The following describes the semantics of operations defined in the
ComputationBuilder
interface. Typically, these operations map onetoone to operations defined in
the RPC interface in
xla_data.proto
.
A note on nomenclature: the generalized data type XLA deals with is an Ndimensional array holding elements of some uniform type (such as 32bit float). Throughout the documentation, array is used to denote an arbitrarydimensional array. For convenience, special cases have more specific and familiar names; for example a vector is a 1dimensional array and a matrix is a 2dimensional array.
BatchNormGrad
See also
ComputationBuilder::BatchNormGrad
and the original batch normalization paper
for a detailed description of the algorithm.
Calculates gradients of batch norm.
BatchNormGrad(operand, scale, mean, variance, grad_output, epsilon, feature_index)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
n dimensional array to be normalized (x) 
scale 
ComputationDataHandle 
1 dimensional array (\(\gamma\)) 
mean 
ComputationDataHandle 
1 dimensional array (\(\mu\)) 
variance 
ComputationDataHandle 
1 dimensional array (\(\sigma^2\)) 
grad_output 
ComputationDataHandle 
Gradients passed to BatchNormTraining (\( \nabla y\)) 
epsilon 
float 
Epsilon value (\(\epsilon\)) 
feature_index 
int64 
Index to feature dimension in operand 
For each feature in the feature dimension (feature_index
is the index for the
feature dimension in operand
), the operation calculates the gradients with
respect to operand
, offset
and scale
across all the other dimensions. The
feature_index
must be a valid index for the feature dimension in operand
.
The three gradients are defined by the following formulas (Assuming a
4dimensional tensor as operand
and (l) is the index for feature dimension):
\( coef_l = \frac{1}{mwh}\sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h (\nabla y_{ijkl} * (x_{ijkl}  \mu_l) / (\sigma^2_{l}+\epsilon)) \)
\( \nabla x_{ijkl} = \gamma_{l} * (1/\sqrt{\sigma^2_{l}+\epsilon}) * [\nabla y_{ijkl}  mean(\nabla y)  (x_{ijkl}  \mu_{l}) * coef_l] \)
\( \nabla \beta_l = \sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h \nabla y_{ijkl} \)
\( \nabla \gamma_l = \sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h \nabla y_{ijkl} * ((x_{ijkl}  \mu_l) / \sqrt{\sigma^2_{l}+\epsilon}) \)
The inputs mean
and variance
represents moments value
across batch and spatial dimensions.
The output type is a tuple of three handles:
Outputs  Type  Semantics 

grad_operand 
ComputationDataHandle 
gradient with respect to input 
operand (\( \nabla x\)) 
grad_scale 
ComputationDataHandle 
grad_offset 
ComputationDataHandle 
gradient with respect to input offset (\( \nabla \beta\)) 
BatchNormInference
See also
ComputationBuilder::BatchNormInference
and
the original batch normalization paper
for a detailed description of the algorithm.
Normalizes an array across batch and spatial dimensions.
BatchNormInference(operand, scale, offset, mean, variance, epsilon, feature_index)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
n dimensional array to be normalized 
scale 
ComputationDataHandle 
1 dimensional array 
offset 
ComputationDataHandle 
1 dimensional array 
mean 
ComputationDataHandle 
1 dimensional array 
variance 
ComputationDataHandle 
1 dimensional array 
epsilon 
float 
Epsilon value 
feature_index 
int64 
Index to feature dimension in operand 
For each feature in the feature dimension (feature_index
is the index for the
feature dimension in operand
), the operation calculates the mean and variance
across all the other dimensions and uses the mean and variance to normalize each
element in operand
. The feature_index
must be a valid index for the feature
dimension in operand
.
BatchNormInference
is equivalent to calling BatchNormTraining
without
computing mean
and variance
for each batch. It uses the input mean
and
variance
instead as estimated values. The purpose of this op is to reduce
latency in inference, hence the name BatchNormInference
.
The output is an ndimensional, normalized array with the same shape as input
operand
.
BatchNormTraining
See also
ComputationBuilder::BatchNormTraining
and
the original batch normalization paper
for a detailed description of the algorithm.
Normalizes an array across batch and spatial dimensions.
BatchNormTraining(operand, scale, offset, epsilon, feature_index)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
n dimensional array to be normalized (x) 
scale 
ComputationDataHandle 
1 dimensional array (\(\gamma\)) 
offset 
ComputationDataHandle 
1 dimensional array (\(\beta\)) 
epsilon 
float 
Epsilon value (\(\epsilon\)) 
feature_index 
int64 
Index to feature dimension in operand 
For each feature in the feature dimension (feature_index
is the index for the
feature dimension in operand
), the operation calculates the mean and variance
across all the other dimensions and uses the mean and variance to normalize each
element in operand
. The feature_index
must be a valid index for the feature
dimension in operand
.
The algorithm goes as follows for each batch in operand
\(x\) that
contains m
elements with w
and h
as the size of spatial dimensions
(assuming operand
is an 4 dimensional array):

Calculates batch mean \(\mu_l\) for each feature
l
in feature dimension: \(\mu_l=\frac{1}{mwh}\sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h x_{ijkl}\) 
Calculates batch variance \(\sigma^2_l\): \(\sigma^2_l=\frac{1}{mwh}\sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h (x_{ijkl}  \mu_l)^2\)

Normalizes, scales and shifts: \(y_{ijkl}=\frac{\gamma_l(x_{ijkl}\mu_l)}{\sqrt[2]{\sigma^2_l+\epsilon}}+\beta_l\)
The epsilon value, usually a small number, is added to avoid dividebyzero errors.
The output type is a tuple of three ComputationDataHandle
s:
Outputs  Type  Semantics 

output 
ComputationDataHandle 
n dimensional array with the same shape as input operand (y) 
batch_mean 
ComputationDataHandle 
1 dimensional array (\(\mu\)) 
batch_var 
ComputationDataHandle 
1 dimensional array (\(\sigma^2\)) 
The batch_mean
and batch_var
are moments calculated across the batch and
spatial dimensions using the formulas above.
BitcastConvertType
See also
ComputationBuilder::BitcastConvertType
.
Similar to a tf.bitcast
in TensorFlow, performs an elementwise bitcast
operation from a data shape to a target shape. The dimensions must match, and
the conversion is an elementwise one; e.g. s32
elements become f32
elements
via bitcast routine. Bitcast is implemented as a lowlevel cast, so machines
with different floatingpoint representations will give different results.
BitcastConvertType(operand, new_element_type)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
array of type T with dims D 
new_element_type 
PrimitiveType 
type U 
The dimensions of the operand and the target shape must match. The bitwidth of the source and destination element types must be equal. The source and destination element types must not be tuples.
Broadcast
See also
ComputationBuilder::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
See also
ComputationBuilder::Call
.
Invokes a computation with the given arguments.
Call(computation, args...)
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 
The arity and types of the args
must match the parameters of the
computation
. It is allowed to have no args
.
Clamp
See also
ComputationBuilder::Clamp
.
Clamps an operand to within the range between a minimum and maximum value.
Clamp(min, operand, max)
Arguments  Type  Semantics 

min 
ComputationDataHandle 
array of type T 
operand 
ComputationDataHandle 
array of type T 
max 
ComputationDataHandle 
array of type T 
Given an operand and minimum and maximum values, returns the operand if it is in
the range between the minimum and maximum, else returns the minimum value if the
operand is below this range or the maximum value if the operand is above this
range. That is, clamp(a, x, b) = min(max(a, x), b)
.
All three arrays must be the same shape. Alternatively, as a restricted form of
broadcasting, min
and/or max
can be a scalar of type T
.
Example with scalar min
and max
:
let operand: s32[3] = {1, 5, 9};
let min: s32 = 0;
let max: s32 = 6;
==>
Clamp(min, operand, max) = s32[3]{0, 5, 6};
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 
inorder, 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
compiletimeconstant vector of dimension indices. The dimension indices must be
an inorder (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
See also
ComputationBuilder::ConcatInDim
.
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 rank0 values
cannot be concatenated (as it's impossible to name the dimension along which the
concatenation occurs).
1dimensional example:
Concat({ {2, 3}, {4, 5}, {6, 7}}, 0)
>>> {2, 3, 4, 5, 6, 7}
2dimensional 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:
Conditional
See also ComputationBuilder::Conditional
.
Conditional(pred, true_operand, true_computation, false_operand,
false_computation)
Arguments  Type  Semantics 

pred 
ComputationDataHandle 
Scalar of type PRED 
true_operand 
ComputationDataHandle 
Argument of type T_0 
true_computation 
Computation 
Computation of type T_0 > S 
false_operand 
ComputationDataHandle 
Argument of type T_1 
false_computation 
Computation 
Computation of type T_1 > S 
Executes true_computation
if pred
is true
, false_computation
if pred
is false
, and returns the result.
The true_computation
must take in a single argument of type T_0
and will be
invoked with true_operand
which must be of the same type. The
false_computation
must take in a single argument of type T_1
and will be
invoked with false_operand
which must be of the same type. The type of the
returned value of true_computation
and false_computation
must be the same.
Note that only one of true_computation
and false_computation
will be
executed depending on the value of pred
.
Conv (convolution)
See also
ComputationBuilder::Conv
.
As ConvWithGeneralPadding, but the padding is specified in a shorthand way as
either SAME or VALID. SAME padding pads the input (lhs
) with zeroes so that
the output has the same shape as the input when not taking striding into
account. VALID padding simply means no padding.
ConvWithGeneralPadding (convolution)
See also
ComputationBuilder::ConvWithGeneralPadding
.
Computes a convolution of the kind used in neural networks. Here, a convolution can be thought of as a ndimensional window moving across a ndimensional 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> 
size n array of kernel strides 
padding 
ArraySlice<pair<int64, int64>> 
size n array of (low, high) padding 
lhs_dilation 
ArraySlice<int64> 
size n lhs dilation factor 
: : : array  
rhs_dilation 
ArraySlice<int64> 
size n 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 then
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:
outputz
: Thez
dimension of the output.inputz
: The size of this dimension should equal the size of thez
dimension in lhs.spatial_dims
: Describes then
spatial dimensions that define the nd 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 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 d1 holes are implicitly
placed between each of the entries in that dimension, increasing the size of the
array. The holes are filled with a noop value, which for convolution means
zeroes.
Dilation of the rhs is also called atrous convolution. For more details, see
tf.nn.atrous_conv2d
. Dilation of the lhs is also called transposed
convolution. For more details, see tf.nn.conv2d_transpose
.
The output shape has these dimensions, in this order:
batch
: Same size asbatch
on the input (lhs
).z
: Same size asoutputz
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 elementwise products between the two
boxes (similar to a dot product). That is the output value.
Note that if outputz
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 outputz
coordinate. So you could think of it as 5
separate convolutions with a different filter for each of them.
Here is pseudocode 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;
}
ConvertElementType
See also
ComputationBuilder::ConvertElementType
.
Similar to an elementwise static_cast
in C++, performs an elementwise
conversion operation from a data shape to a target shape. The dimensions must
match, and the conversion is an elementwise one; e.g. s32
elements become
f32
elements via an s32
tof32
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 
The dimensions of the operand and the target shape must match. The source and destination element types must not be tuples.
A conversion such as T=s32
to U=f32
will perform a normalizing inttofloat
conversion routine such as roundtonearesteven.
let a: s32[3] = {0, 1, 2};
let b: f32[3] = convert(a, f32);
then b == f32[3]{0.0, 1.0, 2.0}
CrossReplicaSum
See also
ComputationBuilder::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, 5.25)
respectively on the two replicas, then the output value from this op will be
(4.0, 7.75)
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
See also
ComputationBuilder::CustomCall
.
Call a userprovided 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 userprovided function must not have sideeffects and its execution must be idempotent.
Dot
See also
ComputationBuilder::Dot
.
Dot(lhs, rhs)
Arguments  Type  Semantics 

lhs 
ComputationDataHandle 
array of type T 
rhs 
ComputationDataHandle 
array of type T 
The exact semantics of this operation depend on the ranks of the operands:
Input  Output  Semantics 

vector [n] dot vector [n] 
scalar  vector dot product 
matrix [m x k] dot vector [k] 
vector [m]  matrixvector multiplication 
matrix [m x k] dot matrix [k x n] 
matrix [m x n]  matrixmatrix multiplication 
The operation performs sum of products over the last dimension of lhs
and the
onebeforelast dimension of rhs
. These are the "contracted" dimensions. The
contracted dimensions of lhs
and rhs
must be of the same size. In practice,
it can be used to perform dot products between vectors, vector/matrix
multiplications or matrix/matrix multiplications.
DotGeneral
See also
ComputationBuilder::DotGeneral
.
DotGeneral(lhs, rhs, dimension_numbers)
Arguments  Type  Semantics 

lhs 
ComputationDataHandle 
array of type T 
rhs 
ComputationDataHandle 
array of type T 
dimension_numbers 
DotDimensionNumbers 
array of type T 
As Dot, but allows contracting and batch dimension numbers to be specified for both the 'lhs' and 'rhs'.
DotDimensionNumbers Fields  Type  Semantics 

'lhs_contracting_dimensions'  repeated int64  'lhs' contracting dimension numbers 
'rhs_contracting_dimensions'  repeated int64  'rhs' contracting dimension numbers 
'lhs_batch_dimensions'  repeated int64  'lhs' batch dimension numbers 
'rhs_batch_dimensions'  repeated int64  'rhs' batch dimension numbers 
DotGeneral performs the sum of products over contracting dimensions specified in 'dimension_numbers'.
Associated contracting dimension numbers from the 'lhs' and 'rhs' do not need to be the same, but must be listed in the same order in both 'lhs/rhs_contracting_dimensions' arrays and have the same dimension sizes. There must be exactly one contracting dimension on both 'lhs' and 'rhs'.
Example with contracting dimension numbers:
lhs = { {1.0, 2.0, 3.0},
{4.0, 5.0, 6.0} }
rhs = { {1.0, 1.0, 1.0},
{2.0, 2.0, 2.0} }
DotDimensionNumbers dnums;
dnums.add_lhs_contracting_dimensions(1);
dnums.add_rhs_contracting_dimensions(1);
DotGeneral(lhs, rhs, dnums) > { {6.0, 12.0},
{15.0, 30.0} }
Associated batch dimension numbers from the 'lhs' and 'rhs' must have the same dimension number, must be listed in the same order in both arrays, must have the same dimension sizes, and must be ordered before contracting and noncontracting/nonbatch dimension numbers.
Example with batch dimension numbers (batch size 2, 2x2 matrices):
lhs = { { {1.0, 2.0},
{3.0, 4.0} },
{ {5.0, 6.0},
{7.0, 8.0} } }
rhs = { { {1.0, 0.0},
{0.0, 1.0} },
{ {1.0, 0.0},
{0.0, 1.0} } }
DotDimensionNumbers dnums;
dnums.add_lhs_contracting_dimensions(2);
dnums.add_rhs_contracting_dimensions(1);
dnums.add_lhs_batch_dimensions(0);
dnums.add_rhs_batch_dimensions(0);
DotGeneral(lhs, rhs, dnums) > { { {1.0, 2.0},
{3.0, 4.0} },
{ {5.0, 6.0},
{7.0, 8.0} } }
Input  Output  Semantics 

[b0, m, k] dot [b0, k, n] 
[b0, m, n]  batch matmul 
[b0, b1, m, k] dot [b0, b1, k, n] 
[b0, b1, m, n]  batch matmul 
It follows that the resulting dimension number starts with the batch dimension, then the 'lhs' noncontracting/nonbatch dimension, and finally the 'rhs' noncontracting/nonbatch dimension.
DynamicSlice
See also
ComputationBuilder::DynamicSlice
.
DynamicSlice extracts a subarray 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 outofbounds slice indices (generated by incorrect runtime
calculation of 'start_indices') is currently implementationdefined.
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. 
1dimensional 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}
2dimensional 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
See also
ComputationBuilder::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 subarray 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 outofbounds slice indices (generated by incorrect runtime
calculation of 'start_indices') is currently implementationdefined.
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 outofbounds 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. 
1dimensional 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}
2dimensional 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} }
Elementwise binary arithmetic operations
See also
ComputationBuilder::Add
.
A set of elementwise binary arithmetic operations is supported.
Op(lhs, rhs)
Where Op
is one of Add
(addition), Sub
(subtraction), Mul
(multiplication), Div
(division), Rem
(remainder), Max
(maximum), Min
(minimum), LogicalAnd
(logical AND), or LogicalOr
(logical OR).
Arguments  Type  Semantics 

lhs 
ComputationDataHandle 
lefthandside operand: array of type T 
rhs 
ComputationDataHandle 
righthandside operand: array of type T 
The arguments' shapes have to be either similar or compatible. See the broadcasting documentation about what it means for shapes to be compatible. The result of an operation has a shape which is the result of broadcasting the two input arrays. In this variant, operations between arrays of different ranks are not supported, unless one of the operands is a scalar.
When Op
is Rem
, the sign of the result is taken from the dividend, and the
absolute value of the result is always less than the divisor's absolute value.
An alternative variant with differentrank broadcasting support exists for these operations:
Op(lhs, rhs, broadcast_dimensions)
Where Op
is the same as above. This variant of the operation should be used
for arithmetic operations between arrays of different ranks (such as adding a
matrix to a vector).
The additional broadcast_dimensions
operand is a slice of integers used to
expand the rank of the lowerrank operand up to the rank of the higherrank
operand. broadcast_dimensions
maps the dimensions of the lowerrank shape to
the dimensions of the higherrank shape. The unmapped dimensions of the expanded
shape are filled with dimensions of size one. Degeneratedimension broadcasting
then broadcasts the shapes along these degenerate dimensions to equalize the
shapes of both operands. The semantics are described in detail on the
broadcasting page.
Elementwise comparison operations
See also
ComputationBuilder::Eq
.
A set of standard elementwise binary comparison operations is supported. Note that standard IEEE 754 floatingpoint comparison semantics apply when comparing floatingpoint types.
Op(lhs, rhs)
Where Op
is one of Eq
(equalto), Ne
(not equalto), Ge
(greaterorequalthan), Gt
(greaterthan), Le
(lessorequalthan), Lt
(lessthan).
Arguments  Type  Semantics 

lhs 
ComputationDataHandle 
lefthandside operand: array of type T 
rhs 
ComputationDataHandle 
righthandside operand: array of type T 
The arguments' shapes have to be either similar or compatible. See the
broadcasting documentation about what it means for shapes to
be compatible. The result of an operation has a shape which is the result of
broadcasting the two input arrays with the element type PRED
. In this variant,
operations between arrays of different ranks are not supported, unless one of
the operands is a scalar.
An alternative variant with differentrank broadcasting support exists for these operations:
Op(lhs, rhs, broadcast_dimensions)
Where Op
is the same as above. This variant of the operation should be used
for comparison operations between arrays of different ranks (such as adding a
matrix to a vector).
The additional broadcast_dimensions
operand is a slice of integers specifying
the dimensions to use for broadcasting the operands. The semantics are described
in detail on the broadcasting page.
Elementwise unary functions
ComputationBuilder supports these elementwise unary functions:
Abs(operand)
Elementwise abs x > x
.
Ceil(operand)
Elementwise ceil x > ⌈x⌉
.
Cos(operand)
Elementwise cosine x > cos(x)
.
Exp(operand)
Elementwise natural exponential x > e^x
.
Floor(operand)
Elementwise 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)
Elementwise natural logarithm x > ln(x)
.
LogicalNot(operand)
Elementwise logical not x > !(x)
.
Neg(operand)
Elementwise negation x > x
.
Sign(operand)
Elementwise sign operation x > sgn(x)
where
using the comparison operator of the element type of operand
.
Tanh(operand)
Elementwise 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).
Gather
The XLA gather operation stitches together several slices (each slice at a potentially different runtime offset) of an input tensor into an output tensor.
General Semantics
See also
ComputationBuilder::Gather
.
For a more intuitive description, see the "Informal Description" section below.
gather(operand, gather_indices, output_window_dims, elided_window_dims, window_bounds, gather_dims_to_operand_dims)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
The tensor we’re gathering from. 
gather_indices 
ComputationDataHandle 
Tensor containing the starting indices of the slices we're we're stitching together into the output tensor. 
index_vector_dim 
int64 
The dimension in gather_indices that contains the starting indices. 
output_window_dims 
ArraySlice<int64> 
The set of dimensions in the output shape that are window dimensions (defined below). Not all window dimensions may be present in the output shape. 
elided_window_dims 
ArraySlice<int64> 
The set of window dimensions that are not present in the output shape. window_bounds[i] must be 1 for all i in elided_window_dims . 
window_bounds 
ArraySlice<int64> 
window_bounds[i] is the bounds for window dimension i . This includes both the window dimensions that are explicitly part of the output shape (via output_window_dims ) and the window dimensions that are elided (via elided_window_dims ). 
gather_dims_to_operand_dims 
ArraySlice<int64> 
A dimension map (the array is interpreted as mapping i to gather_dims_to_operand_dims[i] ) from the gather indices in gather_indices to the operand index space. It has to be onetoone and total. 
For every index Out
in the output tensor, we compute two things (more
precisely described later):

An index into
gather_indices.rank
1
dimensions ofgather_indices
, which gives us a starting index of a slice, operand slice, in the operand tensor. Thesegather_indices.rank
1
dimensions are all the dimensions ingather_indices
exceptindex_vector_dim
. 
A window index that has the same rank as the operand. This index is composed of the values in
Out
at dimensionsoutput_window_dims
, embedded with zeroes according toelided_window_dims
.
The window index is the relative index of the element in operand slice that
should be present in the output at index Out
.
The output is a tensor of rank output_window_dims.size
+ gather_indices.rank
 1
. Additionally, as a shorthand, we define output_gather_dims
of type
ArraySlice<int64>
as the set of dimensions in the output shape but not in
output_window_dims
, in ascending order. E.g. if the output tensor has rank
5
, output_window_dims
is {2
, 4
} then output_gather_dims
is {0
, 1
,
3
}
If index_vector_dim
is equal to gather_indices.rank
we implicitly
consider gather_indices
to have a trailing 1
dimension (i.e. if
gather_indices
was of shape [6,7]
and index_vector_dim
is 2
then
we implicitly consider the shape of gather_indices
to be [6,7,1]
).
The bounds for the output tensor along dimension i
is computed as follows:
 If
i
is present inoutput_gather_dims
(i.e. is equal tooutput_gather_dims[k]
for somek
) then we pick the corresponding dimension bounds out ofgather_indices.shape
, skippingindex_vector_dim
(i.e. pickgather_indices.shape.dims
[k
] ifk
<index_vector_dim
andgather_indices.shape.dims
[k
+1
] otherwise).  If
i
is present inoutput_window_dims
(i.e. equal tooutput_window_dims
[k
] for somek
) then we pick the corresponding bound out ofwindow_bounds
after accounting forelided_window_dims
(i.e. we pickadjusted_window_bounds
[k
] whereadjusted_window_bounds
iswindow_bounds
with the bounds at indiceselided_window_dims
removed).
The operand index In
corresponding to an output index Out
is computed as
follows:
 Let
G
= {Out
[k
] fork
inoutput_gather_dims
}. UseG
to slice out vectorS
such thatS
[i
] =gather_indices
[Combine(G
,i
)] where Combine(A, b) inserts b at positionindex_vector_dim
into A. Note that this is well defined even ifG
is empty  ifG
is empty thenS
=gather_indices
.  Create an index,
S
_{in}, intooperand
usingS
by scatteringS
using thegather_dims_to_operand_dims
map (S
_{in} is the starting indices for operand slice mentioned above). More precisely:S
_{in}[gather_dims_to_operand_dims
[k
]] =S
[k
] ifk
<gather_dims_to_operand_dims.size
.S
_{in}[_
] =0
otherwise.
 Create an index
W
_{in} intooperand
by scattering the indices at the output window dimensions inOut
according to theelided_window_dims
set (W
_{in} is the window index mentioned above). More precisely:W
_{in}[window_dims_to_operand_dims
(k
)] =Out
[k
] ifk
<output_window_dims.size
(window_dims_to_operand_dims
is defined below).W
_{in}[_
] =0
otherwise.
In
isW
_{in} +S
_{in} where + is elementwise addition.
window_dims_to_operand_dims
is the monotonic function with domain [0
,
output_window_dims.size
) and range [0
, operand.rank
) \
elided_window_dims
. So if, e.g., output_window_dims.size
is 4
,
operand.rank
is 6
and elided_window_dims
is {0
, 2
} then
window_dims_to_operand_dims
is {0
→1
, 1
→3
, 2
→4
, 3
→5
}.
Informal Description and Examples
index_vector_dim
is set to gather_indices.rank
 1
in all of the
examples that follow. More interesting values for index_vector_dim
does not change the operation fundamentally, but makes the visual representation
more cumbersome.
To get an intuition on how all of the above fits together, let's look at an
example that gathers 5 slices of shape [8,6]
from a [16,11]
tensor. The
position of a slice into the [16,11]
tensor can be represented as an index
vector of shape S64[2]
, so the set of 5 positions can be represented as a
S64[5,2]
tensor.
The behavior of the gather operation can then be depicted as an index
transformation that takes [G
,W
_{0},W
_{1}], an index in
the output shape, and maps it to an element in the input tensor in the following
way:
We first select an (X
,Y
) vector from the gather indices tensor using G
.
The element in the output tensor at index
[G
,W
_{0},W
_{1}] is then the element in the input
tensor at index [X
+W
_{0},Y
+W
_{1}].
window_bounds
is [8,6]
, which decides the range of W_{0} and
W_{1}, and this in turn decides the bounds of the slice.
This gather operation acts as a batch dynamic slice with G
as the batch
dimension.
The gather indices may be multidimensional. For instance, a more general
version of the example above using a "gather indices" tensor of shape [4,5,2]
would translate indices like this:
Again, this acts as a batch dynamic slice G
_{0} and
G
_{1} as the batch dimensions. The window bounds are still [8,6]
.
The gather operation in XLA generalizes the informal semantics outlined above in the following ways:

We can configure which dimensions in the output shape are the window dimensions (dimensions containing
W
_{0},W
_{1} in the last example). The output gather dimensions (dimensions containingG
_{0},G
_{1} in the last example) are defined to be the output dimensions that are not window dimensions. 
The number of output window dimensions explicitly present in the output shape may be smaller than the input rank. These "missing" dimensions, which are listed explicitly as
elided_window_dims
, must have a window bound of1
. Since they have a window bound of1
the only valid index for them is0
and eliding them does not introduce ambiguity. 
The slice extracted from the "Gather Indices" tensor ((
X
,Y
) in the last example) may have fewer elements than the input tensor rank, and an explicit mapping dictates how the index should be expanded to have the same rank as the input.
As a final example, we use (2) and (3) to implement tf.gather_nd
:
G
_{0} and G
_{1} are used to slice out a starting index
from the gather indices tensor as usual, except the starting index has only one
element, X
. Similarly, there is only one output window index with the value
W
_{0}. However, before being used as indices into the input tensor,
these are expanded in accordance to "Gather Index Mapping"
(gather_dims_to_operand_dims
in the formal description) and "Window Mapping"
(window_dims_to_operand_dims
in the formal description) into
[0
,W
_{0}] and [X
,0
] respectively, adding up to
[X
,W
_{0}]. In other words, the output index
[G
_{0},G
_{1},W
_{0}] maps to the input index
[GatherIndices
[G
_{0},G
_{1},0
],X
] which gives us
the semantics for tf.gather_nd
.
window_bounds
for this case is [1,11]
. Intuitively this means that every
index X
in the gather indices tensor picks an entire row and the result is the
concatenation of all these rows.
GetTupleElement
See also
ComputationBuilder::GetTupleElement
.
Indexes into a tuple with a compiletimeconstant value.
The value must be a compiletimeconstant 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.
See also tf.tuple
.
Infeed
See also
ComputationBuilder::Infeed
.
Infeed(shape)
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. 
Reads a single data item from the implicit Infeed streaming interface of the
device, interpreting the data as the given shape and its layout, and returns a
ComputationDataHandle
of the data. Multiple Infeed operations are allowed in a
computation, but there must be a total order among the Infeed operations. For
example, two Infeeds in the code below have a total order since there is a
dependency between the while loops.
result1 = while (condition, init = init_value) {
Infeed(shape)
}
result2 = while (condition, init = result1) {
Infeed(shape)
}
Nested tuple shapes are not supported. For an empty tuple shape, the Infeed operation is effectively a noop and proceeds without reading any data from the Infeed of the device.
Map
See also
ComputationBuilder::Map
.
Map(operands..., computation)
Arguments  Type  Semantics 

operands 
sequence of N ComputationDataHandle s 
N arrays of types T_0..T_{N1} 
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 
dimensions 
int64 array 
array of map dimensions 
static_operands 
sequence of M ComputationDataHandle s 
M arrays of arbitrary type 
Applies a scalar function over the given operands
arrays, producing an array
of the same dimensions where each element is the result of the mapped function
applied to the corresponding elements in the input arrays with static_operands
given as additional input to computation
.
The mapped function is an arbitrary computation with the restriction that it has
N inputs of scalar type T
and a single output with type S
. The output has
the same dimensions as the operands except that the element type T is replaced
with S.
For example: Map(op1, op2, op3, computation, par1)
maps elem_out <
computation(elem1, elem2, elem3, par1)
at each (multidimensional) index in the
input arrays to produce the output array.
Pad
See also
ComputationBuilder::Pad
.
Pad(operand, padding_value, padding_config)
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 
Expands the given operand
array by padding around the array as well as between
the elements of the array with the given padding_value
. padding_config
specifies the amount of edge padding and the interior padding for each
dimension.
PaddingConfig
is a repeated field of PaddingConfigDimension
, which contains
three fields for each dimension: edge_padding_low
, edge_padding_high
, and
interior_padding
. edge_padding_low
and edge_padding_high
specify the
amount of padding added at the lowend (next to index 0) and the highend (next
to the highest index) of each dimension respectively. The amount of edge padding
can be negative  the absolute value of negative padding indicates the number
of elements to remove from the specified dimension. interior_padding
specifies
the amount of padding added between any two elements in each dimension. Interior
padding occurs logically before edge padding, so in the case of negative edge
padding elements are removed from the interiorpadded operand. This operation is
a noop if the edge padding pairs are all (0, 0) and the interior padding values
are all 0. The figure below shows examples of different edge_padding
and
interior_padding
values for a twodimensional array.
Recv
See also
ComputationBuilder::Recv
.
Recv(shape, channel_handle)
Arguments  Type  Semantics 

shape 
Shape 
shape of the data to receive 
channel_handle 
ChannelHandle 
unique identifier for each send/recv pair 
Receives data of the given shape from a Send
instruction in another
computation that shares the same channel handle. Returns a
ComputationDataHandle for the received data.
The client API of Recv
operation represents synchronous communication.
However, the instruction is internally decomposed into 2 HLO instructions
(Recv
and RecvDone
) to enable asynchronous data transfers. See also
HloInstruction::CreateRecv
and HloInstruction::CreateRecvDone
.
Recv(const Shape& shape, int64 channel_id)
Allocates resources required to receive data from a Send
instruction with the
same channel_id. Returns a context for the allocated resources, which is used
by a following RecvDone
instruction to wait for the completion of the data
transfer. The context is a tuple of {receive buffer (shape), request identifier
(U32)} and it can only be used by a RecvDone
instruction.
RecvDone(HloInstruction context)
Given a context created by a Recv
instruction, waits for the data transfer to
complete and returns the received data.
Reduce
See also
ComputationBuilder::Reduce
.
Applies a reduction function to an array.
Reduce(operand, init_value, computation, dimensions)
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 
Conceptually, this operation reduces one or more dimensions in the input array
into scalars. The rank of the result array is rank(operand)  len(dimensions)
.
init_value
is the initial value used for every reduction and may also be
inserted anywhere during computation if the backend chooses to do so. So in
most cases init_value
should be an identity of the reduction function (for
example, 0 for addition).
The evaluation order of the reduction function is arbitrary and may be nondeterministic. Therefore, the reduction function should not be overly sensitive to reassociation.
Some reduction functions like addition are not strictly associative for floats. However, if the range of the data is limited, floatingpoint addition is close enough to being associative for most practical uses. It is possible to conceive of some completely nonassociative reductions, however, and these will produce incorrect or unpredictable results in XLA reductions.
As an example, when reducing across the one dimension in a 1D array with values
[10, 11, 12, 13], with reduction function f
(this is computation
) then that
could be computed as
f(10, f(11, f(12, f(init_value, 13)))
but there are also many other possibilities, e.g.
f(init_value, f(f(10, f(init_value, 11)), f(f(init_value, 12), f(13,
init_value))))
The following is a rough pseudocode example of how reduction could be implemented, using summation as the reduction computation with an initial value of 0.
result_shape < remove all dims in dimensions from operand_shape
# Iterate over all elements in result_shape. The number of r's here is equal
# to the rank of the result
for r0 in range(result_shape[0]), r1 in range(result_shape[1]), ...:
# Initialize this result element
result[r0, r1...] < 0
# Iterate over all the reduction dimensions
for d0 in range(dimensions[0]), d1 in range(dimensions[1]), ...:
# Increment the result element with the value of the operand's element.
# The index of the operand's element is constructed from all ri's and di's
# in the right order (by construction ri's and di's together index over the
# whole operand shape).
result[r0, r1...] += operand[ri... di]
Here's an example of reducing a 2D array (matrix). The shape has rank 2, dimension 0 of size 2 and dimension 1 of size 3:
Results of reducing dimensions 0 or 1 with an "add" function:
Note that both reduction results are 1D arrays. The diagram shows one as column and another as row just for visual convenience.
For a more complex example, here is a 3D array. Its rank is 3, dimension 0 of size 4, dimension 1 of size 2 and dimension 2 of size 3. For simplicity, the values 1 to 6 are replicated across dimension 0.
Similarly to the 2D example, we can reduce just one dimension. If we reduce dimension 0, for example, we get a rank2 array where all values across dimension 0 were folded into a scalar:
 4 8 12 
 16 20 24 
If we reduce dimension 2, we also get a rank2 array where all values across dimension 2 were folded into a scalar:
 6 15 
 6 15 
 6 15 
 6 15 
Note that the relative order between the remaining dimensions in the input is preserved in the output, but some dimensions may get assigned new numbers (since the rank changes).
We can also reduce multiple dimensions. Addreducing dimensions 0 and 1 produces
the 1D array  20 28 36 
.
Reducing the 3D array over all its dimensions produces the scalar 84
.
ReducePrecision
See also
ComputationBuilder::ReducePrecision
.
Models the effect of converting floatingpoint values to a lowerprecision format (such as IEEEFP16) and back to the original format. The number of exponent and mantissa bits in the lowerprecision format can be specified arbitrarily, although all bit sizes may not be supported on all hardware implementations.
ReducePrecision(operand, mantissa_bits, exponent_bits)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
array of floatingpoint type T . 
exponent_bits 
int32 
number of exponent bits in lowerprecision format 
mantissa_bits 
int32 
number of mantissa bits in lowerprecision format 
The result is an array of type T
. The input values are rounded to the nearest
value representable with the given number of mantissa bits (using "ties to even"
semantics), and any values that exceed the range specified by the number of
exponent bits are clamped to positive or negative infinity. NaN
values are
retained, although they may be converted to canonical NaN
values.
The lowerprecision format must have at least one exponent bit (in order to
distinguish a zero value from an infinity, since both have a zero mantissa), and
must have a nonnegative number of mantissa bits. The number of exponent or
mantissa bits may exceed the corresponding value for type T
; the corresponding
portion of the conversion is then simply a noop.
ReduceWindow
See also
ComputationBuilder::ReduceWindow
.
Applies a reduction function to all elements in each window of the input
multidimensional array, producing an output multidimensional 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
nondeterministic. 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 onedimensional vector of
data values, and then refines this vector into a new shape. The input arguments
are an arbitrary array of type T, a compiletimeconstant vector of dimension
indices, and a compiletimeconstant 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 slowestvarying dimension (most major) to
fastestvarying 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}}};
Inorder 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}};
Outoforder 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 singleelement 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)
See also
ComputationBuilder::Rev
.
Rev(operand, dimensions)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
array of type T 
dimensions 
ArraySlice<int64> 
dimensions to reverse 
Reverses the order of elements in the operand
array along the specified
dimensions
, generating an output array of the same shape. Each element of the
operand array at a multidimensional index is stored into the output array at a
transformed index. The multidimensional index is transformed by reversing the
index in each dimension to be reversed (i.e., if a dimension of size N is one of
the reversing dimensions, its index i is transformed into N  1  i).
One use for the Rev
operation is to reverse the convolution weight array along
the two window dimensions during the gradient computation in neural networks.
RngNormal
See also
ComputationBuilder::RngNormal
.
Constructs an output of a given shape with random numbers generated following
mu
and sigma
, and 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
See also
ComputationBuilder::RngUniform
.
Constructs an output of a given shape with random numbers generated following
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 
Select
See also
ComputationBuilder::Select
.
Constructs an output array from elements of two input arrays, based on the values of a predicate array.
Select(pred, on_true, on_false)
Arguments  Type  Semantics 

pred 
ComputationDataHandle 
array of type PRED 
on_true 
ComputationDataHandle 
array of type T 
on_false 
ComputationDataHandle 
array of type T 
The arrays on_true
and on_false
must have the same shape. This is also the
shape of the output array. The array pred
must have the same dimensionality as
on_true
and on_false
, with the PRED
element type.
For each element P
of pred
, the corresponding element of the output array is
taken from on_true
if the value of P
is true
, and from on_false
if the
value of P
is false
. As a restricted form of broadcasting
, pred
can be a scalar of type PRED
. In this case, the
output array is taken wholly from on_true
if pred
is true
, and from
on_false
if pred
is false
.
Example with nonscalar pred
:
let pred: PRED[4] = {true, false, false, true};
let v1: s32[4] = {1, 2, 3, 4};
let v2: s32[4] = {100, 200, 300, 400};
==>
Select(pred, v1, v2) = s32[4]{1, 200, 300, 4};
Example with scalar pred
:
let pred: PRED = true;
let v1: s32[4] = {1, 2, 3, 4};
let v2: s32[4] = {100, 200, 300, 400};
==>
Select(pred, v1, v2) = s32[4]{1, 2, 3, 4};
Selections between tuples are supported. Tuples are considered to be scalar
types for this purpose. If on_true
and on_false
are tuples (which must have
the same shape!) then pred
has to be a scalar of type PRED
.
SelectAndScatter
See also
ComputationBuilder::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
nondeterministic. Therefore, the scatter
function should not be overly
sensitive to reassociation. See the discussion about associativity in the
context of Reduce
for more details.
Send
See also
ComputationBuilder::Send
.
Send(operand, channel_handle)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
data to send (array of type T) 
channel_handle 
ChannelHandle 
unique identifier for each send/recv pair 
Sends the given operand data to a Recv
instruction in another computation
that shares the same channel handle. Does not return any data.
Similar to the Recv
operation, the client API of Send
operation represents
synchronous communication, and is internally decomposed into 2 HLO instructions
(Send
and SendDone
) to enable asynchronous data transfers. See also
HloInstruction::CreateSend
and HloInstruction::CreateSendDone
.
Send(HloInstruction operand, int64 channel_id)
Initiates an asynchronous transfer of the operand to the resources allocated by
the Recv
instruction with the same channel id. Returns a context, which is
used by a following SendDone
instruction to wait for the completion of the
data transfer. The context is a tuple of {operand (shape), request identifier
(U32)} and it can only be used by a SendDone
instruction.
SendDone(HloInstruction context)
Given a context created by a Send
instruction, waits for the data transfer to
complete. The instruction does not return any data.
Scheduling of channel instructions
The execution order of the 4 instructions for each channel (Recv
, RecvDone
,
Send
, SendDone
) is as below.
Recv
happens beforeSend
Send
happens beforeRecvDone
Recv
happens beforeRecvDone
Send
happens beforeSendDone
When the backend compilers generate a linear schedule for each computation that communicates via channel instructions, there must not be cycles across the computations. For example, below schedules lead to deadlocks.
Slice
See also
ComputationBuilder::Slice
.
Slicing extracts a subarray from the input array. The subarray is of the same rank as the input and contains the values inside a bounding box within the input array where the dimensions and indices of the bounding box are given as arguments to the slice operation.
Slice(operand, start_indices, limit_indices)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
N dimensional array of type T 
start_indices 
ArraySlice<int64> 
List of N integers containing the starting indices of the slice for each dimension. Values must be greater than or equal to zero. 
limit_indices 
ArraySlice<int64> 
List of N integers containing the ending indices (exclusive) for the slice for each dimension. Each value must be strictly greater than the respective start_indices value for the dimension and less than or equal to the size of the dimension. 
1dimensional example:
let a = {0.0, 1.0, 2.0, 3.0, 4.0}
Slice(a, {2}, {4}) produces:
{2.0, 3.0}
2dimensional 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} }
Slice(b, {2, 1}, {4, 3}) produces:
{ { 7.0, 8.0},
{10.0, 11.0} }
Sort
See also
ComputationBuilder::Sort
.
Sorts the elements in the operand.
Sort(operand)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
The operand to sort 
Transpose
See also the tf.reshape
operation.
Transpose(operand)
Arguments  Type  Semantics 

operand 
ComputationDataHandle 
The operand to transpose. 
permutation 
ArraySlice<int64> 
How to permute the dimensions. 
Permutes the operand dimensions with the given permutation, so
∀ i . 0 ≤ i < rank ⇒ input_dimensions[permutation[i]] = output_dimensions[i]
.
This is the same as Reshape(operand, permutation, Permute(permutation, operand.shape.dimensions)).
Tuple
See also
ComputationBuilder::Tuple
.
A tuple containing a variable number of data handles, each of which has its own shape.
This is analogous to std::tuple
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);
Tuples can be deconstructed (accessed) via the GetTupleElement
operation.
While
See also
ComputationBuilder::While
.
While(condition, body, init)
Arguments  Type  Semantics 

condition 
Computation 
Computation of type T > PRED which defines the termination condition of the loop. 
body 
Computation 
Computation of type T > T which defines the body of the loop. 
init 
T 
Initial value for the parameter of condition and body . 
Sequentially executes the body
until the condition
fails. This is similar to
a typical while loop in many other languages except for the differences and
restrictions listed below.
 A
While
node returns a value of typeT
, which is the result from the last execution of thebody
.  The shape of the type
T
is statically determined and must be the same across all iterations. While
nodes are not allowed to be nested. (This restriction may be lifted in the future on some targets.)
The T parameters of the computations are initialized with the init
value in
the first iteration and are automatically updated to the new result from body
in each subsequent iteration.
One main use case of the While
node is to implement the repeated execution of
training in neural networks. Simplified pseudocode is shown below with a graph
that represents the computation. The code can be found in
while_test.cc
.
The type T
in this example is a Tuple
consisting of an int32
for the
iteration count and a vector[10]
for the accumulator. For 1000 iterations, the
loop keeps adding a constant vector to the accumulator.
// Pseudocode for the computation.
init = {0, zero_vector[10]} // Tuple of int32 and float[10].
result = init;
while (result(0) < 1000) {
iteration = result(0) + 1;
new_vector = result(1) + constant_vector[10];
result = {iteration, new_vector};
}