[NBKCoreKit] Modular multiplicative inverse.

oscbyspro · Oct 31, 2023 · 9ea179f · 9ea179f
1 parent 99262f5
commit 9ea179f
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Showing 2 changed files with 63 additions and 12 deletions.
diff --git a/Sources/NBKCoreKit/Private/NBKProperBinaryInteger+ModularMultiplicativeInverse.swift b/Sources/NBKCoreKit/Private/NBKProperBinaryInteger+ModularMultiplicativeInverse.swift
@@ -21,18 +21,16 @@ extension NBK.ProperBinaryInteger {
     ///
     /// - Returns: A value from `0` to `modulus` or `nil`.
     ///
-    @inlinable public static func modularMultiplicativeInverse(of integer: Integer, mod modulus: Integer) -> Integer? {
+    @inlinable public static func modularMultiplicativeInverse(of lhs: Integer, mod rhs: Integer) -> Integer? {
         //=--------------------------------------=
-        let lhsIsLessThanZero = integer.isLessThanZero
-        let rhsIsLessThanZero = modulus.isLessThanZero
+        let lhsIsLessThanZero = lhs.isLessThanZero
+        let rhsIsLessThanZero = rhs.isLessThanZero
         //=--------------------------------------=
         if  rhsIsLessThanZero { return nil }
         //=--------------------------------------=
-        guard let unsigned = Magnitude.modularMultiplicativeInverse(of: integer.magnitude, mod: modulus.magnitude) else { return nil }
-        //=--------------------------------------=
-        var inverse = Integer(sign: NBK.sign(lhsIsLessThanZero), magnitude: unsigned)!
-        if  inverse.isLessThanZero { inverse += modulus }
-        return inverse as Integer as Integer as Integer
+        guard  let magnitude  = Magnitude.modularMultiplicativeInverse(
+        sign:  NBK.sign(lhsIsLessThanZero), magnitude: lhs.magnitude, mod: rhs.magnitude) else { return nil }
+        return Integer(sign: NBK.Sign.plus, magnitude: magnitude)!
     }
 }
 
@@ -46,23 +44,24 @@ extension NBK.ProperBinaryInteger where Integer: NBKUnsignedInteger {
     // MARK: Utilities
     //=------------------------------------------------------------------------=
 
-    /// Returns the modular multiplicative inverse of `integer` modulo `modulus`, if it exists.
+    /// Returns the modular multiplicative inverse of `sign` and `magnitude` modulo `modulus`, if it exists.
     ///
     /// - Returns: A value from `0` to `modulus` or `nil`.
     ///
-    @inlinable public static func modularMultiplicativeInverse(of integer: Integer, mod modulus: Integer) -> Integer? {
+    @inlinable public static func modularMultiplicativeInverse(sign: NBK.Sign, magnitude: Integer, mod modulus: Integer) -> Integer? {
         //=--------------------------------------=
         switch modulus.compared(to: 1 as Integer.Digit) {
         case  1: break;
         case  0: return Integer.zero
         default: return nil }
         //=--------------------------------------=
-        let extended = self.greatestCommonDivisorByEuclideanAlgorithm10(of: integer, and: modulus)
+        let extended = self.greatestCommonDivisorByEuclideanAlgorithm10(of: magnitude, and: modulus)
         //=--------------------------------------=
         guard extended.result.compared(to: 1 as Integer.Digit).isZero else {
             return nil // the arguments must be coprime
         }
         //=--------------------------------------=
-        return extended.iteration.isOdd ? modulus - extended.lhsCoefficient : extended.lhsCoefficient
+        Swift.assert(extended.lhsCoefficient.isMoreThanZero)
+        return (sign == .minus) == extended.iteration.isEven ? modulus - extended.lhsCoefficient : extended.lhsCoefficient
     }
 }
diff --git a/Tests/NBKCoreKitBenchmarks/Private/NBKProperBinaryInteger+ModularMultiplicativeInverse.swift b/Tests/NBKCoreKitBenchmarks/Private/NBKProperBinaryInteger+ModularMultiplicativeInverse.swift
@@ -0,0 +1,52 @@
+//=----------------------------------------------------------------------------=
+// This source file is part of the Numberick open source project.
+//
+// Copyright (c) 2023 Oscar Byström Ericsson
+// Licensed under Apache License, Version 2.0
+//
+// See http://www.apache.org/licenses/LICENSE-2.0 for license information.
+//=----------------------------------------------------------------------------=
+
+#if !DEBUG
+
+import NBKCoreKit
+import XCTest
+
+private typealias W = [UInt]
+private typealias X = [UInt64]
+private typealias Y = [UInt32]
+
+//*============================================================================*
+// MARK: * NBK x Proper Binary Integer x Modular Multiplicative Inverse
+//*============================================================================*
+
+final class NBKProperBinaryIntegerBenchmarksOnModularMultiplicativeInverse: XCTestCase {
+
+    typealias T = NBK.PBI
+
+    //=------------------------------------------------------------------------=
+    // MARK: Tests x Binary Algorithm
+    //=------------------------------------------------------------------------=
+
+    func testInt8s() {
+        for _ in 0 ..< 50 {
+            for lhs in Int8.min ... Int8.max {
+                for rhs in Int8.min ... Int8.max {
+                    NBK.blackHole(T.modularMultiplicativeInverse(of: lhs, mod: rhs))
+                }
+            }
+        }
+    }
+
+    func testUInt8s() {
+        for _ in 0 ..< 50 {
+            for lhs in UInt8.min ... UInt8.max {
+                for rhs in UInt8.min ... UInt8.max {
+                    NBK.blackHole(T.modularMultiplicativeInverse(of: lhs, mod: rhs))
+                }
+            }
+        }
+    }
+}
+
+#endif