Adds two sizes or indices. If either operand is an error it will be propagated to the result. The operands can be of type size or index. If at least one of the operands can hold an error, i.e. if it is of type size, the result must be of type size. If error propagation is not possible because both operands are of type index then the result may be of type size or index.

This operation takes multiple input shapes or extent tensors and returns some combination of their dimensions. This can be best seen with examples below.

The result is undefined, but still side-effect free, in cases where the inputs have differing ranks or differ in extents of shared dimensions.

Example: %s0 = shape.any [2,?], [?,3] // [2,3] %s1 = shape.any [?,?], [1,2] // [1,2]

Used to simplify constraints as any single failing precondition is enough to prevent execution.

"assuming" operations represent an execution order restriction to the compiler, information for dependent code to rely on (by assuming), and nothing else. They should not exist after a program is fully lowered and ready to execute.

Example: %w0 = shape.cstr_broadcastable [2,2], [3,1,2] // Passing %w1 = shape.cstr_broadcastable [2,2], [3,2] // Failure %w2 = shape.cstr_eq [1,2], [1,2], [1,2] // Passing %wf = shape.assuming_all %w0, %w1 // Failure %wt = shape.assuming_all %w0, %w2 // Passing

Executes the region assuming all witnesses are true.

"assuming" operations represent an execution order restriction to the compiler, information for dependent code to rely on (by assuming), and nothing else. They should not exist after a program is fully lowered and ready to execute.

This yield operation represents a return operation within the shape.assuming operation region. The operation takes variable number of operands and produces no results. The operand number and types must match the number and types of parent shape.assuming results.

Returns the broadcasted shape for input shapes or extent tensors. The rest of this description is simplified for the 2 input case but can be extended to more inputs. Both operands can be of type shape.shape or tensor<?xindex>. The result is of type shape.shape and, if both operands are tensors, may be of type tensor<?xindex>.

If the two operand shapes are of different rank the smaller one is padded with 1's from the left. The resulting broadcasted shape is then defined as

result[i] = lhs[i] if lhs[i] == rhs[i] = lhs[i] if rhs[i] == 1 = rhs[i] if lhs[i] == 1.

In case the resulting shape is undefined, i.e. if corresponding extents are different from each other but none is 1, the result is an error shape. Likewise error values are propagated if any of the operands holds an error value. If the result type is an extent tensor (and can therefore not hold the error value) the behavior may be undefined. The optional string attribute can be used to describe the error case.

Creates a shape whose dimensions consist of first the dimensions from lhs followed by the dimensions of rhs.

Example: concat([2,3], [4,5]) -> [2,3,4,5] concat([], []) -> [] concat([], [4,5,6]) -> [4,5,6]

Creates a constant shape or extent tensor. The individual extents are given as the shape attribute. The number of these values equals the shape's rank.

%0 = shape.const_shape [] : !shape.shape
%1 = shape.const_shape [1, 2, 3] : !shape.shape
%2 = shape.const_shape [4, 5, 6] : tensor<3xindex>

Creates a shape.size type representing the constant size given by value.

%x = shape.const_size 10

This operation represents a statically known witness result. This can be often used to canonicalize/fold constraint and assuming code that will always pass.

%0 = shape.const_shape [1,2,3]
%1 = shape.const_shape [1,2,3]
%w0 = shape.cstr_eq(%0, %1) // Can be folded to "const_witness true"
%w1 = shape.const_witness true
%w2 = shape.assuming_all(%w0, %w2) // Can be folded to "const_witness true"

Given input shapes or extent tensors, return a witness specifying if they are broadcastable. This broadcastable follows the same logic as what shape.broadcast documents.

"cstr" operations represent runtime assertions.

Example: %w0 = shape.cstr_broadcastable [2,2], [3,1,2] // Passing %w1 = shape.cstr_broadcastable [2,2], [3,2] // Failure

Given 1 or more input shapes, determine if all shapes are the exact same.

"cstr" operations represent runtime assertions.

Example: %w0 = shape.cstr_eq [1,2], [1,2], [1,2] // Passing %w1 = shape.cstr_eq [2,2], [1,2] // Failure

Represents a runtime assertion that an i1 is true. It returns a !shape.witness to order this assertion.

For simplicity, prefer using other cstr_* ops if they are available for a given constraint.

Example: %bool = ... %w0 = shape.cstr_require %bool, "msg" // Passing if %bool is true.

Since this op can be used to express many different possible assertions (depending on whatever computation calculated pred), the msg should clarify the nature of the assertion for users.

Prints the input dim or shape and passes through input.

Note: This is intended for testing and debugging only.

Gets the extent indexed by dim from the shape of the value operand. If the index is error or out-of-bound then it returns an invalid size if the return type carries error information else the behavior is undefined.

This is a convenience op that performs the equivalent of getting the extent of a shape (e.g., dim(x, i) == get_extent(shape_of(x), i)).

Divides two sizes or indices. If either operand is an error it will be propagated to the result. The operands can be of type size or index. If at least one of the operands can hold an error, i.e. if it is of type size, the result must be of type size. If error propagation is not possible because both operands are of type index then the result may be of type size or index. If both operands and result are of type index, their runtime values could be negative. The result is rounded toward negative infinity, i.e. floor(lhs / rhs), such that

div(lhs, rhs) * rhs + mod(lhs, rhs) = lhs

always holds. If any of the values is of type size, the behavior for negative value is undefined.

Creates a shape from a 1D integral tensor of extents. The rank of the resulting shape equals the number of elements in the tensor, and the extents match the values of the elements.

Creates a shape from multiple SSA values representing the extents of the shape.

// Rank 2 shape.
%s0 = shape.from_extents %a, %b
// Rank 0 shape.
%s1 = shape.from_extents

An operation with a name containing a single SSACFG region which represents a shape transfer function or helper function for shape transfer function.

Represents a list of shape functions and the ops whose shape transfer functions they represent.

Example:

shape.function_library {
  func @same_result_shape(%arg: !shape.value_shape) -> !shape.shape {
    %0 = shape_of %arg : !shape.value_shape -> !shape.shape
    return %0 : !shape.shape
  }
} mapping {
  std.atan = @same_result_shape
}

Gets the extent indexed by dim from the shape operand. If the shape is an error then it returns an invalid size.

Converts a standard index to a shape.size. This operation and its inverse, size_to_index, facilitate index conversion between the standard and the shape dialect.

The behavior is undefined for negative indices.

Given multiple input shapes or extent tensors, return a predicate specifying if they are broadcastable. This broadcastable follows the same logic as what shape.broadcast documents.

Concretely, shape.is_broadcastable returning true implies that shape.broadcast will not give an error, and shape.cstr_broadcastable will not result in an assertion failure. Similarly, false implies an error or assertion failure.

Example: %true = shape.is_broadcastable [2,2], [3,1,2] %false = shape.is_broadcastable [2,2], [3,2]

Computes the elementwise maximum of two sizes or shapes with equal ranks. If either operand is an error, then an error will be propagated to the result. If the input types mismatch or the ranks do not match, then the result is an error.

An operation that computes the least general shape or dim of input operands. This effectively asserts that corresponding static dimensions are equal. The behavior is to match each element of the shape/size and propagate the most restrictive information, returning an invalid shape if there are contradictory requirements. E.g., using pseudo code

shape.meet([*], [*]) -> [*]
shape.meet([*], [1, ?]) -> [1, ?]
shape.meet([1, 2], [1, ?]) -> [1, 2]
shape.meet([*], [1, 2]) -> [1, 2]
shape.meet([], []) -> []
shape.meet([], [*]) -> []
shape.meet([], [?, ?]) -> [invalid]
shape.meet([1, ?], [2, ?, ?]) -> [invalid]

shape.meet also allows specifying an optional error string, that may be used to return an error to the user upon mismatch of dimensions.

%c = shape.meet %a, %b, error="<reason>" : !shape.shape, !shape.shape -> !shape.shape

Computes the elementwise minimum of two sizes or shapes with equal ranks. If either operand is an error, then an error will be propagated to the result. If the input types mismatch or the ranks do not match, then the result is an error.

Multiplies two sizes or indices. If either operand is an error it will be propagated to the result. The operands can be of type size or index. If at least one of the operands can hold an error, i.e. if it is of type size, the result must be of type size. If error propagation is not possible because both operands are of type index then the result may be of type size or index.

Returns the number of elements for a given shape which is the product of its extents. If the argument is of type shape then the result will be of type size and potential errors will be propagated. Otherwise, if the argument is and extent tensor tensor<?xindex> then the result will be of type index.

Returns the rank of the shape or extent tensor, i.e. the number of extents.

An operation that takes as input a shape or extent tensor, and a number of initial values. This operation has a region that is applied repeatedly for every extent of the input. Starting with the initial values, the individual extents are then aggregated as defined by the associated region.

Conceptually this op performs the following reduction:

res[] = init;
for (int i = 0, i < shape.rank(); i++) {
  res = reduce(i, shape[i], res[0], ..., res[n]);
}

Where reduce represents the region attached and the result of the reduce op is the last computed output of the reduce region. As an example, the number of elements can be computed as follows:

func.func @reduce(%shape : !shape.shape, %init : !shape.size) ->
    !shape.size {
  %num_elements = shape.reduce(%shape, %init) -> !shape.size  {
    ^bb0(%index: index, %dim: !shape.size, %acc: !shape.size):
      %updated_acc = "shape.mul"(%acc, %dim) :
        (!shape.size, !shape.size) -> !shape.size
      shape.yield %updated_acc : !shape.size
  }
  return %num_elements : !shape.size
}

The shape.return operation represents a return operation within a function. The operation takes variable number of operands and produces no results.

Takes one or more shape or extent tensor operands and determines whether they are equal. When extent tensors are compared to shapes they are regarded as their equivalent non-error shapes. Error shapes can be tested for equality like any other shape value, meaning that the error value is equal to itself.

The operation takes a value or a shaped operand as an argument and it returns a shape or extent tensor.

Converts a shape.size to a standard index. This operation and its inverse, index_to_size, facilitate index conversion between the standard and the shape dialect. The behavior is undefined for unknown and invalid arguments.

Splits a shape at a given dimension index, returning two shapes. If index is negative, it is treated as indexing from the back of the shape. This negative-handling behavior is important when handling unranked shapes, where the positive index is not necessarily knowable due to a dynamic number of leading dimensions. If the result is in extent tensor form out of bounds indices result in undefined behavior.

Examples: - split_at([4,5,6], index=0) -> [], [4,5,6] - split_at([4,5,6], index=1) -> [4], [5,6] - split_at([4,5,6], index=2) -> [4,5], [6] - split_at([4,5,6], index=3) -> [4,5,6], [] - split_at([4,5,6], index=4) -> error - split_at([4,5,6], index=-1) -> [4,5], [6] - split_at([4,5,6], index=-2) -> [4], [5,6] - split_at([4,5,6], index=-3) -> [], [4,5,6] - split_at([4,5,6], index=-4) -> error

Requires: - index is in the range [-rank(operand),rank(operand)]

Converts a shape to a 1D integral tensor of extents. The number of elements in the tensor equals the rank of the shape, and the elements equal the extents of the shape.

If the shape represents an error, this op's behavior is undefined.

The operations takes a ValueShape and returns a Shape corresponding to the value. If the input value cannot be shape (e.g., not a 1D tensor of integral value representing sizes) then this propagages the error shape. E.g.,

// The following
%0 = arith.constant dense<[1,2]> : tensor<2xi32>
%shape = shape.value_as_shape %0 : tensor<2xi32> -> !shape.shape
// is equivalent to
%shape' = shape.const_shape [1, 2] : !shape.shape

This operation is the complement of shape_of wrt ValueShape values.

The operation takes !shape.value_shape, a.k.a. (value, shape) tuple as an argument, and returns its value. The behavior is undefined for unknown and invalid arguments.

Returns ValueShape with the shape updated to match the shape operand. That is a new ValueShape tuple is created with value equal to operand's value and shape equal to shape. If the ValueShape and given shape are non-conformant, then the returned ValueShape will represent an error of this mismatch. Similarly if either inputs are in an error state, then an error is propagated.

Usage: %0 = shape.with_shape %1, %2 : tensor<...>, !shape.shape

This is used, for example, where one combines shape function calculations and/or call one shape function from another. E.g.,

func.func @shape_foobah(%a: !shape.value_shape,
                   %b: !shape.value_shape,
                   %c: !shape.value_shape) -> !shape.shape {
  %0 = call @shape_foo(%a, %b) :
    (!shape.value_shape, !shape.value_shape) -> !shape.shape
  %1 = shape.with_shape %b, %0 : !shape.value_shape, !shape.shape
  %2 = call @shape_bah(%c, %1) :
    (!shape.value_shape, !shape.value_shape) -> !shape.shape
  return %2 : !shape.shape
}

This op need not be a refinement of the shape. In non-error cases the input ValueShape's value and shape are conformant and so too for the output, but the result may be less specified than operand's shape as shape is merely used to construct the new ValueShape. If join behavior is desired then a join op should be used.