sort: improve average quicksort performance

Revert "Revert "sort: improve average quicksort performance""
This reverts commit 30b87bb.

See https://golang.org/cl/15688 for the CL being replayed.

Change-Id: I2ba36334003f4971f95a10536adfdd86be9a50de
Reviewed-on: https://go-review.googlesource.com/17389
Run-TryBot: Brad Fitzpatrick <[email protected]>
Reviewed-by: Russ Cox <[email protected]>

src/sort/example_multi_test.go

@@ -122,10 +122,10 @@ func Example_sortMultiKeys() {
 	fmt.Println("By language,<lines,user:", changes)
 
 	// Output:
-	// By user: [{dmr C 100} {glenda Go 200} {gri Smalltalk 80} {gri Go 100} {ken Go 200} {ken C 150} {r Go 100} {r C 150} {rsc Go 200}]
+	// By user: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
 	// By user,<lines: [{dmr C 100} {glenda Go 200} {gri Smalltalk 80} {gri Go 100} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
 	// By user,>lines: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken Go 200} {ken C 150} {r C 150} {r Go 100} {rsc Go 200}]
-	// By language,<lines: [{dmr C 100} {ken C 150} {r C 150} {gri Go 100} {r Go 100} {ken Go 200} {glenda Go 200} {rsc Go 200} {gri Smalltalk 80}]
+	// By language,<lines: [{dmr C 100} {ken C 150} {r C 150} {r Go 100} {gri Go 100} {ken Go 200} {glenda Go 200} {rsc Go 200} {gri Smalltalk 80}]
 	// By language,<lines,user: [{dmr C 100} {ken C 150} {r C 150} {gri Go 100} {r Go 100} {glenda Go 200} {ken Go 200} {rsc Go 200} {gri Smalltalk 80}]
 
 }

src/sort/sort.go

@@ -72,7 +72,7 @@ func heapSort(data Interface, a, b int) {
 	}
 }
 
-// Quicksort, following Bentley and McIlroy,
+// Quicksort, loosely following Bentley and McIlroy,
 // ``Engineering a Sort Function,'' SP&E November 1993.
 
 // medianOfThree moves the median of the three values data[m0], data[m1], data[m2] into data[m1].
@@ -111,59 +111,82 @@ func doPivot(data Interface, lo, hi int) (midlo, midhi int) {
 
 	// Invariants are:
 	//	data[lo] = pivot (set up by ChoosePivot)
-	//	data[lo <= i < a] = pivot
-	//	data[a <= i < b] < pivot
-	//	data[b <= i < c] is unexamined
-	//	data[c <= i < d] > pivot
-	//	data[d <= i < hi] = pivot
-	//
-	// Once b meets c, can swap the "= pivot" sections
-	// into the middle of the slice.
+	//	data[lo < i < a] < pivot
+	//	data[a <= i < b] <= pivot
+	//	data[b <= i < c] unexamined
+	//	data[c <= i < hi-1] > pivot
+	//	data[hi-1] >= pivot
 	pivot := lo
-	a, b, c, d := lo+1, lo+1, hi, hi
+	a, c := lo+1, hi-1
+
+	for ; a != c && data.Less(a, pivot); a++ {
+	}
+	b := a
 	for {
-		for b < c {
-			if data.Less(b, pivot) { // data[b] < pivot
-				b++
-			} else if !data.Less(pivot, b) { // data[b] = pivot
-				data.Swap(a, b)
-				a++
-				b++
-			} else {
-				break
-			}
+		for ; b != c && !data.Less(pivot, b); b++ { // data[b] <= pivot
 		}
-		for b < c {
-			if data.Less(pivot, c-1) { // data[c-1] > pivot
-				c--
-			} else if !data.Less(c-1, pivot) { // data[c-1] = pivot
-				data.Swap(c-1, d-1)
-				c--
-				d--
-			} else {
-				break
-			}
+		for ; b != c && data.Less(pivot, c-1); c-- { // data[c-1] > pivot
 		}
-		if b >= c {
+		if b == c {
 			break
 		}
-		// data[b] > pivot; data[c-1] < pivot
+		// data[b] > pivot; data[c-1] <= pivot
 		data.Swap(b, c-1)
 		b++
 		c--
 	}
-
-	n := min(b-a, a-lo)
-	swapRange(data, lo, b-n, n)
-
-	n = min(hi-d, d-c)
-	swapRange(data, c, hi-n, n)
-
-	return lo + b - a, hi - (d - c)
+	// If hi-c<3 then there are duplicates (by property of median of nine).
+	// Let be a bit more conservative, and set border to 5.
+	protect := hi-c < 5
+	if !protect && hi-c < (hi-lo)/4 {
+		// Lets test some points for equality to pivot
+		dups := 0
+		if !data.Less(pivot, hi-1) { // data[hi-1] = pivot
+			data.Swap(c, hi-1)
+			c++
+			dups++
+		}
+		if !data.Less(b-1, pivot) { // data[b-1] = pivot
+			b--
+			dups++
+		}
+		// m-lo = (hi-lo)/2 > 6
+		// b-lo > (hi-lo)*3/4-1 > 8
+		// ==> m < b ==> data[m] <= pivot
+		if !data.Less(m, pivot) { // data[m] = pivot
+			data.Swap(m, b-1)
+			b--
+			dups++
+		}
+		// if at least 2 points are equal to pivot, assume skewed distribution
+		protect = dups > 1
+	}
+	if protect {
+		// Protect against a lot of duplicates
+		// Add invariant:
+		//	data[a <= i < b] unexamined
+		//	data[b <= i < c] = pivot
+		for {
+			for ; a != b && !data.Less(b-1, pivot); b-- { // data[b] == pivot
+			}
+			for ; a != b && data.Less(a, pivot); a++ { // data[a] < pivot
+			}
+			if a == b {
+				break
+			}
+			// data[a] == pivot; data[b-1] < pivot
+			data.Swap(a, b-1)
+			a++
+			b--
+		}
+	}
+	// Swap pivot into middle
+	data.Swap(pivot, b-1)
+	return b - 1, c
 }
 
 func quickSort(data Interface, a, b, maxDepth int) {
-	for b-a > 7 {
+	for b-a > 12 { // Use ShellSort for slices <= 12 elements
 		if maxDepth == 0 {
 			heapSort(data, a, b)
 			return
@@ -181,6 +204,13 @@ func quickSort(data Interface, a, b, maxDepth int) {
 		}
 	}
 	if b-a > 1 {
+		// Do ShellSort pass with gap 6
+		// It could be written in this simplified form cause b-a <= 12
+		for i := a + 6; i < b; i++ {
+			if data.Less(i, i-6) {
+				data.Swap(i, i-6)
+			}
+		}
 		insertionSort(data, a, b)
 	}
 }