5100935: No way to access the 64-bit integer multiplication of 64-bit CPUs efficiently

Add methods multiplyFull() and multiplyHigh() to Math and StrictMath.

Reviewed-by: darcy

jdk/src/java.base/share/classes/java/lang/Math.java

@@ -1059,6 +1059,53 @@ public final class Math {
         return (int)value;
     }
 
+    /**
+     * Returns the exact mathematical product of the arguments.
+     *
+     * @param x the first value
+     * @param y the second value
+     * @return the result
+     */
+    public static long multiplyFull(int x, int y) {
+        return (long)x * (long)y;
+    }
+
+    /**
+     * Returns as a {@code long} the most significant 64 bits of the 128-bit
+     * product of two 64-bit factors.
+     *
+     * @param x the first value
+     * @param y the second value
+     * @return the result
+     */
+    public static long multiplyHigh(long x, long y) {
+        if (x < 0 || y < 0) {
+            // Use technique from section 8-2 of Henry S. Warren, Jr.,
+            // Hacker's Delight (2nd ed.) (Addison Wesley, 2013), 173-174.
+            long x1 = x >> 32;
+            long x2 = x & 0xFFFFFFFFL;
+            long y1 = y >> 32;
+            long y2 = y & 0xFFFFFFFFL;
+            long z2 = x2 * y2;
+            long t = x1 * y2 + (z2 >>> 32);
+            long z1 = t & 0xFFFFFFFFL;
+            long z0 = t >> 32;
+            z1 += x2 * y1;
+            return x1 * y1 + z0 + (z1 >> 32);
+        } else {
+            // Use Karatsuba technique with two base 2^32 digits.
+            long x1 = x >>> 32;
+            long y1 = y >>> 32;
+            long x2 = x & 0xFFFFFFFFL;
+            long y2 = y & 0xFFFFFFFFL;
+            long A = x1 * y1;
+            long B = x2 * y2;
+            long C = (x1 + x2) * (y1 + y2);
+            long K = C - A - B;
+            return (((B >>> 32) + K) >>> 32) + A;
+        }
+    }
+
     /**
      * Returns the largest (closest to positive infinity)
      * {@code int} value that is less than or equal to the algebraic quotient.

jdk/src/java.base/share/classes/java/lang/StrictMath.java

@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 1999, 2015, Oracle and/or its affiliates. All rights reserved.
+ * Copyright (c) 1999, 2016, Oracle and/or its affiliates. All rights reserved.
  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
  *
  * This code is free software; you can redistribute it and/or modify it
@@ -831,6 +831,33 @@ public final class StrictMath {
         return Math.toIntExact(value);
     }
 
+    /**
+     * Returns the exact mathematical product of the arguments.
+     *
+     * @param x the first value
+     * @param y the second value
+     * @return the result
+     * @see Math#multiplyFull(long,long)
+     * @since 1.9
+     */
+    public static long multiplyFull(int x, int y) {
+        return Math.multiplyFull(x, y);
+    }
+
+    /**
+     * Returns as a {@code long} the most significant 64 bits of the 128-bit
+     * product of two 64-bit factors.
+     *
+     * @param x the first value
+     * @param y the second value
+     * @return the result
+     * @see Math#multiplyHigh(long,long)
+     * @since 1.9
+     */
+    public static long multiplyHigh(long x, long y) {
+        return Math.multiplyHigh(x, y);
+    }
+
     /**
      * Returns the largest (closest to positive infinity)
      * {@code int} value that is less than or equal to the algebraic quotient.

jdk/test/java/lang/Math/MultiplicationTests.java

@@ -0,0 +1,113 @@
+/*
+ * Copyright (c) 2016, Oracle and/or its affiliates. All rights reserved.
+ * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
+ *
+ * This code is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License version 2 only, as
+ * published by the Free Software Foundation.
+ *
+ * This code is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ * version 2 for more details (a copy is included in the LICENSE file that
+ * accompanied this code).
+ *
+ * You should have received a copy of the GNU General Public License version
+ * 2 along with this work; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+ *
+ * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
+ * or visit www.oracle.com if you need additional information or have any
+ * questions.
+ */
+
+/*
+ * @test
+ * @library /lib/testlibrary/
+ * @build jdk.testlibrary.*
+ * @run main MultiplicationTests
+ * @bug 5100935
+ * @summary Tests for multiplication methods (use -Dseed=X to set PRNG seed)
+ * @key randomness
+ */
+
+import java.math.BigInteger;
+import jdk.testlibrary.RandomFactory;
+
+public class MultiplicationTests {
+    private MultiplicationTests(){}
+
+    // Number of random products to test.
+    private static final int COUNT = 1 << 16;
+
+    // Initialize shared random number generator
+    private static java.util.Random rnd = RandomFactory.getRandom();
+
+    // Calculate high 64 bits of 128 product using BigInteger.
+    private static long multiplyHighBigInt(long x, long y) {
+        return BigInteger.valueOf(x).multiply(BigInteger.valueOf(y))
+            .shiftRight(64).longValue();
+    }
+
+    // Check Math.multiplyHigh(x,y) against multiplyHighBigInt(x,y)
+    private static boolean check(long x, long y) {
+        long p1 = multiplyHighBigInt(x, y);
+        long p2 = Math.multiplyHigh(x, y);
+        if (p1 != p2) {
+            System.err.printf("Error - x:%d y:%d p1:%d p2:%d\n", x, y, p1, p2);
+            return false;
+        } else {
+            return true;
+        }
+    }
+
+    private static int testMultiplyHigh() {
+        int failures = 0;
+
+        // check some boundary cases
+        long[][] v = new long[][]{
+            {0L, 0L},
+            {-1L, 0L},
+            {0L, -1L},
+            {1L, 0L},
+            {0L, 1L},
+            {-1L, -1L},
+            {-1L, 1L},
+            {1L, -1L},
+            {1L, 1L},
+            {Long.MAX_VALUE, Long.MAX_VALUE},
+            {Long.MAX_VALUE, -Long.MAX_VALUE},
+            {-Long.MAX_VALUE, Long.MAX_VALUE},
+            {Long.MAX_VALUE, Long.MIN_VALUE},
+            {Long.MIN_VALUE, Long.MAX_VALUE},
+            {Long.MIN_VALUE, Long.MIN_VALUE}
+        };
+
+        for (long[] xy : v) {
+            if(!check(xy[0], xy[1])) {
+                failures++;
+            }
+        }
+
+        // check some random values
+        for (int i = 0; i < COUNT; i++) {
+            if (!check(rnd.nextLong(), rnd.nextLong())) {
+                failures++;
+            }
+        }
+
+        return failures;
+    }
+
+    public static void main(String argv[]) {
+        int failures = testMultiplyHigh();
+
+        if (failures > 0) {
+            System.err.println("Multiplication testing encountered "
+                               + failures + " failures.");
+            throw new RuntimeException();
+        } else {
+            System.out.println("MultiplicationTests succeeded");
+        }
+    }
+}