Optimized HashTable.index

(`ops/s`, smaller is better)

`Before (9c5d3f8)`:
```scala
[info] # Run complete. Total time: 00:08:15
[info]
[info] Benchmark                                     (size)  Mode  Cnt      Score      Error  Units
[info] s.c.immutable.VectorMapBenchmark.groupBy          10  avgt   20    645.594 ±    9.435  ns/op
[info] s.c.immutable.VectorMapBenchmark.groupBy         100  avgt   20   2084.216 ±   37.814  ns/op
[info] s.c.immutable.VectorMapBenchmark.groupBy        1000  avgt   20  19878.481 ±  262.404  ns/op
[info] s.c.mutable.HashMapBenchmark.get                  10  avgt   20    689.941 ±    5.850  ns/op
[info] s.c.mutable.HashMapBenchmark.get                 100  avgt   20   7357.330 ±   45.956  ns/op
[info] s.c.mutable.HashMapBenchmark.get                1000  avgt   20  95767.200 ± 1550.771  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate      10  avgt   20    509.181 ±    2.683  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate     100  avgt   20   5563.301 ±   32.335  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate    1000  avgt   20  71965.365 ± 1809.738  ns/op
[info] s.c.mutable.HashMapBenchmark.put                  10  avgt   20    247.270 ±    3.972  ns/op
[info] s.c.mutable.HashMapBenchmark.put                 100  avgt   20   5646.185 ±  106.172  ns/op
[info] s.c.mutable.HashMapBenchmark.put                1000  avgt   20  81303.663 ±  954.938  ns/op
```

`Changed modulo to bitwise and in hash calculation (4c729fe)`:
```scala
[info] Benchmark                                     (size)  Mode  Cnt      Score      Error  Units
[info] s.c.immutable.VectorMapBenchmark.groupBy          10  avgt   20    631.291 ±    9.269  ns/op
[info] s.c.immutable.VectorMapBenchmark.groupBy         100  avgt   20   2077.885 ±   59.737  ns/op
[info] s.c.immutable.VectorMapBenchmark.groupBy        1000  avgt   20  15458.278 ±  317.347  ns/op
[info] s.c.mutable.HashMapBenchmark.get                  10  avgt   20    678.013 ±    4.453  ns/op
[info] s.c.mutable.HashMapBenchmark.get                 100  avgt   20   7258.522 ±   76.088  ns/op
[info] s.c.mutable.HashMapBenchmark.get                1000  avgt   20  94748.845 ± 1226.120  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate      10  avgt   20    498.042 ±    5.006  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate     100  avgt   20   5243.154 ±  110.372  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate    1000  avgt   20  68194.752 ±  655.436  ns/op
[info] s.c.mutable.HashMapBenchmark.put                  10  avgt   20    257.275 ±    1.411  ns/op
[info] s.c.mutable.HashMapBenchmark.put                 100  avgt   20   5318.532 ±  152.923  ns/op
[info] s.c.mutable.HashMapBenchmark.put                1000  avgt   20  79607.160 ±  651.779  ns/op

```

`Optimized HashTable.index (6cc1504)`:
```scala
[info] Benchmark                                     (size)  Mode  Cnt      Score      Error  Units
[info] s.c.immutable.VectorMapBenchmark.groupBy          10  avgt   20    616.164 ±    4.712  ns/op
[info] s.c.immutable.VectorMapBenchmark.groupBy         100  avgt   20   2034.447 ±   14.495  ns/op
[info] s.c.immutable.VectorMapBenchmark.groupBy        1000  avgt   20  14712.164 ±  119.983  ns/op
[info] s.c.mutable.HashMapBenchmark.get                  10  avgt   20    679.046 ±    6.872  ns/op
[info] s.c.mutable.HashMapBenchmark.get                 100  avgt   20   7242.097 ±   41.244  ns/op
[info] s.c.mutable.HashMapBenchmark.get                1000  avgt   20  95342.919 ± 1521.328  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate      10  avgt   20    488.034 ±    4.554  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate     100  avgt   20   4883.123 ±   59.268  ns/op
[info] s.c.mutable.HashMapBenchmark.getOrElseUpdate    1000  avgt   20  65174.034 ±  496.759  ns/op
[info] s.c.mutable.HashMapBenchmark.put                  10  avgt   20    267.983 ±    1.797  ns/op
[info] s.c.mutable.HashMapBenchmark.put                 100  avgt   20   5097.351 ±  104.538  ns/op
[info] s.c.mutable.HashMapBenchmark.put                1000  avgt   20  78772.540 ±  543.935  ns/op
```

Summary, i.e. the effect of this PR, according to the benchmarks:
* `groupBy` has a `~35%` speedup
* `get` didn't change
* `getOrElseUpdate` has a `~10%` speedup
* `put` has a `~3%` speedup

Note: caching the `exponent` to a local private field (`Byte` or `Int`) didn't have any performance advantage (only a minor slowdown was measured, possibly because it's accessed via an interface now)

2 files changed, 177 insertions, 7 deletions

diff --git a/src/library/scala/collection/mutable/HashTable.scala b/src/library/scala/collection/mutable/HashTable.scala
index 9cb40e3f50..776eafaccc 100644
--- a/src/library/scala/collection/mutable/HashTable.scala
+++ b/src/library/scala/collection/mutable/HashTable.scala
@@ -360,14 +360,14 @@ trait HashTable[A, Entry >: Null <: HashEntry[A, Entry]] extends HashTable.HashU
 
   protected def elemEquals(key1: A, key2: A): Boolean = (key1 == key2)
 
-  // Note:
-  // we take the most significant bits of the hashcode, not the lower ones
-  // this is of crucial importance when populating the table in parallel
-  protected final def index(hcode: Int) = {
+  /**
+    * Note: we take the most significant bits of the hashcode, not the lower ones
+    * this is of crucial importance when populating the table in parallel
+    */
+  protected final def index(hcode: Int): Int = {
     val ones = table.length - 1
-    val improved = improve(hcode, seedvalue)
-    val shifted = (improved >> (32 - java.lang.Integer.bitCount(ones))) & ones
-    shifted
+    val exponent = Integer.numberOfLeadingZeros(ones)
+    (improve(hcode, seedvalue) >>> exponent) & ones
   }
 
   protected def initWithContents(c: HashTable.Contents[A, Entry]) = {
diff --git a/test/benchmarks/src/main/scala/scala/BitManipulationBenchmark.scala b/test/benchmarks/src/main/scala/scala/BitManipulationBenchmark.scala
new file mode 100644
index 0000000000..23e303ede0
--- /dev/null
+++ b/test/benchmarks/src/main/scala/scala/BitManipulationBenchmark.scala
@@ -0,0 +1,170 @@
+package scala.collection
+
+import org.openjdk.jmh.annotations._
+import org.openjdk.jmh.infra._
+import org.openjdk.jmh.runner.IterationType
+import benchmark._
+import java.util.concurrent.TimeUnit
+
+@BenchmarkMode(Array(Mode.AverageTime))
+@Fork(2)
+@Threads(1)
+@Warmup(iterations = 10)
+@Measurement(iterations = 10)
+@OutputTimeUnit(TimeUnit.NANOSECONDS)
+@State(Scope.Benchmark)
+class BitManipulationBenchmark {
+  val powersOfTwo = Array(1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824)
+
+  //////////////////////////////////////////////
+
+  @Benchmark def withIntegerBitCount(bh: Blackhole) {
+    for (v <- powersOfTwo) {
+      val leadingZeros = withIntegerBitCount(v)
+      // assert (leadingZeros == withLoop(v), s"$leadingZeros != ${withLoop(v)} ($v)")
+      bh.consume(leadingZeros)
+    }
+  }
+
+  private def withIntegerBitCount(v: Int) = Integer.SIZE - Integer.bitCount(v - 1)
+
+  //////////////////////////////////////////////
+
+  @Benchmark def withIntegerNumberOfLeadingZeros(bh: Blackhole) {
+    for (v <- powersOfTwo) {
+      val leadingZeros = withIntegerNumberOfLeadingZeros(v)
+      // assert (leadingZeros == withLoop(v), s"$leadingZeros != ${withLoop(v)} ($v)")
+      bh.consume(leadingZeros)
+    }
+  }
+
+  private def withIntegerNumberOfLeadingZeros(v: Int) = Integer.numberOfLeadingZeros(v - 1)
+
+  //////////////////////////////////////////////
+
+  @Benchmark def withLoop(bh: Blackhole) {
+    for (v <- powersOfTwo) {
+      val leadingZeros = withLoop(v)
+      bh.consume(leadingZeros)
+    }
+  }
+
+  private def withLoop(v: Int): Int = {
+    var r = Integer.SIZE
+    var copy = v >> 1
+    while (copy != 0) {
+      r -= 1
+      copy = copy >> 1
+    }
+    r
+  }
+
+  //////////////////////////////////////////////
+
+  @Benchmark def withMatch(bh: Blackhole) {
+    for (v <- powersOfTwo) {
+      val leadingZeros = withMatch(v)
+      // assert (leadingZeros == withLoop(v), s"$leadingZeros != ${withLoop(v)} ($v)")
+      bh.consume(leadingZeros)
+    }
+  }
+
+  private def withMatch(i: Int) = i match {
+    case 1 => 32
+    case 2 => 31
+    case 4 => 30
+    case 8 => 29
+    case 16 => 28
+    case 32 => 27
+    case 64 => 26
+    case 128 => 25
+    case 256 => 24
+    case 512 => 23
+    case 1024 => 22
+    case 2048 => 21
+    case 4096 => 20
+    case 8192 => 19
+    case 16384 => 18
+    case 32768 => 17
+    case 65536 => 16
+    case 131072 => 15
+    case 262144 => 14
+    case 524288 => 13
+    case 1048576 => 12
+    case 2097152 => 11
+    case 4194304 => 10
+    case 8388608 => 9
+    case 16777216 => 8
+    case 33554432 => 7
+    case 67108864 => 6
+    case 134217728 => 5
+    case 268435456 => 4
+    case 536870912 => 3
+    case 1073741824 => 2
+  }
+
+
+  //////////////////////////////////////////////
+
+  @Benchmark def with2DeBruijn(bh: Blackhole) {
+    for (v <- powersOfTwo) {
+      val leadingZeros = with2DeBruijn(v)
+      // assert (leadingZeros == withLoop(v), s"$leadingZeros != ${withLoop(v)} ($v)")
+      bh.consume(leadingZeros)
+    }
+  }
+
+  // https://graphics.stanford.edu/~seander/bithacks.html#IntegerLogDeBruijn
+  private val multiplyDeBruijnBitPosition2 = Array(32, 31, 4, 30, 3, 18, 8, 29, 2, 10, 12, 17, 7, 15, 28, 24, 1, 5, 19, 9, 11, 13, 16, 25, 6, 20, 14, 26, 21, 27, 22, 23)
+
+  private def with2DeBruijn(v: Int) = multiplyDeBruijnBitPosition2((v * 0x077CB531) >>> 27)
+
+
+  //////////////////////////////////////////////
+
+  @Benchmark def withBinSearch(bh: Blackhole) {
+    for (v <- powersOfTwo) {
+      val leadingZeros = withBinSearch(v)
+      // assert (leadingZeros == withLoop(v), s"$leadingZeros != ${withLoop(v)} ($v)")
+      bh.consume(leadingZeros)
+    }
+  }
+
+  private def withBinSearch(v: Int) =
+    if (v < 65536) if (v < 256) if (v < 16) if (v < 4) if (v == 1) 32 else 31
+    else if (v == 4) 30 else 29
+    else if (v < 64) if (v == 16) 28 else 27
+    else if (v == 64) 26 else 25
+    else if (v < 4096) if (v < 1024) if (v == 256) 24 else 23
+    else if (v == 1024) 22 else 21
+    else if (v < 16384) if (v == 4096) 20 else 19
+    else if (v == 16384) 18 else 17
+    else if (v < 16777216) if (v < 1048576) if (v < 262144) if (v == 65536) 16 else 15
+    else if (v == 262144) 14 else 13
+    else if (v < 4194304) if (v == 1048576) 12 else 11
+    else if (v == 4194304) 10 else 9
+    else if (v < 268435456) if (v < 67108864) if (v == 16777216) 8 else 7
+    else if (v == 67108864) 6 else 5
+    else if (v < 1073741824) if (v == 268435456) 4 else 3
+    else if (v == 1073741824) 2 else 1
+
+  //////////////////////////////////////////////
+
+  @Benchmark def withSumBinSearch(bh: Blackhole) {
+    for (v <- powersOfTwo) {
+      val leadingZeros = withSumBinSearch(v)
+      // assert(leadingZeros == withLoop(v), s"$leadingZeros != ${withLoop(v)} ($v)")
+      bh.consume(leadingZeros)
+    }
+  }
+
+  private def withSumBinSearch(v: Int): Int = {
+    var exponent = Integer.SIZE
+    var remaining = v
+    if (remaining >= 65536) { remaining >>>= 16; exponent = 16 }
+    if (remaining >= 256) { remaining >>>= 8; exponent -= 8 }
+    if (remaining >= 16) { remaining >>>= 4; exponent -= 4 }
+    if (remaining >= 4) { remaining >>>= 2; exponent -= 2 }
+    if (remaining >= 2) exponent - 1 else exponent
+  }
+}
\ No newline at end of file