensor:
    """
    Exposes the pointer as a Tensor without taking ownership of the original data.
    The pointer must remain valid for the entire lifetime of the created Tensor.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.
    """
    r = Tensor.empty(*shape, **kwargs)
    assert isinstance(r.device, str)
    cast(Buffer, r.uop.buffer).allocate(external_ptr=ptr)
    return r

  @staticmethod
  def from_url(url:str, gunzip:bool=False, **kwargs) -> Tensor:
    """
    Creates a Tensor from a URL.

    This is the preferred way to access Internet resources.
    It currently returns a DISK Tensor, but in the future it may return an HTTP Tensor.
    This also will soon become lazy (when possible) and not print progress without DEBUG.

    The `gunzip` flag will gzip extract the resource and return an extracted Tensor.
    """
    return Tensor(fetch(url, gunzip=gunzip), **kwargs)

  _seed: int = int(time.time())
  _device_seeds: dict[str, Tensor] = {}
  _device_rng_counters: dict[str, Tensor] = {}
  @staticmethod
  def manual_seed(seed=0) -> None:
    """
    Sets the seed for random operations.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.rand(5).numpy())
    print(Tensor.rand(5).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)  # reset to the same seed
    print(Tensor.rand(5).numpy())
    print(Tensor.rand(5).numpy())
    ```
    """
    Tensor._seed, Tensor._device_seeds, Tensor._device_rng_counters = seed, {}, {}

  @staticmethod
  def _threefry_random_bits(key:Tensor, counts0:Tensor, counts1:Tensor) -> Tensor:
    x = (counts1.cast(dtypes.uint64) << 32) | counts0.cast(dtypes.uint64)
    x = x._apply_uop(UOp.threefry, (key[1]._broadcast_to(x.shape).cast(dtypes.uint64) << 32) | key[0]._broadcast_to(x.shape).cast(dtypes.uint64))
    counts0, counts1 = (x & 0xffffffff).cast(dtypes.uint32), ((x >> 32) & 0xffffffff).cast(dtypes.uint32)
    return counts0.cat(counts1)

  @staticmethod
  def rand(*shape, device:str|None=None, dtype:DTypeLike|None=None, contiguous:bool=True, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with random values from a uniform distribution over the interval `[0, 1)`.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.rand(2, 3)
    print(t.numpy())
    ```
    """
    dt = to_dtype(dtype or dtypes.default_float)
    if not dtypes.is_float(dt): raise ValueError(f"rand only supports float dtypes, got {dt}")
    if not all_int(shape:=argfix(*shape)) or not all(s >= 0 for s in shape): raise ValueError(f"invalid input {shape=}")
    if device is not None and not isinstance(device, str): raise ValueError(f"rand only supports single device, got {device=}")
    device = cast(str, canonicalize_device(device))

    # if shape has 0, return zero tensor
    if (numel := prod(shape)) == 0: return Tensor.zeros(shape, device=device, dtype=dt, **kwargs)
    num = ceildiv(numel * dt.itemsize, 4)

    # generate per device seeds and rng counter if we haven't seen this device yet
    if device not in Tensor._device_seeds:
      Tensor._device_seeds[device] = Tensor(
        [int.from_bytes(hashlib.sha256(len(Tensor._device_seeds).to_bytes(4, "big")).digest(), "big"), Tensor._seed],
        device=device, dtype=dtypes.uint32, requires_grad=False)
      Tensor._device_rng_counters[device] = Tensor([0, 0], device=device, dtype=dtypes.uint32, requires_grad=False).contiguous()

    # increment rng counter for devices
    new_low = Tensor._device_rng_counters[device][0:1] + (num & 0xffffffff)
    new_high = Tensor._device_rng_counters[device][1:2] + (num >> 32) + (new_low < Tensor._device_rng_counters[device][0]).cast(dtypes.uint32)
    Tensor._device_rng_counters[device].assign(new_low.cat(new_high))

    low = Tensor._device_rng_counters[device][0:1] - (num & 0xffffffff)
    high = Tensor._device_rng_counters[device][1:2] - (num >> 32) - (Tensor._device_rng_counters[device][0] < (num & 0xffffffff)).cast(dtypes.uint32)

    # threefry random bits
    bits_list = []
    for i in range(0, num, dtypes.uint32.max):
      chunk_num = min(num - i, dtypes.uint32.max)
      c_low = low + (i & 0xffffffff)
      c_high = high + (i >> 32) + (c_low < low).cast(dtypes.uint32)
      new_key = Tensor._threefry_random_bits(Tensor._device_seeds[device], c_low, c_high)
      counts0 = Tensor.arange(ceildiv(chunk_num, 2), device=device, dtype=dtypes.uint32, requires_grad=False)
      counts1 = counts0 + ceildiv(chunk_num, 2)
      bits_list.append(Tensor._threefry_random_bits(new_key, counts0, counts1)[:chunk_num])
    bits = Tensor.cat(*bits_list)

    # bitcast to uint with same number of bits
    _, nmant = dtypes.finfo(dt)
    uint_dtype = {1: dtypes.uint8, 2: dtypes.uint16, 4: dtypes.uint32, 8: dtypes.uint64}[dt.itemsize]
    bits = bits.bitcast(uint_dtype)
    # only randomize the mantissa bits and set the exponent to 1
    one = Tensor.ones_like(bits, device=bits.device, dtype=dt).bitcast(uint_dtype)
    bits = bits.rshift(dt.bitsize - nmant).bitwise_or(one)
    # bitcast back to the original dtype and reshape
    out = bits.bitcast(dt)[:numel].sub(1).reshape(shape).requires_grad_(kwargs.get("requires_grad"))
    return out.contiguous() if contiguous else out

  # ***** creation helper functions *****

  @staticmethod
  def full(shape:tuple[sint, ...], fill_value:ConstType, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with the given value.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.full((2, 3), 42).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.full((2, 3), False).numpy())
    ```
    """
    return Tensor(fill_value, _force_unique=True, **kwargs).reshape((1, )*len(new_shape := argfix(shape))).expand(new_shape)

  @staticmethod
  def invalid(*shape, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with Invalid.

    This is an alternative to Tensor.empty when you want an "anonymous" buffer.

    Eventually Tensor.empty will be replaced by this.
    """
    return Tensor.full(argfix(*shape), Invalid, **kwargs)

  @staticmethod
  def zeros(*shape, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with zeros.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.zeros(2, 3).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.zeros(2, 3, dtype=dtypes.int32).numpy())
    ```
    """
    return Tensor.full(argfix(*shape), 0.0, **kwargs)

  @staticmethod
  def ones(*shape, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with ones.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.ones(2, 3).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.ones(2, 3, dtype=dtypes.int32).numpy())
    ```
    """
    return Tensor.full(argfix(*shape), 1.0, **kwargs)

  @staticmethod
  def arange(start, stop=None, step=1, **kwargs) -> Tensor:
    """
    Returns a 1-D tensor of size `ceil((stop - start) / step)` with values from `[start, stop)`, with spacing between values given by `step`.

    If `stop` is not specified, values are generated from `[0, start)` with the given `step`.

    If `stop` is specified, values are generated from `[start, stop)` with the given `step`.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.arange(5).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.arange(5, 10).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.arange(5, 10, 2).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.arange(5.5, 10, 2).numpy())
    ```
    """
    if stop is None: stop, start = start, 0
    dtype = kwargs.pop("dtype", dtypes.default_float if any(isinstance(x, float) for x in (start, stop, step)) else dtypes.default_int)
    if start < (dt:=to_dtype(dtype)).min or dt.max < (stop-step): raise ValueError(f"arange [{start}, {stop}) is not representable in dtype {dtype}")
    # NOTE: this matches numpy, torch raises RuntimeError if stop-start and step have different signs
    if (output_len:=ceildiv(stop-start, step)) <= 0: return Tensor([], dtype=dtype, **kwargs)
    return (Tensor.full((output_len,), step, dtype=dtype, **kwargs)._cumalu(0, Ops.ADD) + (start - step)).cast(dtype)

  @staticmethod
  def linspace(start:int|float, stop:int|float, steps:int, **kwargs) -> Tensor:
    """
    Returns a 1-D tensor of `steps` evenly spaced values from `start` to `stop`, inclusive.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.linspace(0, 10, 5).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.linspace(-1, 1, 5).numpy())
    ```
    """
    if steps < 0: raise ValueError("number of steps must be non-negative")
    if (dtype := to_dtype(kwargs.pop("dtype", dtypes.default_float))) == dtypes.bool: raise ValueError("linspace with bool dtype is not supported")
    if steps == 1: return Tensor([start], dtype=dtype, **kwargs)
    return (start + Tensor.arange(steps, **kwargs) * ((stop - start) / (steps - 1))).cast(dtype)

  @staticmethod
  def eye(n:int, m:int|None=None, dtype=None, device=None, requires_grad:bool|None=None) -> Tensor:
    """
    Returns a 2-D tensor with `n` rows and `m` columns, with ones on the diagonal and zeros elsewhere.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.eye(3).numpy())
    ```

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.eye(2, 4).numpy())
    ```
    """
    m_ = n if m is None else m
    if n < 0 or m_ < 0: raise ValueError(f"cannot have negative {n=}, {m_=}")
    t = (Tensor.arange(n, device=device).unsqueeze(-1) == Tensor.arange(m_, device=device))
    return t.cast(dtype or dtypes.default_float).requires_grad_(requires_grad)

  def _multi_like(self, fxn, *args, **kwargs) -> Tensor:
    dtype = kwargs.pop("dtype", self.dtype)
    if kwargs.get("device") is not None: raise RuntimeError("cannot specify `device` on `*_like` of a multi device tensor")
    if self.uop.axis is None: return fxn(self.shape, *args, dtype=dtype, **kwargs).shard(self.device)
    stacked = UOp.mstack(*[fxn(self.uop.shard_shape, *args, device=d, dtype=dtype, **kwargs).uop for d in self.device])
    return Tensor(stacked.multi(self.uop.axis))

  def full_like(self, fill_value:ConstType, dtype=None, device=None, requires_grad=None) -> Tensor:
    """
    Creates a tensor with the same shape as `self`, filled with the given value.
    If `dtype` is not specified, the dtype of `self` is used.

    You can pass in the `device` keyword argument to control device of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.ones(2, 3)
    print(Tensor.full_like(t, 42).numpy())
    ```
    """
    if device is not None:
      if isinstance(self.device, tuple): raise RuntimeError("cannot specify `device` on `full_like` of a multi device tensor")
      return Tensor.full(self.shape, fill_value, dtype=dtype or self.dtype, device=device).requires_grad_(requires_grad)
    if requires_grad:
      return Tensor.full(self.shape, fill_value, dtype=dtype or self.dtype, device=self.device).requires_grad_(requires_grad)
    return self.const_like(fill_value) if dtype is None else self.const_like(fill_value).cast(dtype)

  def rand_like(self, **kwargs) -> Tensor:
    """
    Creates a tensor with the same shape and sharding as `self`, filled with random values from a uniform distribution over the interval `[0, 1)`.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.ones(2, 3)
    print(Tensor.rand_like(t).numpy())
    ```
    """
    if isinstance(self.device, tuple): return self._multi_like(Tensor.rand, **kwargs)
    return Tensor.rand(*self.shape, device=kwargs.pop("device", self.device), dtype=kwargs.pop("dtype", self.dtype), **kwargs)

  # ***** random functions *****

  def randn_like(self, dtype:DTypeLike|None=None, requires_grad:bool|None=None, **kwargs) -> Tensor:
    """
    Creates a tensor with the same shape and sharding as `self`, filled with random values from a normal distribution with mean 0 and variance 1.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.ones(2, 3)
    print(Tensor.randn_like(t).numpy())
    ```
    """
    src = self.stack(self).rand_like(**{**kwargs, "dtype": dtypes.float32})
    # https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
    return (src[0].mul(2*math.pi).cos().mul((1 - src[1]).log().mul(-2).sqrt()).cast(dtype or self.dtype)).requires_grad_(requires_grad)

  @staticmethod
  def randn(*shape, dtype:DTypeLike|None=None, requires_grad:bool|None=None, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with random values from a normal distribution with mean `0` and standard deviation `1`.
    If `dtype` is not specified, the default type is used.

    You can pass in the `device` keyword argument to control device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.randn(2, 3).numpy())
    ```
    """
    return Tensor.empty(*shape, **kwargs).randn_like(dtype=dtype, requires_grad=requires_grad)

  @staticmethod
  def randint(*shape, low=0, high=10, dtype=dtypes.int32, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with random integer values generated uniformly from the interval `[low, high)`.
    If `dtype` is not specified, the default type is used.

    You can pass in the `device` keyword argument to control device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.randint(2, 3, low=5, high=10).numpy())
    ```
    """
    if not all_int([low, high]): raise TypeError(f"{low=} and {high=} must be integers")
    if not dtypes.is_int(dtype := to_dtype(dtype)): raise TypeError(f"{dtype=} must be int")
    return Tensor.uniform(*shape, low=low, high=high, dtype=dtype, **kwargs)

  @staticmethod
  def normal(*shape, mean=0.0, std=1.0, requires_grad:bool|None=None, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with random values from a normal distribution with the given `mean` and standard deviation `std`.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.normal(2, 3, mean=10, std=2).numpy())
    ```
    """
    return (std * Tensor.randn(*shape, **kwargs) + mean).requires_grad_(requires_grad)

  @staticmethod
  def uniform(*shape, low=0.0, high=1.0, dtype:DTypeLike|None=None, requires_grad:bool|None=None, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with random values from a uniform distribution over the interval `[low, high)`.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.uniform(2, 3, low=2, high=10).numpy())
    ```
    """
    return (((high-low) * Tensor.rand(*shape, **kwargs)).cast(dtype or dtypes.default_float) + low).requires_grad_(requires_grad)

  @staticmethod
  def scaled_uniform(*shape, **kwargs) -> Tensor:
    """
    Creates a tensor with the given shape, filled with random values from a uniform distribution
    over the interval `[-prod(shape)**-0.5, prod(shape)**-0.5)`.

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.scaled_uniform(2, 3).numpy())
    ```
    """
    return Tensor.uniform(*shape, low=-1.0, high=1.0, **kwargs).mul(prod(argfix(*shape))**-0.5)

  @staticmethod
  def glorot_uniform(*shape, **kwargs) -> Tensor:
    """
    <https://www.tensorflow.org/api_docs/python/tf/keras/initializers/GlorotUniform>

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.glorot_uniform(2, 3).numpy())
    ```
    """
    bound = (6 / (argfix(*shape)[0]+prod(argfix(*shape)[1:]))) ** 0.5
    return Tensor.uniform(*shape, low=-bound, high=bound, **kwargs)

  @staticmethod
  def kaiming_uniform(*shape, a:float = 0.01, **kwargs) -> Tensor:
    """
    <https://pytorch.org/docs/stable/_modules/torch/nn/init.html#kaiming_uniform_>

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.kaiming_uniform(2, 3).numpy())
    ```
    """
    bound = (6 / (1 + a ** 2) / prod(argfix(*shape)[1:])) ** 0.5
    return Tensor.uniform(*shape, low=-bound, high=bound, **kwargs)

  @staticmethod
  def kaiming_normal(*shape, a:float = 0.01, **kwargs) -> Tensor:
    """
    <https://pytorch.org/docs/stable/_modules/torch/nn/init.html#kaiming_normal_>

    You can pass in `dtype` and `device` keyword arguments to control the data type and device of the tensor.
    Additionally, all other keyword arguments are passed to the constructor of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.kaiming_normal(2, 3).numpy())
    ```
    """
    std = (2 / (1 + a ** 2) / prod(argfix(*shape)[1:])) ** 0.5
    return Tensor.normal(*shape, mean=0.0, std=std, **kwargs)

  @staticmethod
  def randperm(n:int, device=None, dtype=dtypes.int32, **kwargs) -> Tensor:
    """
    Returns a tensor with a random permutation of integers from `0` to `n-1`.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    print(Tensor.randperm(6).numpy())
    ```
    """
    return Tensor.rand(n, device=device, **kwargs).argsort().cast(dtype)

  def multinomial(self:Tensor, num_samples:int = 1, replacement:bool = False) -> Tensor:
    """
    Returns a tensor with `num_samples` indices sampled from a multinomial distribution weighted by `self`.

    NOTE: `replacement=False` for `num_samples > 1` is not supported yet.
    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor([1, 2, 3, 4])
    print(t.multinomial(20, replacement=True).numpy())
    ```
    """
    assert 1 <= self.ndim <= 2 and num_samples > 0, f"{self.ndim=} must be 1 or 2 dim, {num_samples=} must be positive"
    assert replacement or num_samples == 1, "no replacement only supports num_samples = 1"
    weight = self.unsqueeze(0) if self.ndim == 1 else self
    cdf = (cw := weight.cumsum(1).float()) / cw[:, -1].unsqueeze(1)
    unif_samples = Tensor.rand(num_samples, cdf.shape[0], 1).to(self.device)
    indices = (unif_samples.expand((-1, -1, cdf.shape[1])) >= cdf).sum(2).permute((1, 0))
    return (indices.squeeze(0) if self.ndim == 1 else indices).cast(dtypes.int32)

  # ***** toposort and backward pass *****

  def gradient(self, *targets:Tensor, gradient:Tensor|None=None) -> list[Tensor]:
    """
    Computes the gradient of the targets with respect to self.

    ```python exec="true" source="above" session="tensor" result="python"
    x = Tensor.eye(3)
    y = Tensor([[2.0,0,-2.0]])
    z = y.matmul(x).sum()
    dx, dy = z.gradient(x, y)

    print(dx.tolist())  # dz/dx
    print(dy.tolist())  # dz/dy
    ```
    """
    assert gradient is not None or self.shape == tuple(), "when no gradient is provided, backward must be called on a scalar tensor"
    if not (self.is_floating_point() and all(t.is_floating_point() for t in targets)): raise RuntimeError("only float Tensors have gradient")
    if gradient is None: gradient = Tensor(1.0, dtype=self.dtype, device=self.device, requires_grad=False)
    target_uops = [x.uop for x in targets]
    grads = compute_gradient(self.uop, gradient.uop, set(target_uops))
    ret:list[Tensor] = []
    for x in target_uops:
      if (y:=grads.get(x)) is None: y = x.const_like(0)
      ret.append(Tensor(y))
    return ret

  def backward(self, gradient:Tensor|None=None) -> Tensor:
    """
    Propagates the gradient of a tensor backwards through the computation graph.
    If the 'gradient' argument is not provided, the tensor must be a scalar, and the gradient is implicitly set to 1.0.
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1.0, 2.0, 3.0, 4.0], requires_grad=True)
    t.sum().backward()
    print(t.grad.numpy())
    ```
    """
    all_uops = self.uop.toposort()
    tensors_need_grad: list[Tensor] = [t for tref in all_tensors if (t:=tref()) is not None and \
                                       t.uop in all_uops and t.requires_grad]
    # clear contexts
    for t,g in zip(tensors_need_grad, self.gradient(*tensors_need_grad, gradient=gradient)):
      assert g.shape == t.shape, f"grad shape must match tensor shape, {g.shape!r} != {t.shape!r}"
      if t.grad is None: t.grad = g
      else: t.grad.assign(t.grad + g.to(t.grad.device))
    return self

  # ***** movement ops *****

  def _mop(self, op:Ops, arg) -> Tensor: return self._apply_uop(UOp._mop, extra_args=(op,), arg=arg)
  def _rop(self, op:Ops, axis:tuple[int, ...]) -> Tensor: return self._apply_uop(UOp._rop, op=op, axis=axis)

  def _pad_constant(self, pX:tuple[tuple[sint, sint], ...], value:float) -> Tensor:
    # shrink first for negative pads, then pad with only non-negative values
    has_neg = not all(resolve(p >= 0) for p in flatten(pX))
    X = self.shrink(tuple((-smin(pB,0),smin(pA+s,s)) for (pB,pA),s in zip(pX, self.shape))) if has_neg else self
    pads = tuple((smax(pB,0), smax(pA,0)) for pB,pA in pX) if has_neg else pX
    if value == 0: return X._apply_uop(UOp.pad, arg=pads)
    return X._apply_uop(UOp.pad, arg=pads) + Tensor.ones_like(X)._apply_uop(UOp.pad, arg=pads).where(0, value)

  def _pad_circular(self, pX:tuple[tuple[sint, sint], ...]) -> Tensor:
    if any(pB>sh or pA>sh for (pB,pA),sh in zip(pX, self.shape)): raise ValueError('Padding value causes wrapping around more than once.')
    if any(pB<0 or pA<0 for pB,pA in pX): raise NotImplementedError("Negative pads with circular pads is not supported")
    orig_shape, X = self.shape, self.repeat(tuple(1 + bool(pB) + bool(pA) for pB,pA in pX))
    return X.shrink(tuple((0 if pB == 0 else osh-pB, xsh if pA == 0 else xsh-osh+pA) for (pB,pA),osh,xsh in zip(pX, orig_shape, X.shape)))

  def _pad_reflect_replicate(self, pX:tuple[tuple[sint, sint], ...], mode:str) -> Tensor:
    X, pads = self, tuple((smax(pB,0), smax(pA,0)) for pB,pA in pX)
    for d,(pB,pA) in enumerate(pads):
      if mode == "reflect":
        if pB >= (s:=X.shape[d]) or pA>=s: raise ValueError(f"Padding ({pB}, {pA}) should be less than the input size={s} for dim={d}.")
        slcB, slcA = slice(pB,0,-1), slice(s-2 if s-2>=0 else None, s-2-pA if s-2-pA>=0 else None, -1)
        xB, xA = (X[[slc if i == d else slice(None) for i in range(X.ndim)]] if p > 0 else None for slc, p in ((slcB, pB), (slcA, pA)))
      else:
        shrB, shrA = tuple((0,1) if i==d else None for i in range(X.ndim)), tuple((X.shape[i]-1,X.shape[i]) if i==d else None for i in range(X.ndim))
        xB, xA = (X.shrink(shr).expand(tuple(p if i==d else None for i in range(X.ndim))) if p > 0 else None for shr, p in ((shrB, pB), (shrA, pA)))
      X = Tensor.cat(*(X_ for X_ in (xB, X, xA) if X_ is not None), dim=d)
    # shrink after for negative pads (reflection/replication must see full data first)
    return X.shrink(tuple((-min(pB,0), min(pA+s,s)) for (pB,pA),s in zip(pX, X.shape)))

  def pad(self, padding:Sequence[sint]|Sequence[tuple[sint, sint]|None], mode:str="constant", value:float=0.0) -> Tensor:
    """
    Returns a tensor with padding applied based on the input `padding`.

    `padding` supports two padding structures:

    1. Flat padding: `(padding_left, padding_right, padding_top, padding_bottom, ...)`
        - This structure matches PyTorch's pad.
        - `padding` length must be even.

    2. Group padding: `(..., (padding_top, padding_bottom), (padding_left, padding_right))`
        - This structure matches pad for JAX, NumPy, TensorFlow, and others.
        - For each axis, padding can be `None`, meaning no padding, or a tuple `(start, end)`.
        - `padding` must have the same length as `self.ndim`.

    Padding values can be negative, resulting in dimension shrinks that work similarly to Python negative slices.
    Padding modes is selected with `mode` which supports `constant`, `reflect` and `replicate`.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(9).reshape(1, 1, 3, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.pad((1, 2, 0, -1)).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.pad(((None, None, (0, -1), (1, 2)))).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.pad((1, 2, 0, -1), value=-float('inf')).numpy())
    ```
    """
    # normalize to grouped format
    if all(isinstance(p, (int,UOp)) for p in padding):
      if len(padding)%2 != 0: raise ValueError("Flat padding must have even number of pads")
      pX = _flat_to_grouped(tuple(cast(Sequence[sint], padding)) + (0,0)*(self.ndim - len(padding)//2))
    else: pX = tuple((0,0) if p is None else p for p in cast(Sequence[tuple[sint, sint]|None], padding))
    if len(pX) != self.ndim: raise ValueError(f"padding length is improper, {padding=} {self.ndim=}")
    # dispatch
    if mode == "constant": return self._pad_constant(pX, value)
    assert all_int(self.shape), f"does not support symbolic shape {self.shape}"
    if mode == "circular": return self._pad_circular(pX)
    if mode in {"reflect", "replicate"}: return self._pad_reflect_replicate(pX, mode)
    raise NotImplementedError(f"{mode=} is not supported")

  def _getitem(self, indices, v: Tensor|None = None) -> Tensor:
    # wrap single index into a list
    if (isinstance(indices, list) and all_int(indices)) or not isinstance(indices, (tuple, list)): indices = [indices]
    x, indices = self, self._normalize_indices(list(indices))

    indices_parsed, dim = [], 0
    for index in indices:
      size = 1 if index is None else self.shape[dim]
      boundary, stride = [0, size], 1  # defaults
      match index:
        case Tensor():
          if not dtypes.is_int(index.dtype): raise IndexError(f"index dtype {index.dtype} is not supported")
          assert isinstance(size, int), "size must be an int"
          index = (index < 0).where(index+size, index).to(self.device)  # treat negative index values
        case list() | tuple():
          if not dtypes.is_int((ti:=Tensor(index)).dtype): raise IndexError(f"{index=} contains non-int element")
          index = Tensor([i+size if i<0 else i for i in fully_flatten(index)], self.device, requires_grad=False).reshape(ti.shape)
        case int() | UOp(): # sint
          if index >= size or index < -size: raise IndexError(f"{index=} is out of bounds with {size=}")
          # TODO: is this right for (negative) symbolic?
          boundary = [index, index+1] if index >= 0 else [index+size, index+size+1]
        case slice():
          if index.step == 0: raise ValueError(f"{index=} cannot have 0 as step")
          start, stop = 0 if index.start is None else index.start, size if index.stop is None else index.stop
          step = 1 if index.step is None else index.step
          boundary, stride = [start, stop], step
          if all(isinstance(s, int) for s in (start,stop,step)):
            # handle int slicing
            # if we're slicing a symbolic dimension into a int dimension, we can slice until the bind size
            # TODO: right now this is using vmax instead of the bind size because jit doesnt update the bound value of the returned tensor
            if isinstance(size, UOp): size = int(size.vmax)
            *boundary, stride = index.indices(cast(SupportsIndex, size))
            if stride * (boundary[1] - boundary[0]) < 0: boundary = [0, 0]
            elif stride < 0: boundary = [boundary[1] + 1, boundary[0] + 1]
            # update size for slice
            size = ceildiv((boundary[1] - boundary[0]), abs(stride))
          elif resolve(step == 1, False) and all(isinstance(s,sint) for s in (start, stop)) and resolve((stop-start) > 0, False):
            # simple symbolic slice
            size = cast(sint, cast(UOp, (stop - start)).ssimplify())
          else: raise TypeError(f"slice {index=} is not supported")
        case None: pass # do nothing
        case _: raise IndexError(f"{type(index).__name__} indexing is not supported")
      indices_parsed.append({"index":index, "size":size, "boundary":tuple(boundary), "stride":stride})
      if index is not None: dim += 1

    # movement op indexing
    if mops := [i for i in indices_parsed if i['index'] is not None]:
      # flip negative strides
      x = x.shrink(tuple(m['boundary'] for m in mops)).flip(tuple(i for i, m in enumerate(mops) if m['stride'] < 0))
      strides = tuple(abs(m['stride']) for m in mops)
      # apply stride
      if any(st != 1 for st in strides):
        # pad shape to multiple of stride
        if not all_int(x.shape): raise RuntimeError("symbolic shape not supported")
        x = x.pad_to(tuple(round_up(s, st) for s, st in zip(x.shape, strides)))
        x = x.reshape(tuple(flatten((s // st, st) for s, st in zip(x.shape, strides))))
        x = x.shrink(tuple(flatten(((0, s), (0, 1)) for s in x.shape[::2]))).reshape(x.shape[::2])

    # dim injection from None (size 1) and dim collapse by skipping sint dims
    x_dims = [p for p in indices_parsed if not isinstance(p['index'], sint)]
    x = x.reshape(tuple(p['size'] for p in x_dims))

    # tensor indexing
    if tops := [(d, p) for d, p in enumerate(x_dims) if isinstance(p['index'], Tensor)]:
      dims, tensors, masks = [d for d, _ in tops], cast(list[Tensor], [p['index'] for _, p in tops]), []
      big_shape = _broadcast_shape(*(t.shape for t in tensors))

      # consecutive tensor indices with int shapes: use linear indexing instead of one-hot masks
      consecutive = dims == list(range(dims[0], dims[0] + len(dims)))
      if v is None and len(dims) > 1 and consecutive and all_int(ishp := tuple(x.shape[d] for d in dims)):
        strides = tuple(prod(ishp[i+1:]) for i in range(len(dims)))
        try: linear_idx = functools.reduce(Tensor.add, (t._broadcast_to(big_shape) * s for t, s in zip(tensors, strides)))
        except ValueError as err: raise IndexError(f"cannot broadcast indices: {err}") from err
        valid = functools.reduce(Tensor.__and__, ((t >= 0) & (t < s) for t, s in zip(tensors, ishp)))
        pre, post = x.shape[:dims[0]], x.shape[dims[-1]+1:]
        x = x.reshape(pre + (prod(ishp),) + post)[tuple([slice(None)] * len(pre)) + (valid.where(linear_idx, 0),)]
        return valid.reshape((1,) * len(pre) + big_shape + (1,) * len(post)).where(x, 0)

      pre_reduce_shape = x.shape[:dims[0]] + big_shape + x.shape[dims[0]:]

      # create index masks
      for dim, tensor in zip(dims, tensors):
        try: i = tensor.reshape(tensor.shape + (1,)*(x.ndim - dims[0])).expand(pre_reduce_shape)
        except ValueError as err: raise IndexError(f"cannot broadcast indices: {err}") from err
        masks.append(i._one_hot_along_dim(num_classes=x.shape[dim], dim=(dim - x.ndim)))

      # reduce masks to 1 mask
      mask: Tensor = functools.reduce(lambda x,y: x.mul(y), masks)

      # inject 1's for the extra dims added in create masks
      reshape_arg = x.shape[:dims[0]] + (1,) * len(big_shape) + x.shape[dims[0]:]
      # sum reduce the extra dims introduced in create masks
      x_pre = x  # save collapsed shape for advanced setitem
      x = (mask.where(x.reshape(reshape_arg), 0)).sum(sum_axis:=tuple(d + len(big_shape) for d in dims), dtype=x.dtype)

      # special permute case
      if (permuted := dims[0] != 0 and len(dims) != 1 and tuple(dims) != tuple(range(dims[0], dims[-1]+1))):
        mask, x = (y.permute(*range(dims[0], dims[0]+len(big_shape)), *range(0, dims[0]), *range(dims[0]+len(big_shape), y.ndim)) for y in (mask, x))

      if v is None: return x  # advanced getitem
      # advanced setitem: resolve tensor dims in collapsed space, then fall through to basic setitem path
      vb = v.cast(self.dtype)._broadcast_to(_broadcast_shape(x.shape, v.shape))
      for dim in sum_axis: vb = vb.unsqueeze(dim)  # add back reduced dims from sum
      start = dims[0] if not permuted else 0
      vb = _masked_setitem(x_pre, vb, mask, tuple(range(start, start + len(big_shape))))
    elif v is None: return x  # basic getitem
    # basic setitem: broadcast v, reshape to self.ndim (unsqueeze int dims, squeeze None dims)
    else: vb = v.cast(self.dtype)._broadcast_to(x.shape)
    vb = vb.reshape(tuple(1 if isinstance(p['index'], sint) else p['size'] for p in indices_parsed if p['index'] is not None))
    per_dim = []
    for d, m in enumerate(mops):
      (s, e), st = m['boundary'], abs(m['stride'])
      if st != 1 and vb.shape[d] > 1:  # un-stride: interleave with zeros
        vb = vb.unsqueeze(d+1)
        vb = vb.pad_to(tuple(st if j == d+1 else None for j in range(vb.ndim)))
        vb = vb.reshape(vb.shape[:d] + (vb.shape[d]*vb.shape[d+1],) + vb.shape[d+2:])
        vb = vb.shrink_to(tuple(e-s if j == d else None for j in range(self.ndim)))
      idx = Tensor.arange(self.shape[d], device=self.device).reshape([1]*d + [self.shape[d]] + [1]*(self.ndim - d - 1))
      per_dim.append((idx >= s) & (idx < e) & (((e-1-idx) if m['stride'] < 0 else (idx-s)) % st == 0))
    vb = vb.flip(tuple(d for d, m in enumerate(mops) if m['stride'] < 0))
    vb = vb.pad(tuple((m['boundary'][0], self.shape[d] - m['boundary'][1]) for d, m in enumerate(mops)))
    return (functools.reduce(lambda a, b: a & b, per_dim) if per_dim else Tensor(True, dtype=dtypes.bool, device=self.device)).where(vb, self)

  def __getitem__(self, indices) -> Tensor:
    """
    Retrieves a sub-tensor using indexing.

    Supported Index Types: `int | slice | Tensor | None | list | tuple | Ellipsis`

    Examples:
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(12).reshape(3, 4)
    print(t.numpy())
    ```

    - Int Indexing: Select an element or sub-tensor using integers for each dimension.
      ```python exec="true" source="above" session="tensor" result="python"
      print(t[1, 2].numpy())
      ```

    - Slice Indexing: Select a range of elements using slice notation (`start:end:stride`).
      ```python exec="true" source="above" session="tensor" result="python"
      print(t[0:2, ::2].numpy())
      ```

    - Tensor Indexing: Use another tensor as indices for advanced indexing. Using `tuple` or `list` here also works.
      ```python exec="true" source="above" session="tensor" result="python"
      print(t[Tensor([2, 0, 1]), Tensor([1, 2, 3])].numpy())
      ```

    - `None` Indexing: Add a new dimension to the tensor.
      ```python exec="true" source="above" session="tensor" result="python"
      print(t[:, None].shape)
      ```

    NOTE: Out-of-bounds indexing results in a value of `0`.
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 2, 3])
    print(t[Tensor([4, 3, 2])].numpy())
    ```
    """
    return self._getitem(indices)

  def __setitem__(self, indices, v:Tensor|PyConst|list|tuple) -> None:
    if isinstance(v, Tensor) and v.dtype != self.dtype: raise RuntimeError(f"setitem dtype mismatch: {self.dtype=} != {v.dtype=}")
    if self.requires_grad or (isinstance(v, Tensor) and v.requires_grad):
      # for +=/-=, v's graph references self.uop through the view — exclude those from the stale-use check
      v_uop, v_bw = (v.uop, v.uop.backward_slice) if isinstance(v, Tensor) else (None, {})
      if any(self.uop in t.uop.backward_slice for tref in all_tensors
             if (t:=tref()) is not None and t is not self and t.uop is not v_uop and t.uop not in v_bw):
        raise RuntimeError("can't setitem on a tensor that already has other uses and requires grad")
      if not isinstance(v, Tensor): v = Tensor(v, device=self.device, dtype=self.dtype)
      # __iadd__/__isub__ creates AFTER(view, STORE(view, computed)); unwrap to get the computed value
      if v.uop.op is Ops.AFTER and any(s.op is Ops.STORE for s in v.uop.src[1:]): v = v._apply_uop(lambda x: x.src[1].src[1])
      self.replace(self._getitem(indices, v))
      return
    idx = [indices] if (isinstance(indices, list) and all_int(indices)) or not isinstance(indices, (tuple, list)) else list(indices)
    is_disk = isinstance(self.device, str) and self.device.startswith("DISK")
    if any(isinstance(i, (Tensor, list, tuple)) for i in idx): # advanced setitem
      if is_disk: raise RuntimeError("advanced setitem is not supported for DISK tensors")
      if not isinstance(v, Tensor): v = Tensor(v, device=self.device, dtype=self.dtype)
      self.assign(self._getitem(indices, v))
    elif is_disk or self.uop.is_realized or self.uop.base.op is Ops.BUFFER or self.uop._base_buffer_is_realized(): # basic setitem
      view = self[indices]
      if isinstance(v, Tensor) and v.uop.op is Ops.AFTER and v.uop in view.uop.base.src: return
      view.assign(v)
    else: # basic setitem, self is not realized
      if not isinstance(v, Tensor): v = Tensor(v, device=self.device, dtype=self.dtype)
      # __iadd__/__isub__ creates AFTER(view, STORE(view, computed)); unwrap to get the computed value
      if v.uop.op is Ops.AFTER and any(s.op is Ops.STORE for s in v.uop.src[1:]): v = v._apply_uop(lambda x: x.src[1].src[1])
      self.replace(self._getitem(indices, v))

  def __delitem__(self, indices) -> None:
    raise TypeError("Tensor does not support deleting items")

  def gather(self:Tensor, dim:int, index:Tensor) -> Tensor:
    """
    Gathers values along an axis specified by `dim`.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 2], [3, 4]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.gather(1, Tensor([[0, 0], [1, 0]])).numpy())
    ```
    """
    assert index.ndim == self.ndim, f"self.ndim must equal index.ndim, {self.ndim=}, {index.ndim=}"
    dim = self._resolve_dim(dim)
    assert all(s >= i for d,(s,i) in enumerate(zip(self.shape, index.shape)) if d != dim), "requires self.shape[d] >= index.shape[d] for all d != dim"
    index = index.to(self.device)
    x = self.shrink_to(tuple(i if d != dim else None for d,i in enumerate(index.shape))).unsqueeze(-1).transpose(-1, dim)
    return (index.unsqueeze(-1)._one_hot_along_dim(self.shape[dim]).where(x, 0)).sum(-1, dtype=self.dtype)

  def cat(self:Tensor, *args:Tensor, dim:int=0) -> Tensor:
    """
    Concatenates self with other `Tensor` in `args` along an axis specified by `dim`.
    All tensors must have the same shape except in the concatenating dimension.

    ```python exec="true" source="above" session="tensor" result="python"
    t0, t1, t2 = Tensor([[1, 2]]), Tensor([[3, 4]]), Tensor([[5, 6]])
    print(t0.cat(t1, t2, dim=0).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t0.cat(t1, t2, dim=1).numpy())
    ```
    """
    dim = self._resolve_dim(dim)
    for arg in args: assert arg.ndim==self.ndim and all(ti==ai for i,(ti,ai) in enumerate(zip(self.shape, arg.shape)) if i!=dim)
    tensors = [self, *args]
    dim_cumsum = list(itertools.accumulate([t.shape[dim] for t in tensors], initial=0))
    for i,t in enumerate(tensors): tensors[i] = t.pad([(dim_cumsum[i], dim_cumsum[-1]-dim_cumsum[i+1]) if j==dim else None for j in range(t.ndim)])
    return functools.reduce(Tensor.add, tensors)

  def stack(self:Tensor, *args:Tensor, dim:int=0) -> Tensor:
    """
    Concatenates self with other `Tensor` in `args` along a new dimension specified by `dim`.

    ```python exec="true" source="above" session="tensor" result="python"
    t0, t1, t2 = Tensor([1, 2]), Tensor([3, 4]), Tensor([5, 6])
    print(t0.stack(t1, t2, dim=0).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t0.stack(t1, t2, dim=1).numpy())
    ```
    """
    # checks for shapes and number of dimensions delegated to cat
    return Tensor.cat(*[t.unsqueeze(dim) for t in argfix(self, *args)], dim=dim)

  def masked_select(self, mask):
    """
    Selects elements from `self` based on the boolean `mask`.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
    mask = Tensor([[True, False, True], [False, True, False], [False, False, True]])
    print(t.numpy())
    print(mask.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.masked_select(mask).numpy())
    ```
    """
    if not dtypes.is_bool(mask.dtype): raise RuntimeError(f"masked_select expects bool mask tensor, got {mask.dtype}")
    x, mask = self.flatten(), mask._broadcast_to(self.shape).flatten()
    mask_cumsum = mask.cumsum()
    counts = Tensor.zeros(mask_cumsum[-1].item(), dtype=dtypes.int32)
    idxs = counts.scatter(0, mask_cumsum, 1, reduce='add').cumsum()
    return x[idxs]

  def nonzero(self) -> Tensor:
    """
    Returns the indices of the elements that are non-zero.

    Returns a 2D tensor where each row is the index of a non-zero element.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 0, 2, 0, 3])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.nonzero().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 0], [0, 2]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.nonzero().numpy())
    ```
    """
    mask = (self != 0).flatten()
    indices = Tensor.stack(*[Tensor.arange(s, device=self.device).reshape(*[1]*i, s, *[1]*(self.ndim-i-1)).expand(self.shape).flatten()
                             for i, s in enumerate(self.shape)], dim=-1)
    return indices.masked_select(mask.unsqueeze(-1).expand(*mask.shape, self.ndim)).reshape(-1, self.ndim)

  def masked_fill(self:Tensor, mask:Tensor, value:Tensor|PyConst) -> Tensor:
    """
    Replaces `self` with `value` wherever the elements of `mask` are True.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 2, 3, 4, 5])
    mask = Tensor([True, False, True, False, False])
    print(t.masked_fill(mask, -12).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 2, 3, 4, 5])
    mask = Tensor([True, False, True, False, False])
    value = Tensor([-1, -2, -3, -4, -5])
    print(t.masked_fill(mask, value).numpy())
    ```
    """
    return mask.where(value, self)

  # ***** reduce ops *****

  def allclose(self, other:Tensor, rtol:float=1e-05, atol:float=1e-08, equal_nan=False) -> bool:
    """
    Check if all self and other are close. Return True or False.
    """
    return bool(self.isclose(other, rtol=rtol, atol=atol, equal_nan=equal_nan).all().item())

  def keccak(self, cfg:str|tuple[int, int]="sha3_256"):
    """
    Calculates a Keccak hash over the last dimension. Uses "sha3_256" by default.

    ```python exec="false" source="above" session="tensor" result="python"
    t = Tensor(b"Hello World!").keccak()
    print(t.data().hex())
    ```
    """

    # https://keccak.team/keccak_specs_summary.html

    def ctensor(l: Sequence[PyConst], dtype: DType = dtypes.uint64):
      # TODO: contiguous is here for compile speed
      return Tensor.stack(*(Tensor(v, dtype=dtype, device=self.device) for v in l)).contiguous()
    rot_offsets = [44, 43, 21, 14, 28, 20, 3, 45, 61, 1, 6, 25, 8, 18, 27, 36, 10, 15, 56, 62, 55, 39, 41, 2]
    rot_offsets_v0, rot_offsets_v1 =  ctensor([0] + [1 << v for v in rot_offsets]), ctensor([1] + [1 << (64 - v) for v in rot_offsets])

    # calculated from π step
    reorder_indexes = ctensor([0,6,12,18,24,3,9,10,16,22,1,7,13,19,20,4,5,11,17,23,2,8,14,15,21], dtype=dtypes.int32)
    rnd_const_masks = [ctensor([v]).pad((0, 24)) for v in (1, 0x8082, 0x800000000000808a, 0x8000000080008000, 0x808b, 0x80000001, 0x8000000080008081,
    0x8000000000008009, 0x8a, 0x88, 0x80008009, 0x8000000a, 0x8000808b, 0x800000000000008b, 0x8000000000008089, 0x8000000000008003,
    0x8000000000008002, 0x8000000000000080, 0x800a, 0x800000008000000a, 0x8000000080008081, 0x8000000000008080, 0x80000001, 0x8000000080008008)]

    rate, dsbyte = {"sha3_224": (144, 6), "sha3_256": (136, 6), "shake_128": (168, 31)}[cfg] if isinstance(cfg, str) else cfg
    data, data_pad = self.bitcast(dtypes.uint8).reshape(prod(self.shape[:-1]), self.shape[-1]), rate - (self.shape[-1] * self.dtype.itemsize % rate)
    # pad batches then pad blocks
    data = data.pad((None, (0, data_pad))).reshape(bs := data.shape[0], -1, rate).pad((None, None, (0, 200 - rate)))

    # create pad mask
    lbe = prod(data.shape[1:]) + rate - data_pad - 200
    if data_pad == 1: mb = [(lbe, 0), (1, dsbyte ^ 0x80), (200 - rate, 0)]
    else: mb = [(lbe, 0), (1, dsbyte), (data_pad - 2, 0), (1, 0x80), (200 - rate, 0)]
    pad_mask = Tensor.cat(*(Tensor(v, dtype=dtypes.uint8, device=data.device).expand(l) for l, v in mb if l > 0)).unsqueeze(0)

    data = (data.flatten(1) ^ pad_mask).reshape(*data.shape[:2], 200).bitcast(dtypes.uint64)

    state = Tensor.zeros(bs, 25, device=self.device, dtype=dtypes.uint64)
    for k in range(int(data.shape[1])):
      state = state ^ data.shrink((None, (k, k+1), None)).squeeze(1)
      for i in range(24): # f1600
        # θ step
        p = state.reshape(bs, 5, 5).transpose(2, 1)
        t1 = (p[:,:,0] ^ p[:,:,1] ^ p[:,:,2] ^ p[:,:,3] ^ p[:,:,4]).roll(-1, 1) # xor reduce
        state = state ^ (t1.roll(2, 1).bitwise_xor((t1 << 1) ^ (t1 >> 63)).unsqueeze(2).expand(bs, 5, 5).transpose(2, 1).flatten(1))
        # ρ and π steps
        state = state[:, reorder_indexes]
        state = (state * rot_offsets_v0).bitwise_or(state // rot_offsets_v1).reshape(bs, 5, 5)
        # χ and ι step
        state = state.bitwise_xor(~state.roll(shifts=-1, dims=2) & state.roll(shifts=-2, dims=2))
        state = state.flatten(1) ^ rnd_const_masks[i]
      # NOTE: there was a kernelize here to prevent internal stack from growing propotional to data size, do we need something else?
    return state.bitcast(dtypes.uint8)[:,:(obytes:=(200 - rate) // 2)].reshape(*self.shape[:-1], obytes)

  def _hash_1mb(self) -> Tensor:
    assert self.dtype == dtypes.uint8, "only support uint8 tensors for hashing"
    assert self.ndim == 2, "only support batched 1d tensors"
    assert self.shape[1] == 1024 * 1024, "only support messages of 1mb"

    blocks = self.shape[0] * self.shape[1] // 4096
    data = self.reshape(blocks, 4096)
    block_hashes = data.keccak("shake_128").reshape(self.shape[0], 4096)
    return block_hashes.keccak("shake_128").reshape(self.shape[0], 16)

  def hash(self) -> Tensor:
    """
    Calculates a 16-byte hash of the tensor.
    ```python exec="false source="above" session="tensor" result="python"
    t = Tensor(b"Hello World!").hash()
    print(t.data().hex())
    ```
    """

    data = self.flatten().bitcast(dtypes.uint8)
    if (tsize := data.shape[0]) % 2**20 != 0: data = data.pad((0, 2**20 - tsize % 2**20))
    base_chunks = ceildiv(data.shape[0], 2**20)
    tree_depth = math.ceil(math.log(base_chunks, 65536)) if base_chunks > 1 else 0

    level_chunks = base_chunks
    for _ in range(tree_depth + 1):
      data = data.reshape(level_chunks, 2**20)._hash_1mb().flatten()
      if (tsize := data.shape[0]) % 2**20 != 0: data = data.pad((0, 2**20 - tsize % 2**20))
      level_chunks = ceildiv(data.shape[0], 2**20)

    return data[:16]

  def _softmax(self, axis, dtype:DTypeLike|None=None) -> tuple[Tensor, Tensor, Tensor]:
    m = self - self.max(axis=axis, keepdim=True).detach()
    if dtype is not None: m = m.cast(dtype)
    e = m.exp()
    return m, e, e.sum(axis=axis, keepdim=True)

  def softmax(self, axis=-1, dtype:DTypeLike|None=None) -> Tensor:
    """
    Applies the softmax function to the tensor along the specified axis.

    Rescales the elements of the tensor such that they lie in the range [0, 1] and sum to 1.

    You can pass in the `axis` keyword argument to control the axis along which the softmax is computed.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.randn(2, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.softmax().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.softmax(axis=0).numpy())
    ```
    """
    _, e, ss = self._softmax(axis, dtype)
    return e.div(ss)

  def log_softmax(self, axis=-1, dtype:DTypeLike|None=None) -> Tensor:
    """
    Applies the log-softmax function to the tensor along the specified axis.

    The log-softmax function is a numerically stable alternative to the softmax function in log space.

    You can pass in the `axis` keyword argument to control the axis along which the log-softmax is computed.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.randn(2, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.log_softmax().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.log_softmax(axis=0).numpy())
    ```
    """
    m, _, ss = self._softmax(axis, dtype)
    return m - ss.log()

  def normalize(self, p:float=2.0, dim:int=1, eps:float=1e-12) -> Tensor:
    """
    Performs Lp normalization of the tensor along the specified dimension.

    See: https://pytorch.org/docs/stable/generated/torch.nn.functional.normalize.html

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.randn(2, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.normalize().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.normalize(p=1, dim=0).numpy())
    ```
    """
    if p == 0: return self / (self != 0).sum(dim, keepdim=True).maximum(eps)
    return self / self.abs().pow(p).sum(dim, keepdim=True).pow(1/p).maximum(eps)

  def logsumexp(self, axis=None, keepdim=False) -> Tensor:
    """
    Computes the log-sum-exp of the tensor along the specified axis or axes.

    The log-sum-exp function is a numerically stable way to compute the logarithm of the sum of exponentials.

    You can pass in `axis` and `keepdim` keyword arguments to control the axis along
    which the log-sum-exp is computed and whether the reduced dimensions are retained.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.randn(2, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.logsumexp().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.logsumexp(axis=0).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.logsumexp(axis=1).numpy())
    ```
    """
    m = self.max(axis=axis, keepdim=True)
    return (self - m).exp().sum(axis=axis, keepdim=keepdim).log() + (m if keepdim else m.squeeze(axis))

  def logcumsumexp(self, axis=0) -> Tensor:
    """
    Computes the log-cumsum-exp of the tensor along the specified axis or axes.

    The log-cumsum-exp function is a numerically stable way to compute the logarithm of the cumulative sum of exponentials.

    You can pass in the `axis` keyword argument to control the axis along which
    the log-cumsum-exp is computed.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.randn(2, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.logcumsumexp().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.logcumsumexp(axis=0).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.logcumsumexp(axis=1).numpy())
    ```
    """
    if self.ndim == 0: return self
    x = self.transpose(axis, -1)
    last_dim_size = x.shape[-1]
    x_unsqueezed = x.unsqueeze(-2).expand((None,)*(self.ndim-1)+(last_dim_size, None))
    x_cummax, _ = x.cummax(-1)
    mask = Tensor.ones(last_dim_size, last_dim_size, requires_grad=False, device=self.device).tril()
    ret = mask.where(x_unsqueezed - x_cummax.unsqueeze(-1), self.dtype.min).exp().sum(-1).log() + x_cummax
    return ret.transpose(-1, axis)

  def argmax(self, axis=None, keepdim=False) -> Tensor:
    """
    Returns the indices of the maximum value of the tensor along the specified axis.

    You can pass in `axis` and `keepdim` keyword arguments to control the axis along
    which the maximum is computed and whether the reduced dimensions are retained.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 0, 2], [5, 4, 3]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.argmax().numpy()) # Returns the index of the maximum value in the flattened tensor.
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.argmax(axis=0).numpy()) # Returns the indices of the maximum values along axis 0.
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.argmax(axis=1).numpy()) # Returns the indices of the maximum values along axis 1.
    ```
    """
    if axis is None: return self.flatten().argmax(0)
    axis = self._resolve_dim(axis)
    m = self == self.max(axis=axis, keepdim=True)
    idx = m * Tensor.arange(self.shape[axis],0,-1, requires_grad=False, device=self.device).reshape(self.shape[axis], *[1]*(self.ndim-axis-1))
    return (self.shape[axis]-idx.max(axis=axis, keepdim=keepdim)).cast(dtypes.int32)

  def argmin(self, axis=None, keepdim=False) -> Tensor:
    """
    Returns the indices of the minimum value of the tensor along the specified axis.

    You can pass in `axis` and `keepdim` keyword arguments to control the axis along
    which the minimum is computed and whether the reduced dimensions are retained.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 0, 2], [5, 4, 3]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.argmin().numpy()) # Returns the index of the minimum value in the flattened tensor.
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.argmin(axis=0).numpy()) # Returns the indices of the minimum values along axis 0.
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.argmin(axis=1).numpy()) # Returns the indices of the minimum values along axis 1.
    ```
    """
    return self._inverse().argmax(axis=axis, keepdim=keepdim)

  @staticmethod
  def einsum(formula:str, *operands:Tensor|Sequence[Tensor], dtype:DTypeLike|None=None) -> Tensor:
    """
    Sums the product of the elements of the input tensors according to a formula based on the Einstein summation convention.

    See: https://pytorch.org/docs/stable/generated/torch.einsum.html

    ```python exec="true" source="above" session="tensor" result="python"
    x = Tensor([[1, 2], [3, 4]])
    y = Tensor([[5, 6], [7, 8]])
    print(Tensor.einsum("ij,ij->", x, y).numpy())
    ```
    """
    xs, formula = list(argfix(*operands)), formula.replace(" ", "")
    # expand ellipsis to letters, determine output
    if "..." in formula:
      ell, lhs = "".join(c for c in string.ascii_letters if c not in formula), (formula.split("->") + [""])[0]
      ell_n = [max(0, x.ndim - len(s) + 3) if "..." in s else 0 for s, x in zip(lhs.split(","), xs)]
      for i, (s, x) in enumerate(zip(inputs := lhs.split(","), xs)): inputs[i] = s.replace("...", ell[max(ell_n)-ell_n[i]:max(ell_n)])
      lhs, auto = ",".join(inputs), "".join(sorted(c for c in lhs if lhs.count(c) == 1 and c.isalpha() and c not in ell))
      formula = f"{lhs}->{formula.split('->')[1].replace('...', ell[:max(ell_n)]) if '->' in formula else ell[:max(ell_n)] + auto}"
    lhs, rhs = formula.split("->") if "->" in formula else (formula, "".join(sorted(c for c in formula if formula.count(c)==1 and c.isalpha())))
    inputs = lhs.split(",")
    if len(xs) != len(inputs): raise ValueError(f"number of operands doesn't match, expected {len(inputs)}, got {len(xs)}")
    # trace: take diagonal when letter repeats in single input
    for i, (s, x) in enumerate(zip(inputs, xs)):
      for c in set(s):
        while s.count(c) > 1:
          j, k, n = s.index(c), s.index(c, s.index(c)+1), cast(int, x.shape[s.index(c)])
          perm = [d for d in range(x.ndim) if d not in (j,k)]+[j,k]
          x = x.permute(perm).flatten(-2).pad(((0,0),)*(x.ndim-2)+((0,n),)).unflatten(-1,(n,n+1))[...,0] if x.ndim > 2 else x.diagonal()
          s = s[:k] + s[k+1:]
      inputs[i], xs[i] = s, x
    # check sizes and build sorted alphabet
    sz = merge_dicts([dict(zip(s, x.shape)) for s, x in zip(inputs, xs)])
    alpha = sorted(sz)
    # align all tensors to alphabet, multiply, sum non-output, permute to output order
    xs = [x.permute(*[s.index(c) for c in sorted(s)]).reshape([sz[c] if c in s else 1 for c in alpha]).expand([sz[c] for c in alpha]) if s else x
          for s, x in zip(inputs, xs)]
    return functools.reduce(lambda a,b:a*b, xs).sum([i for i,c in enumerate(alpha) if c not in rhs], dtype=dtype).permute(argsort(argsort(list(rhs))))

  # ***** processing ops *****

  def _resolve_pool_pads(self, padding:int|Sequence[int], dims:int) -> Sequence[int]:
    if not isinstance(padding, int) and not (len(padding) == 2*dims or len(padding) == dims):
      raise ValueError(f"Padding must be an int or a sequence of length {dims} or {2*dims}, but got {padding=} for {self.shape=} with {dims=}.")
    return [padding]*2*dims if isinstance(padding, int) else (padding if len(padding) == 2*dims else [p for p in padding for _ in range(2)][::-1])

  def _apply_ceil_mode(self, pads:Sequence[int], k_:tuple[sint, ...], s_:int|tuple[int, ...], d_:int|tuple[int, ...]) -> list[int]:
    (d_,s_), i_ = (make_tuple(x, len(k_)) for x in (d_,s_)), self.shape[-len(k_):]
    pads, grouped_pads = list(pads), _flat_to_grouped(pads)
    # https://arxiv.org/pdf/1603.07285 section 5.1, relationship 15.
    o_ = [ceildiv(i+pB+pA - (d*(k-1)+1), s) + 1 for i,d,k,s,(pB,pA) in zip(i_,d_,k_,s_,grouped_pads)]
    for dim,(o,i,s,k,d,(pB,pA)) in enumerate(zip(o_,i_,s_,k_,d_,grouped_pads)):
      # we have to do additional padding before `_pool` so that `o_` in `_pool` is calculated correctly
      # `s*(o-1) + (d*(k-1)+1) - (i+pB+pA)` -> last_sliding_window_start + full_kernel_size - padded_input_shape
      # we decrease padding in the case that a sliding window starts in the end padded region, thereby decreasing `o_` in `_pool`
      # `smax(s*(o-1) - (pB+i-1), 0)` -> last_sliding_window_start - (pad_before + input_size - zero_offset)
      pads[-1-dim*2] += s*(o-1) + (d*(k-1)+1) - (i+pB+pA) - smax(s*(o-1) - (pB+i-1), 0)
    return pads

  # NOTE: these work for more than 2D
  def avg_pool2d(self, kernel_size:tuple[int, ...]=(2,2), stride=None, dilation=1, padding:int|tuple[int, ...]=0,
                 ceil_mode=False, count_include_pad=True) -> Tensor:
    """
    Applies average pooling over a tensor.

    This function supports three different types of `padding`

    1. `int` (single value):
      Applies the same padding value uniformly to all spatial dimensions.

    2. `tuple[int, ...]` (length = number of spatial dimensions):
      Specifies a distinct padding value for each spatial dimension in the form `(padding_height, padding_width, ...)`.

    3. `tuple[int, ...]` (length = 2 * number of spatial dimensions):
      Specifies explicit padding for each side of each spatial dimension in the form
      `(padding_left, padding_right, padding_top, padding_bottom, ...)`.

    When `ceil_mode` is set to `True`, output shape will be determined using ceil division.
    When `count_include_pad` is set to `False`, zero padding will not be included in the averaging calculation.

    NOTE: unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(25).reshape(1, 1, 5, 5)
    print(t.avg_pool2d().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.avg_pool2d(ceil_mode=True).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.avg_pool2d(padding=1).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.avg_pool2d(padding=1, count_include_pad=False).numpy())
    ```
    """
    axis = tuple(range(-len(k_ := make_tuple(kernel_size, 2)), 0))
    def pool(x:Tensor, padding_:Sequence[int]) -> Tensor: return x.pad(padding_)._pool(k_, stride if stride is not None else k_, dilation)
    reg_pads = self._resolve_pool_pads(padding, len(k_))
    ceil_pads = self._apply_ceil_mode(reg_pads, k_, stride if stride is not None else k_, dilation)
    if not count_include_pad:
      pads = ceil_pads if ceil_mode else reg_pads
      return pool(self, pads).sum(axis) / pool(self.ones_like(), pads).sum(axis)
    if not ceil_mode: return pool(self, reg_pads).mean(axis)
    return pool(self, ceil_pads).sum(axis) / pool(self.pad(reg_pads).ones_like(), tuple(cp-rp for cp,rp in zip(ceil_pads, reg_pads))).sum(axis)

  def max_pool2d(self, kernel_size:tuple[int, ...]=(2,2), stride=None, dilation=1, padding:int|tuple[int, ...]=0,
                 ceil_mode=False, return_indices=False) -> Tensor | tuple[Tensor, Tensor]:
    """
    Applies max pooling over a tensor.

    This function supports three different types of `padding`

    1. `int` (single value):
      Applies the same padding value uniformly to all spatial dimensions.

    2. `tuple[int, ...]` (length = number of spatial dimensions):
      Specifies a distinct padding value for each spatial dimension in the form `(padding_height, padding_width, ...)`.

    3. `tuple[int, ...]` (length = 2 * number of spatial dimensions):
      Specifies explicit padding for each side of each spatial dimension in the form
      `(padding_left, padding_right, padding_top, padding_bottom, ...)`.

    When `ceil_mode` is set to `True`, output shape will be determined using ceil division.
    When `return_indices` is set to `True`, the argmax will be returned along with the max values.

    NOTE: unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(25).reshape(1, 1, 5, 5)
    print(t.max_pool2d().numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.max_pool2d(ceil_mode=True).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.max_pool2d(padding=1).numpy())
    ```
    """
    axis = tuple(range(-len(k_ := make_tuple(kernel_size, 2)), 0))
    pads = self._resolve_pool_pads(padding, len(k_))
    if ceil_mode: pads = self._apply_ceil_mode(pads, k_, stride if stride is not None else k_, dilation)
    pooled = self.pad(pads, value=self.dtype.min)._pool(k_, stride if stride is not None else k_, dilation)
    if not return_indices: return pooled.max(axis)
    spatial_sz = int(math.prod(spatial_shape := self.shape[-len(k_):]))
    idx = Tensor.arange(spatial_sz,0,-1, requires_grad=False, device=self.device).reshape(spatial_shape)
    m = pooled == pooled.max(axis, keepdim=True)
    idx = m * idx.pad(pads, value=idx.dtype.min)._pool(k_, stride if stride is not None else k_, dilation)
    return pooled.max(axis), spatial_sz - idx.max(axis)

  def max_unpool2d(self, indices:Tensor, kernel_size:tuple[int, ...]=(2,2), stride=None, dilation=1, padding:int|tuple[int, ...]=0, output_size=None):
    """
    Performs a partial inverse of `max_pool2d` using the indices from the argmax.

    When `output_size` is provided, the output shape disambiguates to the provided shape.

    NOTE: unlike PyTorch, this implementation is not limited to only 2d pooling and instead works for any number of dimensions.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(1, 17).reshape(1, 1, 4, 4)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    output, indices = Tensor.max_pool2d(t, return_indices=True)
    print(output.numpy())
    print(indices.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.max_unpool2d(output, indices).numpy())
    ```
    """
    bs,c,*spatial_shape = self.shape
    if output_size is None:
      k_,d_,s_ = (make_tuple(x, len(spatial_shape)) for x in (kernel_size, dilation, stride if stride is not None else kernel_size))
      p_ = _flat_to_grouped(self._resolve_pool_pads(padding, len(spatial_shape)))
      # https://arxiv.org/pdf/1603.07285 inverse of relationship 15 in section 5.1.
      output_size = tuple((i-1)*s - (pB+pA) + (d*(k-1)+1) for i,k,d,s,(pA,pB) in zip(spatial_shape,k_,d_,s_,p_))
    else: output_size = output_size[-len(spatial_shape):]
    ret = (indices.reshape(bs,c,1,-1)._one_hot_along_dim(prod(output_size), 2).where(self.reshape(bs,c,1,-1), 0)).sum(3)
    return ret.reshape(bs,c,*output_size)

  def conv2d(self, weight:Tensor, bias:Tensor|None=None, groups=1, stride=1, dilation=1, padding:int|tuple[int, ...]=0,
             dtype:DTypeLike|None=None) -> Tensor:
    """
    Applies a convolution over a tensor with a given `weight` and optional `bias`.

    This function supports three different types of `padding`

    1. `int` (single value):
      Applies the same padding value uniformly to all spatial dimensions.

    2. `tuple[int, ...]` (length = number of spatial dimensions):
      Specifies a distinct padding value for each spatial dimension in the form `(padding_height, padding_width, ...)`.

    3. `tuple[int, ...]` (length = 2 * number of spatial dimensions):
      Specifies explicit padding for each side of each spatial dimension in the form
      `(padding_left, padding_right, padding_top, padding_bottom, ...)`.

    NOTE: unlike PyTorch, this implementation is not limited to only 2d convolutions and instead works for any number of dimensions.

    See: https://pytorch.org/docs/stable/generated/torch.nn.Conv2d.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(9).reshape(1, 1, 3, 3)
    w = Tensor.ones(1, 1, 2, 2)
    print(t.conv2d(w).numpy())
    ```
    """
    if IMAGE: return self.image_conv2d(weight, bias, groups, stride, dilation, padding, dtype)
    (bs,cin_), (cout,cin), HW = self.shape[:2], weight.shape[:2], weight.shape[2:]
    padding_ = self._resolve_pool_pads(padding, len(HW))
    assert groups*cin == cin_ and len(self.shape) == len(weight.shape),\
        f"Input Tensor shape {self.shape} does not match the shape of the weights {weight.shape}. ({groups*cin} vs. {cin_})"

    # conv2d is a pooling op (with padding)
    x = self.pad(padding_)._pool(HW, stride, dilation)   # (bs, groups*cin, oy, ox, H, W)
    rcout, oyx = cout//groups, x.shape[2:-len(HW)]
    if not all(x == 3 for x in HW) or stride != 1 or dilation != 1 or not WINO:
      # normal conv
      x = x.reshape(bs, groups, cin, 1, *oyx, *HW).expand(bs, groups, cin, rcout, *oyx, *HW)\
        .permute(0,1,3,*[4+i for i in range(len(oyx))],2,*[4+len(oyx)+i for i in range(len(HW))])

      # conv! broadcasted to (bs, groups, rcout, *oyx, cin, *HW)
      ret = (x * weight.reshape(1, groups, rcout, *[1] * len(oyx), cin, *HW))\
        .sum([-1-i for i in range(1+len(oyx))], keepdim=True, dtype=dtype).reshape(bs, cout, *oyx)
      return ret if bias is None else ret.add(bias.reshape(1, -1, *[1] * len(HW)))

    HWI, HWO = (6,) * len(HW), (4,) * len(HW)  # F(4x4,3x3) winograd tiles
    winograd_G = [[1/4, 0, 0], [-1/6, -1/6, -1/6], [-1/6, 1/6, -1/6], [1/24, 1/12, 1/6], [1/24, -1/12, 1/6], [0, 0, 1]]
    winograd_Bt = [[4, 0, -5, 0, 1, 0], [0, -4, -4, 1, 1, 0], [0, 4, -4, -1, 1, 0], [0, -2, -1, 2, 1, 0], [0, 2, -1, -2, 1, 0], [0, 4, 0, -5, 0, 1]]
    winograd_At = [[1, 1, 1, 1, 1, 0], [0, 1, -1, 2, -2, 0], [0, 1, 1, 4, 4, 0], [0, 1, -1, 8, -8, 1]] # applying At in pre-order doubles compile time

    # TODO: stride == dilation
    # use padding to round up to 4x4 output tiles
    # (bs, cin_, tyx, HWI)
    pads = [[padding_[i*2], padding_[i*2+1] + (-(dim+sum(padding_[i*2:(i+1)*2])-2) % 4)] for i, dim in enumerate(reversed(self.shape[-len(HW):]))]
    d = self.pad(sum(pads, []))._pool(HWI, HWO)
    # move HW to the front: # (HWI, bs, cin_, tyx)
    d = d.permute(*range(len(d.shape)-len(HW),len(d.shape)), *range(len(d.shape)-len(HW)))
    tyx = d.shape[-len(HWI):]  # dim of tiling

    g = weight.permute(*range(len(weight.shape)-len(HW),len(weight.shape)), *range(len(weight.shape)-len(HW)))  # move HW to the front

    # compute 6x6 winograd tiles: GgGt, BtdB
    # (HWI, groups * rcout, cin) -> (HWI, bs=1, groups, rcout, cin, tyx=(1,1))
    gfactors = _apply_winograd_matrix(winograd_G, g, len(HW)).reshape(*HWI, 1, groups, rcout, cin, *([1]*len(tyx)))
    # (HWI, bs, cin_, tyx) -> (HWI, bs, groups, 1 ,cin, *tyx)
    dfactors = _apply_winograd_matrix(winograd_Bt, d, len(HW)).reshape(*HWI, bs, groups, 1, cin, *tyx)

    # matmul; sum across cin: (HWI, bs, groups, rcout, *tyx); then HWI -> HWO: (HWO, bs, groups, rcout, *tyx)
    ret = _apply_winograd_matrix(winograd_At, (gfactors * dfactors).sum(axis=-1-len(HW), dtype=dtype), len(HW))

    # interleave tyx and HWO: (bs, groups, rcout, oy, HO, ox, WO)
    ret = ret.permute([*range(len(HW), len(ret.shape)-len(HW)), *[i+o for i in range(len(HW)) for o in [len(ret.shape)-len(HW),0]]])
    # merge groups and rcout, tyx and HWO: (bs, groups, cout, *yx), shrink to final
    ret = ret.reshape(bs, cout, *[c * HWO[i] for i, c in enumerate(tyx)]).shrink_to(bs, cout, *oyx)

    return (ret if bias is None else ret.add(bias.reshape(1, -1, *[1 for _ in range(len(HW))]))).contiguous().contiguous_backward()

  def conv_transpose2d(self, weight:Tensor, bias:Tensor|None=None, groups=1, stride=1, dilation=1, padding=0, output_padding=0) -> Tensor:
    """
    Applies a transposed convolution over a tensor with a given `weight` and optional `bias`.

    This function supports three different types of `padding`

    1. `int` (single value):
      Applies the same padding value uniformly to all spatial dimensions.

    2. `tuple[int, ...]` (length = number of spatial dimensions):
      Specifies a distinct padding value for each spatial dimension in the form `(padding_height, padding_width, ...)`.

    3. `tuple[int, ...]` (length = 2 * number of spatial dimensions):
      Specifies explicit padding for each side of each spatial dimension in the form
      `(padding_left, padding_right, padding_top, padding_bottom, ...)`.

    NOTE: unlike PyTorch, this implementation is not limited to only 2d transposed convolutions and instead works for any number of dimensions.

    See: https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(9).reshape(1, 1, 3, 3)
    w = Tensor.ones(1, 1, 2, 2)
    print(t.conv_transpose2d(w).numpy())
    ```
    """
    x, w = self, weight.unflatten(0, (groups, -1)).transpose(1, 2).flip(*range(3, len(weight.shape)+1))
    HW = weight.shape[2:]
    padding = _flat_to_grouped(self._resolve_pool_pads(padding, len(HW)))
    stride, dilation, output_padding = [make_tuple(x, len(HW)) for x in (stride, dilation, output_padding)]
    if any(s>1 for s in stride):
      # handle strides: (k) -> reshape -> (k,1) -> pad -> (k,s) -> reshape -> (k*s) -> shrink (k-(s-1))
      x = x.reshape(None, None, *flatten((k,1) for k in x.shape[2:]))
      x = x.pad((None, None, *flatten((None,(0,s-1)) for s in stride)))
      x = x.reshape(None, None, *[k*s for k,s in zip(x.shape[2::2], stride)])
      x = x.shrink_to(None, None, *[k-(s-1) for k,s in zip(x.shape[2:], stride)])
    padding = flatten((((k-1)*d-pB,(k-1)*d-pA+op) for k,d,(pB,pA),op in reversed(list(zip(HW, dilation, padding, output_padding)))))
    return x.conv2d(w.flatten(end_dim=1), groups=groups, bias=bias, dilation=dilation, padding=padding)

  def dot(self, w:Tensor, dtype:DTypeLike|None=None) -> Tensor:
    if IMAGE: return self.image_dot(w, dtype)
    return super().dot(w, dtype=dtype)

  def _cumalu(self, axis:int, op:Ops, _include_initial=False) -> Tensor:
    assert self.shape[axis] != 0 and op in (Ops.ADD, Ops.MAX, Ops.MUL)
    pl_sz = self.shape[axis] - int(not _include_initial)
    pooled = self.transpose(axis,-1).pad((pl_sz, -int(_include_initial)), value=identity_element(op, self.dtype))._pool((self.shape[axis],))
    return getattr(pooled, {Ops.ADD: "sum", Ops.MAX: "max", Ops.MUL: "prod"}[op])(-1).transpose(axis, -1)

  def _split_cumalu(self, axis:int, op:Ops) -> Tensor:
    axis = self._resolve_dim(axis)
    if self.ndim == 0 or 0 in self.shape: return self
    # TODO: someday the optimizer will find this on its own
    # for now this is a two stage cumsum
    SPLIT = 256
    if not isinstance(s:=self.shape[axis], int) or s <= SPLIT*2: return self._cumalu(axis, op)
    ret = self.transpose(axis,-1).pad((round_up(s, SPLIT)-s, 0), value=identity_element(op, self.dtype)).unflatten(-1, (-1, SPLIT))._cumalu(-1, op)
    base = ret[..., -1]._cumalu(-1, op, _include_initial=True)
    base = base.unsqueeze(-1).expand(*base.shape, ret.shape[-1])
    def fix(x: Tensor) -> Tensor: return x.flatten(start_dim=-2)[..., -s:].transpose(axis,-1)
    return getattr(fix(ret), {Ops.ADD: "add", Ops.MAX: "maximum", Ops.MUL: "mul"}[op])(fix(base))

  def cumsum(self, axis:int=0) -> Tensor:
    """
    Computes the cumulative sum of the tensor along the specified `axis`.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.ones(2, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.cumsum(1).numpy())
    ```
    """
    return self._split_cumalu(axis, Ops.ADD)

  def cumprod(self, axis:int) -> Tensor:
    """
    Computes the cumulative product of the elements of the tensor along the specified `axis`.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.arange(1, 7).reshape(2, 3)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.cumprod(axis=0).numpy())
    ```
    """
    return self._split_cumalu(axis, Ops.MUL)

  def cummax(self, axis:int=0) -> tuple[Tensor, Tensor]:
    """
    Computes the cumulative max of the tensor along `axis`, returning (values, indices).

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([0, 1, -1, 2, -2, 3, -3])
    values, indices = t.cummax(0)
    print(values.numpy())
    print(indices.numpy())
    ```
    """
    if self.ndim == 0: return self._split_cumalu(axis, Ops.MAX), Tensor.zeros(self.shape, dtype=dtypes.int32, device=self.device)
    values, n = self._split_cumalu(axis, Ops.MAX), int(self.shape[axis])
    x, values_t = self.transpose(axis, -1), values.transpose(axis, -1)
    match = (x.unsqueeze(-1) == values_t.unsqueeze(-2)) * Tensor.ones(n, n, requires_grad=False, device=self.device).triu()
    idx = (-(match * Tensor.arange(n, 0, -1, requires_grad=False, device=self.device).reshape(n, 1)).max(-2) + n).cast(dtypes.int32)
    return values, idx.transpose(-1, axis)

  def cummin(self, axis:int=0) -> tuple[Tensor, Tensor]:
    """
    Computes the cumulative min of the tensor along `axis`, returning (values, indices).

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([0, 1, -1, 2, -2, 3, -3])
    values, indices = t.cummin(0)
    print(values.numpy())
    print(indices.numpy())
    ```
    """
    values, indices = self._inverse().cummax(axis)
    return values._inverse(), indices

  @staticmethod
  def _tri(r:sint, c:sint, diagonal=0, device=None, requires_grad:bool|None=None) -> Tensor:
    return (Tensor.arange(r, device=device).unsqueeze(-1) + diagonal <= Tensor.arange(c, device=device)).requires_grad_(requires_grad)

  def triu(self, diagonal:sint=0) -> Tensor:
    """
    Returns the upper triangular part of the tensor, the other elements are set to 0.

    The argument `diagonal` determines which diagonal is on the boundary. `diagonal = 0` means the main diagonal.
    Positive `diagonal` means above the main diagonal, and negative `diagonal` means below the main diagonal.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.triu(diagonal=0).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.triu(diagonal=1).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.triu(diagonal=-1).numpy())
    ```
    """
    return Tensor._tri(self.shape[-2], self.shape[-1], diagonal=diagonal, device=self.device).where(self, self.zeros_like())

  def tril(self, diagonal:sint=0) -> Tensor:
    """
    Returns the lower triangular part of the tensor, the other elements are set to 0.

    The argument `diagonal` determines which diagonal is on the boundary. `diagonal = 0` means the main diagonal.
    Positive `diagonal` means above the main diagonal, and negative `diagonal` means below the main diagonal.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.tril(diagonal=0).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.tril(diagonal=1).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.tril(diagonal=-1).numpy())
    ```
    """
    return Tensor._tri(self.shape[-2], self.shape[-1], diagonal=diagonal+1, device=self.device).where(self.zeros_like(), self)

  def interpolate(self, size:tuple[int, ...], mode:str="linear", align_corners:bool=False) -> Tensor:
    """
    Downsamples or Upsamples to the input `size`, accepts 0 to N batch dimensions.

    The interpolation algorithm is selected with `mode` which currently only supports `linear`, `nearest` and `nearest-exact`.
    To run `bilinear` or `trilinear`, pass in a 2D or 3D size.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 2, 3, 4], [21, 22, 23, 24], [41, 42, 43, 44]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.interpolate(size=(2,3), mode="linear").numpy())
    ```
    """
    assert isinstance(size, (tuple,list)) and all_int(size) and 0 < len(size) <= self.ndim, f"invalid {size=}"
    assert mode in ("linear", "nearest", "nearest-exact"), "only supports linear, nearest or nearest-exact interpolate"
    assert not (align_corners and mode != "linear"), "align_corners option can only be set with the interpolating mode linear"
    x, expand = self, list(self.shape)
    for i in range(-1,-len(size)-1,-1):
      scale = (int(self.shape[i]) - int(align_corners)) / (size[i] - int(align_corners))
      arr, reshape = Tensor.arange(size[i], dtype=dtypes.float32, device=self.device), [1] * self.ndim
      reshape[i] = expand[i] = size[i]
      if mode == "linear":
        index = (scale*arr if align_corners else (scale*(arr+0.5))-0.5).clip(0, self.shape[i]-1)
        low, high, perc = [y.reshape(reshape).expand(expand) for y in (index.floor().int(), index.ceil().int(), index - index.floor())]
        x = x.gather(i, low).lerp(x.gather(i, high), perc)
      else:
        index = (scale*(arr+0.5) if mode=="nearest-exact" else scale*arr).cast(dtypes.int32).reshape(reshape).expand(expand)
        x = x.gather(i, index)
    return x.cast(self.dtype)

  def _pre_scatter(self, dim:int, index:Tensor, src:Tensor) -> tuple[Tensor, Tensor]:
    index, dim = index.to(self.device), self._resolve_dim(dim)
    assert index.ndim == self.ndim == src.ndim, f"self.ndim, index.ndim and src.ndim must all equal, {self.ndim=} {index.ndim=} {src.ndim=}"
    assert all((d == dim or self_ >= index_) and src_ >= index_ for d,(self_,index_,src_) in enumerate(zip(self.shape, index.shape, src.shape))), \
      f"All dimensions of {index.shape=} should be <= to all dimensions of {src.shape=} and all dimensions except dimension {dim} of {self.shape=}"
    if self.dtype != src.dtype: raise RuntimeError(f"expect {self.dtype=} to be equal to {src.dtype=}")
    # shrink src to index shape to shrink away the unused values
    src = src.shrink_to(index.shape)
    # prepare src and mask for reduce with respect to dim
    src = src.unsqueeze(-1).expand(*src.shape, self.shape[dim]).transpose(-1, dim)
    mask = index.unsqueeze(-1)._one_hot_along_dim(self.shape[dim]).transpose(-1, dim)
    # pad src and mask to self.shape so that reduce can be done with padded values as no-ops
    return src.pad_to(*self.shape, None), mask.pad_to(*self.shape, None)

  def scatter(self, dim:int, index:Tensor, src:Tensor|PyConst, reduce:Literal['multiply', 'add']|None=None) -> Tensor:
    """
    Scatters `src` values along an axis specified by `dim`.
    Apply `add` or `multiply` reduction operation with `reduce`.

    NOTE: To use the `reduce` argument with a Tensor `src`, see `Tensor.scatter_reduce`.

    ```python exec="true" source="above" session="tensor" result="python"
    src = Tensor.arange(1, 11).reshape(2, 5)
    print(src.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    index = Tensor([[0, 1, 2, 0]])
    print(Tensor.zeros(3, 5, dtype=src.dtype).scatter(0, index, src).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    index = Tensor([[0, 1, 2], [0, 1, 4]])
    print(Tensor.zeros(3, 5, dtype=src.dtype).scatter(1, index, src).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.full((2, 4), 2.0).scatter(1, Tensor([[2], [3]]), 1.23, reduce='multiply').numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.full((2, 4), 2.0).scatter(1, Tensor([[2], [3]]), 1.23, reduce='add').numpy())
    ```
    """
    if reduce not in {None, "add", "multiply"}: raise TypeError(f"{reduce=} must be one of None, 'multiply', or 'add'")
    if reduce and isinstance(src, Tensor): raise TypeError("Tensor src is not supported with reduce arg. see scatter_reduce")
    if not isinstance(src, Tensor): src = index.full_like(src, device=self.device, dtype=self.dtype)
    if reduce == "add": return self.scatter_reduce(dim, index, src, "sum", include_self=True)
    if reduce == "multiply": return self.scatter_reduce(dim, index, src, "prod", include_self=True)
    src, mask = self._pre_scatter(dim, index, src)
    return _masked_setitem(self, src, mask, (-1,))

  def scatter_reduce(self, dim:int, index:Tensor, src:Tensor, reduce:Literal["sum", "prod", "mean", "amax", "amin"],
                     include_self:bool=True) -> Tensor:
    """
    Scatters `src` values along an axis specified by `dim`.
    Apply `"sum"`, `"prod"`, `"mean"`, `"amax"`, or `"amin"` reduction operations with `reduce`.

    Set `include_self=False` to exclude values in the `self` Tensor from the reduction.

    ```python exec="true" source="above" session="tensor" result="python"
    src = Tensor.arange(1, 11).cast(dtypes.float).reshape(2, 5)
    print(src.numpy())
    index = Tensor([[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]])
    print(index.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.ones(1, 5, dtype=src.dtype).scatter_reduce(0, index, src, reduce='sum').numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.ones(1, 5, dtype=src.dtype).scatter_reduce(0, index, src, reduce='prod').numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor.ones(1, 5, dtype=src.dtype).scatter_reduce(0, index, src, reduce='mean', include_self=False).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor([[-10, 20, 0, 5, 10]], dtype=src.dtype).scatter_reduce(0, index, src, reduce='amax').numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor([[-10, 20, 0, 5, 10]], dtype=src.dtype).scatter_reduce(0, index, src, reduce='amin').numpy())
    ```
    """
    src, mask = self._pre_scatter(dim, index, src)
    def _inv_mask(a:Tensor|PyConst, b:Tensor|PyConst) -> Tensor: return mask.any(-1).logical_not().where(a, b)
    if reduce == "sum": return mask.where(src, 0).sum(-1).add(self if include_self else _inv_mask(self, 0))
    if reduce == "prod": return mask.where(src, 1).prod(-1).mul(self if include_self else _inv_mask(self, 1))
    if reduce == "amax": return mask.where(src, m := src.dtype.min).max(-1).maximum(self if include_self else _inv_mask(self, m))
    if reduce == "amin": return mask.where(src, m := src.dtype.max).min(-1).minimum(self if include_self else _inv_mask(self, m))
    if reduce == "mean":
      count = mask.where(1, 0).sum(-1).add(1 if include_self else _inv_mask(1, 0))
      return mask.where(src, 0).sum(-1).add(self if include_self else _inv_mask(self, 0)).div(count)
    raise RuntimeError(f"{reduce=} must be one of 'sum', 'prod', 'mean', 'amax', 'amin'")

  def sort(self, dim:int=-1, descending:bool=False) -> tuple[Tensor, Tensor]:
    """
    Performs a bitonic sort on the tensor along the specified dimension.

    Order of indices for equivalent elements is always preserved.

    See: https://en.wikipedia.org/wiki/Bitonic_sorter

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[0.1, 0.5, 1.2, 3.4, 2.1], [2.2, 1.9, 0.3, 4.5, 0.8]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    sorted_values, indices = t.sort(dim=1, descending=True)
    print(sorted_values.numpy())
    print(indices.numpy())
    ```
    """
    x, dim = self, self._resolve_dim(dim)
    if (orig_len := int(x.shape[dim])) <= 1: return x, x.zeros_like(dtype=dtypes.default_int)
    # pad to power of 2
    n_stages = (orig_len-1).bit_length()
    pads = tuple((0, 2**n_stages - orig_len) if i == dim else None for i in range(x.ndim))
    x = x.pad(pads, value=x.dtype.min if descending else x.dtype.max).unflatten(dim, (2,)*n_stages)
    # https://en.wikipedia.org/wiki/Bitonic_sorter#/media/File:BitonicSort1.svg
    for stage in range(1, n_stages+1):
      if stage != n_stages:
        # flip so arrows of green boxes point the same way as blue boxes
        crossover_dim = dim + n_stages - stage - 1
        blue_box, green_box = x.split(1, crossover_dim)
        flip_dims = tuple(-i for i in range(1, stage+1+(self.ndim-dim)))
        x = (blue_box.cat(green_box.flip(flip_dims), dim=crossover_dim)).contiguous()
      for substage in range(stage-1, -1, -1):
        partner_dim = dim + n_stages - substage - 1
        x_top, x_bottom = x.split(1, partner_dim)
        x_larger, x_smaller = x_top.maximum(x_bottom), x_top.minimum(x_bottom)
        x = (x_larger.cat(x_smaller, dim=partner_dim) if descending else x_smaller.cat(x_larger, dim=partner_dim)).contiguous()
      if stage != n_stages:
        # flip wires back to undo the crossover
        blue_box, flipped_green_box = x.split(1, crossover_dim)
        x = blue_box.cat(flipped_green_box.flip(flip_dims), dim=crossover_dim)
    x = x.flatten(dim, dim+n_stages-1).shrink_to(self.shape)
    # compute indices for sorted values
    mask = Tensor.ones(orig_len, orig_len, dtype=dtypes.bool, device=self.device).tril().reshape((None, None) + (1,)*(self.ndim-dim-1))
    def compute_counts(t:Tensor): return (mask & (t.unsqueeze(dim) == t.unsqueeze(dim+1))).sum(dim+1)
    count_orig, count_sorted = compute_counts(self), compute_counts(x)
    cond = (self.unsqueeze(dim+1) == x.unsqueeze(dim)) & (count_orig.unsqueeze(dim+1) == count_sorted.unsqueeze(dim))
    idx = Tensor.arange(orig_len, device=self.device).reshape(tuple(orig_len if i == dim else 1 for i in range(x.ndim)))
    idx = (cond * idx.unsqueeze(dim+1)).sum(dim)
    return x, idx

  def argsort(self, dim:int=-1, descending:bool=False) -> Tensor:
    """
    Returns the indices that sort input tensor along given `dimension` in given `descending` order by value.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[2, 3, 4, 1], [1, 4, 3, 2]])
    print(t.argsort().numpy())
    ```
    """
    return self.sort(dim, descending)[1]

  def topk(self, k:int, dim:int=-1, largest:bool=True, sorted_:bool=True) -> tuple[Tensor, Tensor]:
    """
    Computes the top-k elements of the tensor along the specified `dim`.

    Order of indices for equivalent elements is always preserved.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[0.1, 0.5, 1.2, 3.4, 2.1], [2.2, 1.9, 0.3, 4.5, 0.8]])
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    topk_values, topk_indices = t.topk(2, dim=1)
    print(topk_values.numpy())
    print(topk_indices.numpy())
    ```
    """
    if not sorted_: raise NotImplementedError("topk with sorted_=False is not supported")
    if k > self.shape[dim:=self._resolve_dim(dim)]: raise ValueError(f"selected index {k=} is out of range")
    x, idx = self.sort(dim, descending=largest)
    topk_shape = tuple(k if i == dim else None for i in range(self.ndim))
    return x.shrink_to(topk_shape), idx.shrink_to(topk_shape)

  # ***** unary ops *****

  def contiguous(self, *args, **kwargs) -> Tensor:
    """
    Returns a contiguous tensor.
    """
    return self._apply_uop(UOp.contiguous, extra_args=args, **kwargs)

  def contiguous_backward(self) -> Tensor:
    """
    Inserts a contiguous operation in the backward pass.
    """
    return self._apply_uop(UOp.contiguous_backward)

  # ***** broadcasted elementwise ops *****

  def ufix(self, x) -> Tensor:
    # TODO: x:ConstType|UOp does not work because mixin only accepts Self | ConstType
    assert isinstance(x, (*get_args(ConstType), UOp)), f"{type(x)=}, {x=}"
    dtype = self.dtype if dtypes.is_float(self.dtype) or (dtypes.is_int(self.dtype) and isinstance(x, (int, InvalidType))) else None
    return Tensor(x, self.device, dtype, requires_grad=False)

  def div(self, x:Tensor|ConstType|UOp, reverse=False, rounding_mode:Literal["trunc", "floor"]|None=None) -> Tensor:
    """
    Divides `self` by `x`.
    Equivalent to `self / x`.
    Supports broadcasting to a common shape, type promotion, and integer, float, boolean inputs.
    `div` performs true division.

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.randn(4)
    print(t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.div(3).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor([1, 4, 10]).div(Tensor([2, 3, 4])).numpy())
    ```
    """
    numerator, denominator = self._broadcasted(x, reverse)
    d = numerator.cast(least_upper_float(numerator.dtype)) * denominator.cast(least_upper_float(denominator.dtype)).reciprocal()
    output_dtype = numerator.dtype if dtypes.is_int(numerator.dtype) else d.dtype
    if dtypes.is_int(dt:=least_upper_dtype(numerator.dtype, denominator.dtype)) and rounding_mode is not None:
      numerator, denominator = numerator.cast(dt), denominator.cast(dt)
      if rounding_mode == "trunc": return numerator.idiv(denominator)
      if rounding_mode == "floor":
        truncate_div, truncate_mod = numerator.idiv(denominator), numerator._binop(Ops.MOD, denominator, False)
        opposite_sign = ((numerator>0)&(denominator<0)) | ((numerator<0)&(denominator>0))
        return (opposite_sign&(truncate_mod!=0)).where(truncate_div-1, truncate_div)
    if rounding_mode == "trunc": return d.trunc().cast(output_dtype)
    if rounding_mode == "floor": return d.floor().cast(output_dtype)
    if rounding_mode is not None: raise RuntimeError(f"{rounding_mode=} is not supported")
    return d

  def mod(self, x:Tensor|ConstType, reverse=False) -> Tensor:
    """
    Mod `self` by `x`.
    Equivalent to `self % x`.
    Supports broadcasting to a common shape, type promotion, and integer inputs.

    ```python exec="true" source="above" session="tensor" result="python"
    print(Tensor([-4, 7, 5, 4, -7, 8]).mod(Tensor([2, -3, 8, -2, 3, 5])).numpy())
    ```
    """
    a, b = self._broadcasted(x, reverse)
    return a - a.div(b, rounding_mode="floor") * b

  def where(self:Tensor, x:Tensor|ConstType|sint, y:Tensor|ConstType|sint) -> Tensor:
    """
    Returns a tensor of elements selected from either `x` or `y`, depending on `self`.
    `output_i = x_i if self_i else y_i`.

    ```python exec="true" source="above" session="tensor" result="python"
    cond = Tensor([[True, True, False], [True, False, False]])
    print(cond.where(1, 3).numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    cond = Tensor.randn(2, 3)
    print(cond.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print((cond > 0).where(cond, -float("inf")).numpy())
    ```
    """
    if isinstance(x, Tensor): x, y = x._broadcasted(y)
    elif isinstance(y, Tensor): y, x = y._broadcasted(x)
    else: x, y = Tensor(x, self.device, requires_grad=False)._broadcasted(y)
    out_shape = _broadcast_shape(self.shape, x.shape)
    return self.cast(dtypes.bool)._broadcast_to(out_shape)._apply_uop(UOp.where, x._broadcast_to(out_shape), y._broadcast_to(out_shape))

  # ***** op wrappers *****

  # TODO: combine with UOps __floordiv__
  def __floordiv__(self, x): return self.div(x, rounding_mode="floor")
  def __rfloordiv__(self, x): return self.div(x, rounding_mode="floor", reverse=True)

  def __ifloordiv__(self, x) -> Tensor: return self.assign(self.__floordiv__(x))

  # unlike Tensors, UOps are immutable, so these don't go in mixin
  def __iadd__(self, x) -> Tensor: return self.assign(self.add(x)) # type: ignore[misc]
  def __isub__(self, x) -> Tensor: return self.assign(self.sub(x)) # type: ignore[misc]
  def __imul__(self, x) -> Tensor: return self.assign(self.mul(x)) # type: ignore[misc]
  def __itruediv__(self, x) -> Tensor: return self.assign(self.div(x)) # type: ignore[misc]
  def __ipow__(self, x) -> Tensor: return self.assign(self.pow(x)) # type: ignore[misc]
  def __iand__(self, x) -> Tensor: return self.assign(self.bitwise_and(x)) # type: ignore[misc]
  def __ior__(self, x) -> Tensor: return self.assign(self.bitwise_or(x)) # type: ignore[misc]
  def __ixor__(self, x) -> Tensor: return self.assign(self.bitwise_xor(x)) # type: ignore[misc]
  def __ilshift__(self, x) -> Tensor: return self.assign(self.lshift(x)) # type: ignore[misc]
  def __irshift__(self, x) -> Tensor: return self.assign(self.rshift(x)) # type: ignore[misc]
  def __imatmul__(self, x) -> Tensor: return self.assign(self.matmul(x)) # type: ignore[misc]

  def __eq__(self, x) -> Tensor: return self.eq(x)                      # type: ignore[override]

  # ***** encoding/decoding ops *****

  def decode_hevc_frame(self, frame_pos:Variable, shape:tuple[int,...], state:Tensor, ref_frames:list[Tensor]|None=None) -> Tensor:
    """
    Creates a Tensor by decoding an HEVC frame chunk.

    You must provide the output shape of the decoded data (`shape`), the HEVC context (`vstate`), and, if required by the chunk,
    the reference frames (`ref_frames`).
    """
    ref_frames = [x.contiguous() for x in ref_frames or []]
    assert frame_pos.op is Ops.BIND, "frame_pos must be a bound Variable"
    srcs = (out:=Tensor.empty(*shape, device=self.device, dtype=self.dtype), self.contiguous(), state.contiguous(), *ref_frames)
    fn = UOp(Ops.CUSTOM_FUNCTION, dtypes.void, src=(frame_pos.src[0], *[UOp.const(dtypes.int, s) for s in shape]), arg="encdec")
    return Tensor(out.uop.after(fn.call(*[s.uop for s in srcs], frame_pos)))

  # ***** functional nn ops *****

  def linear(self, weight:Tensor, bias:Tensor|None=None, dtype:DTypeLike|None=None) -> Tensor:
    """
    Applies a linear transformation to `self` using `weight` and `bias`.

    See: https://pytorch.org/docs/stable/generated/torch.nn.Linear.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[1, 2], [3, 4]])
    weight = Tensor([[1, 2], [3, 4]])
    bias = Tensor([1, 2])
    print(t.linear(weight, bias).numpy())
    ```
    """
    if dtype is not None: return self.cast(dtype).linear(weight.cast(dtype), bias.cast(dtype) if bias is not None else bias)
    x = self.mul(weight) if len(weight.shape) == 1 else self.dot(weight)
    return x.add(bias) if bias is not None else x

  def sequential(self, ll:list[Callable[[Tensor], Tensor]]) -> Tensor:
    """
    Applies a sequence of functions to `self` chaining the output of each function to the input of the next.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([1, 2, 3])
    print(t.sequential([lambda x: x * 2, lambda x: x + 1]).numpy())
    ```
    """
    return functools.reduce(lambda x,f: f(x), ll, self)

  def layernorm(self, axis:int|tuple[int,...]=-1, eps:float=1e-5) -> Tensor:
    """
    Applies Layer Normalization over a mini-batch of inputs.

    - Paper: https://arxiv.org/abs/1607.06450v1

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.randn(8, 10, 16) * 2 + 8
    print(t.mean().item(), t.std().item())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = t.layernorm()
    print(t.mean().item(), t.std().item())
    ```
    """
    y = (self - self.mean(axis, keepdim=True))
    return y.mul((y*y).mean(axis, keepdim=True).add(eps).rsqrt())

  def batchnorm(self, weight:Tensor|None, bias:Tensor|None, mean:Tensor, invstd:Tensor, axis:int|tuple[int, ...]=1) -> Tensor:
    """
    Applies Batch Normalization over a mini-batch of inputs.

    - Paper: https://arxiv.org/abs/1502.03167

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.randn(8, 4, 16, 16) * 2 + 8
    print(t.mean().item(), t.std().item())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = t.batchnorm(None, None, t.mean(axis=(0,2,3)), t.var(axis=(0,2,3)).add(1e-5).rsqrt())
    print(t.mean().item(), t.std().item())
    ```
    """
    axis_ = argfix(axis)
    shape = tuple(s if ax in axis_ else 1 for ax, s in enumerate(self.shape))
    x = self - mean.reshape(shape)
    if weight is not None: x = x * weight.reshape(shape)
    ret = x.mul(invstd.reshape(shape) if len(invstd.shape) == len(axis_) else invstd)
    return (ret + bias.reshape(shape)) if bias is not None else ret

  def dropout(self, p=0.5) -> Tensor:
    """
    Applies dropout to `self`.

    NOTE: dropout is only applied when `Tensor.training` is `True`.

    - Paper: https://jmlr.org/papers/v15/srivastava14a.html

    ```python exec="true" source="above" session="tensor" result="python"
    Tensor.manual_seed(42)
    t = Tensor.randn(2, 2)
    with Tensor.train():
      print(t.dropout().numpy())
    ```
    """
    if not 0 <= p <= 1: raise ValueError(f"{p=} is out of range [0, 1]")
    if not Tensor.training or p == 0: return self
    if p == 1: return self.zeros_like()
    return (Tensor.rand_like(self, requires_grad=False, dtype=dtypes.default_float, contiguous=False) >= p).contiguous().where(self, 0) / (1.0 - p)

  # helper function commonly used for indexing
  def _one_hot_along_dim(self:Tensor, num_classes:sint, dim:int=-1) -> Tensor:
    if not dtypes.is_int(self.dtype): raise RuntimeError(f"_one_hot_along_dim expects int index tensor, getting {self.dtype}")
    offset = self.ndim - self._resolve_dim(dim) - 1
    dt = dtypes.int64 if sint_to_uop(num_classes).overflows(dtypes.int32) else dtypes.int32
    return self == Tensor.arange(num_classes, dtype=dt, device=self.device, requires_grad=False).reshape((num_classes,) + (1,) * offset)

  def one_hot(self, num_classes:int=-1) -> Tensor:
    """
    Converts `self` to a one-hot tensor.

    `num_classes` defaults to -1, which means num_classes will be inferred as max(self) + 1.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([0, 1, 3, 3, 4])
    print(t.one_hot(5).numpy())
    ```
    """
    if not dtypes.is_int(self.dtype): raise RuntimeError(f"expect integer dtype, getting {self.dtype=}")
    if num_classes == -1: num_classes = int(self.max().item())+1
    return self[..., None]._one_hot_along_dim(num_classes).where(1, 0)

  def scaled_dot_product_attention(self, key:Tensor, value:Tensor, attn_mask:Tensor|None=None, dropout_p:float=0.0,
                                   is_causal:bool=False, enable_gqa:bool=False) -> Tensor:
    """
    Computes scaled dot-product attention.
    `self` is the query tensor, `key` is the key tensor, and `value` is the value tensor.

    - Paper: https://arxiv.org/abs/1706.03762v7

    ```python exec="true" source="above" session="tensor" result="python"
    q = Tensor.randn(2, 4, 8)
    k = Tensor.randn(2, 4, 8)
    v = Tensor.randn(2, 4, 8)
    print(q.scaled_dot_product_attention(k, v).numpy())
    ```
    """
    # GQA: https://docs.pytorch.org/docs/stable/generated/torch.nn.functional.scaled_dot_product_attention.html
    if enable_gqa:
      key = key.repeat_interleave(int(self.shape[-3] // key.shape[-3]), dim=-3)
      value = value.repeat_interleave(int(self.shape[-3] // value.shape[-3]), dim=-3)

    q = self
    qk = q.matmul(key.transpose(-2,-1), dtype=least_upper_dtype(q.dtype, key.dtype, dtypes.float32)) / math.sqrt(q.shape[-1])
    # handle attention mask
    if is_causal:
      if attn_mask is not None: raise RuntimeError("cannot set attn_mask when is_causal=True")
      attn_mask = qk.ones_like(requires_grad=False, dtype=dtypes.bool).tril()
    if attn_mask is not None:
      if attn_mask.dtype == dtypes.bool: attn_mask = attn_mask.where(0, -float("inf"))
      qk = qk + attn_mask
    return qk.cast(self.dtype).softmax(-1).dropout(dropout_p) @ value

  def _do_reduction(self, reduction:ReductionStr="mean") -> Tensor:
    if reduction == "none": return self
    if reduction == "sum": return self.sum()
    if reduction == "mean": return self.mean()
    raise ValueError(f"{reduction=} must be one of {get_args(ReductionStr)}")

  def binary_crossentropy(self, Y:Tensor, reduction:ReductionStr="mean") -> Tensor:
    """
    Computes the binary cross-entropy loss between `self` and `Y`.

    See: https://pytorch.org/docs/stable/generated/torch.nn.BCELoss.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([0.1, 0.9, 0.2])
    Y = Tensor([0, 1, 0])
    print(t.binary_crossentropy(Y).item())
    ```
    """
    return (-Y*self.log() - (1-Y)*(1-self).log())._do_reduction(reduction)

  def binary_crossentropy_logits(self, Y:Tensor, reduction:ReductionStr="mean", pos_weight:Tensor|None=None) -> Tensor:
    """
    Computes the binary cross-entropy loss between `self` and `Y` where `self` is logits.

    See: https://pytorch.org/docs/stable/generated/torch.nn.BCEWithLogitsLoss.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([-1, 2, -3])
    Y = Tensor([0, 1, 0])
    print(t.binary_crossentropy_logits(Y).item())
    ```
    """
    log_p, log_1_minus_p = self.logsigmoid(), (-self).logsigmoid()
    return (-((1 if pos_weight is None else pos_weight) * Y * log_p + (1-Y) * log_1_minus_p))._do_reduction(reduction)

  def sparse_categorical_crossentropy(self, Y:Tensor, ignore_index:int=-1, label_smoothing=0.0, reduction:ReductionStr="mean") -> Tensor:
    """
    Computes the sparse categorical cross-entropy loss between `self` and `Y`.

    NOTE: `self` is logits and `Y` is the target labels.
    NOTE: unlike PyTorch, this function expects the class axis to be -1

    See: https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[-1, 2, -3], [1, -2, 3]])
    Y = Tensor([1, 2])
    print(t.sparse_categorical_crossentropy(Y).item())
    ```
    """
    assert 0.0 <= label_smoothing <= 1.0, "label_smoothing must be in [0.0, 1.0]"
    log_probs = self.log_softmax()
    loss_mask = (Y != ignore_index) if ignore_index != -1 else Y.ones_like(dtype=dtypes.bool)
    y = Y.to(self.device).unsqueeze(-1)._one_hot_along_dim(self.shape[-1], dim=-1) * loss_mask.unsqueeze(-1)
    smoothing = label_smoothing * (log_probs.mean(-1) * loss_mask)
    unreduced = ((1 - label_smoothing) * (log_probs * y).sum(-1) + smoothing)
    return -unreduced.sum() / loss_mask.sum() if reduction == "mean" else -unreduced._do_reduction(reduction)

  def cross_entropy(self, Y:Tensor, reduction:ReductionStr="mean", label_smoothing:float=0.0) -> Tensor:
    """
    Computes the cross entropy loss between input logits and target.

    NOTE: `self` are logits and `Y` are the target labels or class probabilities.

    See: https://pytorch.org/docs/stable/generated/torch.nn.functional.cross_entropy.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[-1, 2, -3], [1, -2, 3]])
    Y = Tensor([1, 2])
    print(t.cross_entropy(Y).item())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[-1, 2, -3], [1, -2, 3]])
    Y = Tensor([1, 2])
    print(t.cross_entropy(Y, reduction='none').numpy())
    ```
    """
    assert 0.0 <= label_smoothing <= 1.0, "label_smoothing must be in [0.0, 1.0]"
    classes_dim = 0 if self.ndim == 1 else 1
    if self.shape != Y.shape:
      if self.max(classes_dim).shape != Y.shape: raise RuntimeError(f"shape mismatch: {self.shape=}, {Y.shape=}")
      Y = Y.unsqueeze(classes_dim)._one_hot_along_dim(num_classes=self.shape[classes_dim], dim=classes_dim)
    Y = (1 - label_smoothing)*Y + label_smoothing / int(Y.shape[classes_dim])
    return -self.log_softmax(classes_dim).mul(Y).sum(classes_dim)._do_reduction(reduction)

  def nll_loss(self, Y:Tensor, weight:Tensor|None=None, ignore_index:int|None=None, reduction:ReductionStr="mean") -> Tensor:
    """
    Computes the negative log likelihood loss between log-probabilities and target labels.

    NOTE: `self` is log-probabilities and `Y` is the Y labels or class probabilities.

    See: https://pytorch.org/docs/stable/generated/torch.nn.functional.nll_loss.html

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[-1, 2, -3], [1, -2, 3]])
    Y = Tensor([1, 2])
    print(t.log_softmax().nll_loss(Y).item())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[-1, 2, -3], [1, -2, 3]])
    Y = Tensor([1, 2])
    print(t.log_softmax().nll_loss(Y, reduction='none').numpy())
    ```
    """
    weight = Y.ones_like(requires_grad=False) if weight is None else weight[Y]
    masked_weight = weight if ignore_index is None else weight * (Y != ignore_index)
    nll = -self.gather(1, Y.unsqueeze(1)).squeeze(1) * masked_weight
    return nll.sum() / masked_weight.sum() if reduction == "mean" else nll._do_reduction(reduction)

  def newton_schulz(self, steps:int, params:tuple[int, ...], eps:float=1.0e-7) -> Tensor:
    """
    Performs the newton-schulz algorithm for odd polynomials. The degree of the odd polynomial depends on the number of params.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor.randn(4, 4)
    print(t.newton_schulz(steps=5, params=(2,-1.5,0.5)).numpy())
    ```
    """
    assert self.ndim > 1, "NS only works for two or more dims"
    if self.shape[-2] > self.shape[-1]: return self.transpose(-2, -1).newton_schulz(steps, params, eps).transpose(-2, -1)
    G = self / (self.square().sum(axis=(-2, -1), keepdim=True).sqrt() + eps)
    for _ in range(steps):
      G = cast(Tensor, sum(p * functools.reduce(lambda x, y: (y @ y.transpose(-2, -1)) @ x, [G]*i, G) for i,p in enumerate(params)))
    return G

  def qr(self) -> tuple[Tensor, Tensor]:
    assert self.ndim > 1, f"expected two or more dimensions, got {self.ndim}"
    b_shape, m, n = self.shape[:-2], int(self.shape[-2]), int(self.shape[-1])
    R = self.clone()
    Q = Tensor.eye(m, dtype=self.dtype).reshape((1,) * len(b_shape) + (m, m)).expand(b_shape + (m, m))
    for i in range(min(m, n)):
      x = R[..., i:m, i]
      norm = x.square().sum(-1).sqrt()
      s = (x[..., 0] != 0).where(-x[..., 0].sign(), -1)
      u1 = x[..., 0] - s * norm
      w = x.unsqueeze(-1) / (norm != 0).where(u1, 1).reshape(b_shape + (1, 1))
      w[..., 0, 0] = 1
      tau = (-s * u1 / (norm != 0).where(norm, 1)).reshape(b_shape + (1, 1))
      tau = (norm != 0).reshape(b_shape + (1, 1)).where(tau, 0)
      R[..., i:m, :] = R[..., i:m, :] - (w * tau) @ (w.transpose(-2, -1) @ R[..., i:m, :])
      Q[..., :, i:m] = Q[..., :, i:m] - (Q[..., :, i:m] @ w) @ (tau * w).transpose(-2, -1)
    return Q,R

  def svd(self, full_matrices = True) -> tuple[Tensor, Tensor, Tensor]:
    #partial implementation of https://www.netlib.org/lapack/lawnspdf/lawn169.pdf , pg 26
    assert self.ndim > 1, f"expected two or more dimensions, got {self.ndim}"
    b_shape, m, n = self.shape[:-2], int(self.shape[-2]), int(self.shape[-1])
    #preprocess the matrix
    Q, R = (self.qr() if m >= n else self.transpose(-2, -1).qr())
    num, q_num = min(m, n), max(m, n)
    # TODO: codegen infinite loop without contiguous
    U = R.shrink(tuple([None] * len(b_shape) + [(0, num), (0, num)])).contiguous()
    V = Tensor.eye(num, dtype=self.dtype).reshape((1,) * len(b_shape) + (num, num)).expand(b_shape + (num, num)).contiguous()
    #prepare round robin pairing
    permute, inverse_permute = Tensor.arange(0, num, dtype=dtypes.int), Tensor.zeros(num, dtype=dtypes.int)
    permute[num//2:num] = permute[num//2:num].flip(0)
    inverse_permute[permute] = Tensor.arange(num, dtype=dtypes.int)
    def one_round_jacobi(U, V,permute,inverse_permute):
      #pair all the columns
      V_permuted, runoff_V = (V[..., permute].split(num - 1, -1)) if num % 2 == 1 else (V[..., permute], None)
      V_left, V_right = V_permuted.split(num//2, -1)
      U_permuted, runoff_U = (U[..., permute].split(num - 1, -1)) if num % 2 == 1 else (U[..., permute], None)
      U_left, U_right = U_permuted.split(num//2, -1)
      #compute the jacobi rotations for each pairing
      gamma = (U_left * U_right).sum(-2).reshape(b_shape + (1, num//2))
      alpha, beta = U_permuted.square().sum(-2).unsqueeze(-2).split(num//2, -1)
      rot = gamma != 0
      tau = (beta - alpha) / (2 * rot.where(gamma, 1))
      t = (tau != 0).where(tau.sign(), 1) / (tau.abs() + (1 + tau.square()).sqrt())
      t = rot.where(t, 0)
      c = 1 / (1 + t.square()).sqrt()
      s = c * t
      #apply the rotations
      U_left, U_right = c * U_left - s * U_right, s * U_left + c * U_right
      U = U_left.cat(U_right.cat(runoff_U, dim = -1) if num % 2 == 1 else U_right, dim = -1)[..., inverse_permute]
      V_left, V_right = c * V_left - s * V_right, s * V_left + c * V_right
      V = V_left.cat(V_right.cat(runoff_V, dim = -1) if num % 2 == 1 else V_right, dim = -1)[..., inverse_permute]
      #prepare the next round robin pairings
      if num % 2 == 1: permute = ((permute - 1) % num)
      else: permute = permute[0].reshape(1).cat(((permute[1:num] - 2) % (num - 1)) + 1)
      inverse_permute = inverse_permute.scatter(0,permute,Tensor.arange(num,dtype=dtypes.int32))
      return U, V, permute, inverse_permute
    max_iterations, iterations_per_round = 1, int(num * math.log2(num) * 2 + 2)#sorta heuristic, most use num*log2(num)
    for _ in range(max_iterations * iterations_per_round): U, V, permute, inverse_permute = one_round_jacobi(U, V, permute, inverse_permute)
    #extract singular values and sort. construct U from Q
    S, indices = U.square().sum(-2).sqrt().sort(dim = -1, descending=True)
    new_indices = indices.reshape(b_shape + (1, num)).expand(b_shape + (num, num))
    U = U.gather(-1, new_indices) / (S != 0).where(S, 1).unsqueeze(-2)
    V = V.gather(-1, new_indices)

    padded_u = Tensor.eye(q_num, dtype=U.dtype).reshape((1,) * len(b_shape) + (q_num, q_num)).expand(b_shape + (q_num, q_num))
    padded_u[..., 0:num, 0:num] = U
    U = Q @ padded_u
    if not full_matrices: U, V = U[..., 0:num], V[..., 0:num]
    return (U, S, V.transpose(-2,-1)) if m >= n else (V, S, U.transpose(-2, -1))

  # ***** Tensor Properties *****

  def nbytes(self) -> int:
    """
    Returns the total number of bytes of all elements in the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([8, 9], dtype=dtypes.float)
    print(t.nbytes())
    ```
    """
    return int(self.numel()) * self.element_size()

  def size(self, dim:int|None=None) -> sint|tuple[sint, ...]:
    """
    Returns the size of the tensor. If `dim` is specified, return the length along dimension `dim`. Otherwise return the shape of the tensor.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([[4, 5, 6], [7, 8, 9]])
    print(t.size())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    print(t.size(dim=1))
    ```
    """
    return self.shape if dim is None else self.shape[dim]

  # ***** cast ops *****

  def cast(self, dtype:DTypeLike) -> Tensor:
    """
    Casts `self` to the given `dtype`.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([-1, 2.5, 3], dtype=dtypes.float)
    print(t.dtype, t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = t.cast(dtypes.int32)
    print(t.dtype, t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = t.cast(dtypes.uint8)
    print(t.dtype, t.numpy())
    ```
    """
    return self if self.dtype == (dt:=to_dtype(dtype)) else self._apply_uop(UOp.cast, dtype=dt)

  def bitcast(self, dtype:DTypeLike) -> Tensor:
    """
    Bitcasts `self` to the given `dtype` of the same itemsize.

    `self` must not require a gradient.

    ```python exec="true" source="above" session="tensor" result="python"
    t = Tensor([-1, 2, 3], dtype=dtypes.int32)
    print(t.dtype, t.numpy())
    ```
    ```python exec="true" source="above" session="tensor" result="python"
    t = t.bitcast(dtypes.uint32)
    print(t.dtype, t.numpy())
    ```
    """
    if self.requires_grad: raise RuntimeError("can't backprop through bitcast")
    dt = to_dtype(dtype)
    if (ns:=dt.itemsize) != (os:=self.dtype.itemsize) and (self.shape[-1]*os) % ns != 0: raise RuntimeError("unsupported size in bitcast")
    if (not isinstance(self.device, str) or not self.device.startswith("DISK")) and ns != os:
      new_uint, old_uint = to_dtype(f"uint{8*ns}"), to_dtype(f"uint{8*os}")
      tmp = self.bitcast(old_uint)
      if ns > os:
        tmp = tmp.reshape(self.shape[:-1] + (self.shape[-1]//(rate := ns//os), rate))
        nones = (None,) * (tmp.ndim - 1)
        return functools.reduce(Tensor.add, (tmp.shrink(nones + ((i, i+1),)).cast(new_uint)<<8*i*os for i in range(rate))).squeeze(-1).bitcast(dtype)
      return Tensor.stack(*(tmp>>8*i*ns for i in range(os//ns)), dim=-1).flatten(-2).cast(new_uint).bitcast(dtype)
    return self._apply_uop(UOp.bitcast, dtype=dt) if self.dtype != dt else self

  # *** image Tensor function replacements ***

  def image_dot(self, w:Tensor, dtype:DTypeLike|None=None) -> Tensor:
    # NOTE: we use a 1x1 conv2d to do the matmul. mxk @ kxn = (1,k,m,1).conv2d(n,k,1,1)
    if not (self.ndim > 0 and w.ndim > 0): raise RuntimeError(f"both tensors need to be at least 1D, got {self.ndim=}, {w.ndim=}")
    if self.shape[-1] != w.shape[-min(w.ndim, 2)]: raise RuntimeError(f"cannot image_dot {self.shape} and {w.shape}")

    bs, groups, cin, cout = prod(self.shape[0:-2]), prod(w.shape[0:-2]), w.shape[-2], w.shape[-1]
    out_shape_t = self.shape[0:-2] + (cout,-1) if len(self.shape) > 1 else (cout,)

    # NOTE: with NHWC we can remove the transposes
    # bs x groups*cin x H x W
    cx = self.transpose(self.ndim-1, self.ndim-2).reshape(bs//groups, groups*cin, -1, 1)
    # groups*cout x cin x H, W
    cw = w.transpose(w.ndim-1, w.ndim-2).reshape(groups*cout, cin, 1, 1)
    return cx.image_conv2d(cw, groups=groups, dtype=dtype).reshape(out_shape_t).transpose(self.ndim-1, self.ndim-2)

  def image_conv2d(self, weight:Tensor, bias:Tensor|None=None, groups=1, stride=1, dilation=1, padding=0, dtype=None) -> Tensor:
    dtsz = 2 if FLOAT16 else 4

    (bs,_,iy,ix), (cout,cin,H,W) = self.shape, weight.shape
    x, w = self, weight.reshape(groups, (rcout := cout//groups), cin, H, W)

    padding_neg, padding_pos = [min(0, p) for p in self._resolve_pool_pads(padding, 2)], [max(0, p) for p in self._resolve_pool_pads(padding, 2)]
    x = x.pad(padding_neg)
    iy, ix = x.shape[2:]

    # hack for non multiples of 4 on cin
    if cin % 4 != 0 and not (cin == 1 and groups%4 == 0):
      x = x.reshape(bs, groups, cin, iy, ix)   # do this always?
      added_input_channels = 4 - (cin % 4)
      cin = cin + added_input_channels
      w = w.pad_to(None, None, cin, None, None)
      x = x.pad_to(None, None, cin, None, None).reshape(bs, groups*cin, iy, ix)

    # hack for non multiples of 4 on rcout
    added_output_channels = 0
    if rcout % 4 != 0 and not (rcout == 1 and groups%4 == 0):
      added_output_channels = 4 - (rcout % 4)
      rcout += added_output_channels
      cout = groups * rcout
      w = w.pad_to(None, rcout, None, None, None)

    # packed (note: flipping bs and iy would make the auto-padding work)
    x = x.permute(0,2,3,1)
    cin_last = iy == 1 and ix == 1
    if cin == 1: w = w.reshape(cout//4,4,H,W).permute(0,2,3,1)
    elif cin_last: w = w.reshape(cout//4,4,cin//4,4,H,W).permute(0,4,2,5,1,3)
    else: w = w.reshape(cout//4,4,cin//4,4,H,W).permute(0,4,2,5,3,1)

    # contiguous creates the image, and early realize static weights (TODO: test for the static weight)
    def is_pow2(v): return v > 0 and v & (v - 1) == 0
    # pad dimension i to amt with invalids
    def ipad(t, i, amt):
      shape = (None,)*i + (amt,) + (None,)*(t.ndim-i-1)
      return Tensor(True, device=t.device).expand(t.shape).pad_to(shape).where(t.pad_to(shape), Invalid) if amt != t.shape[i] else t

    # align a dimension, use at to specify the dimension to pad in, defaults to first
    def pad_align(t, dim, at=None, force=False):
      # align to 64 pixels when height is real, otherwise 64 bytes is sufficient
      align = (64 // dtsz) if prod(t.shape[:dim]) == 1 or prod(t.shape) < 16384 * 4 else 256
      return ipad(t, at:=at or dim, round_up(t.shape[at] + int(force), align // math.gcd(prod(t.shape[dim:]) // t.shape[at], align)))

    # bank conflicts
    if cin >= 8 and is_pow2(cin // 4):
      x, w = pad_align(x.reshape(bs, iy, ix, groups, cin // 4, 4), 2, at=4, force=True), pad_align(w, 1, at=2, force=True)
    else: x, w = pad_align(x, 2), pad_align(w, 1)

    if FLOAT16: x, w = x.cast(dtypes.half).contiguous().cast(dtypes.float), w.cast(dtypes.half).contiguous().cast(dtypes.float)
    else: x, w = x.contiguous(), w.contiguous()

    # undo alignment hacks
    if cin >= 8 and is_pow2(cin // 4): x, w = x[:, :, :ix, :, :cin // 4, :], w[:, :H, :cin // 4, ...]
    else: x, w = x[:, :, :ix, :], w[:, :H, ...]

    # expand out
    rcin_hi, rcin_lo = (cin//4, 4) if cin >= 4 else (1, 1)
    group_shape, rcout_expand = (groups//4, 4) if cin == 1 else (groups, 1), (rcout//4, 4) if rcout >= 4 else (1, 1)
    x = x.reshape(bs, iy, -1, groups, rcin_hi, rcin_lo)
    if cin_last: w = w.reshape(cout//4, H, rcin_hi, W, 4, rcin_lo)
    else: w = w.reshape(cout//4, H, rcin_hi, W, rcin_lo, 4).permute(0,1,2,3,5,4)

    # prepare input
    x = x.permute(0,3,4,5,1,2).pad(padding_pos)._pool((H,W), stride, dilation)# -> (bs, groups, rcin_hi, rcin_lo, oy, ox, H, W)
    x = x.permute(0,4,5,1,2,3,6,7).reshape(bs, (oy := x.shape[4]), (ox := x.shape[5]), *group_shape, 1, 1, rcin_hi, rcin_lo, H, W)

    # prepare weights
    w = w.permute(0,4,2,5,1,3).reshape((1, 1, 1, *group_shape, *rcout_expand, rcin_hi, rcin_lo, H, W))

    added_ox = 0
    assert isinstance(ox, int) and isinstance(cout, int)
    if (ox * cout) % (64 // dtsz):
      added_ox = round_up(ox, 64 // (dtsz * math.gcd(cout, 64 // dtsz))) - ox
      ox = ox + added_ox
      x = x.pad_to(None, None, ox, None, None, None, None, None, None, None, None)

    # the conv!
    ret = (x*w).cast(dtypes.float32).sum((-4, -3, -2, -1), dtype=dtype)

    if added_ox:
      ret = ret.reshape(bs, oy, ox, groups, rcout)[:, :, :-added_ox, ...]
      ox = ox - added_ox

    # undo hack for non multiples of 4 on C.rcout
    if added_output_channels != 0:
      ret = ret.reshape(bs, oy, ox, groups, rcout)[:, :, :, :, :-added_output_channels]
      cout = groups * (rcout - added_output_channels)

    # NCHW output
    ret = ret.reshape(bs, oy, ox, cout).permute(0,3,1,2)
    return ret if bias is None else ret.add(bias.reshape(1, -1, 1, 1))

P = ParamSpec("P")
T = TypeVar("T")

# this tracks the tensor.py METADATA, contextvars.ContextVar was switched to this due to thread safety issues
class _ContextVar(Generic[T]):
  def __init__(self, default:T): self.state:T = default
  def get(self) -> T: return self.state
  def set(self, x:T) -> T:
    ret, self.state = self.state, x
    return ret
_METADATA: _ContextVar[Metadata|None] = _ContextVar(default=None)

def _metadata_wrapper(fn: Callable[P, T]) -> Callable[P, T]:
  def _wrapper(*args: P.args, **kwargs: P.kwargs) -> T:
    if TRACEMETA < 1 or _METADATA.get() is not None: return fn(*args, **kwargs)

    if TRACEMETA >= 2:
      caller_frame = sys._getframe(frame := 1)
      caller_module = caller_frame.f_globals.get("__name__", None)
      caller_func = caller_frame.f_code.co_name
      if caller_module is None: return fn(*args, **kwargs)

      # if its called from nn we want to step up frames until we are out of nn
      while caller_module.startswith("tinygrad.nn") and "optim" not in caller_module:
        caller_frame = sys._getframe(frame := frame + 1)
        caller_module = caller_frame.f_globals.get("__name__", None)
        if caller_module is None: return fn(*args, **kwargs)

      # if its called from a lambda in tinygrad we want to look two more frames up
      if caller_module.startswith("tinygrad") and caller_func == "<lambda>": caller_frame = sys._getframe(frame := frame + 2)
      caller_module = caller_frame.f_globals.get("__name__", None)
      if caller_module is None: return fn(*args, **kwargs)
      caller_func = caller_frame.f_code.co_name
      caller_lineno = caller_frame.f_lineno

      caller = f"{caller_module}:{caller_lineno}::{caller_func}"
    else: caller = ""

    token = _METADATA.set(Metadata(name=fn.__name__, caller=caller))
    with cpu_profile(TracingKey(fn.__name__), "USER"):
      ret = fn(*args, **kwargs)
    _METADATA.set(token)
    return ret
  return _wrapper

if TRACEMETA >= 1:
  for name, fn in inspect.getmembers(Tensor, inspect.isfunction):
    if name in ["__class__", "__init__", "__new__", "__repr__", "backward", "sequential", "gradient"]: continue
    setattr(Tensor, name, functools.wraps(fn)(_metadata_wrapper(fn)))