Implement the NackModule as part of the new jitter buffer.

webrtc/base/mod_ops.h

Index: webrtc/base/mod_ops.h
diff --git a/webrtc/base/mod_ops.h b/webrtc/base/mod_ops.h
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+/*
+ *  Copyright (c) 2016 The WebRTC project authors. All Rights Reserved.
+ *
+ *  Use of this source code is governed by a BSD-style license
+ *  that can be found in the LICENSE file in the root of the source
+ *  tree. An additional intellectual property rights grant can be found
+ *  in the file PATENTS.  All contributing project authors may
+ *  be found in the AUTHORS file in the root of the source tree.
+ */
+
+#ifndef WEBRTC_BASE_MOD_OPS_H_
+#define WEBRTC_BASE_MOD_OPS_H_
+
+#include <limits>
+#include <type_traits>
+
+#include "webrtc/base/checks.h"
+
+#define MOD_OPS_ASSERT_TYPE_IS_UNSIGNED(T) \
+  static_assert(std::numeric_limits<T>::is_integer && \
+                !std::numeric_limits<T>::is_signed, \
+               "ModNum type must be of unsigned integer.")
+
+namespace webrtc {
+
+template <size_t M> inline size_t Add(size_t a , size_t b) {

[torbjorng (webrtc), 2016/02/29 17:23:46]

Why use size_t and not T? Using T seems cleaner, but also is more general as it
would allow correct operation for T = 'unsigned long long" on a 32-bit machine
where size_t is just 32 bits.

[philipel, 2016/03/01 09:29:34]

Having to specify the type makes it less practical to use, for example
Add<1000>(a, b) would become Add<uint16_t, 1000>(a, b).

You are right about this being incorrect for uint64_t on a 32 bit machine, but I
would rather just change the type to uint64_t to keep it as easy to use as
possible.

[torbjorng (webrtc), 2016/03/01 14:13:35]

On 32-bit machines, uint64_t is a quite poor choice, generating a complex set of
branches for most arithmetic and comparisons.

+  size_t add = b % M;
+  if (a + add < a)
+    return M - a + add;

[torbjorng (webrtc), 2016/02/29 17:23:46]

This looks incorrect, a should not be subtracted as (a) and (-a) are not in
general the same residue class (mod M). Some expression like (add + a - M) is
required. You may rearrange that to your taste; intermediate subtype overflow
will not matter here.

Note that if (a) is not a principal residue (mod M) this return statement will
also not return principal residues.

[philipel, 2016/03/01 09:29:34]

Yepp, this implementation is clearly wrong. A was assumed to be a principal
residue in the ModNum class so this detail is a residue (huehuehue) of that
implementation.

[torbjorng (webrtc), 2016/03/01 14:13:35]

Whether a principal residue or not, that code was incorrect.

[philipel, 2016/03/01 15:28:38]

Reading my own comment in hindsight I realize I was not very clear. Yes, the
calculation was wrong regardless of 'a' being a principal residue or not.

+  return (a + add) % M;
+}
+
+template <size_t M> inline size_t Subtract(size_t a, size_t b) {
+  size_t sub = b % M;
+  if (a < sub)
+    return M - (sub - a);
+  return a - sub;

[torbjorng (webrtc), 2016/02/29 17:23:46]

Note that if a is not a principal residue (mod M) this return statement will not
necessarily yield principal residues.

[philipel, 2016/03/01 09:29:34]

True.

+}
+
+
+// Calculates the forward difference between two numbers.
+//
+// Example:
+// uint8_t a = 253;
+// uint8_t b = 2;
+//
+// ForwardDiff(a, b) == 4
+//
+//   252   253   254   255    0     1     2     3
+// #################################################
+// |     |  a  |     |     |     |     |  b  |     |
+// #################################################
+//          |----->----->----->----->----->
+//
+// ForwardDiff(b, a) == 251
+//
+//   252   253   254   255    0     1     2     3
+// #################################################
+// |     |  a  |     |     |     |     |  b  |     |
+// #################################################
+// -->----->                              |----->---
+//
+template <typename T> inline T ForwardDiff(T a, T b) {
+  MOD_OPS_ASSERT_TYPE_IS_UNSIGNED(T);
+  return a <= b ? b - a : std::numeric_limits<T>::max() - (a - b);
+}
+
+// Calculates the reverse difference between two numbers.
+//
+// Example:
+// uint8_t a = 253;
+// uint8_t b = 2;
+//
+// ReverseDiff(a, b) == 251
+//
+//   252   253   254   255    0     1     2     3
+// #################################################
+// |     |  a  |     |     |     |     |  b  |     |
+// #################################################
+//          <-----<-----<-----<-----<-----|
+//
+// ReverseDiff(b, a) == 5
+//
+//   252   253   254   255    0     1     2     3
+// #################################################
+// |     |  a  |     |     |     |     |  b  |     |
+// #################################################
+// ---<-----|                             |<-----<--
+//
+template <typename T> inline T ReverseDiff(T a, T b) {
+  MOD_OPS_ASSERT_TYPE_IS_UNSIGNED(T);
+  return a < b ? std::numeric_limits<T>::max() - (b - a) : a - b;
+}
+
+template <typename T> inline bool AheadOrAt(T a, T b) {
+  MOD_OPS_ASSERT_TYPE_IS_UNSIGNED(T);
+  return ForwardDiff(b, a) < std::numeric_limits<T>::max() / 2;
+}
+
+template <typename T> inline bool AheadOf(T a, T b) {
+  MOD_OPS_ASSERT_TYPE_IS_UNSIGNED(T);
+  return a != b && AheadOrAt(a, b);
+}
+
+}  // namespace webrtc
+
+#endif  // WEBRTC_BASE_MOD_OPS_H_