A Discrete-Event Network Simulator
API
codel-queue-disc.cc
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1 /*
2  * Copyright (c) 2012 Andrew McGregor
3  *
4  * This program is free software; you can redistribute it and/or modify
5  * it under the terms of the GNU General Public License version 2 as
6  * published by the Free Software Foundation;
7  *
8  * This program is distributed in the hope that it will be useful,
9  * but WITHOUT ANY WARRANTY; without even the implied warranty of
10  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11  * GNU General Public License for more details.
12  *
13  * You should have received a copy of the GNU General Public License
14  * along with this program; if not, write to the Free Software
15  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
16  *
17  * Codel, the COntrolled DELay Queueing discipline
18  * Based on ns2 simulation code presented by Kathie Nichols
19  *
20  * This port based on linux kernel code by
21  * Authors: Dave Täht <d@taht.net>
22  * Eric Dumazet <edumazet@google.com>
23  *
24  * Ported to ns-3 by: Andrew McGregor <andrewmcgr@gmail.com>
25  */
26 
27 #include "codel-queue-disc.h"
28 
29 #include "ns3/abort.h"
30 #include "ns3/drop-tail-queue.h"
31 #include "ns3/enum.h"
32 #include "ns3/log.h"
33 #include "ns3/object-factory.h"
34 #include "ns3/uinteger.h"
35 
36 namespace ns3
37 {
38 
39 NS_LOG_COMPONENT_DEFINE("CoDelQueueDisc");
40 
48 /* borrowed from the linux kernel */
49 static inline uint32_t
50 ReciprocalDivide(uint32_t A, uint32_t R)
51 {
52  return (uint32_t)(((uint64_t)A * R) >> 32);
53 }
54 
55 /* end kernel borrowings */
56 
61 static uint32_t
63 {
64  Time time = Simulator::Now();
65  uint64_t ns = time.GetNanoSeconds();
66 
67  return static_cast<uint32_t>(ns >> CODEL_SHIFT);
68 }
69 
70 NS_OBJECT_ENSURE_REGISTERED(CoDelQueueDisc);
71 
72 TypeId
74 {
75  static TypeId tid =
76  TypeId("ns3::CoDelQueueDisc")
78  .SetGroupName("TrafficControl")
79  .AddConstructor<CoDelQueueDisc>()
80  .AddAttribute("UseEcn",
81  "True to use ECN (packets are marked instead of being dropped)",
82  BooleanValue(false),
85  .AddAttribute("UseL4s",
86  "True to use L4S (only ECT1 packets are marked at CE threshold)",
87  BooleanValue(false),
90  .AddAttribute(
91  "MaxSize",
92  "The maximum number of packets/bytes accepted by this queue disc.",
94  MakeQueueSizeAccessor(&QueueDisc::SetMaxSize, &QueueDisc::GetMaxSize),
95  MakeQueueSizeChecker())
96  .AddAttribute("MinBytes",
97  "The CoDel algorithm minbytes parameter.",
98  UintegerValue(1500),
100  MakeUintegerChecker<uint32_t>())
101  .AddAttribute("Interval",
102  "The CoDel algorithm interval",
103  StringValue("100ms"),
105  MakeTimeChecker())
106  .AddAttribute("Target",
107  "The CoDel algorithm target queue delay",
108  StringValue("5ms"),
110  MakeTimeChecker())
111  .AddAttribute("CeThreshold",
112  "The CoDel CE threshold for marking packets",
113  TimeValue(Time::Max()),
115  MakeTimeChecker())
116  .AddTraceSource("Count",
117  "CoDel count",
119  "ns3::TracedValueCallback::Uint32")
120  .AddTraceSource("LastCount",
121  "CoDel lastcount",
123  "ns3::TracedValueCallback::Uint32")
124  .AddTraceSource("DropState",
125  "Dropping state",
127  "ns3::TracedValueCallback::Bool")
128  .AddTraceSource("DropNext",
129  "Time until next packet drop",
131  "ns3::TracedValueCallback::Uint32");
132 
133  return tid;
134 }
135 
138  m_count(0),
139  m_lastCount(0),
140  m_dropping(false),
141  m_recInvSqrt(~0U >> REC_INV_SQRT_SHIFT),
142  m_firstAboveTime(0),
143  m_dropNext(0)
144 {
145  NS_LOG_FUNCTION(this);
146 }
147 
149 {
150  NS_LOG_FUNCTION(this);
151 }
152 
153 uint16_t
154 CoDelQueueDisc::NewtonStep(uint16_t recInvSqrt, uint32_t count)
155 {
157  uint32_t invsqrt = ((uint32_t)recInvSqrt) << REC_INV_SQRT_SHIFT;
158  uint32_t invsqrt2 = ((uint64_t)invsqrt * invsqrt) >> 32;
159  uint64_t val = (3LL << 32) - ((uint64_t)count * invsqrt2);
160 
161  val >>= 2; /* avoid overflow */
162  val = (val * invsqrt) >> (32 - 2 + 1);
163  return static_cast<uint16_t>(val >> REC_INV_SQRT_SHIFT);
164 }
165 
166 uint32_t
167 CoDelQueueDisc::ControlLaw(uint32_t t, uint32_t interval, uint32_t recInvSqrt)
168 {
170  return t + ReciprocalDivide(interval, recInvSqrt << REC_INV_SQRT_SHIFT);
171 }
172 
173 bool
175 {
176  NS_LOG_FUNCTION(this << item);
177 
178  if (GetCurrentSize() + item > GetMaxSize())
179  {
180  NS_LOG_LOGIC("Queue full -- dropping pkt");
182  return false;
183  }
184 
185  bool retval = GetInternalQueue(0)->Enqueue(item);
186 
187  // If Queue::Enqueue fails, QueueDisc::DropBeforeEnqueue is called by the
188  // internal queue because QueueDisc::AddInternalQueue sets the trace callback
189 
190  NS_LOG_LOGIC("Number packets " << GetInternalQueue(0)->GetNPackets());
191  NS_LOG_LOGIC("Number bytes " << GetInternalQueue(0)->GetNBytes());
192 
193  return retval;
194 }
195 
196 bool
198 {
199  NS_LOG_FUNCTION(this);
200  bool okToDrop;
201 
202  if (!item)
203  {
204  m_firstAboveTime = 0;
205  return false;
206  }
207 
208  Time delta = Simulator::Now() - item->GetTimeStamp();
209  NS_LOG_INFO("Sojourn time " << delta.As(Time::MS));
210  uint32_t sojournTime = Time2CoDel(delta);
211 
212  if (CoDelTimeBefore(sojournTime, Time2CoDel(m_target)) ||
214  {
215  // went below so we'll stay below for at least q->interval
216  NS_LOG_LOGIC("Sojourn time is below target or number of bytes in queue is less than "
217  "minBytes; packet should not be dropped");
218  m_firstAboveTime = 0;
219  return false;
220  }
221  okToDrop = false;
222  if (m_firstAboveTime == 0)
223  {
224  /* just went above from below. If we stay above
225  * for at least q->interval we'll say it's ok to drop
226  */
227  NS_LOG_LOGIC("Sojourn time has just gone above target from below, need to stay above for "
228  "at least q->interval before packet can be dropped. ");
230  }
231  else if (CoDelTimeAfter(now, m_firstAboveTime))
232  {
233  NS_LOG_LOGIC("Sojourn time has been above target for at least q->interval; it's OK to "
234  "(possibly) drop packet.");
235  okToDrop = true;
236  }
237  return okToDrop;
238 }
239 
242 {
243  NS_LOG_FUNCTION(this);
244 
245  Ptr<QueueDiscItem> item = GetInternalQueue(0)->Dequeue();
246  if (!item)
247  {
248  // Leave dropping state when queue is empty
249  m_dropping = false;
250  NS_LOG_LOGIC("Queue empty");
251  return nullptr;
252  }
253  uint32_t ldelay = Time2CoDel(Simulator::Now() - item->GetTimeStamp());
254  if (item && m_useL4s)
255  {
256  uint8_t tosByte = 0;
257  if (item->GetUint8Value(QueueItem::IP_DSFIELD, tosByte) &&
258  (((tosByte & 0x3) == 1) || (tosByte & 0x3) == 3))
259  {
260  if ((tosByte & 0x3) == 1)
261  {
262  NS_LOG_DEBUG("ECT1 packet " << static_cast<uint16_t>(tosByte & 0x3));
263  }
264  else
265  {
266  NS_LOG_DEBUG("CE packet " << static_cast<uint16_t>(tosByte & 0x3));
267  }
268 
269  if (CoDelTimeAfter(ldelay, Time2CoDel(m_ceThreshold)) &&
271  {
272  NS_LOG_LOGIC("Marking due to CeThreshold " << m_ceThreshold.GetSeconds());
273  }
274  return item;
275  }
276  }
277 
278  uint32_t now = CoDelGetTime();
279 
280  NS_LOG_LOGIC("Popped " << item);
281  NS_LOG_LOGIC("Number packets remaining " << GetInternalQueue(0)->GetNPackets());
282  NS_LOG_LOGIC("Number bytes remaining " << GetInternalQueue(0)->GetNBytes());
283 
284  // Determine if item should be dropped
285  bool okToDrop = OkToDrop(item, now);
286  bool isMarked = false;
287 
288  if (m_dropping)
289  { // In the dropping state (sojourn time has gone above target and hasn't come down yet)
290  // Check if we can leave the dropping state or next drop should occur
291  NS_LOG_LOGIC("In dropping state, check if it's OK to leave or next drop should occur");
292  if (!okToDrop)
293  {
294  /* sojourn time fell below target - leave dropping state */
295  NS_LOG_LOGIC("Sojourn time goes below target, it's OK to leave dropping state.");
296  m_dropping = false;
297  }
298  else if (CoDelTimeAfterEq(now, m_dropNext))
299  {
300  while (m_dropping && CoDelTimeAfterEq(now, m_dropNext))
301  {
302  ++m_count;
304  // It's time for the next drop. Drop the current packet and
305  // dequeue the next. The dequeue might take us out of dropping
306  // state. If not, schedule the next drop.
307  // A large amount of packets in queue might result in drop
308  // rates so high that the next drop should happen now,
309  // hence the while loop.
310  if (m_useEcn && Mark(item, TARGET_EXCEEDED_MARK))
311  {
312  isMarked = true;
313  NS_LOG_LOGIC("Sojourn time is still above target and it's time for next drop "
314  "or mark; marking "
315  << item);
316  NS_LOG_LOGIC("Running ControlLaw for input m_dropNext: " << (double)m_dropNext /
317  1000000);
319  NS_LOG_LOGIC("Scheduled next drop at " << (double)m_dropNext / 1000000);
320  goto end;
321  }
322  NS_LOG_LOGIC(
323  "Sojourn time is still above target and it's time for next drop; dropping "
324  << item);
326 
327  item = GetInternalQueue(0)->Dequeue();
328 
329  if (item)
330  {
331  NS_LOG_LOGIC("Popped " << item);
332  NS_LOG_LOGIC("Number packets remaining " << GetInternalQueue(0)->GetNPackets());
333  NS_LOG_LOGIC("Number bytes remaining " << GetInternalQueue(0)->GetNBytes());
334  }
335 
336  if (!OkToDrop(item, now))
337  {
338  /* leave dropping state */
339  NS_LOG_LOGIC("Leaving dropping state");
340  m_dropping = false;
341  }
342  else
343  {
344  /* schedule the next drop */
345  NS_LOG_LOGIC("Running ControlLaw for input m_dropNext: " << (double)m_dropNext /
346  1000000);
348  NS_LOG_LOGIC("Scheduled next drop at " << (double)m_dropNext / 1000000);
349  }
350  }
351  }
352  }
353  else
354  {
355  // Not in the dropping state
356  // Decide if we have to enter the dropping state and drop the first packet
357  NS_LOG_LOGIC("Not in dropping state; decide if we have to enter the state and drop the "
358  "first packet");
359  if (okToDrop)
360  {
361  if (m_useEcn && Mark(item, TARGET_EXCEEDED_MARK))
362  {
363  isMarked = true;
364  NS_LOG_LOGIC("Sojourn time goes above target, marking the first packet "
365  << item << " and entering the dropping state");
366  }
367  else
368  {
369  // Drop the first packet and enter dropping state unless the queue is empty
370  NS_LOG_LOGIC("Sojourn time goes above target, dropping the first packet "
371  << item << " and entering the dropping state");
373  item = GetInternalQueue(0)->Dequeue();
374  if (item)
375  {
376  NS_LOG_LOGIC("Popped " << item);
377  NS_LOG_LOGIC("Number packets remaining " << GetInternalQueue(0)->GetNPackets());
378  NS_LOG_LOGIC("Number bytes remaining " << GetInternalQueue(0)->GetNBytes());
379  }
380  OkToDrop(item, now);
381  }
382  m_dropping = true;
383  /*
384  * if min went above target close to when we last went below it
385  * assume that the drop rate that controlled the queue on the
386  * last cycle is a good starting point to control it now.
387  */
388  int delta = m_count - m_lastCount;
389  if (delta > 1 && CoDelTimeBefore(now - m_dropNext, 16 * Time2CoDel(m_interval)))
390  {
391  m_count = delta;
393  }
394  else
395  {
396  m_count = 1;
398  }
400  NS_LOG_LOGIC("Running ControlLaw for input now: " << (double)now);
402  NS_LOG_LOGIC("Scheduled next drop at " << (double)m_dropNext / 1000000 << " now "
403  << (double)now / 1000000);
404  }
405  }
406 end:
407  ldelay = Time2CoDel(Simulator::Now() - item->GetTimeStamp());
408  // In Linux, this branch of code is executed even if the packet has been marked
409  // according to the target delay above. If the ns-3 code were to do the same here,
410  // it would result in two counts of mark in the queue statistics. Therefore, we
411  // use the isMarked flag to suppress a second attempt at marking.
412  if (!isMarked && item && !m_useL4s && m_useEcn &&
414  {
415  NS_LOG_LOGIC("Marking due to CeThreshold " << m_ceThreshold.GetSeconds());
416  }
417  return item;
418 }
419 
420 Time
422 {
423  return m_target;
424 }
425 
426 Time
428 {
429  return m_interval;
430 }
431 
432 uint32_t
434 {
435  return m_dropNext;
436 }
437 
438 bool
439 CoDelQueueDisc::CoDelTimeAfter(uint32_t a, uint32_t b)
440 {
441  return ((int64_t)(a) - (int64_t)(b) > 0);
442 }
443 
444 bool
445 CoDelQueueDisc::CoDelTimeAfterEq(uint32_t a, uint32_t b)
446 {
447  return ((int64_t)(a) - (int64_t)(b) >= 0);
448 }
449 
450 bool
451 CoDelQueueDisc::CoDelTimeBefore(uint32_t a, uint32_t b)
452 {
453  return ((int64_t)(a) - (int64_t)(b) < 0);
454 }
455 
456 bool
457 CoDelQueueDisc::CoDelTimeBeforeEq(uint32_t a, uint32_t b)
458 {
459  return ((int64_t)(a) - (int64_t)(b) <= 0);
460 }
461 
462 uint32_t
464 {
465  return static_cast<uint32_t>(t.GetNanoSeconds() >> CODEL_SHIFT);
466 }
467 
468 bool
470 {
471  NS_LOG_FUNCTION(this);
472  if (GetNQueueDiscClasses() > 0)
473  {
474  NS_LOG_ERROR("CoDelQueueDisc cannot have classes");
475  return false;
476  }
477 
478  if (GetNPacketFilters() > 0)
479  {
480  NS_LOG_ERROR("CoDelQueueDisc cannot have packet filters");
481  return false;
482  }
483 
484  if (GetNInternalQueues() == 0)
485  {
486  // add a DropTail queue
490  }
491 
492  if (GetNInternalQueues() != 1)
493  {
494  NS_LOG_ERROR("CoDelQueueDisc needs 1 internal queue");
495  return false;
496  }
497 
498  return true;
499 }
500 
501 void
503 {
504  NS_LOG_FUNCTION(this);
505 }
506 
507 } // namespace ns3
AttributeValue implementation for Boolean.
Definition: boolean.h:37
A CoDel packet queue disc.
bool CheckConfig() override
Check whether the current configuration is correct.
uint32_t GetDropNext()
Get the time for next packet drop while in the dropping state.
static uint16_t NewtonStep(uint16_t recInvSqrt, uint32_t count)
Calculate the reciprocal square root of m_count by using Newton's method http://en....
static constexpr const char * OVERLIMIT_DROP
Overlimit dropped packet.
static uint32_t ControlLaw(uint32_t t, uint32_t interval, uint32_t recInvSqrt)
Determine the time for next drop CoDel control law is t + m_interval/sqrt(m_count).
static constexpr const char * TARGET_EXCEEDED_DROP
Sojourn time above target.
uint16_t m_recInvSqrt
Reciprocal inverse square root.
bool CoDelTimeBeforeEq(uint32_t a, uint32_t b)
Check if CoDel time a is preceding or equal to b.
void InitializeParams() override
Initialize parameters (if any) before the first packet is enqueued.
Time m_ceThreshold
Threshold above which to CE mark.
Time GetInterval()
Get the interval.
Ptr< QueueDiscItem > DoDequeue() override
Remove a packet from queue based on the current state If we are in dropping state,...
uint32_t m_minBytes
Minimum bytes in queue to allow a packet drop.
bool CoDelTimeAfterEq(uint32_t a, uint32_t b)
Check if CoDel time a is successive or equal to b.
static constexpr const char * CE_THRESHOLD_EXCEEDED_MARK
Sojourn time above CE threshold.
TracedValue< uint32_t > m_count
Number of packets dropped since entering drop state.
bool m_useL4s
True if L4S is used (ECT1 packets are marked at CE threshold)
bool OkToDrop(Ptr< QueueDiscItem > item, uint32_t now)
Determine whether a packet is OK to be dropped.
TracedValue< uint32_t > m_lastCount
Last number of packets dropped since entering drop state.
Time m_target
5 ms target queue delay
uint32_t Time2CoDel(Time t)
Return the unsigned 32-bit integer representation of the input Time object.
CoDelQueueDisc()
CoDelQueueDisc Constructor.
uint32_t m_firstAboveTime
Time to declare sojourn time above target.
Time GetTarget()
Get the target queue delay.
bool m_useEcn
True if ECN is used (packets are marked instead of being dropped)
TracedValue< bool > m_dropping
True if in dropping state.
bool CoDelTimeAfter(uint32_t a, uint32_t b)
Check if CoDel time a is successive to b.
bool CoDelTimeBefore(uint32_t a, uint32_t b)
Check if CoDel time a is preceding b.
bool DoEnqueue(Ptr< QueueDiscItem > item) override
Add a packet to the queue.
static constexpr const char * TARGET_EXCEEDED_MARK
Sojourn time above target.
Time m_interval
100 ms sliding minimum time window width
TracedValue< uint32_t > m_dropNext
Time to drop next packet.
static TypeId GetTypeId()
Get the type ID.
Introspection did not find any typical Config paths.
Smart pointer class similar to boost::intrusive_ptr.
Definition: ptr.h:78
QueueDisc is an abstract base class providing the interface and implementing the operations common to...
Definition: queue-disc.h:184
void AddInternalQueue(Ptr< InternalQueue > queue)
Add an internal queue to the tail of the list of queues.
Definition: queue-disc.cc:577
QueueSize GetCurrentSize()
Get the current size of the queue disc in bytes, if operating in bytes mode, or packets,...
Definition: queue-disc.cc:519
uint32_t GetNPackets() const
Get the number of packets stored by the queue disc.
Definition: queue-disc.cc:436
uint32_t GetNBytes() const
Get the amount of bytes stored by the queue disc.
Definition: queue-disc.cc:443
Ptr< InternalQueue > GetInternalQueue(std::size_t i) const
Get the i-th internal queue.
Definition: queue-disc.cc:595
void DropAfterDequeue(Ptr< const QueueDiscItem > item, const char *reason)
Perform the actions required when the queue disc is notified of a packet dropped after dequeue.
Definition: queue-disc.cc:766
std::size_t GetNQueueDiscClasses() const
Get the number of queue disc classes.
Definition: queue-disc.cc:665
QueueSize GetMaxSize() const
Get the maximum size of the queue disc.
Definition: queue-disc.cc:450
std::size_t GetNPacketFilters() const
Get the number of packet filters.
Definition: queue-disc.cc:622
bool SetMaxSize(QueueSize size)
Set the maximum size of the queue disc.
Definition: queue-disc.cc:478
std::size_t GetNInternalQueues() const
Get the number of internal queues.
Definition: queue-disc.cc:602
bool Mark(Ptr< QueueDiscItem > item, const char *reason)
Marks the given packet and, if successful, updates the counters associated with the given reason.
Definition: queue-disc.cc:817
void DropBeforeEnqueue(Ptr< const QueueDiscItem > item, const char *reason)
Perform the actions required when the queue disc is notified of a packet dropped before enqueue.
Definition: queue-disc.cc:726
Class for representing queue sizes.
Definition: queue-size.h:96
AttributeValue implementation for QueueSize.
static Time Now()
Return the current simulation virtual time.
Definition: simulator.cc:199
Hold variables of type string.
Definition: string.h:56
Simulation virtual time values and global simulation resolution.
Definition: nstime.h:105
int64_t GetNanoSeconds() const
Get an approximation of the time stored in this instance in the indicated unit.
Definition: nstime.h:417
double GetSeconds() const
Get an approximation of the time stored in this instance in the indicated unit.
Definition: nstime.h:402
@ MS
millisecond
Definition: nstime.h:117
static Time Max()
Maximum representable Time Not to be confused with Max(Time,Time).
Definition: nstime.h:296
AttributeValue implementation for Time.
Definition: nstime.h:1423
a unique identifier for an interface.
Definition: type-id.h:60
TypeId SetParent(TypeId tid)
Set the parent TypeId.
Definition: type-id.cc:935
Hold an unsigned integer type.
Definition: uinteger.h:45
#define DEFAULT_CODEL_LIMIT
#define REC_INV_SQRT_SHIFT
Ptr< const AttributeAccessor > MakeBooleanAccessor(T1 a1)
Create an AttributeAccessor for a class data member, or a lone class get functor or set method.
Definition: boolean.h:86
Ptr< const AttributeChecker > MakeBooleanChecker()
Definition: boolean.cc:124
Ptr< const AttributeAccessor > MakeTimeAccessor(T1 a1)
Create an AttributeAccessor for a class data member, or a lone class get functor or set method.
Definition: nstime.h:1424
Ptr< const AttributeAccessor > MakeUintegerAccessor(T1 a1)
Create an AttributeAccessor for a class data member, or a lone class get functor or set method.
Definition: uinteger.h:46
#define NS_LOG_ERROR(msg)
Use NS_LOG to output a message of level LOG_ERROR.
Definition: log.h:254
#define NS_LOG_COMPONENT_DEFINE(name)
Define a Log component with a specific name.
Definition: log.h:202
#define NS_LOG_DEBUG(msg)
Use NS_LOG to output a message of level LOG_DEBUG.
Definition: log.h:268
#define NS_LOG_LOGIC(msg)
Use NS_LOG to output a message of level LOG_LOGIC.
Definition: log.h:282
#define NS_LOG_FUNCTION_NOARGS()
Output the name of the function.
#define NS_LOG_FUNCTION(parameters)
If log level LOG_FUNCTION is enabled, this macro will output all input parameters separated by ",...
#define NS_LOG_INFO(msg)
Use NS_LOG to output a message of level LOG_INFO.
Definition: log.h:275
Ptr< T > CreateObjectWithAttributes(Args... args)
Allocate an Object on the heap and initialize with a set of attributes.
#define NS_OBJECT_ENSURE_REGISTERED(type)
Register an Object subclass with the TypeId system.
Definition: object-base.h:46
@ BYTES
Use number of bytes for queue size.
Definition: queue-size.h:46
Ptr< const TraceSourceAccessor > MakeTraceSourceAccessor(T a)
Create a TraceSourceAccessor which will control access to the underlying trace source.
QueueDiscSizePolicy
Enumeration of the available policies to handle the queue disc size.
Definition: queue-disc.h:107
@ SINGLE_INTERNAL_QUEUE
Used by queue discs with single internal queue.
Definition: queue-disc.h:108
Every class exported by the ns3 library is enclosed in the ns3 namespace.
static int64_t CoDelGetTime()
Returns the current time translated in CoDel time representation.
static const int CODEL_SHIFT
Number of bits discarded from the time representation.
Ptr< const AttributeChecker > MakeTimeChecker(const Time min, const Time max)
Helper to make a Time checker with bounded range.
Definition: time.cc:535
static uint32_t ReciprocalDivide(uint32_t A, uint32_t R)
Performs a reciprocal divide, similar to the Linux kernel reciprocal_divide function.