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// Copyright 2007, 2008 Google Inc.
// Authors: Jeff Dean, Sanjay Ghemawat, Lincoln Smith
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// See the License for the specific language governing permissions and
// limitations under the License.
#include <config.h>
#include <stdint.h> // uint32_t
#include "compile_assert.h"
#include "logging.h"
namespace open_vcdiff {
// Rabin-Karp hasher module -- this is a faster version with different
// constants, so it's not quite Rabin-Karp fingerprinting, but its behavior is
// close enough for most applications.
// Definitions common to all hash window sizes.
class RollingHashUtil {
// Multiplier for incremental hashing. The compiler should be smart enough to
// convert (val * kMult) into ((val << 8) + val).
static const uint32_t kMult = 257;
// All hashes are returned modulo "kBase". Current implementation requires
// kBase <= 2^32/kMult to avoid overflow. Also, kBase must be a power of two
// so that we can compute modulus efficiently.
static const uint32_t kBase = (1 << 23);
// Returns operand % kBase, assuming that kBase is a power of two.
static inline uint32_t ModBase(uint32_t operand) {
return operand & (kBase - 1);
// Given an unsigned integer "operand", returns an unsigned integer "result"
// such that
// result < kBase
// and
// ModBase(operand + result) == 0
static inline uint32_t FindModBaseInverse(uint32_t operand) {
// The subtraction (0 - operand) produces an unsigned underflow for any
// operand except 0. The underflow results in a (very large) unsigned
// number. Binary subtraction is used instead of unary negation because
// some compilers (e.g. Visual Studio 7+) produce a warning if an unsigned
// value is negated.
// The C++ mod operation (operand % kBase) may produce different results for
// different compilers if operand is negative. That is not a problem in
// this case, since all numbers used are unsigned, and ModBase does its work
// using bitwise arithmetic rather than the % operator.
return ModBase(uint32_t(0) - operand);
// Here's the heart of the hash algorithm. Start with a partial_hash value of
// 0, and run this HashStep once against each byte in the data window to be
// hashed. The result will be the hash value for the entire data window. The
// Hash() function, below, does exactly this, albeit with some refinements.
static inline uint32_t HashStep(uint32_t partial_hash,
unsigned char next_byte) {
return ModBase((partial_hash * kMult) + next_byte);
// Use this function to start computing a new hash value based on the first
// two bytes in the window. It is equivalent to calling
// HashStep(HashStep(0, ptr[0]), ptr[1])
// but takes advantage of the fact that the maximum value of
// (ptr[0] * kMult) + ptr[1] is not large enough to exceed kBase, thus
// avoiding an unnecessary ModBase operation.
static inline uint32_t HashFirstTwoBytes(const char* ptr) {
return (static_cast<unsigned char>(ptr[0]) * kMult)
+ static_cast<unsigned char>(ptr[1]);
// Making these private avoids copy constructor and assignment operator.
// No objects of this type should be constructed.
RollingHashUtil(const RollingHashUtil&); // NOLINT
void operator=(const RollingHashUtil&);
// window_size must be >= 2.
template<int window_size>
class RollingHash {
// Perform global initialization that is required in order to instantiate a
// RollingHash. This function *must* be called (preferably on startup) by any
// program that uses a RollingHash. It is harmless to call this function more
// than once. It is not thread-safe, but calling it from two different
// threads at the same time can only cause a memory leak, not incorrect
// behavior. Make sure to call it before spawning any threads that could use
// RollingHash.
static void Init();
// Initialize hasher to maintain a window of the specified size. You need an
// instance of this type to use UpdateHash(), but Hash() does not depend on
// remove_table_, so it is static.
RollingHash() {
if (!remove_table_) {
VCD_DFATAL << "RollingHash object instantiated"
" before calling RollingHash::Init()" << VCD_ENDL;
// Compute a hash of the window "ptr[0, window_size - 1]".
static uint32_t Hash(const char* ptr) {
uint32_t h = RollingHashUtil::HashFirstTwoBytes(ptr);
for (int i = 2; i < window_size; ++i) {
h = RollingHashUtil::HashStep(h, ptr[i]);
return h;
// Update a hash by removing the oldest byte and adding a new byte.
// UpdateHash takes the hash value of buffer[0] ... buffer[window_size -1]
// along with the value of buffer[0] (the "old_first_byte" argument)
// and the value of buffer[window_size] (the "new_last_byte" argument).
// It quickly computes the hash value of buffer[1] ... buffer[window_size]
// without having to run Hash() on the entire window.
// The larger the window, the more advantage comes from using UpdateHash()
// (which runs in time independent of window_size) instead of Hash().
// Each time window_size doubles, the time to execute Hash() also doubles,
// while the time to execute UpdateHash() remains constant. Empirical tests
// have borne out this statement.
uint32_t UpdateHash(uint32_t old_hash,
const char old_first_byte,
const char new_last_byte) const {
uint32_t partial_hash = RemoveFirstByteFromHash(old_hash, old_first_byte);
return RollingHashUtil::HashStep(partial_hash, new_last_byte);
// Given a full hash value for buffer[0] ... buffer[window_size -1], plus the
// value of the first byte buffer[0], this function returns a *partial* hash
// value for buffer[1] ... buffer[window_size -1]. See the comments in
// Init(), below, for a description of how the contents of remove_table_ are
// computed.
static uint32_t RemoveFirstByteFromHash(uint32_t full_hash,
unsigned char first_byte) {
return RollingHashUtil::ModBase(full_hash + remove_table_[first_byte]);
// We keep a table that maps from any byte "b" to
// (- b * pow(kMult, window_size - 1)) % kBase
static const uint32_t* remove_table_;
// For each window_size, fill a 256-entry table such that
// the hash value of buffer[0] ... buffer[window_size - 1]
// + remove_table_[buffer[0]]
// == the hash value of buffer[1] ... buffer[window_size - 1]
// See the comments in Init(), below, for a description of how the contents of
// remove_table_ are computed.
template<int window_size>
const uint32_t* RollingHash<window_size>::remove_table_ = NULL;
// Init() checks to make sure that the static object remove_table_ has been
// initialized; if not, it does the considerable work of populating it. Once
// it's ready, the table can be used for any number of RollingHash objects of
// the same window_size.
template<int window_size>
void RollingHash<window_size>::Init() {
VCD_COMPILE_ASSERT(window_size >= 2,
if (remove_table_ == NULL) {
// The new object is placed into a local pointer instead of directly into
// remove_table_, for two reasons:
// 1. remove_table_ is a pointer to const. The table is populated using
// the non-const local pointer and then assigned to the global const
// pointer once it's ready.
// 2. No other thread will ever see remove_table_ pointing to a
// partially-initialized table. If two threads happen to call Init()
// at the same time, two tables with the same contents may be created
// (causing a memory leak), but the results will be consistent
// no matter which of the two tables is used.
uint32_t* new_remove_table = new uint32_t[256];
// Compute multiplier. Concisely, it is:
// pow(kMult, (window_size - 1)) % kBase,
// but we compute the power in integer form.
uint32_t multiplier = 1;
for (int i = 0; i < window_size - 1; ++i) {
multiplier =
RollingHashUtil::ModBase(multiplier * RollingHashUtil::kMult);
// For each character removed_byte, compute
// remove_table_[removed_byte] ==
// (- (removed_byte * pow(kMult, (window_size - 1)))) % kBase
// where the power operator "pow" is taken in integer form.
// If you take a hash value fp representing the hash of
// buffer[0] ... buffer[window_size - 1]
// and add the value of remove_table_[buffer[0]] to it, the result will be
// a partial hash value for
// buffer[1] ... buffer[window_size - 1]
// that is to say, it no longer includes buffer[0].
// The following byte at buffer[window_size] can then be merged with this
// partial hash value to arrive quickly at the hash value for a window that
// has advanced by one byte, to
// buffer[1] ... buffer[window_size]
// In fact, that is precisely what happens in UpdateHash, above.
uint32_t byte_times_multiplier = 0;
for (int removed_byte = 0; removed_byte < 256; ++removed_byte) {
new_remove_table[removed_byte] =
// Iteratively adding the multiplier in this loop is equivalent to
// computing (removed_byte * multiplier), and is faster
byte_times_multiplier =
RollingHashUtil::ModBase(byte_times_multiplier + multiplier);
remove_table_ = new_remove_table;
} // namespace open_vcdiff