ModArith

ModArith attributes

AffineMapAttr

An Attribute containing an AffineMap object

Syntax:

affine-map-attribute ::= `affine_map` `<` affine-map `>`

Examples:

affine_map<(d0) -> (d0)>
affine_map<(d0, d1, d2) -> (d0, d1)>

Parameters:

ArrayAttr

A collection of other Attribute values

Syntax:

array-attribute ::= `[` (attribute-value (`,` attribute-value)*)? `]`

An array attribute is an attribute that represents a collection of attribute values.

Examples:

[]
[10, i32]
[affine_map<(d0, d1, d2) -> (d0, d1)>, i32, "string attribute"]

Parameters:

DenseArrayAttr

A dense array of integer or floating point elements.

A dense array attribute is an attribute that represents a dense array of primitive element types. Contrary to DenseIntOrFPElementsAttr this is a flat unidimensional array which does not have a storage optimization for splat. This allows to expose the raw array through a C++ API as ArrayRef<T> for compatible types. The element type must be bool or an integer or float whose bitwidth is a multiple of 8. Bool elements are stored as bytes.

This is the base class attribute. Access to C++ types is intended to be managed through the subclasses DenseI8ArrayAttr, DenseI16ArrayAttr, DenseI32ArrayAttr, DenseI64ArrayAttr, DenseF32ArrayAttr, and DenseF64ArrayAttr.

Syntax:

dense-array-attribute ::= `array` `<` (integer-type | float-type)
                                      (`:` tensor-literal)? `>`

Examples:

array<i8>
array<i32: 10, 42>
array<f64: 42., 12.>

When a specific subclass is used as argument of an operation, the declarative assembly will omit the type and print directly:

[1, 2, 3]

Parameters:

DenseIntOrFPElementsAttr

An Attribute containing a dense multi-dimensional array of integer or floating-point values

Syntax:

tensor-literal ::= integer-literal | float-literal | bool-literal | [] | [tensor-literal (, tensor-literal)* ]
dense-intorfloat-elements-attribute ::= `dense` `<` tensor-literal `>` `:`
                                        ( tensor-type | vector-type )

A dense int-or-float elements attribute is an elements attribute containing a densely packed vector or tensor of integer or floating-point values. The element type of this attribute is required to be either an IntegerType or a FloatType.

Examples:

// A splat tensor of integer values.
dense<10> : tensor<2xi32>
// A tensor of 2 float32 elements.
dense<[10.0, 11.0]> : tensor<2xf32>

Parameters:

DenseResourceElementsAttr

An Attribute containing a dense multi-dimensional array backed by a resource

Syntax:

dense-resource-elements-attribute ::=
  `dense_resource` `<` resource-handle `>` `:` shaped-type

A dense resource elements attribute is an elements attribute backed by a handle to a builtin dialect resource containing a densely packed array of values. This class provides the low-level attribute, which should only be interacted with in very generic terms, actual access to the underlying resource data is intended to be managed through one of the subclasses, such as; DenseBoolResourceElementsAttr, DenseUI64ResourceElementsAttr, DenseI32ResourceElementsAttr, DenseF32ResourceElementsAttr, DenseF64ResourceElementsAttr, etc.

Examples:

"example.user_op"() {attr = dense_resource<blob1> : tensor<3xi64> } : () -> ()

{-#
dialect_resources: {
    builtin: {
      blob1: "0x08000000010000000000000002000000000000000300000000000000"
    }
  }
#-}

Parameters:

DenseStringElementsAttr

An Attribute containing a dense multi-dimensional array of strings

Syntax:

dense-string-elements-attribute ::= `dense` `<` attribute-value `>` `:`
                                    ( tensor-type | vector-type )

A dense string elements attribute is an elements attribute containing a densely packed vector or tensor of string values. There are no restrictions placed on the element type of this attribute, enabling the use of dialect specific string types.

Examples:

// A splat tensor of strings.
dense<"example"> : tensor<2x!foo.string>
// A tensor of 2 string elements.
dense<["example1", "example2"]> : tensor<2x!foo.string>

Parameters:

DictionaryAttr

An dictionary of named Attribute values

Syntax:

dictionary-attribute ::= `{` (attribute-entry (`,` attribute-entry)*)? `}`

A dictionary attribute is an attribute that represents a sorted collection of named attribute values. The elements are sorted by name, and each name must be unique within the collection.

Examples:

{}
{attr_name = "string attribute"}
{int_attr = 10, "string attr name" = "string attribute"}

Parameters:

FloatAttr

An Attribute containing a floating-point value

Syntax:

float-attribute ::= (float-literal (`:` float-type)?)
                  | (hexadecimal-literal `:` float-type)

A float attribute is a literal attribute that represents a floating point value of the specified float type. It can be represented in the hexadecimal form where the hexadecimal value is interpreted as bits of the underlying binary representation. This form is useful for representing infinity and NaN floating point values. To avoid confusion with integer attributes, hexadecimal literals must be followed by a float type to define a float attribute.

Examples:

42.0         // float attribute defaults to f64 type
42.0 : f32   // float attribute of f32 type
0x7C00 : f16 // positive infinity
0x7CFF : f16 // NaN (one of possible values)
42 : f32     // Error: expected integer type

Parameters:

IntegerAttr

An Attribute containing a integer value

Syntax:

integer-attribute ::= (integer-literal ( `:` (index-type | integer-type) )?)
                      | `true` | `false`

An integer attribute is a literal attribute that represents an integral value of the specified integer or index type. i1 integer attributes are treated as boolean attributes, and use a unique assembly format of either true or false depending on the value. The default type for non-boolean integer attributes, if a type is not specified, is signless 64-bit integer.

Examples:

10 : i32
10    // : i64 is implied here.
true  // A bool, i.e. i1, value.
false // A bool, i.e. i1, value.

Parameters:

IntegerSetAttr

An Attribute containing an IntegerSet object

Syntax:

integer-set-attribute ::= `affine_set` `<` integer-set `>`

Examples:

affine_set<(d0) : (d0 - 2 >= 0)>

Parameters:

OpaqueAttr

An opaque representation of another Attribute

Syntax:

opaque-attribute ::= dialect-namespace `<` attr-data `>`

Opaque attributes represent attributes of non-registered dialects. These are attribute represented in their raw string form, and can only usefully be tested for attribute equality.

Examples:

#dialect<"opaque attribute data">

Parameters:

SparseElementsAttr

An opaque representation of a multi-dimensional array

Syntax:

sparse-elements-attribute ::= `sparse` `<` attribute-value `,`
                              attribute-value `>` `:`
                              ( tensor-type | vector-type )

A sparse elements attribute is an elements attribute that represents a sparse vector or tensor object. This is where very few of the elements are non-zero.

The attribute uses COO (coordinate list) encoding to represent the sparse elements of the elements attribute. The indices are stored via a 2-D tensor of 64-bit integer elements with shape [N, ndims], which specifies the indices of the elements in the sparse tensor that contains non-zero values. The element values are stored via a 1-D tensor with shape [N], that supplies the corresponding values for the indices.

Example:

sparse<[[0, 0], [1, 2]], [1, 5]> : tensor<3x4xi32>

// This represents the following tensor:
///  [[1, 0, 0, 0],
///   [0, 0, 5, 0],
///   [0, 0, 0, 0]]

Parameters:

StringAttr

An Attribute containing a string

Syntax:

string-attribute ::= string-literal (`:` type)?

A string attribute is an attribute that represents a string literal value.

Examples:

"An important string"
"string with a type" : !dialect.string

Parameters:

SymbolRefAttr

An Attribute containing a symbolic reference to an Operation

Syntax:

symbol-ref-attribute ::= symbol-ref-id (`::` symbol-ref-id)*

A symbol reference attribute is a literal attribute that represents a named reference to an operation that is nested within an operation with the OpTrait::SymbolTable trait. As such, this reference is given meaning by the nearest parent operation containing the OpTrait::SymbolTable trait. It may optionally contain a set of nested references that further resolve to a symbol nested within a different symbol table.

Rationale: Identifying accesses to global data is critical to enabling efficient multi-threaded compilation. Restricting global data access to occur through symbols and limiting the places that can legally hold a symbol reference simplifies reasoning about these data accesses.

See Symbols And SymbolTables for more information.

Examples:

@flat_reference
@parent_reference::@nested_reference

Parameters:

TypeAttr

An Attribute containing a Type

Syntax:

type-attribute ::= type

A type attribute is an attribute that represents a type object.

Examples:

i32
!dialect.type

Parameters:

UnitAttr

An Attribute value of unit type

Syntax:

unit-attribute ::= `unit`

A unit attribute is an attribute that represents a value of unit type. The unit type allows only one value forming a singleton set. This attribute value is used to represent attributes that only have meaning from their existence.

One example of such an attribute could be the swift.self attribute. This attribute indicates that a function parameter is the self/context parameter. It could be represented as a boolean attribute(true or false), but a value of false doesn’t really bring any value. The parameter either is the self/context or it isn’t.

Examples:

// A unit attribute defined with the `unit` value specifier.
func.func @verbose_form() attributes {dialectName.unitAttr = unit}

// A unit attribute in an attribute dictionary can also be defined without
// the value specifier.
func.func @simple_form() attributes {dialectName.unitAttr}

ModArithAttr

a typed mod_arith attribute

Syntax:

#mod_arith.int<
  ::mlir::heir::mod_arith::ModArithType,   # type
  mlir::IntegerAttr   # value
>

Example:

#attr = 123:i32
#attr_verbose = #mod_arith.int<123:i32>

Parameters:

StridedLayoutAttr

An Attribute representing a strided layout of a shaped type

Syntax:

strided-layout-attribute ::= `strided` `<` `[` stride-list `]`
                             (`,` `offset` `:` dimension)? `>`
stride-list ::= /*empty*/
              | dimension (`,` dimension)*
dimension ::= decimal-literal | `?`

A strided layout attribute captures layout information of the memref type in the canonical form. Specifically, it contains a list of strides, one for each dimension. A stride is the number of elements in the linear storage one must step over to reflect an increment in the given dimension. For example, a MxN row-major contiguous shaped type would have the strides [N, 1]. The layout attribute also contains the offset from the base pointer of the shaped type to the first effectively accessed element, expressed in terms of the number of contiguously stored elements.

Strides must be positive and the offset must be non-negative. Both the strides and the offset may be dynamic, i.e. their value may not be known at compile time. This is expressed as a ? in the assembly syntax and as ShapedType::kDynamic in the code. Stride and offset values must satisfy the constraints above at runtime, the behavior is undefined otherwise.

See [Dialects/Builtin.md#memreftype](MemRef type) for more information.

Parameters:

ModArith types

ModArithType

Integer type with modular arithmetic

Syntax:

!mod_arith.int<
  ::mlir::IntegerAttr   # modulus
>

mod_arith.int<p> represents an element of the ring of integers modulo $p$. The modulus attribute is the ring modulus, and mod_arith operations lower to arith operations that produce results in the range [0, modulus), often called the canonical representative.

modulus is specified with an integer type suffix, for example, mod_arith.int<65537 : i32>. This corresponds to the storage type for the modulus, and is i64 by default.

It is required that the underlying integer type should be larger than twice the modulus (have one extra bit of storage space) to avoid signedness issues. For example, when modulus == 2 ** 32 - 1, the underlying type for the modulus should be at least i33, though i64 is a natural choice.

Passes may allow intermediate values that do not always produce a canonical representative in [0, modulus). For example, if the machine storage type is i64, but the modulus fits within an i32, a lowering could allow intermediate arithmetic values to grow to as large as an i64 before reducing them. However, all passes must ensure that values used outside the local scope (e.g., function return values or arguments to calls to linked functions) are appropriately reduced to the canonical representative. modulus is the modulus the arithmetic working with.

Examples:

!Zp1 = !mod_arith.int<7> // implicitly being i64
!Zp2 = !mod_arith.int<65537 : i32>
!Zp3 = !mod_arith.int<536903681 : i64>

Parameters:

ModArith ops

mod_arith.add (heir::mod_arith::AddOp)

Modular addition operation

Syntax:

operation ::= `mod_arith.add` operands attr-dict `:` type($output)

Computes modular addition.

Unless otherwise specified, the operation assumes both inputs are canonical representatives and guarantees the output being canonical representative.

Traits: AlwaysSpeculatableImplTrait, Commutative, Elementwise, SameOperandsAndResultType, Scalarizable, Tensorizable, Vectorizable

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

mod_arith.barrett_reduce (heir::mod_arith::BarrettReduceOp)

Compute the first step of the Barrett reduction.

Syntax:

operation ::= `mod_arith.barrett_reduce` operands attr-dict `:` qualified(type($input))

Let $q$ denote a statically known modulus and $b = 4^{w}$, where $w$ is the smallest bit-width that contains the range $[0, q)$. The Barrett reduce operation computes barret_reduce x = x - floor(x * floor(b / q) / b) * q.

Given $0 <= x < q^2$, then this will compute $(x \mod q)$ or $(x \mod q) + q$.

Traits: SameOperandsAndResultType

Interfaces: InferTypeOpInterface

Attributes:

Operands:

Results:

mod_arith.constant (heir::mod_arith::ConstantOp)

Define a constant value via an attribute.

Example:

%0 = mod_arith.constant 123 : !mod_arith.int<65537:i32>

Traits: AlwaysSpeculatableImplTrait, InferTypeOpAdaptor

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Results:

mod_arith.encapsulate (heir::mod_arith::EncapsulateOp)

Encapsulate an integer into a mod_arith type

Syntax:

operation ::= `mod_arith.encapsulate` operands attr-dict `:` type($input) `->` type($output)

mod_arith.encapsulate converts the integer to be of mod_arith type.

It is required that the bitwidth of the input integer type is the same as that of the storage type of the output mod_arith type.

Examples:

mod_arith.encapsulate %c0 : i32 -> mod_arith.int<65537 : i32>
mod_arith.encapsulate %c1 : i64 -> mod_arith.int<65537>

Traits: AlwaysSpeculatableImplTrait, Elementwise, Scalarizable, Tensorizable, Vectorizable

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

mod_arith.extract (heir::mod_arith::ExtractOp)

Extract the integer stored inside mod_arith type

Syntax:

operation ::= `mod_arith.extract` operands attr-dict `:` type($input) `->` type($output)

mod_arith.extract extracts the integer inside the mod_arith type.

It is required that the bitwidth of the output integer type is the same as that of the storage type of the input mod_arith type.

Examples:

%m0 = mod_arith.encapsulate %c0 : i32 -> mod_arith.int<65537 : i32>
%m1 = mod_arith.encapsulate %c1 : i64 -> mod_arith.int<65537>
%c2 = mod_arith.extract %m0 : mod_arith.int<65537 : i32> -> i32
%c3 = mod_arith.extract %m1 : mod_arith.int<65537> -> i64

Traits: AlwaysSpeculatableImplTrait, Elementwise, Scalarizable, Tensorizable, Vectorizable

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

mod_arith.mac (heir::mod_arith::MacOp)

Modular multiplication-and-accumulation operation

Syntax:

operation ::= `mod_arith.mac` operands attr-dict `:` type($output)

mod_arith.mac x, y, z computes $(x * y) + z$

Unless otherwise specified, the operation assumes all inputs are canonical representatives and guarantees the output being canonical representative.

Traits: AlwaysSpeculatableImplTrait, Elementwise, SameOperandsAndResultType, Scalarizable, Tensorizable, Vectorizable

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

mod_arith.mul (heir::mod_arith::MulOp)

Modular multiplication operation

Syntax:

operation ::= `mod_arith.mul` operands attr-dict `:` type($output)

Computes modular multiplication.

Unless otherwise specified, the operation assumes both inputs are canonical representatives and guarantees the output being canonical representative.

Traits: AlwaysSpeculatableImplTrait, Commutative, Elementwise, SameOperandsAndResultType, Scalarizable, Tensorizable, Vectorizable

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

mod_arith.reduce (heir::mod_arith::ReduceOp)

Reduce the mod arith type to its canonical representative

Syntax:

operation ::= `mod_arith.reduce` operands attr-dict `:` type($output)

mod_arith.reduce x produces $y$, the canonical representative in $[0, q)$ such that $x \equiv y \mod q$.

Examples:

%c0 = arith.constant 65538 : i32
%m0 = mod_arith.encapsulate %c0 : i32 -> mod_arith.int<65537 : i32>
// mod_arith.extract %m0 produces 65538
%m1 = mod_arith.reduce %m0 : mod_arith.int<65537: i32>
// mod_arith.extract %m1 produces 1

Traits: AlwaysSpeculatableImplTrait, Elementwise, SameOperandsAndResultType, Scalarizable, Tensorizable, Vectorizable

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

mod_arith.subifge (heir::mod_arith::SubIfGEOp)

Compute (x >= y) ? x - y : x.

Syntax:

operation ::= `mod_arith.subifge` operands attr-dict `:` qualified(type($output))

Traits: SameOperandsAndResultType

Interfaces: InferTypeOpInterface

Operands:

Results:

mod_arith.sub (heir::mod_arith::SubOp)

Modular subtraction operation

Syntax:

operation ::= `mod_arith.sub` operands attr-dict `:` type($output)

Computes modular subtraction.

Unless otherwise specified, the operation assumes both inputs are canonical representatives and guarantees the output being canonical representative.

Traits: AlwaysSpeculatableImplTrait, Elementwise, SameOperandsAndResultType, Scalarizable, Tensorizable, Vectorizable

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results: