tinygrab/tinygrad/tensor.py

# inspired by https://github.com/karpathy/micrograd/blob/master/micrograd/engine.py
from __future__ import annotations
import time
from functools import partialmethod, reduce
from itertools import accumulate, filterfalse
import operator
import numpy as np
from typing import List, Tuple, Callable, Optional, ClassVar, Type, Union, Sequence, cast
from tinygrad.helpers import ImageDType, argfix, make_pair, getenv, IMAGE, DEBUG, flatten, DType, dtypes
from math import ceil, pi, prod, sqrt, log, cos, copysign
from tinygrad.lazy import Device, LazyBuffer
from tinygrad.ops import LoadOps

# An instantiation of the Function is the Context
class Function:
  def __init__(self, device:str, *tensors:Tensor):
    self.device = device
    self.needs_input_grad = [t.requires_grad for t in tensors]
    self.requires_grad = True if any(self.needs_input_grad) else None if None in self.needs_input_grad else False
    if self.requires_grad: self.parents = tensors

  def forward(self, *args, **kwargs): raise NotImplementedError(f"forward not implemented for {type(self)}")
  def backward(self, *args, **kwargs): raise RuntimeError(f"backward not implemented for {type(self)}")

  @classmethod
  def apply(fxn:Type[Function], *x:Tensor, **kwargs) -> Tensor:
    ctx = fxn(x[0].device, *x)
    ret = Tensor(ctx.forward(*[t.lazydata for t in x], **kwargs), device=ctx.device, requires_grad=ctx.requires_grad)
    if ctx.requires_grad and not Tensor.no_grad: ret._ctx = ctx    # used by autograd engine
    return ret

import tinygrad.mlops as mlops

# **** start with two base classes, Tensor and Function ****

class Tensor:
  __slots__ = "lazydata", "requires_grad", "grad", "_ctx"
  __deletable__ = ('_ctx',)
  training: ClassVar[bool] = False
  no_grad: ClassVar[bool] = False
  default_type: ClassVar[DType] = dtypes.float32

  def __init__(self, data:Union[int, float, list, LazyBuffer, np.ndarray], device:Optional[str]=None, dtype:Optional[DType]=None, requires_grad:Optional[bool]=None):
    assert dtype is None or isinstance(dtype, DType), f"invalid dtype {dtype}"
    device = Device.canonicalize(device)
    # tensors have gradients, buffers do not
    self.grad: Optional[Tensor] = 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: Optional[bool] = requires_grad

    # internal variables used for autograd graph construction
    self._ctx: Optional[Function] = None
    if data.__class__ is LazyBuffer:
      data = cast(LazyBuffer, data) # NOTE: this is a noop, it makes mypy happy
      assert dtype is None or dtype == data.dtype, "dtype doesn't match, and casting isn't supported"
      self.lazydata = data if data.device == device else LazyBuffer.loadop(LoadOps.FROM, data.shape, data.dtype, device, src=data)
      return

    if isinstance(data, (int, float)):
      self.lazydata = LazyBuffer.loadop(LoadOps.CONST, tuple(), dtype or Tensor.default_type, device, data)
      return

    if data.__class__ is list:
      data = np.array(data, dtype=(dtype or Tensor.default_type).np)

    if data.__class__ is np.ndarray:
      data = cast(np.ndarray, data)
      if data.size == 1: # constant fold
        self.lazydata = LazyBuffer.loadop(LoadOps.CONST, tuple(), dtypes.from_np(data.dtype), device, data.flat[0]).reshape(data.shape)
      else:
        data = LazyBuffer.fromCPU(data)
        self.lazydata = data if data.device == device else LazyBuffer.loadop(LoadOps.FROM, data.shape, data.dtype, device, src=data)
      return

    raise RuntimeError(f"can't create Tensor from {data}")

  def __repr__(self):
    return f"<Tensor {self.lazydata!r} on {self.device} with grad {(self.grad.lazydata if self.grad else None)!r}>"

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

  @property
  def device(self) -> str: return self.lazydata.device

  @property
  def shape(self) -> Tuple[int, ...]: return self.lazydata.shape

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

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

  def realize(self) -> Tensor:
    self.lazydata.realize()
    return self

  def assign(self, x) -> Tensor:
    # TODO: this is a hack for writing to DISK
    if self.device.startswith("DISK"):
      if x.__class__ is not Tensor: x = Tensor(x, device="CPU", dtype=self.dtype)
      self.lazydata.realize().realized._copyin(x.numpy())  # type: ignore
      return self
    if x.__class__ is not Tensor: x = Tensor(x, device=self.device, dtype=self.dtype)
    assert self.shape == x.shape and self.device == x.device, f"assign shape mismatch {self.shape} != {x.shape} or device mismatch {self.device} != {x.device}"
    assert not x.requires_grad  # self requires_grad is okay?
    if DEBUG >= 4: print(f"assign {self.lazydata} <- {x.lazydata}")
    if self.lazydata.realized is not None and not getenv("DISALLOW_ASSIGN"): x.lazydata.output_buffer = self.lazydata.realized
    self.lazydata = x.lazydata
    return self

  def detach(self): return Tensor(self.lazydata, device=self.device, requires_grad=False)
  def numpy(self) -> np.ndarray: return self.lazydata.toCPU()

  # TODO: if things are realized this won't work
  def to_(self, device:str):
    assert self.lazydata.realized is None
    self.lazydata.device = device
    if self.grad: self.grad.to_(device)

  def to(self, device:str):
    ret = Tensor(self.lazydata, device)
    if self.grad: ret.grad = self.grad.to(device)
    return ret

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

  @staticmethod
  def _loadop(op, sz, device:Optional[str]=None, dtype:Optional[DType]=None, arg=None, **kwargs):
    return Tensor(LazyBuffer.loadop(op, [sz], Tensor.default_type if dtype is None else dtype, Device.canonicalize(device), arg), dtype=dtype, device=device, **kwargs)

  @staticmethod
  def empty(*shape, **kwargs): return Tensor._loadop(LoadOps.EMPTY, prod(shape), **kwargs).reshape(shape)

  _seed: int = int(time.time())
  @staticmethod
  def manual_seed(seed=0): Tensor._seed = seed

  @staticmethod
  def rand(*shape, **kwargs):
    Tensor._seed += 1
    return Tensor._loadop(LoadOps.RAND, prod(shape), arg=Tensor._seed, **kwargs).reshape(shape)

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

  @staticmethod
  def full(shape:Tuple[int, ...], fill_value, **kwargs): return Tensor(fill_value, **kwargs).reshape([1]*len(new_shape := argfix(shape))).expand(new_shape)

  @staticmethod
  def zeros(*shape, **kwargs): return Tensor.full(argfix(*shape), 0, **kwargs)

  @staticmethod
  def ones(*shape, **kwargs): return Tensor.full(argfix(*shape), 1, **kwargs)

  @staticmethod
  def arange(stop, start=0, step=1, **kwargs): return Tensor.full((ceil((stop-start)/step),), step, **kwargs).cumsum() + (start - step)

  @staticmethod
  def full_like(tensor, fill_value, dtype:Optional[DType]=None, **kwargs):
    return Tensor.full(tensor.shape, fill_value=fill_value, dtype=tensor.dtype if dtype is None else dtype, **kwargs)

  @staticmethod
  def zeros_like(tensor, **kwargs): return Tensor.full_like(tensor, 0, **kwargs)

  @staticmethod
  def ones_like(tensor, **kwargs): return Tensor.full_like(tensor, 1, **kwargs)

  @staticmethod
  def eye(dim, **kwargs): return Tensor([1], **kwargs).slice(((0,dim+1),)).reshape(1, dim+1).expand(dim, dim+1).reshape(dim*(dim+1)).slice(((0,dim*dim),)).reshape(dim, dim)

  def where(self:Tensor, input_:Union[Tensor, float], other:Union[Tensor, float]):
    cond = (self != 0.0)
    return cond * input_ + (1.0 - cond) * other

  # ***** rng hlops *****

  @staticmethod
  def randn(*shape, dtype:Optional[DType]=None, **kwargs) -> Tensor:
    # https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
    src = Tensor.rand(2, *shape, **kwargs)
    return src[0].mul(2*pi).cos().mul((1 - src[1]).log().mul(-2).sqrt()).cast(Tensor.default_type if dtype is None else dtype)

  @staticmethod
  def uniform(*shape, low=-1.0, high=1.0, **kwargs) -> Tensor: return ((high-low) * Tensor.rand(*shape, **kwargs)) + low

  @staticmethod
  def scaled_uniform(*shape, **kwargs) -> Tensor: return Tensor.uniform(*shape, **kwargs).mul(prod(shape)**-0.5)

  # https://www.tensorflow.org/api_docs/python/tf/keras/initializers/GlorotUniform
  @staticmethod
  def glorot_uniform(*shape, **kwargs) -> Tensor: return Tensor.uniform(*shape, **kwargs).mul((6/(shape[0]+prod(shape[1:])))**0.5)

  # https://pytorch.org/docs/stable/_modules/torch/nn/init.html#kaiming_uniform_
  @staticmethod
  def kaiming_uniform(*shape, a:float = 0.01, **kwargs) -> Tensor:
    bound = sqrt(3.0) * sqrt(2.0 / (1 + a ** 2)) / sqrt(prod(shape[1:]))
    return Tensor.uniform(*shape, low=-bound, high=bound, **kwargs)

  # ***** toposort and backward pass *****
  def deepwalk(self):
    def _deepwalk(node, visited, nodes):
      visited.add(node)
      if node._ctx:
        for i in node._ctx.parents:
          if i not in visited: _deepwalk(i, visited, nodes)
        nodes.append(node)
      return nodes
    return _deepwalk(self, set(), [])

  def backward(self):
    assert self.shape == tuple(), f"backward can only be called for scalar tensors, but it has shape {self.shape})"

    # fill in the first grad with one. don't use Tensor.ones because we don't need contiguous
    # this is "implicit gradient creation"
    self.grad = Tensor(1, device=self.device, requires_grad=False)

    for t0 in reversed(self.deepwalk()):
      if not t0.requires_grad:
        del t0._ctx # TODO: does it help to delete this here ever?
        continue
      assert (t0.grad is not None)
      grads = t0._ctx.backward(t0.grad.lazydata)
      grads = [Tensor(g, device=self.device, requires_grad=False) if g is not None else None
        for g in ([grads] if len(t0._ctx.parents) == 1 else grads)]
      for t, g in zip(t0._ctx.parents, grads):
        if g is not None and t.requires_grad:
          assert g.shape == t.shape, f"grad shape must match tensor shape, {g.shape!r} != {t.shape!r}"
          t.grad = g if t.grad is None else (t.grad + g)
      del t0._ctx

  # ***** movement mlops *****
  def reshape(self, shape, *args) -> Tensor:
    new_shape = argfix(shape, *args)
    assert 0 not in new_shape, f"zeros not allowed in shape {new_shape}"
    return mlops.Reshape.apply(self, shape=tuple([-prod(self.shape) // prod(new_shape) if s == -1 else s for s in new_shape]))
  def expand(self, shape, *args) -> Tensor: return mlops.Expand.apply(self, shape=tuple([x if x != -1 else s for s,x in zip(self.shape, argfix(shape, *args))]))
  def permute(self, order, *args) -> Tensor: return mlops.Permute.apply(self, order=argfix(order, *args))
  def flip(self, axis, *args) -> Tensor: return mlops.Flip.apply(self, axis=[x if x >= 0 else x+len(self.shape) for x in argfix(axis, *args)])
  def pad(self, arg:Tuple[Tuple[int, int], ...]) -> Tensor: return mlops.Pad.apply(self, arg=arg) if any(x != (0,0) for x in arg) else self
  def shrink(self, arg:Tuple[Tuple[int, int], ...]) -> Tensor: return mlops.Shrink.apply(self, arg=arg) if any(x != (0,s) for x,s in zip(arg, self.shape)) else self

  # ***** movement hlops *****

  # NOTE: using slice is discouraged and things should migrate to pad and shrink
  def slice(self, arg:Sequence[Optional[Tuple[int, int]]]) -> Tensor:
    arg_ = tuple([a if a is not None else (0,s) for s,a in zip(self.shape, arg)])
    padding = tuple([(max(0, -p[0]), max(0, p[1]-self.shape[i])) for i,p in enumerate(arg_)])
    return self.pad(padding).shrink(tuple([(p[0] + padding[i][0], p[1] + padding[i][0]) for i,p in enumerate(arg_)]))

  # - Negative indices are taken relative to the end of the sequence, so X[-2] returns the 2nd-to-last element
  # - A slice i:j returns the elements with indices in [i, j)
  #    - If omitted, i and j will default to 0 and N, respectively, where N is the length of the sequence
  #    - Negative values for i and j are taken relative to the end of the sequence
  #    - Both i and j will be clamped to the range (-N, N], where N in the length of the sequence
  # - Indexing with np.newaxis or None on a given axis will add a new dimension of size one before that axis
  # - Empty slices are not allowed (tensors with 0s in shape have to be supported first, for all backends).
  # - For a slice [i:j:k] finding the correct indices is delegated to slice.indices(len).
  # - Strides > 1 and < 0 are now allowed!:
  #    - This works by applying Shrink -> [[Flip -> ] Pad -> Reshape -> Shrink] -> Reshape (ops in brackets are optional)
  #    - Idea of stride < 0 support:
  #        - Do the slice first, flip the axes were slice.step is negative, do slice.step -> -slice.step. Go to steps below.
  #    - Idea of stride `s` > 1 support (Pad -> Reshape -> Shrink):
  #        - Instead of doing [::s] on axis [dim_sz], do [:, 0] on axes [dim_sz_padded // s, s].
  #        - So pad dim_sz with as many zeros as needed (dim_sz -> dim_sz_padded) so that reshape to [dim_sz_padded // s, s]
  #          is possible.
  #        - Apply Shrink to do the slice [:, 0] on axes of shapes [dim_sz_padded // s, s].
  def __getitem__(self, val):
    def normalize_int(e, i, dim_sz):
      if -dim_sz <= e < dim_sz: return e if e != -1 else dim_sz-1
      raise IndexError(f"index {e} is out of bounds for dimension {i} with size {self.shape[i]}")
    val = list(val) if isinstance(val, tuple) else [val]
    if (num_slices := sum(isinstance(v, (slice, int)) for v in val)) > len(self.shape):
      raise IndexError(f"too many indices for tensor of dimension {len(self.shape)}")
    orig_slices = list(val)
    ellipses_found = [i for i, v in enumerate(val) if v is Ellipsis]
    if len(ellipses_found) > 0:
      if len(ellipses_found) != 1:
        raise IndexError("an index can only have a single ellipsis ('...')")
      ellipsis_idx = ellipses_found[0]
      orig_slices[ellipsis_idx:ellipsis_idx+1] = [slice(None)] * (len(self.shape) - num_slices)
    else:
      orig_slices += [slice(None)] * (len(self.shape) - num_slices)
    valid_slices = list(filterfalse(lambda x: x is None, orig_slices))
    valid_slices = [v if isinstance(v, slice) else slice(y := normalize_int(v, i, dim_sz), y+1) for i, (v, dim_sz) in enumerate(zip(valid_slices, self.shape))]
    start, stop, strides = zip(*y) if (y := [s.indices(dim_sz) for s, dim_sz in zip(valid_slices, self.shape)]) else ((), (), ())
    new_slice = tuple((s, e)  if st > 0 else (e+1, s+1) for s, e, st in zip(start, stop, strides))
    new_shape = tuple(e - s for s, e in new_slice)
    # Shrink
    sliced_tensor = self.shrink(new_slice)
    # Flip
    if (flip_axes := tuple(i for i, s in enumerate(strides) if s < 0)):
      sliced_tensor = sliced_tensor.flip(axis=flip_axes)
    if any(s > 1 or s < 0 for s in strides):
      # normalize if negative strides
      strides = tuple(abs(s) for s in strides)
      def num_zeros(step, dim_sz): return 0 if step == 1 or (y := dim_sz % step) == 0 else (step - y)
      # Pad: add pad at the end: [dim_sz] -> [dim_sz_padded]
      paddings = tuple((0, num_zeros(s, dim_sz)) for s, dim_sz in zip(strides, sliced_tensor.shape))
      padded_tensor = sliced_tensor.pad(paddings)
      # Reshape: [dim_sz_padded] -> [dim_sz_padded // s, s]
      new_shape = reduce(operator.add, [[sh // s, s] for sh, s in zip(padded_tensor.shape, strides)], [])  # type: ignore
      reshaped_tensor = padded_tensor.reshape(new_shape)
      # Shrink: do [:, 0]
      new_shape = new_shape[::2]
      final_slice = reduce(operator.add, (((0, sh), (0, 1)) for sh in new_shape), ())
      sliced_tensor = reshaped_tensor.shrink(final_slice)
    final_shape = []
    it_shape = iter(new_shape)
    for i in orig_slices:
      if isinstance(i, (int, slice)):
        dim_shape = next(it_shape)
        if isinstance(i, slice): final_shape.append(dim_shape)
      else: # i is None
        final_shape.append(1)
    return sliced_tensor.reshape(tuple(final_shape))  # Reshape

  def cat(self, *args, dim=0):
    dim = (dim + len(self.shape)) if dim < 0 else dim
    assert all(len(y.shape) == len(self.shape) and all(y.shape[i] == s for i,s in enumerate(self.shape) if i != dim) for y in args)
    catargs = [self] + list(args)
    assert all(len(t.shape) != 0 for t in catargs), "zero-dimensional tensor cannot be concatenated"
    shape_cumsum = [0, *accumulate([y.shape[dim] for y in catargs])]
    slc = [[(0, s) for s in self.shape] for _ in catargs]
    for s,k in zip(slc, shape_cumsum):
      s[dim] = (-k, shape_cumsum[-1]-k)
    return reduce(Tensor.__add__, [arg.slice(s) for arg,s in zip(catargs, slc)])

  @staticmethod
  def stack(tensors, dim=0):
    first = tensors[0].unsqueeze(dim)
    unsqueezed_tensors = [tensor.unsqueeze(dim) for tensor in tensors[1:]]
    # checks for shapes and number of dimensions delegated to cat
    return first.cat(*unsqueezed_tensors, dim=dim)

  def repeat(self, repeats):
    base_shape = self.shape
    if len(repeats) > self.ndim:
      base_shape = (1,) * (len(repeats) - self.ndim) + base_shape
    new_shape = [x for i in range(len(base_shape)) for x in [1, base_shape[i]]]
    expand_shape = [x for r,s in zip(repeats, base_shape) for x in [r,s]]
    final_shape = [r*s for r,s in zip(repeats, base_shape)]
    return self.reshape(new_shape).expand(expand_shape).reshape(final_shape)

  # TODO: make this nicer with syntactic sugar in slice
  def chunk(self, num, dim):
    slice_params = [[(0, s) for s in self.shape] for _ in range(num)]
    for i,k in enumerate(range(0, self.shape[dim], self.shape[dim]//num)):
      slice_params[i][dim] = (k, min(self.shape[dim], k+self.shape[dim]//num))
    return [self.slice(p) for p in slice_params]

  def unsqueeze(self, dim):
    if dim < 0: dim = len(self.shape) + dim + 1
    return self.reshape(self.shape[:dim] + (1,) + self.shape[dim:])

  # (padding_left, padding_right, padding_top, padding_bottom)
  def pad2d(self, padding:Union[List[int], Tuple[int, ...]]):
    slc = [(-p0, s+p1) for p0,p1,s in zip(padding[::2], padding[1::2], self.shape[::-1])][::-1]
    return self.slice([(0,s) for s in self.shape[:-(len(padding)//2)]] + slc)

  @property
  def T(self) -> Tensor: return self.transpose()
  def transpose(self, ax1=1, ax2=0) -> Tensor:
    order = list(range(len(self.shape)))
    order[ax1], order[ax2] = order[ax2], order[ax1]
    return self.permute(order)
  def flatten(self, start_dim=0): return self.reshape(shape=tuple(list(self.shape[0:start_dim]) + [-1]))

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

  def _reduce(self, fxn:Type[Function], axis:Optional[Union[int, Tuple[int, ...]]]=None, keepdim=False):
    axis_: List[int] = list(range(len(self.shape))) if axis is None else ([axis] if axis.__class__ is int else list(axis)) # type: ignore
    axis_ = [x if x >= 0 else x+len(self.shape) for x in axis_]
    shape = [self.shape[i] for i in range(len(self.shape)) if i not in axis_]
    ret = fxn.apply(self, new_shape=tuple([1 if i in axis_ else self.shape[i] for i in range(len(self.shape))]))
    return ret if keepdim else ret.reshape(shape=shape)

  def sum(self, axis=None, keepdim=False): return self._reduce(mlops.Sum, axis, keepdim)
  def max(self, axis=None, keepdim=False): return self._reduce(mlops.Max, axis, keepdim)
  def min(self, axis=None, keepdim=False): return -((-self).max(axis=axis, keepdim=keepdim))

  def mean(self, axis=None, keepdim=False):
    out = self.sum(axis=axis, keepdim=keepdim)
    return out * (prod(out.shape)/prod(self.shape))
  def std(self, axis=None, keepdim=False, correction=1):
    square_sum = ((self - self.mean(axis=axis, keepdim=True)).square()).sum(axis=axis, keepdim=keepdim)
    return (square_sum / (prod(self.shape)/prod(square_sum.shape)-correction)).sqrt()
  def _softmax(self, axis):
    m = self - self.max(axis=axis, keepdim=True)
    e = m.exp()
    return m, e, e.sum(axis=axis, keepdim=True)

  def softmax(self, axis=-1):
    _, e, ss = self._softmax(axis)
    return e.div(ss)

  def log_softmax(self, axis=-1):
    m, _, ss = self._softmax(axis)
    return m - ss.log()

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

  def _pool(self, k_:Tuple[int, ...], stride:Union[Tuple[int, ...], int]=1, dilation:Union[Tuple[int, ...], int]=1, _insert_dims=tuple()) -> Tensor:
    assert len(self.shape) >= len(k_), f"can't pool {self.shape} with {k_}"
    s_, d_ = make_pair(stride, len(k_)), make_pair(dilation, len(k_))
    assert len(k_) == len(s_) and len(k_) == len(d_), f"stride/dilation mismatch kernel:{k_} stride:{s_} dilation:{d_}"
    slc_prefix, prefix, i_ = [(0,x) for x in self.shape[0:-len(k_)]], self.shape[0:-len(k_)], self.shape[-len(k_):]
    if any(k > s for k,s in zip(k_, s_)) or any(d != 1 for d in d_):
      o_ = [(i - d * (k-1) - 1)//s + 1 for i,d,k,s in zip(i_, d_, k_, s_)]
      e_ = [ceil(k*(i+d) / i) for k,i,d in zip(k_, i_, d_)]  # expands such that we don't need padding
      xup = self.reshape(*prefix, *([1]*len(_insert_dims)), *flatten((1,i) for i in i_)).expand(*prefix, *_insert_dims, *flatten((e,i) for e,i in zip(e_, i_))).reshape(*prefix, *_insert_dims, *[e*i for e,i in zip(e_, i_)])
      # NOTE: _insert_dims is required because reduces can't be merged (yet)
      prefix += _insert_dims
      slc_prefix += [(0,x) for x in _insert_dims]
      # slide by dilation
      xup = xup.slice(slc_prefix + [(0,k*(i+d)) for k,i,d in zip(k_, i_, d_)])
      xup = xup.reshape(*prefix, *flatten((k,i+d) for k,i,d in zip(k_, i_, d_)))
      xup = xup.slice(slc_prefix + flatten(((0,k), (0,o*s)) for k,o,s in zip(k_, o_, s_)))
      # handle stride, and permute to move reduce to the end
      xup = xup.reshape(*prefix, *flatten((k,o,s) for k,o,s in zip(k_, o_, s_)))
      xup = xup.slice(slc_prefix + flatten(((0,k), (0,o), (0,1)) for k,o in zip(k_, o_)))
      xup = xup.reshape(*prefix, *flatten((k,o) for k,o in zip(k_, o_)))
      return xup.permute(*range(len(prefix)), *[len(prefix)+i*2+1 for i in range(len(k_))], *[len(prefix)+i*2 for i in range(len(k_))])
    # TODO: once the shapetracker can optimize well, remove this alternative implementation. or not if the CPU implementation doesn't use ShapeTracker
    o_ = [(i+(s-k))//s for i,s,k in zip(i_, s_, k_)]
    xup = self.slice(slc_prefix + [(0,o*s) for o,s in zip(o_, s_)])
    xup = xup.reshape(*prefix, *([1]*len(_insert_dims)), *flatten(((o, s) for o,s in zip(o_, s_))))
    if len(_insert_dims):
      xup = xup.expand(*prefix, *_insert_dims, *flatten(((o, s) for o,s in zip(o_, s_))))
      prefix += _insert_dims
      slc_prefix += [(0,x) for x in _insert_dims]
    xup = xup.slice(slc_prefix + flatten(((0,o), (0,k)) for o,k in zip(o_, k_)))
    return xup.permute(*range(len(prefix)), *[len(prefix)+i*2 for i in range(len(k_))], *[len(prefix)+i*2+1 for i in range(len(k_))])

  # NOTE: these work for more than 2D
  def avg_pool2d(self, kernel_size=(2,2), stride=None): return self._pool(make_pair(kernel_size), stride if stride is not None else kernel_size).mean(axis=tuple(range(0-len(make_pair(kernel_size)), 0)))
  def max_pool2d(self, kernel_size=(2,2), stride=None, dilation=1): return self._pool(make_pair(kernel_size), stride if stride is not None else kernel_size, dilation).max(axis=tuple(range(0-len(make_pair(kernel_size)), 0)))

  def conv_transpose2d(self, weight:Tensor, bias:Optional[Tensor]=None, groups=1, stride=1, dilation=1, padding=0, output_padding=0) -> Tensor:
    HW, trailing = weight.shape[2:], list(range(3, len(weight.shape)+1))
    x, w = self, weight.reshape(groups, weight.shape[0]//groups, weight.shape[1], *weight.shape[2:]).permute(0,2,1,*trailing).flip(trailing)
    stride = make_pair(stride, len(HW))
    if any(s>1 for s in stride):
      x = x.reshape(*x.shape[:2], *flatten((k,1) for k in x.shape[2:]))
      x = x.pad(((0,0), (0,0), *flatten(((0,0),(0,s-1)) for s in stride)))
      x = x.reshape(*x.shape[:2], *[k*s for k,s in zip(x.shape[2::2], stride)])
      x = x.shrink(((0,x.shape[0]), (0,x.shape[1]), *[(0,k-(s-1)) for k,s in zip(x.shape[2:], stride)]))
    padding = flatten((((k-1)*d-p,(k-1)*d-p+op) for k,d,p,op in reversed(list(zip(HW, make_pair(dilation, len(HW)), make_pair(padding, len(HW)), make_pair(output_padding, len(HW)))))))
    return x.conv2d(w.reshape(w.shape[0]*w.shape[1],*w.shape[2:]), groups=groups, bias=bias, dilation=dilation, padding=padding)

  def conv2d(self, weight:Tensor, bias:Optional[Tensor]=None, groups=1, stride=1, dilation=1, padding=0) -> Tensor:
    (bs,cin_), (cout,cin), HW = self.shape[:2], weight.shape[:2], weight.shape[2:]
    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_})"
    if isinstance(padding, (tuple,list)): assert len(padding) == 2*len(HW) or len(padding) == len(HW), f"Expected padding of length {2*len(HW)} or {len(HW)}, but got {len(padding)} for tensor of shape {self.shape}"
    padding_ = [padding]*2*len(HW) if isinstance(padding, int) else (padding if len(padding) == 2*len(HW) else [p for p in padding for _ in range(2)][::-1])

    # conv2d is a pooling op (with padding)
    x = self.pad2d(padding_)._pool(HW, stride, dilation)   # (bs, groups*cin, oy, ox, H, W)
    rcout, oyx = cout//groups, x.shape[2:-len(HW)]
    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))])

    # expand the channels with the pool
    # TODO: this reduces the number of kernels, but it's slower!
    #x = self.pad2d(padding_)._pool((H,W), stride, dilation, _insert_dims=(cout//groups,))   # (bs, groups*cin, rcout, oy, ox, H, W)
    #rcout, oy, ox = x.shape[2:5]
    #x = x.reshape(bs, groups, cin, rcout, oy, ox, H, W).permute(0,1,3,4,5,2,6,7)

    # 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).reshape(bs, cout, *oyx)
    return ret if bias is None else ret.add(bias.reshape(1, -1, *[1] * len(HW)))

  def dot(self, w:Tensor) -> Tensor:
    n1, n2 = len(self.shape), len(w.shape)
    assert n1 != 0 and n2 != 0, f"both arguments to matmul need to be at least 1D, but they are {n1}D and {n2}D"
    x = self.reshape(*self.shape[0:-1], *[1]*min(n1-1, n2-1, 1), self.shape[-1])
    w = w.reshape(*w.shape[0:-2], *[1]*min(n1-1, n2-1, 1), *w.shape[-min(n2, 2):]).transpose(-1, -min(n2, 2))
    return (x*w).sum(-1)

  def cumsum(self, axis=0):
    x = self.permute(*(i for i in range(self.ndim) if i != axis), axis)
    return x.reshape(1, 1, -1, self.shape[axis]).conv2d(Tensor.ones(1, 1, 1, self.shape[axis], dtype=self.dtype, device=self.device), padding=(self.shape[axis]-1, 0, 0, 0)).reshape(*x.shape).permute(*range(axis), self.ndim - 1, *range(axis, self.ndim-1))

  # ***** mlops (unary) *****

  def contiguous(self): return mlops.Contiguous.apply(self)
  def log(self): return mlops.Log.apply(self)
  def log2(self): return mlops.Log.apply(self)/log(2)
  def exp(self): return mlops.Exp.apply(self)
  def relu(self): return mlops.Relu.apply(self)
  def sigmoid(self): return mlops.Sigmoid.apply(self)
  def sin(self): return mlops.Sin.apply(self)
  def sqrt(self): return mlops.Sqrt.apply(self)
  def rsqrt(self): return (1/self).sqrt()
  def cos(self): return ((pi/2)-self).sin()
  def tan(self): return self.sin() / self.cos()

  @staticmethod
  def _tri(r:int, c:int, k:int=0, **kwargs) -> Tensor: return Tensor.arange(r, **kwargs).unsqueeze(1).expand(r,c) <= Tensor.arange(c-k, start=-k, **kwargs).unsqueeze(0).expand(r,c)
  def triu(self, k:int=0) -> Tensor: return Tensor._tri(self.shape[-2], self.shape[-1], k=k, dtype=self.dtype).where(self, Tensor.zeros_like(self))
  def tril(self, k:int=0) -> Tensor: return Tensor._tri(self.shape[-2], self.shape[-1], k=k+1, dtype=self.dtype).where(Tensor.zeros_like(self), self)

  # ***** math functions (unary) *****
  def ceil(self: Tensor) -> Tensor:
    b = self.cast(dtypes.int32).contiguous().cast(self.dtype)
    return (self > b).where(b+1, b)
  def floor(self: Tensor) -> Tensor:
    b = self.cast(dtypes.int32).contiguous().cast(self.dtype)
    return (self < b).where(b-1, b)

  def __neg__(self): return 0.0-self
  def square(self): return self*self
  def clip(self, min_, max_): return self.maximum(min_).minimum(max_)
  def abs(self): return self.relu() + (-self).relu()
  def sign(self): return self / (self.abs() + 1e-10)
  def reciprocal(self): return 1.0/self

  # ***** activation functions (unary) *****
  def elu(self, alpha=1.0): return self.relu() - alpha*(1-self.exp()).relu()
  def celu(self, alpha=1.0): return self.maximum(0) + (alpha * ((self / alpha).exp() - 1)).minimum(0)
  def swish(self): return self * self.sigmoid()
  def silu(self): return self.swish()   # The SiLU function is also known as the swish function.
  def relu6(self): return self.relu() - (self-6).relu()
  def hardswish(self): return self * (self+3).relu6() * (1/6)
  def tanh(self): return 2.0 * ((2.0 * self).sigmoid()) - 1.0
  def hardtanh(self, min_val=-1, max_val=1): return self.clip(min_val, max_val)
  def gelu(self): return 0.5 * self * (1 + (self * 0.7978845608 * (1 + 0.044715 * self * self)).tanh())
  def quick_gelu(self): return self * (self * 1.702).sigmoid()
  def leakyrelu(self, neg_slope=0.01): return self.relu() - (-neg_slope*self).relu()
  def mish(self): return self * self.softplus().tanh()
  def softplus(self, beta=1): return (1/beta) * (1 + (self*beta).exp()).log()
  def softsign(self): return self / (1 + self.abs())

  # ***** broadcasted binary mlops *****

  def _broadcasted(self, fxn:Type[Function], other:Union[Tensor, float], reverse:bool=False) -> Tensor:
    dtype = self.dtype if self.dtype != dtypes.bool and self.dtype.__class__ is not ImageDType else dtypes.float32
    x: Tensor = self
    y: Tensor = Tensor(cast(float, other), device=self.device, requires_grad=False, dtype=dtype) if other.__class__ is not Tensor else cast(Tensor, other)
    if reverse: x, y = y, x
    if x.shape == y.shape: return fxn.apply(x, y)

    len_x_shape, len_y_shape = len(x.shape), len(y.shape)
    max_shape = max(len_x_shape, len_y_shape)

    if len_x_shape != max_shape: x = x.reshape((1,) * (max_shape - len_x_shape) + x.shape)
    if len_y_shape != max_shape: y = y.reshape((1,) * (max_shape - len_y_shape) + y.shape)

    shape_ret = tuple([max(x, y) for x, y in zip(x.shape, y.shape)])
    if x.shape != shape_ret: x = x.expand(shape_ret)
    if y.shape != shape_ret: y = y.expand(shape_ret)

    return fxn.apply(x, y)

  def add(self, x:Union[Tensor, float], reverse=False) -> Tensor: return self._broadcasted(mlops.Add, x, reverse) if x.__class__ is Tensor or x else self
  def sub(self, x:Union[Tensor, float], reverse=False) -> Tensor: return self._broadcasted(mlops.Sub, x, reverse) if x.__class__ is Tensor or x or reverse else self
  def mul(self, x:Union[Tensor, float], reverse=False) -> Tensor: return self._broadcasted(mlops.Mul, x, reverse) if x.__class__ is Tensor or x != 1.0 else self
  def div(self, x:Union[Tensor, float], reverse=False) -> Tensor: return self._broadcasted(mlops.Div, x, reverse) if x.__class__ is Tensor or reverse or not x else self.mul(1/x)
  def pow(self, x:Union[Tensor, float], reverse=False) -> Tensor:
    if x.__class__ is not Tensor and not reverse:
      # simple pow identities
      if x < 0: return (1.0/self).pow(-x)
      if x == 2.0: return self*self
      if x == 1.0: return self
      if x == 0.5: return self.sqrt()
    ar = self.abs().log().mul(x).exp() if not reverse or isinstance(x, Tensor) else self.mul(log(abs(x))).exp()
    # correct sign of negative numbers raised to a power (cos has a period of 2pi so we use it here to get the oddness of the power)
    sign = (x * pi).cos() if isinstance(x, Tensor) else cos(x * pi) if not reverse else (self * pi).cos()
    # we only need to correct the sign if the base is negative
    base_sign = ((self.sign() if not reverse else x.sign() if isinstance(x, Tensor) else copysign(1, x)) - 1) / -2
    return ar.mul(sign * base_sign + (1 - base_sign))
  def matmul(self, x:Tensor, reverse=False) -> Tensor: return x.dot(self) if reverse else self.dot(x)

  def maximum(self, x:Union[Tensor, float]) -> Tensor: return self._broadcasted(mlops.Maximum, x)
  def minimum(self, x:Union[Tensor, float]) -> Tensor: return -((-self).maximum(-x))
  def eq(self, x) -> Tensor: return self._broadcasted(mlops.Equal, x, False)

  # ***** binary op wrappers (18 wasted lines to make the typechecker happy) *****

  # NOTE: __pow__ and friends are broken in mypyc with the ** operator
  def __add__(self, x) -> Tensor: return self.add(x)
  def __sub__(self, x) -> Tensor: return self.sub(x)
  def __mul__(self, x) -> Tensor: return self.mul(x)
  def __pow__(self, x) -> Tensor: return self.pow(x)
  def __truediv__(self, x) -> Tensor: return self.div(x)
  def __matmul__(self, x) -> Tensor: return self.matmul(x)

  def __radd__(self, x) -> Tensor: return self.add(x, True)
  def __rsub__(self, x) -> Tensor: return self.sub(x, True)
  def __rmul__(self, x) -> Tensor: return self.mul(x, True)
  def __rpow__(self, x) -> Tensor: return self.pow(x, True)
  def __rtruediv__(self, x) -> Tensor: return self.div(x, True)
  def __rmatmul__(self, x) -> Tensor: return self.matmul(x, True)

  def __iadd__(self, x) -> Tensor: return self.assign(self.add(x))
  def __isub__(self, x) -> Tensor: return self.assign(self.sub(x))
  def __imul__(self, x) -> Tensor: return self.assign(self.mul(x))
  def __ipow__(self, x) -> Tensor: return self.assign(self.pow(x))
  def __itruediv__(self, x) -> Tensor: return self.assign(self.div(x))
  def __imatmul__(self, x) -> Tensor: return self.assign(self.matmul(x))

  def __ge__(self, x) -> Tensor: return self.maximum(x).eq(self)
  def __le__(self, x) -> Tensor: return self.maximum(x).eq(x)
  def __lt__(self, x) -> Tensor: return 1.0-(self>=x)
  def __gt__(self, x) -> Tensor: return 1.0-(self<=x)
  def __eq__(self, x) -> Tensor: return self.eq(x)  # type: ignore # mypy things this should be a bool
  def __ne__(self, x) -> Tensor: return 1.0-self.eq(x)  # type: ignore

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

  def linear(self, weight:Tensor, bias:Optional[Tensor]=None):
    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]]): return reduce(lambda x,f: f(x), ll, self)

  def layernorm(self, axis=-1, eps:float=1e-5) -> Tensor:
    y = (self - self.mean(axis, keepdim=True))
    return y.mul((y*y).mean(axis, keepdim=True).add(eps).rsqrt())

  def batchnorm(self, weight:Optional[Tensor], bias:Optional[Tensor], mean:Tensor, invstd:Tensor) -> Tensor:
    x = (self - mean.reshape(shape=[1, -1, 1, 1]))
    if weight: x = x * weight.reshape(shape=[1, -1, 1, 1])
    ret = x.mul(invstd.reshape(shape=[1, -1, 1, 1]) if len(invstd.shape) == 1 else invstd)
    return (ret + bias.reshape(shape=[1, -1, 1, 1])) if bias else ret

  def dropout(self, p=0.5) -> Tensor:
    if not Tensor.training: return self
    mask = (Tensor.rand(*self.shape, requires_grad=False) >= p).cast(dtypes.bool)
    return self * mask * (1/(1.0 - p))

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

  def cast(self, dtype:DType) -> Tensor: return mlops.Cast.apply(self, dtype=dtype) if self.dtype != dtype else self
  def float(self) -> Tensor: return self.cast(dtypes.float32)
  def half(self) -> Tensor: return self.cast(dtypes.float16)

  # ***** Convenience stuff *****
  @property
  def ndim(self) -> int: return len(self.shape)
  def numel(self) -> int: return prod(self.shape)
  def element_size(self) -> int: return self.dtype.itemsize
  def nbytes(self) -> int: return self.numel() * self.element_size()
  def is_floating_point(self) -> bool: return dtypes.is_float(self.dtype)

# register functions to move between devices
for device in Device._buffers:
  setattr(Tensor, f"{device.lower()}", partialmethod(Tensor.to, device))
  setattr(Tensor, f"{device.lower()}_", partialmethod(Tensor.to_, device))

# if IMAGE>0 we install these replacement functions in Tensor (hack!)
from tinygrad.nn.image import image_conv2d, image_dot
if IMAGE:
  setattr(Tensor, "conv2d", image_conv2d)
  setattr(Tensor, "dot", image_dot)