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 <gri@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>

diff --git a/src/sort/search.go b/src/sort/search.go
index b9640a40aff88e90f3ca9b48aed1a9ce69071ae8..24cc90248c0992fc6be4b802b491c98933fc5d85 100644 (file)
--- a/src/sort/search.go
+++ b/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