faster binary search using Arrays.binarySearch()

Author: TilmanNeumann

src/main/java/de/tilman_neumann/jml/BinarySearch.java

@@ -1,6 +1,6 @@
 /*
  * java-math-library is a Java library focused on number theory, but not necessarily limited to it. It is based on the PSIQS 4.0 factoring project.
- * Copyright (C) 2018-2024 Tilman Neumann - tilman.neumann@web.de
+ * Copyright (C) 2018-2025 Tilman Neumann - tilman.neumann@web.de
  *
  * This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License
  * as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
@@ -13,6 +13,8 @@
  */
 package de.tilman_neumann.jml;
 
+import java.util.Arrays;
+
 import de.tilman_neumann.util.Ensure;
 
 /**
@@ -34,7 +36,7 @@ public class BinarySearch {
 	 * @param x
 	 * @return the insert position
 	 */
-	public int getInsertPosition(int[] array, int maxIndex, int x) {
+	public int getInsertPosition_v1(int[] array, int maxIndex, int x) {
 		if (maxIndex<=0 || array[maxIndex-1] <= x) return maxIndex;
 		int left = 0;
 		int right = maxIndex-1;
@@ -56,6 +58,26 @@ public int getInsertPosition(int[] array, int maxIndex, int x) {
 		return left;
 	}
 
+	/**
+	 * Find the insert position for x into array given that array is sorted bottom-up.
+	 * 
+	 * More precisely:
+	 * If array[maxIndex-1] >  x, return the index of the first entry of array[0].. array[maxIndex-1] greater than x.
+	 * If array[maxIndex-1] <= x, return maxIndex.
+	 * 
+	 * Faster version using Arrays.binarySearch().
+	 * 
+	 * @param array
+	 * @param maxIndex the maximum index to consider, exclusive (may be smaller than the array size)
+	 * @param x
+	 * @return the insert position
+	 */
+	public int getInsertPosition/*_v2*/(int[] array, int maxIndex, int x) {
+		// see @returns in Arrays.binarySearch() javadoc
+		int i = Arrays.binarySearch(array, 0, maxIndex, x);
+		return i >= 0 ? i + 1 : -i - 1;
+	}
+
 	/**
 	 * Find the insert position for x into array given that array is sorted bottom-up.
 	 * 
@@ -68,7 +90,7 @@ public int getInsertPosition(int[] array, int maxIndex, int x) {
 	 * @param x
 	 * @return the insert position
 	 */
-	public int getInsertPosition(byte[] array, int maxIndex, int x) {
+	public int getInsertPosition_v1(byte[] array, int maxIndex, byte x) {
 		if (maxIndex<=0 || array[maxIndex-1] <= x) return maxIndex;
 		int left = 0;
 		int right = maxIndex-1;
@@ -89,4 +111,24 @@ public int getInsertPosition(byte[] array, int maxIndex, int x) {
 		}
 		return left;
 	}
+	
+	/**
+	 * Find the insert position for x into array given that array is sorted bottom-up.
+	 * 
+	 * More precisely:
+	 * If array[maxIndex-1] >  x, return the index of the first entry of array[0].. array[maxIndex-1] greater than x.
+	 * If array[maxIndex-1] <= x, return maxIndex.
+	 * 
+	 * Faster version using Arrays.binarySearch().
+	 * 
+	 * @param array
+	 * @param maxIndex the maximum index to consider, exclusive (may be smaller than the array size)
+	 * @param x
+	 * @return the insert position
+	 */
+	public int getInsertPosition/*_v2*/(byte[] array, int maxIndex, byte x) {
+		// see @returns in Arrays.binarySearch() javadoc
+		int i = Arrays.binarySearch(array, 0, maxIndex, x);
+		return i >= 0 ? i + 1 : -i - 1;
+	}
 }

src/main/java/de/tilman_neumann/jml/factor/siqs/sieve/Sieve03h.java

@@ -201,7 +201,7 @@ public void initializeForAParameter(int d, BigInteger daParam, SolutionArrays so
 		int logP = logPMax;
 		int lastBound = filteredBaseSize;
 		for (int i=logPBoundCount-1; i>0; i--) {
-			lastBound = logPBounds[i] = binarySearch.getInsertPosition(logPArray, lastBound, --logP);
+			lastBound = logPBounds[i] = binarySearch.getInsertPosition(logPArray, lastBound, (byte) --logP);
 			if (DEBUG) LOG.debug("logPBound[" + i + "] = " + logPBounds[i] + ", logP[" + logPBounds[i] + "] = " + logPArray[logPBounds[i]] + ", logP[" + (logPBounds[i]-1) + "] = " + logPArray[logPBounds[i]-1]);
 		}
 		logPBounds[0] = p1Index;

src/main/java/de/tilman_neumann/jml/factor/siqs/sieve/Sieve03hU.java

@@ -202,7 +202,7 @@ public void initializeForAParameter(int d, BigInteger daParam, SolutionArrays so
 		int logP = logPMax;
 		int lastBound = filteredBaseSize;
 		for (int i=logPBoundCount-1; i>0; i--) {
-			lastBound = logPBounds[i] = binarySearch.getInsertPosition(logPArray, lastBound, --logP);
+			lastBound = logPBounds[i] = binarySearch.getInsertPosition(logPArray, lastBound, (byte) --logP);
 			if (DEBUG) LOG.debug("logPBound[" + i + "] = " + logPBounds[i] + ", logP[" + logPBounds[i] + "] = " + logPArray[logPBounds[i]] + ", logP[" + (logPBounds[i]-1) + "] = " + logPArray[logPBounds[i]-1]);
 		}
 		logPBounds[0] = p1Index;