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Operation Semantics

The following describes the semantics of operations defined in the ComputationBuilder interface. Typically, these operations map one-to-one to operations defined in the RPC interface in xla_data.proto.

A note on nomenclature: the generalized data type XLA deals with is an N-dimensional array holding elements of some uniform type (such as 32-bit float). Throughout the documentation, array is used to denote an arbitrary-dimensional array. For convenience, special cases have more specific and familiar names; for example a vector is a 1-dimensional array and a matrix is a 2-dimensional array.

Broadcast

Adds dimensions to an array by duplicating the data in the array.

Broadcast(operand, broadcast_sizes)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	The array to duplicate
`broadcast_sizes`	`ArraySlice<int64>`	The sizes of the new dimensions

The new dimensions are inserted on the left, i.e. if broadcast_sizes has values {a0, ..., aN} and the operand shape has dimensions {b0, ..., bM} then the shape of the output has dimensions {a0, ..., aN, b0, ..., bM}.

The new dimensions index into copies of the operand, i.e.

output[i0, ..., iN, j0, ..., jM] = operand[j0, ..., jM]

For example, if operand is a scalar f32 with value 2.0f, and broadcast_sizes is {2, 3}, then the result will be an array with shape f32[2, 3] and all the values in the result will be 2.0f.

Call

Arguments	Type	Semantics
`computation`	`Computation`	computation of type `T_0, T_1, ..., T_N -> S` with N parameters of arbitrary type
`args`	sequence of N `ComputationDataHandle`s	N arguments of arbitrary type

Collapse

See also ComputationBuilder::Collapse and the tf.reshape operation.

Collapses dimensions of an array into one dimension.

Collapse(operand, dimensions)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	array of type T
`dimensions`	`int64` vector	in-order, consecutive subset of T's dimensions.

Collapse replaces the given subset of the operand's dimensions by a single dimension. The input arguments are an arbitrary array of type T and a compile-time-constant vector of dimension indices. The dimension indices must be an in-order (low to high dimension numbers), consecutive subset of T's dimensions. Thus, {0, 1, 2}, {0, 1}, or {1, 2} are all valid dimension sets, but {1, 0} or {0, 2} are not. They are replaced by a single new dimension, in the same position in the dimension sequence as those they replace, with the new dimension size equal to the product of original dimension sizes. The lowest dimension number in dimensions is the slowest varying dimension (most major) in the loop nest which collapses these dimension, and the highest dimension number is fastest varying (most minor). See the tf.reshape operator if more general collapse ordering is needed.

For example, let v be an array of 24 elements:

let v = f32[4x2x3] { { {10, 11, 12},  {15, 16, 17}},
                    { {20, 21, 22},  {25, 26, 27}},
                    { {30, 31, 32},  {35, 36, 37}},
                    { {40, 41, 42},  {45, 46, 47}}};

// Collapse to a single dimension, leaving one dimension.
let v012 = Collapse(v, {0,1,2});
then v012 == f32[24] {10, 11, 12, 15, 16, 17,
                      20, 21, 22, 25, 26, 27,
                      30, 31, 32, 35, 36, 37,
                      40, 41, 42, 45, 46, 47};

// Collapse the two lower dimensions, leaving two dimensions.
let v01 = Collapse(v, {0,1});
then v01 == f32[4x6] { {10, 11, 12, 15, 16, 17},
                      {20, 21, 22, 25, 26, 27},
                      {30, 31, 32, 35, 36, 37},
                      {40, 41, 42, 45, 46, 47}};

// Collapse the two higher dimensions, leaving two dimensions.
let v12 = Collapse(v, {1,2});
then v12 == f32[8x3] { {10, 11, 12},
                      {15, 16, 17},
                      {20, 21, 22},
                      {25, 26, 27},
                      {30, 31, 32},
                      {35, 36, 37},
                      {40, 41, 42},
                      {45, 46, 47}};

Concatenate

Concatenate composes an array from multiple array operands. The array is of the same rank as each of the input array operands (which must be of the same rank as each other) and contains the arguments in the order that they were specified.

Concatenate(operands..., dimension)

Arguments	Type	Semantics
`operands`	sequence of N `ComputationDataHandle`	N arrays of type T with dimensions [L0, L1, ...]. Requires N >= 1.
`dimension`	`int64`	A value in the interval `[0, N)` that names the dimension to be concatenated between the `operands`.

With the exception of dimension all dimensions must be the same. This is because XLA does not support "ragged" arrays Also note that rank-0 values cannot be concatenated (as it's impossible to name the dimension along which the concatenation occurs).

1-dimensional example:

Concat({ {2, 3}, {4, 5}, {6, 7}}, 0)
>>> {2, 3, 4, 5, 6, 7}

2-dimensional example:

let a = {
  {1, 2},
  {3, 4},
  {5, 6},
};
let b = {
  {7, 8},
};
Concat({a, b}, 0)
>>> {
  {1, 2},
  {3, 4},
  {5, 6},
  {7, 8},
}

Diagram:

ConvertElementType

Similar to an element-wise static_cast in C++, performs an element-wise conversion operation from a data shape to a target shape. The dimensions must match, and the conversion is an element-wise one; e.g. s32 elements become f32 elements via an s32-to-f32 conversion routine.

ConvertElementType(operand, new_element_type)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	array of type T with dims D
`new_element_type`	`PrimitiveType`	type U

If the dimensions of the operand and the target shape do not match, or an invalid conversion is requested (e.g. to/from a tuple) an error will be produced.

A conversion such as T=s32 to U=f32 will perform a normalizing int-to-float conversion routine such as round-to-nearest-even.

Note: The precise float-to-int and visa-versa conversions are currently unspecified, but may become additional arguments to the convert operation in the future. Not all possible conversions have been implemented for all targets.

let a: s32[3] = {0, 1, 2};
let b: f32[3] = convert(a, f32);
then b == f32[3]{0.0, 1.0, 2.0}

Conv (convolution)

ConvWithGeneralPadding (convolution)

Computes a convolution of the kind used in neural networks. Here, a convolution can be thought of as a n-dimensional window moving across a n-dimensional base area and a computation is performed for each possible position of the window.

Arguments	Type	Semantics
`lhs`	`ComputationDataHandle`	rank n+2 array of inputs
`rhs`	`ComputationDataHandle`	rank n+2 array of kernel weights
`window_strides`	`ArraySlice<int64>`	n-d array of kernel strides
`padding`	`ArraySlice<pair<int64, int64>>`	n-d array of (low, high) padding
`lhs_dilation`	`ArraySlice<int64>`	n-d lhs dilation factor array
`rhs_dilation`	`ArraySlice<int64>`	n-d rhs dilation factor array

Let n be the number of spatial dimensions. The lhs argument is a rank n+2 array describing the base area. This is called the input, even though of course the rhs is also an input. In a neural network, these are the input activations. The n+2 dimensions are, in this order:

batch: Each coordinate in this dimension represents an independent input for which convolution is carried out.
z/depth/features: Each (y,x) position in the base area has a vector associated to it, which goes into this dimension.
spatial_dims: Describes the n spatial dimensions that define the base area that the window moves across.

The rhs argument is a rank n+2 array describing the convolutional filter/kernel/window. The dimensions are, in this order:

output-z: The z dimension of the output.
input-z: The size of this dimension should equal the size of the z dimension in lhs.
spatial_dims: Describes the n spatial dimensions that define the n-d window that moves across the base area.

The window_strides argument specifies the stride of the convolutional window in the spatial dimensions. For example, if the stride in a the first spatial dimension is 3, then the window can only be placed at coordinates where the first spatial index is divisible by 3.

The padding argument specifies the amount of zero padding to be applied to the base area. The amount of padding can be negative -- the absolute value of negative padding indicates the number of elements to remove from the specified dimension before doing the convolution. padding[0] specifies the padding for dimension y and padding[1] specifies the padding for dimension x. Each pair has the low padding as the first element and the high padding as the second element. The low padding is applied in the direction of lower indices while the high padding is applied in the direction of higher indices. For example, if padding[1] is (2,3) then there will be a padding by 2 zeroes on the left and by 3 zeroes on the right in the second spatial dimension. Using padding is equivalent to inserting those same zero values into the input (lhs) before doing the convolution.

The lhs_dilation and rhs_dilation arguments specify the dilation factor to be applied to the lhs and rhs, respectively, in each spatial dimension. If the dilation factor in a spatial dimension is d, then d-1 holes are implicitly placed between each of the entries in that dimension, increasing the size of the array. The holes are filled with a no-op value, which for convolution means zeroes.

Dilation of the rhs is also called atrous convolution. For more details, see the tf.nn.atrous_conv2d. Dilation of the lhs is also called deconvolution.

The output shape has these dimensions, in this order:

batch: Same size as batch on the input (lhs).
z: Same size as output-z on the kernel (rhs).
spatial_dims: One value for each valid placement of the convolutional window.

The valid placements of the convolutional window are determined by the strides and the size of the base area after padding.

To describe what a convolution does, consider a 2d convolution, and pick some fixed batch, z, y, x coordinates in the output. Then (y,x) is a position of a corner of the window within the base area (e.g. the upper left corner, depending on how you interpret the spatial dimensions). We now have a 2d window, taken from the base area, where each 2d point is associated to a 1d vector, so we get a 3d box. From the convolutional kernel, since we fixed the output coordinate z, we also have a 3d box. The two boxes have the same dimensions, so we can take the sum of the element-wise products between the two boxes (similar to a dot product). That is the output value.

Note that if output-z is e.g., 5, then each position of the window produces 5 values in the output into the z dimension of the output. These values differ in what part of the convolutional kernel is used - there is a separate 3d box of values used for each output-z coordinate. So you could think of it as 5 separate convolutions with a different filter for each of them.

Here is pseudo-code for a 2d convolution with padding and striding:

for (b, oz, oy, ox) {  // output coordinates
  value = 0;
  for (iz, ky, kx) {  // kernel coordinates and input z
    iy = oy*stride_y + ky - pad_low_y;
    ix = ox*stride_x + kx - pad_low_x;
    if ((iy, ix) inside the base area considered without padding) {
      value += input(b, iz, iy, ix) * kernel(oz, iz, ky, kx);
    }
  }
  output(b, oz, oy, ox) = value;
}

CrossReplicaSum

Computes a sum across replicas.

CrossReplicaSum(operand)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	Array to sum across replicas.

The output shape is the same as the input shape. For example, if there are two replicas and the operand has the value (1.0, 2.5) and (3.0, 5.1) respectively on the two replicas, then the output value from this op will be (4.0, 7.6) on both replicas.

Computing the result of CrossReplicaSum requires having one input from each replica, so if one replica executes a CrossReplicaSum node more times than another, then the former replica will wait forever. Since the replicas are all running the same program, there are not a lot of ways for that to happen, but it is possible when a while loop's condition depends on data from infeed and the data that is infed causes the while loop to iterate more times on one replica than another.

CustomCall

Call a user-provided function within a computation.

CustomCall(target_name, args..., shape)

Arguments	Type	Semantics
`target_name`	`string`	Name of the function. A call instruction will be emitted which targets this symbol name.
`args`	sequence of N `ComputationDataHandle`s	N arguments of arbitrary type, which will be passed to the function.
`shape`	`Shape`	Output shape of the function

The function signature is the same, regardless of the arity or type of args:

extern "C" void target_name(void* out, void** in);

For example, if CustomCall is used as follows:

let x = f32[2] {1,2};
let y = f32[2x3] { {10, 20, 30}, {40, 50, 60}};

CustomCall("myfunc", {x, y}, f32[3x3])

Here is an example of an implementation of myfunc:

extern "C" void myfunc(void* out, void** in) {
  float (&x)[2] = *static_cast<float(*)[2]>(in[0]);
  float (&y)[2][3] = *static_cast<float(*)[2][3]>(in[1]);
  EXPECT_EQ(1, x[0]);
  EXPECT_EQ(2, x[1]);
  EXPECT_EQ(10, y[0][0]);
  EXPECT_EQ(20, y[0][1]);
  EXPECT_EQ(30, y[0][2]);
  EXPECT_EQ(40, y[1][0]);
  EXPECT_EQ(50, y[1][1]);
  EXPECT_EQ(60, y[1][2]);
  float (&z)[3][3] = *static_cast<float(*)[3][3]>(out);
  z[0][0] = x[1] + y[1][0];
  // ...
}

The user-provided function must not have side-effects and its execution must be idempotent.

Note: The opaque nature of the user-provided function restricts optimization opportunities for the compiler. Try to express your computation in terms of native XLA ops whenever possible; only use CustomCall as a last resort.

Dot

Arguments	Type	Semantics
`lhs`	`ComputationDataHandle`	array of type T
`rhs`	`ComputationDataHandle`	array of type T

Input	Output	Semantics
vector [n] `dot` vector [n]	scalar	vector dot product
matrix [m x k] `dot` vector [k]	vector [m]	matrix-vector multiplication
matrix [m x k] `dot` matrix [k x n]	matrix [m x n]	matrix-matrix multiplication

Element-wise binary arithmetic operations

Arguments	Type	Semantics
`lhs`	`ComputationDataHandle`	left-hand-side operand: array of type T
`rhs`	`ComputationDataHandle`	right-hand-side operand: array of type T

Element-wise comparison operations

Arguments	Type	Semantics
`lhs`	`ComputationDataHandle`	left-hand-side operand: array of type T
`rhs`	`ComputationDataHandle`	right-hand-side operand: array of type T

Element-wise unary functions

ComputationBuilder supports these element-wise unary functions:

Abs(operand) Element-wise abs x -> |x|.

Ceil(operand) Element-wise ceil x -> ⌈x⌉.

Exp(operand) Element-wise natural exponential x -> e^x.

Floor(operand) Element-wise floor x -> ⌊x⌋.

IsFinite(operand) Tests whether each element of operand is finite, i.e., is not positive or negative infinity, and is not NaN. Returns an array of PRED values with the same shape as the input, where each element is true if and only if the corresponding input element is finite.

Log(operand) Element-wise natural logarithm x -> ln(x).

LogicalNot(operand) Element-wise logical not x -> !(x).

Neg(operand) Element-wise negation x -> -x.

Sign(operand) Element-wise sign operation x -> sgn(x) where

$$\text{sgn}(x) = \begin{cases} -1 & x < 0\\ 0 & x = 0\\ 1 & x > 0 \end{cases}$$

using the comparison operator of the element type of operand.

Tanh(operand) Element-wise hyperbolic tangent x -> tanh(x).

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	The operand to the function

The function is applied to each element in the operand array, resulting in an array with the same shape. It is allowed for operand to be a scalar (rank 0).

GetTupleElement

Indexes into a tuple with a compile-time-constant value.

The value must be a compile-time-constant so that shape inference can determine the type of the resulting value.

This is analogous to std::get<int N>(t) in C++. Conceptually:

let v: f32[10] = f32[10]{0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
let s: s32 = 5;
let t: (f32[10], s32) = tuple(v, s);
let element_1: s32 = gettupleelement(t, 1);  // Inferred shape matches s32.

Infeed

Argument	Type	Semantics
`shape`	`Shape`	Shape of the data read from the Infeed interface. The layout field of the shape must be set to match the layout of the data sent to the device; otherwise its behavior is undefined.

Map

Arguments	Type	Semantics
`operands`	sequence of N `ComputationDataHandle`s	N arrays of types T_0..T_{N-1}
`computation`	`Computation`	computation of type `T_0, T_1, ..., T_{N + M -1} -> S` with N parameters of type T and M of arbitrary type
`static_operands`	sequence of M `ComputationDataHandle`s	M arrays of arbitrary type

Pad

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	array of type `T`
`padding_value`	`ComputationDataHandle`	scalar of type `T` to fill in the added padding
`padding_config`	`PaddingConfig`	padding amount on both edges (low, high) and between the elements of each dimension

Reduce

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	array of type `T`
`init_value`	`ComputationDataHandle`	scalar of type `T`
`computation`	`Computation`	computation of type `T, T -> T`
`dimensions`	`int64` array	unordered array of dimensions to reduce

ReduceWindow

Applies a reduction function to all elements in each window of the input multi-dimensional array, producing an output multi-dimensional array with the same number of elements as the number of valid positions of the window. A pooling layer can be expressed as a ReduceWindow.

ReduceWindow(operand, init_value, computation, window_dimensions, window_strides, padding)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	N dimensional array containing elements of type T. This is the base area on which the window is placed.
`init_value`	`ComputationDataHandle`	Starting value for the reduction. See Reduce for details.
`computation`	`Computation`	Reduction function of type `T, T -> T`, to apply to all elements in each window
`window_dimensions`	`ArraySlice<int64>`	array of integers for window dimension values
`window_strides`	`ArraySlice<int64>`	array of integers for window stride values
`padding`	`Padding`	padding type for window (Padding\:\:kSame or Padding\:\:kValid)

Below code and figure shows an example of using ReduceWindow. Input is a matrix of size [4x6] and both window_dimensions and window_stride_dimensions are [2x3].

// Create a computation for the reduction (maximum).
Computation max;
{
  ComputationBuilder builder(client_, "max");
  auto y = builder.Parameter(0, ShapeUtil::MakeShape(F32, {}), "y");
  auto x = builder.Parameter(1, ShapeUtil::MakeShape(F32, {}), "x");
  builder.Max(y, x);
  max = builder.Build().ConsumeValueOrDie();
}

// Create a ReduceWindow computation with the max reduction computation.
ComputationBuilder builder(client_, "reduce_window_2x3");
auto shape = ShapeUtil::MakeShape(F32, {4, 6});
auto input = builder.Parameter(0, shape, "input");
builder.ReduceWindow(
    input, *max,
    /*init_val=*/builder.ConstantLiteral(LiteralUtil::MinValue(F32)),
    /*window_dimensions=*/{2, 3},
    /*window_stride_dimensions=*/{2, 3},
    Padding::kValid);

Stride of 1 in a dimension specifies that the position of a window in the dimension is 1 element away from its adjacent window. In order to specify that no windows overlap with each other, window_stride_dimensions should be equal to window_dimensions. The figure below illustrates the use of two different stride values. Padding is applied to each dimension of the input and the calculations are the same as though the input came in with the dimensions it has after padding.

The evaluation order of the reduction function is arbitrary and may be non-deterministic. Therefore, the reduction function should not be overly sensitive to reassociation. See the discussion about associativity in the context of Reduce for more details.

Reshape

See also ComputationBuilder::Reshape and the Collapse operation.

Reshapes the dimensions of an array into a new configuration.

Reshape(operand, new_sizes) Reshape(operand, dimensions, new_sizes)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	array of type T
`dimensions`	`int64` vector	order in which dimensions are collapsed
`new_sizes`	`int64` vector	vector of sizes of new dimensions

Conceptually, reshape first flattens an array into a one-dimensional vector of data values, and then refines this vector into a new shape. The input arguments are an arbitrary array of type T, a compile-time-constant vector of dimension indices, and a compile-time-constant vector of dimension sizes for the result. The values in the dimension vector, if given, must be a permutation of all of T's dimensions; the default if not given is {0, ..., rank - 1}. The order of the dimensions in dimensions is from slowest-varying dimension (most major) to fastest-varying dimension (most minor) in the loop nest which collapses the input array into a single dimension. The new_sizes vector determines the size of the output array. The value at index 0 in new_sizes is the size of dimension 0, the value at index 1 is the size of dimension 1, and so on. The product of the new_size dimensions must equal the product of the operand's dimension sizes. When refining the collapsed array into the multidimensional array defined by new_sizes, the dimensions in new_sizes are ordered from slowest varying (most major) and to fastest varying (most minor).

For example, let v be an array of 24 elements:

let v = f32[4x2x3] { { {10, 11, 12}, {15, 16, 17}},
                    { {20, 21, 22}, {25, 26, 27}},
                    { {30, 31, 32}, {35, 36, 37}},
                    { {40, 41, 42}, {45, 46, 47}}};

In-order collapse:
let v012_24 = Reshape(v, {0,1,2}, {24});
then v012_24 == f32[24] {10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27,
                         30, 31, 32, 35, 36, 37, 40, 41, 42, 45, 46, 47};

let v012_83 = Reshape(v, {0,1,2}, {8,3});
then v012_83 == f32[8x3] { {10, 11, 12}, {15, 16, 17},
                          {20, 21, 22}, {25, 26, 27},
                          {30, 31, 32}, {35, 36, 37},
                          {40, 41, 42}, {45, 46, 47}};

Out-of-order collapse:
let v021_24 = Reshape(v, {1,2,0}, {24});
then v012_24 == f32[24]  {10, 20, 30, 40, 11, 21, 31, 41, 12, 22, 32, 42,
                          15, 25, 35, 45, 16, 26, 36, 46, 17, 27, 37, 47};

let v021_83 = Reshape(v, {1,2,0}, {8,3});
then v021_83 == f32[8x3] { {10, 20, 30}, {40, 11, 21},
                          {31, 41, 12}, {22, 32, 42},
                          {15, 25, 35}, {45, 16, 26},
                          {36, 46, 17}, {27, 37, 47}};

let v021_262 = Reshape(v, {1,2,0}, {2,6,2});
then v021_262 == f32[2x6x2] { { {10, 20}, {30, 40},
                              {11, 21}, {31, 41},
                              {12, 22}, {32, 42}},
                             { {15, 25}, {35, 45},
                              {16, 26}, {36, 46},
                              {17, 27}, {37, 47}}};

As a special case, reshape can transform a single-element array to a scalar and vice versa. For example,

Reshape(f32[1x1] { {5}}, {0,1}, {}) == 5;
Reshape(5, {}, {1,1}) == f32[1x1] { {5}};

Rev (reverse)

RngBernoulli

Constructs an output of a given shape with random numbers generated following the Bernoulli distribution. The parameter needs to be a scalar valued F32 operand while the output shape needs to have elemental type U32.

RngBernoulli(mean, shape)

Arguments	Type	Semantics
`mean`	`ComputationDataHandle`	Scalar of type F32 specifying mean of generated numbers
`shape`	`Shape`	Output shape of type U32

RngNormal

Constructs an output of a given shape with random numbers generated following

the $$N(\mu, \sigma)$$ normal distribution. The parameters mu and sigma, and

output shape have to have elemental type F32. The parameters furthermore have to be scalar valued.

RngNormal(mean, sigma, shape)

Arguments	Type	Semantics
`mu`	`ComputationDataHandle`	Scalar of type F32 specifying mean of generated numbers
`sigma`	`ComputationDataHandle`	Scalar of type F32 specifying standard deviation of generated numbers
`shape`	`Shape`	Output shape of type F32

RngUniform

Constructs an output of a given shape with random numbers generated following

the uniform distribution over the interval $$[a,b)$$. The parameters and output

shape may be either F32, S32 or U32, but the types have to be consistent.

Furthermore, the parameters need to be scalar valued. If $$b <= a$$ the result

is implementation-defined.

RngUniform(a, b, shape)

Arguments	Type	Semantics
`a`	`ComputationDataHandle`	Scalar of type T specifying lower limit of interval
`b`	`ComputationDataHandle`	Scalar of type T specifying upper limit of interval
`shape`	`Shape`	Output shape of type T

SelectAndScatter

This operation can be considered as a composite operation that first computes ReduceWindow on the operand array to select an element from each window, and then scatters the source array to the indices of the selected elements to construct an output array with the same shape as the operand array. The binary select function is used to select an element from each window by applying it across each window, and it is called with the property that the first parameter's index vector is lexicographically less than the second parameter's index vector. The select function returns true if the first parameter is selected and returns false if the second parameter is selected, and the function must hold transitivity (i.e., if select(a, b) and select(b, c) are true, then select(a, c) is also true) so that the selected element does not depend on the order of the elements traversed for a given window.

The function scatter is applied at each selected index in the output array. It takes two scalar parameters:

Current value at the selected index in the output array
The scatter value from source that applies to the selected index

It combines the two parameters and returns a scalar value that's used to update the value at the selected index in the output array. Initially, all indices of the output array are set to init_value.

The output array has the same shape as the operand array and the source array must have the same shape as the result of applying a ReduceWindow operation on the operand array. SelectAndScatter can be used to backpropagate the gradient values for a pooling layer in a neural network.

SelectAndScatter(operand, select, window_dimensions, window_strides, padding, source, init_value, scatter)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	array of type T over which the windows slide
`select`	`Computation`	binary computation of type `T, T -> PRED`, to apply to all elements in each window; returns `true` if the first parameter is selected and returns `false` if the second parameter is selected
`window_dimensions`	`ArraySlice<int64>`	array of integers for window dimension values
`window_strides`	`ArraySlice<int64>`	array of integers for window stride values
`padding`	`Padding`	padding type for window (Padding\:\:kSame or Padding\:\:kValid)
`source`	`ComputationDataHandle`	array of type T with the values to scatter
`init_value`	`ComputationDataHandle`	scalar value of type T for the initial value of the output array
`scatter`	`Computation`	binary computation of type `T, T -> T`, to apply each scatter source element with its destination element

The figure below shows examples of using SelectAndScatter, with the select function computing the maximal value among its parameters. Note that when the windows overlap, as in the figure (2) below, an index of the operand array may be selected multiple times by different windows. In the figure, the element of value 9 is selected by both of the top windows (blue and red) and the binary addition scatter function produces the output element of value 8 (2 + 6).

The evaluation order of the scatter function is arbitrary and may be non-deterministic. Therefore, the scatter function should not be overly sensitive to reassociation. See the discussion about associativity in the context of Reduce for more details.

Select

Arguments	Type	Semantics
`pred`	`ComputationDataHandle`	array of type PRED
`on_true`	`ComputationDataHandle`	array of type T
`on_false`	`ComputationDataHandle`	array of type T

Slice

DynamicSlice

DynamicSlice extracts a sub-array from the input array at dynamic start_indices. The size of the slice in each dimension is passed in size_indices, which specify the end point of exclusive slice intervals in each dimension: [start, start + size). The shape of start_indices must be rank == 1, with dimension size equal to the rank of operand. Note: handling of out-of-bounds slice indices (generated by incorrect runtime calculation of 'start_indices') is currently implementation-defined. Currently, slice indices are computed modulo input dimension sizes to prevent out-of-bound array accesses, but this behavior may change in future implementations.

DynamicSlice(operand, start_indices, size_indices)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	N dimensional array of type T
`start_indices`	`ComputationDataHandle`	Rank 1 array of N integers containing the starting indices of the slice for each dimension. Value must be greater than or equal to zero.
`size_indices`	`ArraySlice<int64>`	List of N integers containing the slice size for each dimension. Each value must be strictly greater than zero, and start + size must be less than or equal to the size of the dimension to avoid wrapping modulo dimension size.

1-dimensional example:

let a = {0.0, 1.0, 2.0, 3.0, 4.0}
let s = {2}

DynamicSlice(a, s, {2}) produces:
  {2.0, 3.0}

2-dimensional example:

let b =
 { {0.0,  1.0,  2.0},
   {3.0,  4.0,  5.0},
   {6.0,  7.0,  8.0},
   {9.0, 10.0, 11.0} }
let s = {2, 1}

DynamicSlice(b, s, {2, 2}) produces:
  { { 7.0,  8.0},
    {10.0, 11.0} }

DynamicUpdateSlice

DynamicUpdateSlice generates a result which is the value of the input array operand, with a slice update overwritten at start_indices. The shape of update determines the shape of the sub-array of the result which is updated. The shape of start_indices must be rank == 1, with dimension size equal to the rank of operand. Note: handling of out-of-bounds slice indices (generated by incorrect runtime calculation of 'start_indices') is currently implementation-defined. Currently, slice indices are computed modulo update dimension sizes to prevent out-of-bound array accesses, but this behavior may change in future implementations.

DynamicUpdateSlice(operand, update, start_indices)

Arguments	Type	Semantics
`operand`	`ComputationDataHandle`	N dimensional array of type T
`update`	`ComputationDataHandle`	N dimensional array of type T containing the slice update. Each dimension of update shape must be strictly greater than zero, and start + update must be less than operand size for each dimension to avoid generating out-of-bounds update indices.
`start_indices`	`ComputationDataHandle`	Rank 1 array of N integers containing the starting indices of the slice for each dimension. Value must be greater than or equal to zero.

1-dimensional example:

let a = {0.0, 1.0, 2.0, 3.0, 4.0}
let u = {5.0, 6.0}
let s = {2}

DynamicUpdateSlice(a, u, s) produces:
  {0.0, 1.0, 5.0, 6.0, 4.0}

2-dimensional example:

let b =
 { {0.0,  1.0,  2.0},
   {3.0,  4.0,  5.0},
   {6.0,  7.0,  8.0},
   {9.0, 10.0, 11.0} }
let u =
 { {12.0,  13.0},
   {14.0,  15.0},
   {16.0,  17.0} }

let s = {1, 1}

DynamicUpdateSlice(b, u, s) produces:
 { {0.0,  1.0,  2.0},
   {3.0, 12.0, 13.0},
   {6.0, 14.0, 15.0},
   {9.0, 16.0, 17.0} }

Operation Semantics