提交代码

2025-03-13 09:20:11 +08:00
parent 6d0c6e28de
commit 980946f316
3443 changed files with 188150 additions and 3 deletions
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+// BarrettMu, a class for performing Barrett modular reduction computations in
+// JavaScript.
+//
+// Requires BigInt.js.
+//
+// Copyright 2004-2005 David Shapiro.
+//
+// You may use, re-use, abuse, copy, and modify this code to your liking, but
+// please keep this header.
+//
+// Thanks!
+// 
+// Dave Shapiro
+// dave@ohdave.com 
+
+function BarrettMu(m)
+{
+	this.modulus = biCopy(m);
+	this.k = biHighIndex(this.modulus) + 1;
+	var b2k = new BigInt();
+	b2k.digits[2 * this.k] = 1; // b2k = b^(2k)
+	this.mu = biDivide(b2k, this.modulus);
+	this.bkplus1 = new BigInt();
+	this.bkplus1.digits[this.k + 1] = 1; // bkplus1 = b^(k+1)
+	this.modulo = BarrettMu_modulo;
+	this.multiplyMod = BarrettMu_multiplyMod;
+	this.powMod = BarrettMu_powMod;
+}
+
+function BarrettMu_modulo(x)
+{
+	var q1 = biDivideByRadixPower(x, this.k - 1);
+	var q2 = biMultiply(q1, this.mu);
+	var q3 = biDivideByRadixPower(q2, this.k + 1);
+	var r1 = biModuloByRadixPower(x, this.k + 1);
+	var r2term = biMultiply(q3, this.modulus);
+	var r2 = biModuloByRadixPower(r2term, this.k + 1);
+	var r = biSubtract(r1, r2);
+	if (r.isNeg) {
+		r = biAdd(r, this.bkplus1);
+	}
+	var rgtem = biCompare(r, this.modulus) >= 0;
+	while (rgtem) {
+		r = biSubtract(r, this.modulus);
+		rgtem = biCompare(r, this.modulus) >= 0;
+	}
+	return r;
+}
+
+function BarrettMu_multiplyMod(x, y)
+{
+	/*
+	x = this.modulo(x);
+	y = this.modulo(y);
+	*/
+	var xy = biMultiply(x, y);
+	return this.modulo(xy);
+}
+
+function BarrettMu_powMod(x, y)
+{
+	var result = new BigInt();
+	result.digits[0] = 1;
+	var a = x;
+	var k = y;
+	while (true) {
+		if ((k.digits[0] & 1) != 0) result = this.multiplyMod(result, a);
+		k = biShiftRight(k, 1);
+		if (k.digits[0] == 0 && biHighIndex(k) == 0) break;
+		a = this.multiplyMod(a, a);
+	}
+	return result;
+}
+