Initial check in of big integer library

third_party/bigint/BigIntegerAlgorithms.cc

Index: third_party/bigint/BigIntegerAlgorithms.cc
diff --git a/third_party/bigint/BigIntegerAlgorithms.cc b/third_party/bigint/BigIntegerAlgorithms.cc
new file mode 100644
index 0000000000000000000000000000000000000000..7edebda76a8e17de58dcb3476bc02e3d6be5a249
--- /dev/null
+++ b/third_party/bigint/BigIntegerAlgorithms.cc
@@ -0,0 +1,70 @@
+#include "BigIntegerAlgorithms.hh"
+
+BigUnsigned gcd(BigUnsigned a, BigUnsigned b) {
+	BigUnsigned trash;
+	// Neat in-place alternating technique.
+	for (;;) {
+		if (b.isZero())
+			return a;
+		a.divideWithRemainder(b, trash);
+		if (a.isZero())
+			return b;
+		b.divideWithRemainder(a, trash);
+	}
+}
+
+void extendedEuclidean(BigInteger m, BigInteger n,
+		BigInteger &g, BigInteger &r, BigInteger &s) {
+	if (&g == &r || &g == &s || &r == &s)
+		throw "BigInteger extendedEuclidean: Outputs are aliased";
+	BigInteger r1(1), s1(0), r2(0), s2(1), q;
+	/* Invariants:
+	 * r1*m(orig) + s1*n(orig) == m(current)
+	 * r2*m(orig) + s2*n(orig) == n(current) */
+	for (;;) {
+		if (n.isZero()) {
+			r = r1; s = s1; g = m;
+			return;
+		}
+		// Subtract q times the second invariant from the first invariant.
+		m.divideWithRemainder(n, q);
+		r1 -= q*r2; s1 -= q*s2;
+
+		if (m.isZero()) {
+			r = r2; s = s2; g = n;
+			return;
+		}
+		// Subtract q times the first invariant from the second invariant.
+		n.divideWithRemainder(m, q);
+		r2 -= q*r1; s2 -= q*s1;
+	}
+}
+
+BigUnsigned modinv(const BigInteger &x, const BigUnsigned &n) {
+	BigInteger g, r, s;
+	extendedEuclidean(x, n, g, r, s);
+	if (g == 1)
+		// r*x + s*n == 1, so r*x === 1 (mod n), so r is the answer.
+		return (r % n).getMagnitude(); // (r % n) will be nonnegative
+	else
+		throw "BigInteger modinv: x and n have a common factor";
+}
+
+BigUnsigned modexp(const BigInteger &base, const BigUnsigned &exponent,
+		const BigUnsigned &modulus) {
+	BigUnsigned ans = 1, base2 = (base % modulus).getMagnitude();
+	BigUnsigned::Index i = exponent.bitLength();
+	// For each bit of the exponent, most to least significant...
+	while (i > 0) {
+		i--;
+		// Square.
+		ans *= ans;
+		ans %= modulus;
+		// And multiply if the bit is a 1.
+		if (exponent.getBit(i)) {
+			ans *= base2;
+			ans %= modulus;
+		}
+	}
+	return ans;
+}