comment on final correction in montMul64()

Author: TilmanNeumann

src/main/java/de/tilman_neumann/jml/factor/ecm/TinyEcm64.java

@@ -1093,7 +1093,7 @@ public static long montMul64(long a, long b, long N, long Nhat) {
 		// Since R=2^64, "x / R" just means to get the high part of x.
 		long r = ab.add_getHigh(Uint128.mul64(t, N));
 		// If the correct result is c, then now r==c or r==c+N.
-		r = r<N ? r : r-N; // required at ecm
+		r = r<N ? r : r-N; // improves performance for N >= 50 bit, degrades it for smaller N
 
 		if (DEBUG) {
 			//LOG.debug(a + " * " + b + " = " + r);

src/main/java/de/tilman_neumann/jml/factor/ecm/TinyEcm64MH.java

@@ -1104,7 +1104,7 @@ public static long montMul64(long a, long b, long N, long Nhat) {
 		// Since R=2^64, "x / R" just means to get the high part of x.
 		long r = ab.add_getHigh(Uint128.mul64SignedMH(t, N));
 		// If the correct result is c, then now r==c or r==c+N.
-		r = r<N ? r : r-N; // required at ecm
+		r = r<N ? r : r-N; // improves performance for N >= 55 bit, degrades it for smaller N
 
 		if (DEBUG) {
 			//LOG.debug(a + " * " + b + " = " + r);

src/main/java/de/tilman_neumann/jml/factor/ecm/TinyEcm64MHInlined.java

@@ -1112,7 +1112,7 @@ public static long montMul64(long a, long b, long N, long Nhat) {
 		long high = abHigh + tNHigh;
 		long r = (low+Long.MIN_VALUE < abLow+Long.MIN_VALUE) ? high + 1 : high;
 		// If the correct result is c, then now r==c or r==c+N.
-		r = r<N ? r : r-N; // required only for N>=62 bit; for smaller N dropping this instruction means a speed gain
+		r = r<N ? r : r-N; // improves performance for N >= 55 bit, degrades it for smaller N
 
 		if (DEBUG) {
 			//LOG.debug(a + " * " + b + " = " + r);

src/main/java/de/tilman_neumann/jml/factor/pollardRho/PollardRhoBrentMontgomery64MHInlined.java

@@ -184,7 +184,7 @@ public static long montMul64(long a, long b, long N, long Nhat) {
 		// Since R=2^64, "x / R" just means to get the high part of x.
 		long low = abLow + tNLow;
 		long high = abHigh + tNHigh;
-		long r = (low+Long.MIN_VALUE < abLow+Long.MIN_VALUE) ? high + 1 : high;
+		long r = (low+Long.MIN_VALUE < abLow+Long.MIN_VALUE) ? high + 1 : high; // this adjustment is very important here
 		// If the correct result is c, then now r==c or r==c+N.
 		// This is fine for this factoring algorithm, because r will 
 		// * either be subjected to another Montgomery multiplication mod N,