sort: optimize average calculation in binary search

Use fewer instructions to calculate the average of i and j without
overflowing at the addition.

Even if both i and j are math.MaxInt{32,64}, the sum fits into a
uint{32,64}. Because the sum of i and j is always ≥ 0, the right
shift by one does the same as a division by two. The result of the
shift operation is at most math.MaxInt{32,64} and fits again into
an int{32,64}.

name              old time/op  new time/op  delta
SearchWrappers-4   153ns ± 3%   143ns ± 6%  -6.33%  (p=0.000 n=90+100)

This calculation is documented in:
https://research.googleblog.com/2006/06/extra-extra-read-all-about-it-nearly.html

Change-Id: I2be7922afc03b3617fce32e59364606c37a83678
Reviewed-on: https://go-review.googlesource.com/36332
Reviewed-by: Robert Griesemer <[email protected]>
Run-TryBot: Robert Griesemer <[email protected]>
TryBot-Result: Gobot Gobot <[email protected]>

Author: davidrjenni

src/sort/search.go

@@ -61,7 +61,7 @@ func Search(n int, f func(int) bool) int {
 	// Invariant: f(i-1) == false, f(j) == true.
 	i, j := 0, n
 	for i < j {
-		h := i + (j-i)/2 // avoid overflow when computing h
+		h := int(uint(i+j) >> 1) // avoid overflow when computing h
 		// i ≤ h < j
 		if !f(h) {
 			i = h + 1 // preserves f(i-1) == false