ModArith

ModArith ops

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

Modular addition operation

Syntax:

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

Computes addition modulo a statically known modulus $q$.

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

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

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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 $(x \mod q) + p$.

Traits: SameOperandsAndResultType

Interfaces: InferTypeOpInterface

Attributes:

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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 {modulus = q} computes $(x * y) + z \mod q$

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

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

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

Modular multiplication operation

Syntax:

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

Computes multiplication modulo a statically known modulus $q$.

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

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

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

Reduce a signed integer to its congruence modulo equivalent

Syntax:

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

mod_arith.reduce x {modulus = q} computes $y \in [0, q)$ such that $x \equiv y \mod n$.

Note this will interpret x as a signed integer. For an unsigned integer, equivalent functionality is: y = arith.remui x.

Traits: SameOperandsAndResultType

Interfaces: InferTypeOpInterface

Attributes:

Operands:

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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 subtraction modulo a statically known modulus $q$.

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

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results: