JDK 8 RFR 8022181: Tune algorithm crossover thresholds in BigInteger

[Brian Burkhalter]

Hello,

Issue:	https://bugs.openjdk.java.net/browse/JDK-8022181
Webrev:	http://cr.openjdk.java.net/~bpb/8022181/webrev/

Based on numerous micro-benchmark test runs on various operating systems and architectures I would like to propose changing the BigInteger algorithm crossover thresholds as indicated in the webrev from which I excerpt here for convenience:

-    private static final int KARATSUBA_THRESHOLD = 50;
+    private static final int KARATSUBA_THRESHOLD = 80;
 
-    private static final int TOOM_COOK_THRESHOLD = 75;
+    private static final int TOOM_COOK_THRESHOLD = 240;
 
-    private static final int KARATSUBA_SQUARE_THRESHOLD = 90;
+    private static final int KARATSUBA_SQUARE_THRESHOLD = 128;

-    private static final int TOOM_COOK_SQUARE_THRESHOLD = 140;
+    private static final int TOOM_COOK_SQUARE_THRESHOLD = 216;
 
-    static final int BURNIKEL_ZIEGLER_THRESHOLD = 50;
+    static final int BURNIKEL_ZIEGLER_THRESHOLD = 80;

-    private static final int SCHOENHAGE_BASE_CONVERSION_THRESHOLD = 8;
+    private static final int SCHOENHAGE_BASE_CONVERSION_THRESHOLD = 20;

Each threshold is approximately the smallest value for which no statistically significant performance regression was observed with respect to the baseline. For the Toom-Cook algorithms, the baselines are the respective Karatsuba algorithms; for the other algorithms, the baselines are the respective algorithms previously implemented in BigInteger. Also, these new suggested thresholds were benchmarked against a performance baseline defined by the previous values of the respective thresholds.

With respect to the potential objection that the proposed thresholds are too high, please note that the values are subject to further refinement in the future. This issue https://bugs.openjdk.java.net/browse/JDK-8029425 has been filed as a reminder to continue to refine these values in the JDK 9 time frame although such fine tuning could as well occur in JDK 8 updates.

Thanks,

Brian