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Fix reference to reduceProduct #228

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Merged
fboemer merged 1 commit into from
Sep 15, 2025
Merged

Fix reference to reduceProduct #228

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19 changes: 18 additions & 1 deletion Sources/ModularArithmetic/Modulus.swift
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Expand Up @@ -327,9 +327,26 @@ public struct ReduceModulus<T: CoreScalarType>: Equatable, Sendable {
/// Performs modular reduction of a product with modulus `p`.
/// - Parameter x: Must be in `[0, p^2)`.
/// - Returns: `x mod p` for `p`.
///
/// Details:
/// - "Dhem, J. F. "Modified version of the Barrett algorithm." Technical report, Technical report (1994).
/// - See also Algorithm 2 from
/// "Knezevic, Miroslav, Frederik Vercauteren, and Ingrid Verbauwhede.
/// "Speeding up Barrett and Montgomery modular multiplications."
/// IEEE Transactions on Compute 2 (2009).
/// Available at
/// https://web.archive.org/web/20170830020846/http://homes.esat.kuleuven.be/~fvercaut/papers/bar_mont.pdf
///
/// / / | x | \ / | 2^(n+alpha) | \ \
/// | floor | |--------| | * floor | |-------------| | |
/// | \ |2^n+beta| / \ | p | / |
/// x mod p = floor |------------------------------------------------------|
/// \ 2^{alpha - beta} /
/// where `x = (x_{n + gamma - 1, ...., x_0)_2``, and modulus `p = (p_{n - 1}, ..., p_0)_2`, `p_{n-1} != 0`, and
/// `gamma <= n`.
/// For `beta = -2` and `\alpha >= \gamma + 1`, we need just a single conditional subtraction.
@inlinable
public func reduceProduct(_ x: T.DoubleWidth) -> T {
// Algorithm 2 from https://homes.esat.kuleuven.be/~fvercaut/papers/bar_mont.pdf
assert(x < T.DoubleWidth(modulus.multipliedFullWidth(by: modulus)))
let n = modulus.significantBitCount
let reduceModulusBeta = -2
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