image/png: optimize the paeth filter implementation.

image/png benchmarks:
benchmark                       old ns/op    new ns/op    delta
BenchmarkPaeth                         10            7  -29.21%
BenchmarkDecodeGray               2381745      2241620   -5.88%
BenchmarkDecodeNRGBAGradient      9535555      8835100   -7.35%
BenchmarkDecodeNRGBAOpaque        8189590      7611865   -7.05%
BenchmarkDecodePaletted           1300688      1301940   +0.10%
BenchmarkDecodeRGB                6760146      6317082   -6.55%
BenchmarkEncodePaletted           6048596      6122666   +1.22%
BenchmarkEncodeRGBOpaque         18891140     19474230   +3.09%
BenchmarkEncodeRGBA              78945350     78552600   -0.50%

Wall time for Denis Cheremisov's PNG-decoding program given in
https://groups.google.com/group/golang-nuts/browse_thread/thread/22aa8a05040fdd49
Before: 2.25s
After:  2.27s
Delta:  +1%

The same program, but with a different PNG input file
(http://upload.wikimedia.org/wikipedia/commons/4/47/PNG_transparency_demonstration_1.png)
and only 100 iterations instead of 1000
Before: 4.78s
After:  4.42s
Delta:  -8%

R=rsc
CC=golang-dev
https://golang.org/cl/6242056

src/pkg/image/png/paeth_test.go

+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package png
+
+import (
+	"testing"
+)
+
+func abs(x int) int {
+	if x < 0 {
+		return -x
+	}
+	return x
+}
+
+// slowPaeth is a slow but simple implementation of the Paeth function.
+// It is a straight port of the sample code in the PNG spec, section 9.4.
+func slowPaeth(a, b, c uint8) uint8 {
+	p := int(a) + int(b) - int(c)
+	pa := abs(p - int(a))
+	pb := abs(p - int(b))
+	pc := abs(p - int(c))
+	if pa <= pb && pa <= pc {
+		return a
+	} else if pb <= pc {
+		return b
+	}
+	return c
+}
+
+func TestPaeth(t *testing.T) {
+	for a := 0; a < 256; a += 15 {
+		for b := 0; b < 256; b += 15 {
+			for c := 0; c < 256; c += 15 {
+				got := paeth(uint8(a), uint8(b), uint8(c))
+				want := slowPaeth(uint8(a), uint8(b), uint8(c))
+				if got != want {
+					t.Errorf("a, b, c = %d, %d, %d: got %d, want %d", a, b, c, got, want)
+				}
+			}
+		}
+	}
+}
+
+func BenchmarkPaeth(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		paeth(uint8(i>>16), uint8(i>>8), uint8(i))
+	}
+}

src/pkg/image/png/reader.go

@@ -98,13 +98,6 @@ type UnsupportedError string
 
 func (e UnsupportedError) Error() string { return "png: unsupported feature: " + string(e) }
 
-func abs(x int) int {
-	if x < 0 {
-		return -x
-	}
-	return x
-}
-
 func min(a, b int) int {
 	if a < b {
 		return a
@@ -241,12 +234,28 @@ func (d *decoder) parsetRNS(length uint32) error {
 	return d.verifyChecksum()
 }
 
-// The Paeth filter function, as per the PNG specification.
+// paeth implements the Paeth filter function, as per the PNG specification.
 func paeth(a, b, c uint8) uint8 {
-	p := int(a) + int(b) - int(c)
-	pa := abs(p - int(a))
-	pb := abs(p - int(b))
-	pc := abs(p - int(c))
+	// This is an optimized version of the sample code in the PNG spec.
+	// For example, the sample code starts with:
+	//	p := int(a) + int(b) - int(c)
+	//	pa := abs(p - int(a))
+	// but the optimized form uses fewer arithmetic operations:
+	//	pa := int(b) - int(c)
+	//	pa = abs(pa)
+	pc := int(c)
+	pa := int(b) - pc
+	pb := int(a) - pc
+	pc = pa + pb
+	if pa < 0 {
+		pa = -pa
+	}
+	if pb < 0 {
+		pb = -pb
+	}
+	if pc < 0 {
+		pc = -pc
+	}
 	if pa <= pb && pa <= pc {
 		return a
 	} else if pb <= pc {