sort: optimize average calculation in symMerge and doPivot.

Change code of the form `i + (j-i)/2` to `int(uint(i+j) >> 1)`.

The optimized average calculation uses fewer instructions to calculate
the average without overflowing at the addition.

Analogous to https://golang.org/cl/36332.

name                 old time/op  new time/op  delta
StableString1K-4     49.6µs ± 3%  49.1µs ± 8%    ~     (p=0.659 n=16+19)
StableInt1K-4         160µs ±10%   148µs ± 5%  -7.29%  (p=0.000 n=20+16)
StableInt1K_Slice-4   139µs ± 4%   136µs ± 3%  -2.52%  (p=0.000 n=20+16)
StableInt64K-4       8.84ms ± 6%  8.57ms ± 5%  -3.07%  (p=0.001 n=20+19)
Stable1e2-4           162µs ±19%   147µs ±16%  -8.79%  (p=0.002 n=20+20)
Stable1e4-4          31.0ms ± 5%  30.6ms ± 5%    ~     (p=0.221 n=20+20)
Stable1e6-4           6.37s ± 3%   6.27s ± 2%  -1.67%  (p=0.000 n=19+20)

Change-Id: I1cea0bcb9ace8ef7e48b8fab772e41b4b2170da9
Reviewed-on: https://go-review.googlesource.com/36570
Run-TryBot: Ian Lance Taylor <iant@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Russ Cox <rsc@golang.org>

3 files changed, 14 insertions, 10 deletions

diff --git a/src/sort/genzfunc.go b/src/sort/genzfunc.go
index 6d2b471b62..3bb7691f6a 100644
--- a/src/sort/genzfunc.go
+++ b/src/sort/genzfunc.go
@@ -115,6 +115,10 @@ func rewriteCall(ce *ast.CallExpr) {
 		// e.g. skip SelectorExpr (data.Less(..) calls)
 		return
 	}
+	// skip casts
+	if ident.Name == "int" || ident.Name == "uint" {
+		return
+	}
 	if len(ce.Args) < 1 {
 		return
 	}
diff --git a/src/sort/sort.go b/src/sort/sort.go
index 72d24efcea..54f92a4217 100644
--- a/src/sort/sort.go
+++ b/src/sort/sort.go
@@ -96,7 +96,7 @@ func swapRange(data Interface, a, b, n int) {
 }
 
 func doPivot(data Interface, lo, hi int) (midlo, midhi int) {
-	m := lo + (hi-lo)/2 // Written like this to avoid integer overflow.
+	m := int(uint(lo+hi) >> 1) // Written like this to avoid integer overflow.
 	if hi-lo > 40 {
 		// Tukey's ``Ninther,'' median of three medians of three.
 		s := (hi - lo) / 8
@@ -447,7 +447,7 @@ func symMerge(data Interface, a, m, b int) {
 		i := m
 		j := b
 		for i < j {
-			h := i + (j-i)/2
+			h := int(uint(i+j) >> 1)
 			if data.Less(h, a) {
 				i = h + 1
 			} else {
@@ -471,7 +471,7 @@ func symMerge(data Interface, a, m, b int) {
 		i := a
 		j := m
 		for i < j {
-			h := i + (j-i)/2
+			h := int(uint(i+j) >> 1)
 			if !data.Less(m, h) {
 				i = h + 1
 			} else {
@@ -485,7 +485,7 @@ func symMerge(data Interface, a, m, b int) {
 		return
 	}
 
-	mid := a + (b-a)/2
+	mid := int(uint(a+b) >> 1)
 	n := mid + m
 	var start, r int
 	if m > mid {
@@ -498,7 +498,7 @@ func symMerge(data Interface, a, m, b int) {
 	p := n - 1
 
 	for start < r {
-		c := start + (r-start)/2
+		c := int(uint(start+r) >> 1)
 		if !data.Less(p-c, c) {
 			start = c + 1
 		} else {
diff --git a/src/sort/zfuncversion.go b/src/sort/zfuncversion.go
index 7abb18a24d..99c95a22c1 100644
--- a/src/sort/zfuncversion.go
+++ b/src/sort/zfuncversion.go
@@ -70,7 +70,7 @@ func swapRange_func(data lessSwap, a, b, n int) {
 
 // Auto-generated variant of sort.go:doPivot
 func doPivot_func(data lessSwap, lo, hi int) (midlo, midhi int) {
-	m := lo + (hi-lo)/2
+	m := int(uint(lo+hi) >> 1)
 	if hi-lo > 40 {
 		s := (hi - lo) / 8
 		medianOfThree_func(data, lo, lo+s, lo+2*s)
@@ -189,7 +189,7 @@ func symMerge_func(data lessSwap, a, m, b int) {
 		i := m
 		j := b
 		for i < j {
-			h := i + (j-i)/2
+			h := int(uint(i+j) >> 1)
 			if data.Less(h, a) {
 				i = h + 1
 			} else {
@@ -205,7 +205,7 @@ func symMerge_func(data lessSwap, a, m, b int) {
 		i := a
 		j := m
 		for i < j {
-			h := i + (j-i)/2
+			h := int(uint(i+j) >> 1)
 			if !data.Less(m, h) {
 				i = h + 1
 			} else {
@@ -217,7 +217,7 @@ func symMerge_func(data lessSwap, a, m, b int) {
 		}
 		return
 	}
-	mid := a + (b-a)/2
+	mid := int(uint(a+b) >> 1)
 	n := mid + m
 	var start, r int
 	if m > mid {
@@ -229,7 +229,7 @@ func symMerge_func(data lessSwap, a, m, b int) {
 	}
 	p := n - 1
 	for start < r {
-		c := start + (r-start)/2
+		c := int(uint(start+r) >> 1)
 		if !data.Less(p-c, c) {
 			start = c + 1
 		} else {