from __future__ import annotations import re import numpy import cupy import cupy._core._routines_manipulation as _manipulation from cupy._core.internal import _normalize_axis_indices from cupy._core._dtype import get_dtype, _raise_if_invalid_cast from cupy._core import internal # Signature parsing code and dimension accessing has been borrowed # from dask # https://github.com/dask/dask/blob/61b578f5a3ad88cbc6a8b9a73ce08c551bd969fa/dask/array/gufunc.py#L12-L55 _DIMENSION_NAME = r'\w+(\?|\|1)?' _CORE_DIMENSION_LIST = '(?:{0:}(?:,{0:})*,?)?'.format(_DIMENSION_NAME) _ARGUMENT = r'\({}\)'.format(_CORE_DIMENSION_LIST) _INPUT_ARGUMENTS = '(?:{0:}(?:,{0:})*,?)?'.format(_ARGUMENT) _OUTPUT_ARGUMENTS = '{0:}(?:,{0:})*'.format( _ARGUMENT ) # Use `'{0:}(?:,{0:})*,?'` if gufunc- # signature should be allowed for length 1 tuple returns _SIGNATURE = '^{:}->{:}$'.format(_INPUT_ARGUMENTS, _OUTPUT_ARGUMENTS) def _parse_gufunc_signature(signature): """Parse and prepare gufunc signature for internal use, we convert each operand into a tuple of dimensions and for each dimension return (name, optional, broadcastable). Additionally, returns the number of unique core dimensions (for later). """ coredims = set() # The code has been modified from dask to support optional dimensions if not isinstance(signature, str): raise TypeError('Signature is not a string') if signature == '' or signature is None: raise ValueError('Signature cannot be empty') signature = signature.replace(' ', '') if not re.match(_SIGNATURE, signature): raise ValueError('Not a valid gufunc signature: {}'.format(signature)) in_txt, out_txt = signature.split('->') ins = [list(x.split(',')) if x != '' else () for x in in_txt[1:-1].split('),(')] outs = [list(y.split(',')) if y != '' else () for y in out_txt[1:-1].split('),(')] # Modify the signature information to be a tuple of # (name, optional, broadcastable) for cds in ins: for i in range(len(cds)): optional = cds[i].endswith('?') broadcastable = cds[i].endswith('|1') # Remove either (can't be both) name = cds[i].removesuffix('?').removesuffix('|1') cds[i] = (name, optional, broadcastable) for cds in outs: for i in range(len(cds)): optional = cds[i].endswith('?') broadcastable = cds[i].endswith('|1') if broadcastable: raise ValueError('Output name cannot indicate |1.') # Remove either (can't be both) name = cds[i].removesuffix('?') cds[i] = (name, optional, broadcastable) ins = [tuple(_) for _ in ins] outs = [tuple(_) for _ in outs] for cds in ins + outs: for cd in cds: coredims.add(cd[0]) # add coredim name return ins, outs, len(coredims) class _OpsRegister: ''' Holds the ops for each dtypes signature like ('ff->f', func1) and allows to do look ups for these ''' class _Op: def __init__(self, in_types, out_types, func): self.func = func self.in_types = tuple(numpy.dtype(i) for i in in_types) self.out_types = tuple(numpy.dtype(o) for o in out_types) self.sig_str = (''.join( in_t.char for in_t in self.in_types) + '->' + ''.join( out_t.char for out_t in self.out_types)) def __init__(self, signatures, default_func, nin, nout, name): self._default_func = default_func self._nin = nin self._nout = nout self._ops = self._process_signatures(signatures) self._name = name def _sig_str_to_tuple(self, sig): sig = sig.replace(' ', '') toks = sig.split('->') if len(toks) != 2: raise ValueError(f'signature {sig} for dtypes is invalid') else: ins, outs = toks return ins, outs def _process_signatures(self, signatures): ops = [] for sig in signatures: if isinstance(sig, tuple): sig, op = sig else: op = self._default_func ins, outs = self._sig_str_to_tuple(sig) # Check the number of inputs and outputs matches the gufunc sig if len(ins) != self._nin: raise ValueError( f'signature {sig} for dtypes is invalid number of inputs ' 'is not consistent with general signature') if len(outs) != self._nout: raise ValueError( f'signature {sig} for dtypes is invalid number of inputs ' 'is not consistent with general signature') ops.append(_OpsRegister._Op(ins, outs, op)) return ops def _determine_from_args(self, args, casting): n = len(args) in_types = tuple(arg.dtype for arg in args) for op in self._ops: op_types = op.in_types for i in range(n): it = in_types[i] ot = op_types[i] if not numpy.can_cast(it, ot, casting=casting): break else: return op return None def _determine_from_dtype(self, dtype): for op in self._ops: op_types = op.out_types for t in op_types: if t != dtype: break else: return op return None def _determine_from_signature(self, signature): # Lets convert the signature as it can be a tuple of tuples # or a string if isinstance(signature, tuple): # create a string to do a look-up on the ops if len(signature) == 1: raise TypeError( 'The use of a length 1 tuple for the ufunc `signature` is' ' not allowed. Use `dtype` or fill the tuple with' ' `None`s.') nin = self._nin nout = self._nout if len(signature) != (nin + nout): raise TypeError( 'A type-tuple must be specified of length 1 or 3 for ufunc' f' {self._name}') signature = ''.join( numpy.dtype(t).char for t in signature[:nin]) + '->' + ''.join( numpy.dtype(t).char for t in signature[nin:nin+nout]) if isinstance(signature, str): is_out = len(signature) == 1 for op in self._ops: if is_out: for t in op.out_types: if t.char != signature: break else: return op else: if op.sig_str == signature: return op raise TypeError('No loop matching the specified signature and' f' casting was found for ufunc {self._name}') def determine_dtype(self, args, dtype, casting, signature): if self._nout != 1: # dtype discovery doesn't yet support this (the rest should) raise NotImplementedError('Multiple output gufuncs not supported') ret_dtype = None func = self._default_func if signature is not None: # TODO(ecastill) use an externally provided signature to # find the typecasting rules op = self._determine_from_signature(signature) elif dtype is not None: if isinstance(dtype, tuple): # TODO(ecastill) support dtype tuples raise RuntimeError('dtype with tuple is not yet supported') op = self._determine_from_dtype(dtype) else: op = self._determine_from_args(args, casting) if op is None: # Should we allow op to be none? if dtype is None: dtype = args[0].dtype for arg in args: ret_dtype = numpy.promote_types(dtype, arg.dtype) else: ret_dtype = get_dtype(dtype) else: # Convert args to the op specified in_types n_args = [] def argname(): return f'ufunc {self._name} input {i}' for i, (arg, in_type) in enumerate(zip(args, op.in_types)): _raise_if_invalid_cast(arg.dtype, in_type, casting, argname) n_args.append(arg.astype(in_type, copy=False)) args = n_args ret_dtype = op.out_types[0] func = op.func return args, ret_dtype, func class _GUFunc: ''' Creates a Generalized Universal Function by wrapping a user provided function with the signature. ``signature`` determines if the function consumes or produces core dimensions. The remaining dimensions in given input arrays (``*args``) are considered loop dimensions and are required to broadcast naturally against each other. Args: func (callable): Function to call like ``func(*args, **kwargs)`` on input arrays (``*args``) that returns an array or tuple of arrays. If multiple arguments with non-matching dimensions are supplied, this function is expected to vectorize (broadcast) over axes of positional arguments in the style of NumPy universal functions. signature (string): Specifies what core dimensions are consumed and produced by ``func``. According to the specification of numpy.gufunc signature. supports_batched (bool, optional): If the wrapped function supports to pass the complete input array with the loop and the core dimensions. Defaults to `False`. Dimensions will be iterated in the `GUFunc` processing code. supports_out (bool, optional): If the wrapped function supports out as one of its kwargs. Defaults to `False`. try_fastcall_func (None, optional): If not None this function is called with same arguments as the gufunc itself. Must return the final result or ``NotImplemented`` if the fast-path is not possible. signatures (list of tuple of str): Contains strings in the form of 'ii->i' with i being the char of a dtype. Each element of the list is a tuple with the string and a alternative function to `func` to be executed when the inputs of the function can be casted as described by this function. name (str, optional): Name for the GUFunc object. If not specified, ``func``'s name is used. doc (str, optional): Docstring for the GUFunc object. If not specified, ``func.__doc__`` is used. ''' def __init__( self, func, signature, *, name=None, doc=None, supports_batched=False, supports_out=False, signatures=None, try_fastcall_func=None): # We would like to create gufuncs from cupy regular ufuncs # so we can avoid most of the __call__ stuff self._func = func self._signature = signature self.__name__ = name if name is not None else func.__name__ self.__doc__ = doc if doc is not None else func.__doc__ # The following are attributes to avoid applying certain steps # when wrapping cupy functions that do some of the gufunc # stuff internally due to CUDA libraries requirements self._supports_batched = supports_batched self._supports_out = supports_out self._try_fastcall_func = try_fastcall_func signatures = signatures if signatures is not None else [] # Preprocess the signature here input_coredimss, output_coredimss, cndim_ix = _parse_gufunc_signature( self._signature) self._core_num_dim_ix = cndim_ix self._core_dims = input_coredimss + output_coredimss self._input_coredimss = input_coredimss self._output_coredimss = output_coredimss # This is pre-calculated to later check the minimum number of # dimensions required per input self._min_dims = [0] * len(input_coredimss) for i, inp in enumerate(input_coredimss): for d in inp: if d[1]: # name, optional, broadcastable self._min_dims[i] += 1 self._nout = len(output_coredimss) self._nin = len(input_coredimss) # Determines the function that will be run depending on the datatypes # Pass a list of signatures that are either the types in format # ii->o or a tuple with the string and a function other than func to be # executed for those types # For some reason _nout is a tuple and now we get it with 0s self._ops_register = _OpsRegister( signatures, self._func, self._nin, self._nout, self.__name__) def _validate_normalize_axes(self, arrays, axes, axis, keepdims): # This code originally came from Dask and was later heavily modified: # https://github.com/dask/dask/blob/61b578f5a3ad88cbc6a8b9a73ce08c551bd969fa/dask/array/gufunc.py#L58-L172 if axes is not None and axis is not None: raise ValueError( 'Only one of `axis` or `axes` keyword arguments ' 'should be given') if axes and not isinstance(axes, list): raise ValueError('`axes` has to be of type list') if keepdims: # Store the number of core dimensions to append into keepdims. keepdims = None for icd in self._input_coredimss: ndim_core = len(icd) if keepdims is not None and keepdims != ndim_core: raise ValueError( '`keepdims` requires all inputs to have the same ' 'number of core dimensions') keepdims = ndim_core for ocd in self._output_coredimss: if len(ocd) > 0: raise ValueError( '`keepdims` can only be used for scalar outputs') if axis is not None: if not isinstance(axis, int): raise ValueError('`axis` argument has to be an integer value') if self._core_num_dim_ix != 1: raise ValueError( '`axis` can be used only, if there is a single shared ' f'core dimension, but {self._core_num_dim_ix} are ' f'present in the signature {self._signature}' ) if not keepdims: axes = [(axis,) if cd else () for cd in self._core_dims] else: # When keepdims is used with axis, it applies to the output axes = [(axis,) if cd else () for cd in self._input_coredimss] axes.extend([(axis,)] * self._nout) elif axes is not None: # Allow a single integer in axes. axes = [(a,) if isinstance(a, int) else a for a in axes] else: axes = [None] * (self._nin + self._nout) if len(axes) == self._nin: for ocd in self._output_coredimss: if len(ocd) > 0: raise ValueError( '`axes` entries for outputs can only be omitted if ' 'none of them has core axes.') # Output axes may be ommitted, fill them in if this is the case. # This seems actually more relaxes as NumPy as of NumPy 2.4. axes.extend([None] * self._nout) elif len(axes) != self._nin + self._nout: raise ValueError( 'The number of `axes` entries is not equal to the number of ' 'input and output arguments. Outputs may only be omitted if ' 'they are all scalar.') return axes[:self._nin], axes[self._nin:], keepdims def _get_transpose(self, i, axs, ndim, n_core_dims): """Normalize the axes tuple and check the bounds may be None at this point. """ if axs is None: if ndim < n_core_dims: raise ValueError( f'Argument {i} has too few dimensions.') return None elif len(axs) != n_core_dims: # NOTE(seberg): Like NumPy, this rejects partial axes when axes # are optional. The kernel (e.g. matmul) would need the info. raise cupy.exceptions.AxisError( f'Number of axes passed for argument {i} does not match the ' f'the number of core dimensions.') axs = _normalize_axis_indices(axs, ndim, sort_axes=False) if axs == tuple(range(ndim-n_core_dims, ndim)): return None # normalize for no transpose needed return tuple(i for i in range(ndim) if i not in axs) + axs def _apply_func_to_inputs(self, func, outer_shape, args, outs): # Apply function # The resulting array is loop_output_dims+the specified dims # Some functions have batching logic inside due to highly # optimized CUDA libraries so we just call them if self._supports_batched or len(outer_shape) == 0: # Check if the function supports out, order and other args if self._supports_out and outs is not None: outs = outs[0] if len(outs) == 1 else outs func(*args, out=outs) else: fouts = func(*args) # TODO(ecastill) improve this check if isinstance(fouts, cupy.ndarray): fouts = (fouts,) for o, fo in zip(outs, fouts): cupy._core.elementwise_copy(fo, o) else: # iterate over first outer dimension and recurse. for i in range(outer_shape[0]): n_args = [a[i] for a in args] n_outs = [o[i] for o in outs] self._apply_func_to_inputs( func, outer_shape[1:], n_args, n_outs) def _update_dims(self, i, core_dims, cd, length): # Helper to update dimensions, just to not repeat error messages. name = cd[0] prev_length = core_dims.get(name, None) if prev_length is None: if cd[2] and length == 1: return # broadcastable, other operand may set it. core_dims[name] = length elif length == 1 and cd[2]: # cd[2] indicates broadcastable # broadcastable core-dim of size 1, ignore it. return elif prev_length != length: if prev_length == -1 or length == -1: raise ValueError( 'An optional core-dimension must be skipped in ' 'all or no inputs.') raise ValueError( f'Input operand {i} has mismatch in its core ' f'dimension {name} with signature {self._signature} ' f'({prev_length} != {length}).') def _setup_operands( self, args, in_axes, outs, out_axes, keepdims, ret_dtype, filter_order, casting): """Set up the operands for the function call, this needs to figure out the actual core axes and shapes and make sure core-dimensions match. We then transpose the core dimensions to the end for the actual operation. This function also sets up the output operands, note that there are two versions. The untransposed ones for user-return and the transposed ones for the actual result. """ core_dims = {} outer_shapes = [] for i, (arg, axs, coredims) in enumerate( zip(args, in_axes, self._input_coredimss)): ndim = arg.ndim n_core_dims = max(self._min_dims[i], min(ndim, len(coredims))) transpose = self._get_transpose(i, axs, ndim, n_core_dims) if transpose is None: outer_shape = arg.shape[:-n_core_dims] core_shape = arg.shape[-n_core_dims:] else: outer_shape = tuple(arg.shape[i] for i in transpose[:-n_core_dims]) core_shape = tuple(arg.shape[i] for i in transpose[-n_core_dims:]) n_skipped = len(coredims) - n_core_dims ommitted_coredims = [] i_coredim = 0 for length in core_shape: # Process the core dimension shape and store the result into # `core_dims` for each dimension. # If there are optional coredims skip them from the front while (cd := coredims[i_coredim])[1] and n_skipped > 0: ommitted_coredims.append(i_coredim) self._update_dims(i, core_dims, cd, -1) i_coredim += 1 n_skipped -= 1 else: i_coredim += 1 self._update_dims(i, core_dims, cd, length) # The above may not have processed all optional dimensions, do it # to ensure errors for missing ones (and simplify output shape). while i_coredim < len(coredims): ommitted_coredims.append(i_coredim) self._update_dims(i, core_dims, coredims[i_coredim], -1) i_coredim += 1 if transpose is not None: args[i] = arg.transpose(transpose) if ommitted_coredims: assert transpose is None # currently guaranteed args[i] = cupy.expand_dims(arg, axis=tuple(ommitted_coredims)) outer_shapes.append(outer_shape) # The outer shape needs to be broadcast across all input operands. bc_outer_shape = internal._broadcast_shapes(outer_shapes) for i, (arg, outer_shape) in enumerate(zip(args, outer_shapes)): # Above, we figured out the transpose and outer shape, we still # need to apply it to broadcast (potentially) if outer_shape != bc_outer_shape: arg = _manipulation.broadcast_to( arg, bc_outer_shape + arg.shape[len(outer_shape):]) args[i] = arg # Figure out the outputs now based on the input shapes and core dims. # (NumPy supports `out=` to fill in shapes sometimes, we do not yet.) untransposed_outs = [] # The return array is the untransposed one. for i, (out, axs, coredims) in enumerate( zip(outs, out_axes, self._output_coredimss)): ommitted_dims = [] if not keepdims: core_shape = [] for i_cd, cd in enumerate(coredims): dim = core_dims.get(cd[0], None) if dim == -1: # Ommit dim in output is core-dim + outer ndim ommitted_dims.append(i_cd + len(bc_outer_shape)) elif dim is None: core_shape.append(1) # should be a |1 core-dim else: core_shape.append(dim) else: assert not self._output_coredimss[i] core_shape = [1] * keepdims shape = bc_outer_shape + tuple(core_shape) trans = self._get_transpose( self._nin + i, axs, len(shape), len(core_shape)) if out is not None: untransposed_outs.append(out) if trans is not None: out = out.transpose(trans) if out.shape != shape: # Inverse transpose for error message (if needed) itrans = range(len(shape)) if trans is not None: itrans = sorted(itrans, key=lambda i: trans[i]) actual = tuple(out.shape[i] for i in itrans) expected = tuple(shape[i] for i in itrans) raise ValueError( f'Output operand {i} has invalid shape {actual} ' f'expected {expected}') _raise_if_invalid_cast( ret_dtype, out.dtype, casting, "out dtype") else: if trans is not None: itrans = sorted(range(len(trans)), key=lambda i: trans[i]) shape = tuple(shape[i] for i in itrans) # Note: Order logic here may be weird/wrong as core dims should # be preferred contiguous. out = cupy.empty(shape, dtype=ret_dtype, order=filter_order) untransposed_outs.append(out) if trans is not None: out = out.transpose(trans) if ommitted_dims: out = cupy.expand_dims(out, axis=tuple(ommitted_dims)) if keepdims: # The core function should not see the keepdims, strip them. out = out[(...,) + (0,) * keepdims] outs[i] = out # The operand "out" may have been transposed return args, outs, untransposed_outs, bc_outer_shape def _determine_order(self, args, order): if order.upper() in ('C', 'K'): # Order is determined to be C to allocate the out array # but we will change the strides of the out array # to be K later in __call__ return 'C' elif order.upper() == 'A': # order is F if all arrays are strictly F order = ('F' if all([a.flags.f_contiguous and not a.flags.c_contiguous for a in args]) else 'C') return order elif order.upper() == 'F': return 'F' else: raise RuntimeError(f'Unknown order {order}') def __call__( self, *args, axes=None, axis=None, keepdims=False, casting='same_kind', dtype=None, signature=None, order='K', out=None): ''' Apply a generalized ufunc. Args: args: Input arguments. Each of them can be a :class:`cupy.ndarray` object or a scalar. The output arguments can be omitted or be specified by the ``out`` argument. axes (List of tuples of int, optional): A list of tuples with indices of axes a generalized ufunc should operate on. For instance, for a signature of ``'(i,j),(j,k)->(i,k)'`` appropriate for matrix multiplication, the base elements are two-dimensional matrices and these are taken to be stored in the two last axes of each argument. The corresponding axes keyword would be ``[(-2, -1), (-2, -1), (-2, -1)]``. For simplicity, for generalized ufuncs that operate on 1-dimensional arrays (vectors), a single integer is accepted instead of a single-element tuple, and for generalized ufuncs for which all outputs are scalars, the output tuples can be omitted. axis (int, optional): A single axis over which a generalized ufunc should operate. This is a short-cut for ufuncs that operate over a single, shared core dimension, equivalent to passing in axes with entries of (axis,) for each single-core-dimension argument and ``()`` for all others. For instance, for a signature ``'(i),(i)->()'``, it is equivalent to passing in ``axes=[(axis,), (axis,), ()]``. keepdims (bool, optional): If this is set to True, axes which are reduced over will be left in the result as a dimension with size one, so that the result will broadcast correctly against the inputs. This option can only be used for generalized ufuncs that operate on inputs that all have the same number of core dimensions and with outputs that have no core dimensions , i.e., with signatures like ``'(i),(i)->()'`` or ``'(m,m)->()'``. If used, the location of the dimensions in the output can be controlled with axes and axis. casting (str, optional): Provides a policy for what kind of casting is permitted. Defaults to ``'same_kind'`` dtype (dtype, optional): Overrides the dtype of the calculation and output arrays. Similar to signature. signature (str or tuple of dtype, optional): Either a data-type, a tuple of data-types, or a special signature string indicating the input and output types of a ufunc. This argument allows you to provide a specific signature for the function to be used if registered in the ``signatures`` kwarg of the ``__init__`` method. If the loop specified does not exist for the ufunc, then a TypeError is raised. Normally, a suitable loop is found automatically by comparing the input types with what is available and searching for a loop with data-types to which all inputs can be cast safely. This keyword argument lets you bypass that search and choose a particular loop. order (str, optional): Specifies the memory layout of the output array. Defaults to ``'K'``.``'C'`` means the output should be C-contiguous, ``'F'`` means F-contiguous, ``'A'`` means F-contiguous if the inputs are F-contiguous and not also not C-contiguous, C-contiguous otherwise, and ``'K'`` means to match the element ordering of the inputs as closely as possible. out (cupy.ndarray): Output array. It outputs to new arrays default. Returns: Output array or a tuple of output arrays. ''' if self._try_fastcall_func is not None: result = self._try_fastcall_func( *args, out=out, axes=axes, axis=axis, keepdims=keepdims, casting=casting, dtype=dtype, signature=signature, order=order) if result is not NotImplemented: return result # this will cast the inputs appropriately args, ret_dtype, func = self._ops_register.determine_dtype( args, dtype, casting, signature) args = list(args) # make args mutable to transpose later if len(args) != self._nin: raise ValueError( 'According to `signature`, `func` requires %d arguments,' ' but %s given' % (self._nin, len(args))) if not isinstance(self._signature, str): raise TypeError('`signature` has to be of type string') if out is None: outs = [None] * self._nout elif not isinstance(out, tuple): if not isinstance(out, cupy.ndarray): raise TypeError('`out` must be a tuple or `cupy.ndarray`') outs = [out] else: outs = list(out) # make outs mutable to transpose later for out in outs: if out is not None and not isinstance(out, cupy.ndarray): raise TypeError( '`out` tuple must contain `cupy.ndarray` or None') filter_order = self._determine_order(args, order) # Preproces axes/axis (does not check out of bound axes) in_axes, out_axes, keepdims = self._validate_normalize_axes( args, axes, axis, keepdims) args, outs, untransposed_outs, outer_shape = self._setup_operands( args, in_axes, outs, out_axes, keepdims, ret_dtype, filter_order, casting) self._apply_func_to_inputs(func, outer_shape, args, outs) if len(untransposed_outs) == 1: return untransposed_outs[0] else: return tuple(untransposed_outs)