strings: use Rabin-Karp algorithm for LastIndex.

benchmark                  old ns/op     new ns/op     delta
BenchmarkSingleMatch       49443         52275         +5.73%
BenchmarkIndex             28.8          27.4          -4.86%
BenchmarkLastIndex         14.5          14.0          -3.45%
BenchmarkLastIndexHard1    3982782       2309200       -42.02%
BenchmarkLastIndexHard2    3985562       2287715       -42.60%
BenchmarkLastIndexHard3    3555259       2282866       -35.79%

LGTM=josharian, nigeltao
R=golang-codereviews, ality, josharian, bradfitz, dave, nigeltao, gobot, nightlyone
CC=golang-codereviews
https://golang.org/cl/102560043

src/pkg/strings/strings.go

@@ -43,13 +43,29 @@ func explode(s string, n int) []string {
 // primeRK is the prime base used in Rabin-Karp algorithm.
 const primeRK = 16777619
 
-// hashstr returns the hash and the appropriate multiplicative
+// hashStr returns the hash and the appropriate multiplicative
 // factor for use in Rabin-Karp algorithm.
-func hashstr(sep string) (uint32, uint32) {
+func hashStr(sep string) (uint32, uint32) {
 	hash := uint32(0)
 	for i := 0; i < len(sep); i++ {
 		hash = hash*primeRK + uint32(sep[i])
+	}
+	var pow, sq uint32 = 1, primeRK
+	for i := len(sep); i > 0; i >>= 1 {
+		if i&1 != 0 {
+			pow *= sq
+		}
+		sq *= sq
+	}
+	return hash, pow
+}
 
+// hashStrRev returns the hash of the reverse of sep and the
+// appropriate multiplicative factor for use in Rabin-Karp algorithm.
+func hashStrRev(sep string) (uint32, uint32) {
+	hash := uint32(0)
+	for i := len(sep) - 1; i >= 0; i-- {
+		hash = hash*primeRK + uint32(sep[i])
 	}
 	var pow, sq uint32 = 1, primeRK
 	for i := len(sep); i > 0; i >>= 1 {
@@ -85,7 +101,8 @@ func Count(s, sep string) int {
 		}
 		return 0
 	}
-	hashsep, pow := hashstr(sep)
+	// Rabin-Karp search
+	hashsep, pow := hashStr(sep)
 	h := uint32(0)
 	for i := 0; i < len(sep); i++ {
 		h = h*primeRK + uint32(s[i])
@@ -139,8 +156,8 @@ func Index(s, sep string) int {
 	case n > len(s):
 		return -1
 	}
-	// Hash sep.
-	hashsep, pow := hashstr(sep)
+	// Rabin-Karp search
+	hashsep, pow := hashStr(sep)
 	var h uint32
 	for i := 0; i < n; i++ {
 		h = h*primeRK + uint32(s[i])
@@ -163,22 +180,41 @@ func Index(s, sep string) int {
 // LastIndex returns the index of the last instance of sep in s, or -1 if sep is not present in s.
 func LastIndex(s, sep string) int {
 	n := len(sep)
-	if n == 0 {
+	switch {
+	case n == 0:
 		return len(s)
-	}
-	c := sep[0]
-	if n == 1 {
+	case n == 1:
 		// special case worth making fast
+		c := sep[0]
 		for i := len(s) - 1; i >= 0; i-- {
 			if s[i] == c {
 				return i
 			}
 		}
 		return -1
+	case n == len(s):
+		if sep == s {
+			return 0
+		}
+		return -1
+	case n > len(s):
+		return -1
 	}
-	// n > 1
-	for i := len(s) - n; i >= 0; i-- {
-		if s[i] == c && s[i:i+n] == sep {
+	// Rabin-Karp search from the end of the string
+	hashsep, pow := hashStrRev(sep)
+	last := len(s) - n
+	var h uint32
+	for i := len(s) - 1; i >= last; i-- {
+		h = h*primeRK + uint32(s[i])
+	}
+	if h == hashsep && s[last:] == sep {
+		return last
+	}
+	for i := last - 1; i >= 0; i-- {
+		h *= primeRK
+		h += uint32(s[i])
+		h -= pow * uint32(s[i+n])
+		if h == hashsep && s[i:i+n] == sep {
 			return i
 		}
 	}

src/pkg/strings/strings_test.go

@@ -168,6 +168,15 @@ func BenchmarkIndex(b *testing.B) {
 	}
 }
 
+func BenchmarkLastIndex(b *testing.B) {
+	if got := Index(benchmarkString, "v"); got != 17 {
+		b.Fatalf("wrong index: expected 17, got=%d", got)
+	}
+	for i := 0; i < b.N; i++ {
+		LastIndex(benchmarkString, "v")
+	}
+}
+
 func BenchmarkIndexByte(b *testing.B) {
 	if got := IndexByte(benchmarkString, 'v'); got != 17 {
 		b.Fatalf("wrong index: expected 17, got=%d", got)
@@ -1087,6 +1096,12 @@ func benchmarkIndexHard(b *testing.B, sep string) {
 	}
 }
 
+func benchmarkLastIndexHard(b *testing.B, sep string) {
+	for i := 0; i < b.N; i++ {
+		LastIndex(benchInputHard, sep)
+	}
+}
+
 func benchmarkCountHard(b *testing.B, sep string) {
 	for i := 0; i < b.N; i++ {
 		Count(benchInputHard, sep)
@@ -1097,6 +1112,10 @@ func BenchmarkIndexHard1(b *testing.B) { benchmarkIndexHard(b, "<>") }
 func BenchmarkIndexHard2(b *testing.B) { benchmarkIndexHard(b, "</pre>") }
 func BenchmarkIndexHard3(b *testing.B) { benchmarkIndexHard(b, "<b>hello world</b>") }
 
+func BenchmarkLastIndexHard1(b *testing.B) { benchmarkLastIndexHard(b, "<>") }
+func BenchmarkLastIndexHard2(b *testing.B) { benchmarkLastIndexHard(b, "</pre>") }
+func BenchmarkLastIndexHard3(b *testing.B) { benchmarkLastIndexHard(b, "<b>hello world</b>") }
+
 func BenchmarkCountHard1(b *testing.B) { benchmarkCountHard(b, "<>") }
 func BenchmarkCountHard2(b *testing.B) { benchmarkCountHard(b, "</pre>") }
 func BenchmarkCountHard3(b *testing.B) { benchmarkCountHard(b, "<b>hello world</b>") }