optimize long multiplications

Author: TilmanNeumann

src/main/java/de/tilman_neumann/jml/factor/squfof/SquFoF31.java

@@ -86,7 +86,7 @@ public long findSingleFactor(long N) {
 				// The cast may be wrong for some bigger kN, but fixing the cast would mean a small performance
 				// penalty, so we ignore it. Return immediately if kN is square.
 				floor_sqrt_kN = (int) Math.sqrt(kN);
-				int diff = (int) (kN - floor_sqrt_kN*(long)floor_sqrt_kN);
+				int diff = (int) (kN - ((long)floor_sqrt_kN) * floor_sqrt_kN);
 				if (diff==0) return gcdEngine.gcd(N, floor_sqrt_kN);
 
 				// search square Q_i
@@ -140,7 +140,7 @@ private Long reverseIteration(int found_P, int found_Q_sqrt) {
 		int b_i = (floor_sqrt_kN-found_P)/found_Q_sqrt; // floor(rational result)
 		int P_i = b_i*found_Q_sqrt + found_P;
 		int Q_i = found_Q_sqrt;
-		int Q_ip1 = (int) ((kN - P_i*(long)P_i)/found_Q_sqrt);
+		int Q_ip1 = (int) ((kN - ((long)P_i) * P_i) / found_Q_sqrt);
 
 		// second iteration step
 		int P_im1, Q_im1;

src/main/java/de/tilman_neumann/jml/factor/squfof/SquFoF31Preload.java

@@ -109,7 +109,7 @@ public long findSingleFactor(long N) {
 				// The cast may be wrong for some bigger kN, but fixing the cast would mean a small performance
 				// penalty, so we ignore it. Return immediately if kN is square.
 				floor_sqrt_kN = (int) Math.sqrt(kN);
-				int diff = (int) (kN - floor_sqrt_kN*(long)floor_sqrt_kN);
+				int diff = (int) (kN - ((long)floor_sqrt_kN) * floor_sqrt_kN);
 				if (diff==0) return gcdEngine.gcd(N, floor_sqrt_kN);
 
 				// search square Q_i
@@ -163,7 +163,7 @@ private Long reverseIteration(int found_P, int found_Q_sqrt) {
 		int b_i = (floor_sqrt_kN-found_P)/found_Q_sqrt; // floor(rational result)
 		int P_i = b_i*found_Q_sqrt + found_P;
 		int Q_i = found_Q_sqrt;
-		int Q_ip1 = (int) ((kN - P_i*(long)P_i)/found_Q_sqrt);
+		int Q_ip1 = (int) ((kN - ((long)P_i) * P_i) / found_Q_sqrt);
 
 		// second iteration step
 		int P_im1, Q_im1;

src/main/java/de/tilman_neumann/jml/modular/ModularSqrt.java

@@ -102,7 +102,7 @@ private int Tonelli_Shanks(BigInteger n, int p) {
 				Ensure.ensureEquals(p-1, mpe.modPow(c, 1<<(M-1), p)); //  -1 == c^(2^(M-1)) (mod p)
 				Ensure.ensureEquals(1, mpe.modPow(t, 1<<(M-1), p));   //   1 == t^(2^(M-1)) (mod p)
 				long nModP = n.mod(BigInteger.valueOf(p)).longValue();
-				Ensure.ensureEquals((R*(long)R) % p, (t*nModP) % p);  // R^2 == t*n (mod p)
+				Ensure.ensureEquals((((long)R) * R) % p, (t*nModP) % p);  // R^2 == t*n (mod p)
 			}
 			boolean foundI = false;
 			int i;
@@ -115,9 +115,9 @@ private int Tonelli_Shanks(BigInteger n, int p) {
 			if (foundI==false) throw new IllegalStateException("Tonelli-Shanks did not find an 'i' < M=" + M);
 
 			int b = mpe.modPow(c, 1<<(M-i-1), p); // c^(2^(M-i-1))
-			R = (int) ((R*(long)b) % p);
-			c = (int) ((b*(long)b) % p);
-			t = (int) ((t*(long)c) % p);
+			R = (int) ((((long)R) * b) % p);
+			c = (int) ((((long)b) * b) % p);
+			t = (int) ((((long)t) * c) % p);
 			M = i;
 		}
 		if (DEBUG) Ensure.ensureEquals(BigInteger.valueOf(R).pow(2).mod(BigInteger.valueOf(p)), n.mod(BigInteger.valueOf(p)));
@@ -148,10 +148,10 @@ private int case5Mod8(BigInteger n, int p) {
 		int k = p>>3; // for p == 5 (mod 8) we need k = (p-5)/8 = p>>3
 		BigInteger n2 = n.shiftLeft(1);
 		int g = mpe.modPow(n2, k, p);
-		BigInteger gSquare = BigInteger.valueOf(g*(long)g);
+		BigInteger gSquare = BigInteger.valueOf(((long)g) * g);
 		BigInteger p_big = BigInteger.valueOf(p);
 		int i = n2.multiply(gSquare).mod(p_big).intValue();
-		int t = n.multiply(BigInteger.valueOf(g*(long)(i-1))).mod(p_big).intValue();
+		int t = n.multiply(BigInteger.valueOf(((long)g) * (i-1))).mod(p_big).intValue();
 		if (DEBUG) Ensure.ensureEquals(BigInteger.valueOf(t).pow(2).mod(p_big), n.mod(p_big));
 		// return the smaller sqrt
 		return t <= (p>>1) ? t : p-t;

src/main/java/de/tilman_neumann/jml/modular/ModularSqrt31.java

@@ -102,7 +102,7 @@ int Tonelli_Shanks(int n, int p) { // not private because used in tests
 				// test invariants from <link>https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm#Proof</link>:
 				Ensure.ensureEquals(p-1, mpe.modPow(c, 1<<(M-1), p));  //  -1 == c^(2^(M-1)) (mod p)
 				Ensure.ensureEquals(1, mpe.modPow(t, 1<<(M-1), p));    //   1 == t^(2^(M-1)) (mod p)
-				Ensure.ensureEquals((R*(long)R) % p, (t*(long)n) % p); // R^2 == t*n (mod p)
+				Ensure.ensureEquals((((long)R) * R) % p, (((long)t) * n) % p); // R^2 == t*n (mod p)
 			}
 			boolean foundI = false;
 			int i;
@@ -115,9 +115,9 @@ int Tonelli_Shanks(int n, int p) { // not private because used in tests
 			if (foundI==false) throw new IllegalStateException("Tonelli-Shanks did not find an 'i' < M=" + M);
 
 			int b = mpe.modPow(c, 1<<(M-i-1), p); // c^(2^(M-i-1))
-			R = (int) ((R*(long)b) % p);
-			c = (int) ((b*(long)b) % p);
-			t = (int) ((t*(long)c) % p);
+			R = (int) ((((long)R) * b) % p);
+			c = (int) ((((long)b) * b) % p);
+			t = (int) ((((long)t) * c) % p);
 			M = i;
 		}
 		if (DEBUG) Ensure.ensureEquals(BigInteger.valueOf(R).pow(2).mod(BigInteger.valueOf(p)), BigInteger.valueOf(n%p));