[Sync] Generalize StringOrdinal to handle ordinal_in_parent field

sync/internal_api/public/base/ordinal.h

+// Copyright (c) 2012 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#ifndef SYNC_INTERNAL_API_PUBLIC_BASE_ORDINAL_H_
+#define SYNC_INTERNAL_API_PUBLIC_BASE_ORDINAL_H_
+
+#include <algorithm>
+#include <cstddef>
+#include <string>
+
+#include "base/basictypes.h"
+#include "base/json/string_escape.h"
+#include "base/logging.h"
+
+namespace syncer {
+
+// An Ordinal<T> is an object that can be used for ordering. The
+// Ordinal<T> class has an unbounded dense strict total order, which
+// mean for any Ordinal<T>s a, b and c:
+//
+//  - a < b and b < c implies a < c (transitivity);
+//  - exactly one of a < b, b < a and a = b holds (trichotomy);
+//  - if a < b, there is a Ordinal<T> x such that a < x < b (density);
+//  - there are Ordinals<T> x and y such that x < a < y (unboundedness).
+//
+// This means that when Ordinal<T> is used for sorting a list, if any
+// item changes its position in the list, only its Ordinal<T> value
+// has to change to represent the new order, and all the other values
+// can stay the same.
+//
+// An Ordinal<T> is internally represented as an array of bytes, so it
+// can be serialized to and deserialized from disk.
+//
+// The Traits class should look like the following:
+//
+//   // Don't forget to #include "base/basictypes.h".
+//   struct MyOrdinalTraits {
+//     // There must be at least two distinct values greater than kZeroDigit
+//     // and less than kMaxDigit.
+//     static const uint8 kZeroDigit = '0';
+//     static const uint8 kMaxDigit = '9';
+//     // kMinLength must be positive.
+//     static const size_t kMinLength = 1;
+//   };
+//
+// An Ordinal<T> is valid iff its corresponding string has at least
+// kMinLength characters, does not contain any characters less than
+// kZeroDigit or greater than kMaxDigit, is not all zero digits, and
+// does not have any unnecessary trailing zero digits.
+//
+// Note that even if the native char type is signed, strings still
+// compare as if their they are unsigned.  (This is explicitly in
+// C++11 but not in C++98, even though all implementations do so
+// anyway in practice.)  Thus, it is safe to use any byte range for
+// Ordinal<T>s.
+template <typename Traits>
+class Ordinal {
+ public:
+  // Functors for use with STL algorithms and containers.
+  class LessThanFn {
+   public:
+    LessThanFn();
+
+    bool operator()(const Ordinal<Traits>& lhs,
+                    const Ordinal<Traits>& rhs) const;
+  };
+
+  class EqualsFn {
+   public:
+    EqualsFn();
+
+    bool operator()(const Ordinal<Traits>& lhs,
+                    const Ordinal<Traits>& rhs) const;
+  };
+
+  // Creates an Ordinal from the given string of bytes. The Ordinal
+  // may be valid or invalid.
+  explicit Ordinal(const std::string& bytes);
+
+  // Creates an invalid Ordinal.
+  Ordinal();
+
+  // Creates a valid initial Ordinal. This is called to create the first
+  // element of Ordinal list (i.e. before we have any other values we can
+  // generate from).
+  static Ordinal CreateInitialOrdinal();
+
+  // Returns true iff this Ordinal is valid.  This takes constant
+  // time.
+  bool IsValid() const;
+
+  // Returns true iff |*this| == |other| or |*this| and |other|
+  // are both invalid.
+  bool EqualsOrBothInvalid(const Ordinal& other) const;
+
+  // Returns a printable string representation of the Ordinal suitable
+  // for logging.
+  std::string ToDebugString() const;
+
+  // All remaining functions can only be called if IsValid() holds.
+  // It is an error to call them if IsValid() is false.
+
+  // Order-related functions.
+
+  // Returns true iff |*this| < |other|.
+  bool LessThan(const Ordinal& other) const;
+
+  // Returns true iff |*this| > |other|.
+  bool GreaterThan(const Ordinal& other) const;
+
+  // Returns true iff |*this| == |other| (i.e. |*this| < |other| and
+  // |other| < |*this| are both false).
+  bool Equals(const Ordinal& other) const;
+
+  // Given |*this| != |other|, returns a Ordinal x such that
+  // min(|*this|, |other|) < x < max(|*this|, |other|). It is an error
+  // to call this function when |*this| == |other|.
+  Ordinal CreateBetween(const Ordinal& other) const;
+
+  // Returns a Ordinal |x| such that |x| < |*this|.
+  Ordinal CreateBefore() const;
+
+  // Returns a Ordinal |x| such that |*this| < |x|.
+  Ordinal CreateAfter() const;
+
+  // Returns the string of bytes representing the Ordinal.  It is
+  // guaranteed that an Ordinal constructed from the returned string
+  // will be valid.
+  std::string ToInternalValue() const;
+
+  // Use of copy constructor and default assignment for this class is allowed.
+
+  // Constants for Ordinal digits.
+  static const uint8 kZeroDigit = Traits::kZeroDigit;
+  static const uint8 kMaxDigit = Traits::kMaxDigit;
+  static const size_t kMinLength = Traits::kMinLength;
+  static const uint8 kOneDigit = kZeroDigit + 1;
+  static const uint8 kMidDigit = kOneDigit + (kMaxDigit - kOneDigit) / 2;
+  static const unsigned int kMidDigitValue = kMidDigit - kZeroDigit;
+  static const unsigned int kMaxDigitValue = kMaxDigit - kZeroDigit;
+  static const unsigned int kRadix = kMaxDigitValue + 1;
+
+  COMPILE_ASSERT(kOneDigit > kZeroDigit, OrdinalOneDigitGreaterThanMinDigit);
+  COMPILE_ASSERT(kMidDigit > kOneDigit, OrdinalMidDigitGreaterThanOneDigit);
+  COMPILE_ASSERT(kMaxDigit > kMidDigit, OrdinalMaxDigitGreaterThanMidDigit);
+  COMPILE_ASSERT(kMinLength > 0, OrdinalMinLengthIsPositive);
+  COMPILE_ASSERT(kMidDigitValue > 1, OrdinalMidDigitValueGreaterThanOne);
+  COMPILE_ASSERT(kMaxDigitValue > kMidDigitValue,
+                 OrdinalMaxDigitValueGreaterThanMidDigitValue);
+  COMPILE_ASSERT(kRadix == kMaxDigitValue + 1,
+                 OrdinalRadixIsMaxDigitValuePlusOne);
+
+ private:
+  // Returns true iff the given byte string satisfies the criteria for
+  // a valid Ordinal.
+  static bool IsValidOrdinalBytes(const std::string& bytes);
+
+  // Returns the length that bytes.substr(0, length) would be with
+  // trailing zero digits removed.
+  static size_t GetLengthWithoutTrailingZeroDigits(
+      const std::string& bytes,
+      size_t length);
+
+  // Returns the digit at position i, padding with zero digits if
+  // required.
+  static uint8 GetDigit(const std::string& bytes, size_t i);
+
+  // Returns the digit value at position i, padding with 0 if required.
+  static int GetDigitValue(const std::string& bytes, size_t i);
+
+  // Adds the given value to |bytes| at position i, carrying when
+  // necessary.  Returns the left-most carry.
+  static int AddDigitValue(std::string* bytes, size_t i, int digit_value);
+
+  // Returns the proper length |bytes| should be resized to, i.e. the
+  // smallest length such that |bytes| is still greater than
+  // |lower_bound| and is still valid.  |bytes| should be greater than
+  // |lower_bound|.
+  static size_t GetProperLength(const std::string& lower_bound,
+                                const std::string& bytes);
+
+  // Compute the midpoint ordinal byte string that is between |start|
+  // and |end|.
+  static std::string ComputeMidpoint(const std::string& start,
+                                     const std::string& end);
+
+  // Create a Ordinal that is lexigraphically greater than |start| and
+  // lexigraphically less than |end|. The returned Ordinal will be roughly
+  // between |start| and |end|.
+  static Ordinal<Traits> CreateOrdinalBetween(const Ordinal<Traits>& start,
+                                              const Ordinal<Traits>& end);
+
+  // The internal byte string representation of the Ordinal.  Never
+  // changes after construction except for assignment.
+  std::string bytes_;
+
+  // A cache of the result of IsValidOrdinalBytes(bytes_).
+  bool is_valid_;
+};
+
+template <typename Traits> const uint8 Ordinal<Traits>::kZeroDigit;
+template <typename Traits> const uint8 Ordinal<Traits>::kMaxDigit;
+template <typename Traits> const size_t Ordinal<Traits>::kMinLength;
+template <typename Traits> const uint8 Ordinal<Traits>::kOneDigit;
+template <typename Traits> const uint8 Ordinal<Traits>::kMidDigit;
+template <typename Traits> const unsigned int Ordinal<Traits>::kMidDigitValue;
+template <typename Traits> const unsigned int Ordinal<Traits>::kMaxDigitValue;
+template <typename Traits> const unsigned int Ordinal<Traits>::kRadix;
+
+template <typename Traits>
+Ordinal<Traits>::LessThanFn::LessThanFn() {}
+
+template <typename Traits>
+bool Ordinal<Traits>::LessThanFn::operator()(const Ordinal<Traits>& lhs,
+                                             const Ordinal<Traits>& rhs) const {
+  return lhs.LessThan(rhs);
+}
+
+template <typename Traits>
+Ordinal<Traits>::EqualsFn::EqualsFn() {}
+
+template <typename Traits>
+bool Ordinal<Traits>::EqualsFn::operator()(const Ordinal<Traits>& lhs,
+                                           const Ordinal<Traits>& rhs) const {
+  return lhs.Equals(rhs);
+}
+
+template <typename Traits>
+Ordinal<Traits>::Ordinal(const std::string& bytes)
+    : bytes_(bytes),
+      is_valid_(IsValidOrdinalBytes(bytes_)) {}
+
+template <typename Traits>
+Ordinal<Traits>::Ordinal() : is_valid_(false) {}
+
+template <typename Traits>
+Ordinal<Traits> Ordinal<Traits>::CreateInitialOrdinal() {
+  std::string bytes(Traits::kMinLength, kZeroDigit);
+  bytes[0] = kMidDigit;
+  return Ordinal(bytes);
+}
+
+template <typename Traits>
+bool Ordinal<Traits>::IsValid() const {
+  DCHECK_EQ(IsValidOrdinalBytes(bytes_), is_valid_);
+  return is_valid_;
+}
+
+template <typename Traits>
+bool Ordinal<Traits>::EqualsOrBothInvalid(const Ordinal& other) const {
+  if (!IsValid() && !other.IsValid())
+    return true;
+
+  if (!IsValid() || !other.IsValid())
+    return false;
+
+  return Equals(other);
+}
+
+template <typename Traits>
+std::string Ordinal<Traits>::ToDebugString() const {
+  std::string debug_string;
+  base::JsonDoubleQuote(bytes_, false /* put_in_quotes */, &debug_string);
+  if (!is_valid_) {
+    debug_string = "INVALID[" + debug_string + "]";
+  }
+  return debug_string;
+}
+
+template <typename Traits>
+bool Ordinal<Traits>::LessThan(const Ordinal& other) const {
+  CHECK(IsValid());
+  CHECK(other.IsValid());
+  return bytes_ < other.bytes_;
+}
+
+template <typename Traits>
+bool Ordinal<Traits>::GreaterThan(const Ordinal& other) const {
+  CHECK(IsValid());
+  CHECK(other.IsValid());
+  return bytes_ > other.bytes_;
+}
+
+template <typename Traits>
+bool Ordinal<Traits>::Equals(const Ordinal& other) const {
+  CHECK(IsValid());
+  CHECK(other.IsValid());
+  return bytes_ == other.bytes_;
+}
+
+template <typename Traits>
+Ordinal<Traits> Ordinal<Traits>::CreateBetween(const Ordinal& other) const {
+  CHECK(IsValid());
+  CHECK(other.IsValid());
+  CHECK(!Equals(other));
+
+  if (LessThan(other)) {
+    return CreateOrdinalBetween(*this, other);
+  } else {
+    return CreateOrdinalBetween(other, *this);
+  }
+}
+
+template <typename Traits>
+Ordinal<Traits> Ordinal<Traits>::CreateBefore() const {
+  CHECK(IsValid());
+  // Create the smallest valid Ordinal of the appropriate length
+  // to be the minimum boundary.
+  const size_t length = bytes_.length();
+  std::string start(length, kZeroDigit);
+  start[length - 1] = kOneDigit;
+  if (start == bytes_) {
+    start[length - 1] = kZeroDigit;
+    start += kOneDigit;
+  }
+
+  // Even though |start| is already a valid Ordinal that is less
+  // than |*this|, we don't return it because we wouldn't have much space in
+  // front of it to insert potential future values.
+  return CreateBetween(Ordinal(start));
+}
+
+template <typename Traits>
+Ordinal<Traits> Ordinal<Traits>::CreateAfter() const {
+  CHECK(IsValid());
+  // Create the largest valid Ordinal of the appropriate length to be
+  // the maximum boundary.
+  std::string end(bytes_.length(), kMaxDigit);
+  if (end == bytes_)
+    end += kMaxDigit;
+
+  // Even though |end| is already a valid Ordinal that is greater than
+  // |*this|, we don't return it because we wouldn't have much space after
+  // it to insert potential future values.
+  return CreateBetween(Ordinal(end));
+}
+
+template <typename Traits>
+std::string Ordinal<Traits>::ToInternalValue() const {
+  CHECK(IsValid());
+  return bytes_;
+}
+
+template <typename Traits>
+bool Ordinal<Traits>::IsValidOrdinalBytes(const std::string& bytes) {
+  const size_t length = bytes.length();
+  if (length < kMinLength)
+    return false;
+
+  bool found_non_zero = false;
+  for (size_t i = 0; i < length; ++i) {
+    const uint8 byte = bytes[i];
+    if (byte < kZeroDigit || byte > kMaxDigit)
+      return false;
+    if (byte > kZeroDigit)
+      found_non_zero = true;
+  }
+  if (!found_non_zero)
+    return false;
+
+  if (length > kMinLength) {
+    const uint8 last_byte = bytes[length - 1];
+    if (last_byte == kZeroDigit)
+      return false;
+  }
+
+  return true;
+}
+
+template <typename Traits>
+size_t Ordinal<Traits>::GetLengthWithoutTrailingZeroDigits(
+    const std::string& bytes, size_t length) {
+  DCHECK(!bytes.empty());
+  DCHECK_GT(length, 0U);
+
+  size_t end_position =
+      bytes.find_last_not_of(static_cast<char>(kZeroDigit), length - 1);
+
+  // If no non kZeroDigit is found then the string is a string of all zeros
+  // digits so we return 0 as the correct length.
+  if (end_position == std::string::npos)
+    return 0;
+
+  return end_position + 1;
+}
+
+template <typename Traits>
+uint8 Ordinal<Traits>::GetDigit(const std::string& bytes, size_t i) {
+  return (i < bytes.length()) ? bytes[i] : kZeroDigit;
+}
+
+template <typename Traits>
+int Ordinal<Traits>::GetDigitValue(const std::string& bytes, size_t i) {
+  return GetDigit(bytes, i) - kZeroDigit;
+}
+
+template <typename Traits>
+int Ordinal<Traits>::AddDigitValue(std::string* bytes,
+                                   size_t i, int digit_value) {
+  DCHECK_GE(i, 0U);
+  DCHECK_LT(i, bytes->length());
+
+  for (int j = i; j >= 0 && digit_value > 0; --j) {
+    int byte_j_value = GetDigitValue(*bytes, j) + digit_value;
+    digit_value = byte_j_value / kRadix;
+    DCHECK_LE(digit_value, 1);
+    byte_j_value %= kRadix;
+    (*bytes)[j] = static_cast<char>(kZeroDigit + byte_j_value);
+  }
+  return digit_value;
+}
+
+template <typename Traits>
+size_t Ordinal<Traits>::GetProperLength(const std::string& lower_bound,
+                                        const std::string& bytes) {
+  CHECK_GT(bytes, lower_bound);
+
+  size_t drop_length =
+      GetLengthWithoutTrailingZeroDigits(bytes, bytes.length());
+  // See if the |ordinal| can be truncated after its last non-zero
+  // digit without affecting the ordering.
+  if (drop_length > kMinLength) {
+    size_t truncated_length =
+        GetLengthWithoutTrailingZeroDigits(bytes, drop_length - 1);
+
+    if (truncated_length > 0 &&
+        bytes.compare(0, truncated_length, lower_bound) > 0)
+      drop_length = truncated_length;
+  }
+  return std::max(drop_length, kMinLength);
+}
+
+template <typename Traits>
+std::string Ordinal<Traits>::ComputeMidpoint(
+    const std::string& start,
+    const std::string& end) {
+  size_t max_size = std::max(start.length(), end.length()) + 1;
+  std::string midpoint(max_size, kZeroDigit);
+
+  // Perform the operation (start + end) / 2 left-to-right by
+  // maintaining a "forward carry" which is either 0 or
+  // kMidDigitValue.  AddDigitValue() is in general O(n), but this
+  // operation is still O(n) despite that; calls to AddDigitValue()
+  // will overflow at most to the last position where AddDigitValue()
+  // last overflowed.
+  int forward_carry = 0;
+  for (size_t i = 0; i < max_size; ++i) {
+    const int sum_value = GetDigitValue(start, i) + GetDigitValue(end, i);
+    const int digit_value = sum_value / 2 + forward_carry;
+    // AddDigitValue returning a non-zero carry would imply that
+    // midpoint[0] >= kMaxDigit, which one can show is impossible.
+    CHECK_EQ(AddDigitValue(&midpoint, i, digit_value), 0);
+    forward_carry = (sum_value % 2 == 1) ? kMidDigitValue : 0;
+  }
+  DCHECK_EQ(forward_carry, 0);
+
+  return midpoint;
+}
+
+template <typename Traits>
+Ordinal<Traits> Ordinal<Traits>::CreateOrdinalBetween(
+    const Ordinal<Traits>& start,
+    const Ordinal<Traits>& end) {
+  CHECK(start.IsValid());
+  CHECK(end.IsValid());
+  CHECK(start.LessThan(end));
+  const std::string& start_bytes = start.ToInternalValue();
+  const std::string& end_bytes = end.ToInternalValue();
+  DCHECK_LT(start_bytes, end_bytes);
+
+  std::string midpoint = ComputeMidpoint(start_bytes, end_bytes);
+  const size_t proper_length = GetProperLength(start_bytes, midpoint);
+  midpoint.resize(proper_length, kZeroDigit);
+
+  DCHECK_GT(midpoint, start_bytes);
+  DCHECK_LT(midpoint, end_bytes);
+
+  Ordinal<Traits> midpoint_ordinal(midpoint);
+  DCHECK(midpoint_ordinal.IsValid());
+  return midpoint_ordinal;
+}
+
+}  // namespace syncer
+
+#endif  // SYNC_INTERNAL_API_PUBLIC_BASE_ORDINAL_H_