reduce toMont inf invMontOp

include/mcl/op.hpp

@@ -54,10 +54,12 @@ struct Op {
 		for Montgomery
 		one = 1
 		R = (1 << (N * sizeof(Unit) * 8)) % p
-		RR = (R * R) % p
+		R2 = (R * R) % p
+		R3 = RR^3
 	*/
 	Unit one[maxOpUnitSize];
-	Unit RR[maxOpUnitSize];
+	Unit R2[maxOpUnitSize];
+	Unit R3[maxOpUnitSize];
 	std::vector<Unit> invTbl;
 	size_t N;
 	size_t bitSize;
@@ -100,11 +102,18 @@ struct Op {
 	}
 	void fromMont(Unit* y, const Unit *x) const
 	{
+		/*
+			M(x, y) = xyR^-1
+			y = M(x, 1) = xR^-1
+		*/
 		mul(y, x, one);
 	}
 	void toMont(Unit* y, const Unit *x) const
 	{
-		mul(y, x, RR);
+		/*
+			y = M(x, R2) = xR^2 R^-1 = xR
+		*/
+		mul(y, x, R2);
 	}
 	void init(const std::string& mstr, int base, size_t maxBitSize, Mode mode);
 	static FpGenerator* createFpGenerator();

src/fp.cpp

@@ -151,13 +151,14 @@ struct OpeFunc {
 		Gmp::getArray(y, N, my);
 	}
 	/*
-		inv(x/R) = (1/x)R -toMont-> 1/x -toMont-> (1/x)R^-1
+		inv(xR) = (1/x)R^-1 -toMont-> 1/x -toMont-> (1/x)R
 	*/
 	static void invMontOp(Unit *y, const Unit *x, const Op& op)
 	{
 		invOp(y, x, op);
-		op.toMont(y, y);
-		op.toMont(y, y);
+		op.mul(y, y, op.R3);
+//		op.toMont(y, y);
+//		op.toMont(y, y);
 	}
 	static inline bool isZeroC(const Unit *x)
 	{
@@ -233,11 +234,15 @@ static void initForMont(Op& op, const Unit *p)
 {
 	const size_t N = op.N;
 	assert(N >= 2);
-	mpz_class t = 1;
-	Gmp::getArray(op.one, N, t);
-	t = (t << (N * 64)) % op.mp;
-	t = (t * t) % op.mp;
-	Gmp::getArray(op.RR, N, t);
+	{
+		mpz_class t = 1, R;
+		Gmp::getArray(op.one, N, t);
+		R = (t << (N * 64)) % op.mp;
+		t = (R * R) % op.mp;
+		Gmp::getArray(op.R2, N, t);
+		t = (R * R * R) % op.mp;
+		Gmp::getArray(op.R3, N, t);
+	}
 	op.rp = getMontgomeryCoeff(p[0]);
 #ifdef USE_MONT_FP
 	FpGenerator *fg = op.fg;