hash/crc32: move reverse representation docs to an example

Updates #8229.

Change-Id: I3e691479d3659ed1b3ff8ebbb71b4fc03f2e67af
Reviewed-on: https://go-review.googlesource.com/9680Reviewed-by: Rob Pike <r@golang.org>

src/hash/crc32/crc32.go

@@ -8,13 +8,6 @@
 //
 // Polynomials are represented in LSB-first form also known as reversed representation.
 //
-// LSB-first representation is a hexadecimal number with n bits, the most
-// significant bit represents the coefficient of x^0 and the least significant
-// bit represents the coefficient of x^(n-1).
-//
-// For example, x^5 + x^2 + x^0 is (binary:10100, hexadecimal:0x14) in 5-bit LSB-first form,
-// as opposed to (binary:00101, hexadecimal:0x05) in MSB-first (normal) form.
-//
 // See http://en.wikipedia.org/wiki/Mathematics_of_cyclic_redundancy_checks#Reversed_representations_and_reciprocal_polynomials
 // for information.
 package crc32

src/hash/crc32/example_test.go

+// Copyright 2015 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 crc32_test
+
+import (
+	"fmt"
+	"hash/crc32"
+)
+
+func ExampleMakeTable() {
+	// In this package, the CRC polynomial is represented in reversed notation,
+	// or LSB-first representation.
+	//
+	// LSB-first representation is a hexadecimal number with n bits, in which the
+	// most significant bit represents the coefficient of x⁰ and the least significant
+	// bit represents the coefficient of xⁿ⁻¹ (the coefficient for xⁿ is implicit).
+	//
+	// For example, CRC32-Q, as defined by the following polynomial,
+	//	x³²+ x³¹+ x²⁴+ x²²+ x¹⁶+ x¹⁴+ x⁸+ x⁷+ x⁵+ x³+ x¹+ x⁰
+	// has the reversed notation 0b11010101100000101000001010000001, so the value
+	// that should be passed to MakeTable is 0xD5828281.
+	crc32q := crc32.MakeTable(0xD5828281)
+	fmt.Printf("%08x\n", crc32.Checksum([]byte("Hello world"), crc32q))
+	// Output:
+	// 2964d064
+}