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Network Working Group                                           S. Floyd
Request for Comments: 2582                                         ACIRI
Category: Experimental                                      T. Henderson
                                                           U.C. Berkeley
                                                              April 1999


       The NewReno Modification to TCP's Fast Recovery Algorithm

Status of this Memo

   This memo defines an Experimental Protocol for the Internet
   community.  It does not specify an Internet standard of any kind.
   Discussion and suggestions for improvement are requested.
   Distribution of this memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (1999).  All Rights Reserved.

Abstract

   RFC 2001 [RFC2001] documents the following four intertwined TCP
   congestion control algorithms: Slow Start, Congestion Avoidance, Fast
   Retransmit, and Fast Recovery.  RFC 2581 [RFC2581] explicitly allows
   certain modifications of these algorithms, including modifications
   that use the TCP Selective Acknowledgement (SACK) option [MMFR96],
   and modifications that respond to "partial acknowledgments" (ACKs
   which cover new data, but not all the data outstanding when loss was
   detected) in the absence of SACK.  This document describes a specific
   algorithm for responding to partial acknowledgments, referred to as
   NewReno.  This response to partial acknowledgments was first proposed
   by Janey Hoe in [Hoe95].

1. Introduction

   For the typical implementation of the TCP Fast Recovery algorithm
   described in [RFC2581] (first implemented in the 1990 BSD Reno
   release, and referred to as the Reno algorithm in [FF96]), the TCP
   data sender only retransmits a packet after a retransmit timeout has
   occurred, or after three duplicate acknowledgements have arrived
   triggering the Fast Retransmit algorithm.  A single retransmit
   timeout might result in the retransmission of several data packets,
   but each invocation of the Reno Fast Retransmit algorithm leads to
   the retransmission of only a single data packet.






Floyd & Henderson             Experimental                      [Page 1]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   Problems can arise, therefore, when multiple packets have been
   dropped from a single window of data and the Fast Retransmit and Fast
   Recovery algorithms are invoked.  In this case, if the SACK option is
   available, the TCP sender has the information to make intelligent
   decisions about which packets to retransmit and which packets not to
   retransmit during Fast Recovery.  This document applies only for TCP
   connections that are unable to use the TCP Selective Acknowledgement
   (SACK) option.

   In the absence of SACK, there is little information available to the
   TCP sender in making retransmission decisions during Fast Recovery.
   From the three duplicate acknowledgements, the sender infers a packet
   loss, and retransmits the indicated packet.  After this, the data
   sender could receive additional duplicate acknowledgements, as the
   data receiver acknowledges additional data packets that were already
   in flight when the sender entered Fast Retransmit.

   In the case of multiple packets dropped from a single window of data,
   the first new information available to the sender comes when the
   sender receives an acknowledgement for the retransmitted packet (that
   is the packet retransmitted when Fast Retransmit was first entered).
   If there had been a single packet drop, then the acknowledgement for
   this packet will acknowledge all of the packets transmitted before
   Fast Retransmit was entered (in the absence of reordering).  However,
   when there were multiple packet drops, then the acknowledgement for
   the retransmitted packet will acknowledge some but not all of the
   packets transmitted before the Fast Retransmit.  We call this packet
   a partial acknowledgment.

   Along with several other suggestions, [Hoe95] suggested that during
   Fast Recovery the TCP data sender respond to a partial acknowledgment
   by inferring that the indicated packet has been lost, and
   retransmitting that packet.  This document describes a modification
   to the Fast Recovery algorithm in Reno TCP that incorporates a
   response to partial acknowledgements received during Fast Recovery.
   We call this modified Fast Recovery algorithm NewReno, because it is
   a slight but significant variation of the basic Reno algorithm.  This
   document does not discuss the other suggestions in [Hoe95] and
   [Hoe96], such as a change to the ssthresh parameter during Slow-
   Start, or the proposal to send a new packet for every two duplicate
   acknowledgements during Fast Recovery.  The version of NewReno in
   this document also draws on other discussions of NewReno in the
   literature [LM97].

   We do not claim that the NewReno version of Fast Recovery described
   here is an optimal modification of Fast Recovery for responding to
   partial acknowledgements, for TCPs that are unable to use SACK.
   Based on our experiences with the NewReno modification in the NS



Floyd & Henderson             Experimental                      [Page 2]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   simulator [NS], we believe that this modification improves the
   performance of the Fast Retransmit and Fast Recovery algorithms in a
   wide variety of scenarios, and we are simply documenting it for the
   benefit of the IETF community.  We encourage the use of this
   modification to Fast Recovery, and we further encourage feedback
   about operational experiences with this or related modifications.

2. Definitions

   This document assumes that the reader is familiar with the terms
   MAXIMUM SEGMENT SIZE (MSS), CONGESTION WINDOW (cwnd), and FLIGHT SIZE
   (FlightSize) defined in [RFC2581].  FLIGHT SIZE is defined as in
   [RFC2581] as follows:

      FLIGHT SIZE:
         The amount of data that has been sent but not yet acknowledged.

3. The Fast Retransmit and Fast Recovery algorithms in NewReno

   The standard implementation of the Fast Retransmit and Fast Recovery
   algorithms is given in [RFC2581].  The NewReno modification of these
   algorithms is given below.  This NewReno modification differs from
   the implementation in [RFC2581] only in the introduction of the
   variable "recover" in step 1, and in the response to a partial or new
   acknowledgement in step 5.  The modification defines a "Fast Recovery
   procedure" that begins when three duplicate ACKs are received and
   ends when either a retransmission timeout occurs or an ACK arrives
   that acknowledges all of the data up to and including the data that
   was outstanding when the Fast Recovery procedure began.

   1.  When the third duplicate ACK is received and the sender is not
       already in the Fast Recovery procedure, set ssthresh to no more
       than the value given in equation 1 below.  (This is equation 3
       from [RFC2581]).

         ssthresh = max (FlightSize / 2, 2*MSS)           (1)

       Record the highest sequence number transmitted in the variable
       "recover".

   2.  Retransmit the lost segment and set cwnd to ssthresh plus 3*MSS.
       This artificially "inflates" the congestion window by the number
       of segments (three) that have left the network and which the
       receiver has buffered.

   3.  For each additional duplicate ACK received, increment cwnd by
       MSS.  This artificially inflates the congestion window in order
       to reflect the additional segment that has left the network.



Floyd & Henderson             Experimental                      [Page 3]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   4.  Transmit a segment, if allowed by the new value of cwnd and the
       receiver's advertised window.

   5.  When an ACK arrives that acknowledges new data, this ACK could be
       the acknowledgment elicited by the retransmission from step 2, or
       elicited by a later retransmission.

       If this ACK acknowledges all of the data up to and including
       "recover", then the ACK acknowledges all the intermediate
       segments sent between the original transmission of the lost
       segment and the receipt of the third duplicate ACK.  Set cwnd to
       either (1) min (ssthresh, FlightSize + MSS); or (2) ssthresh,
       where ssthresh is the value set in step 1; this is termed
       "deflating" the window.  (We note that "FlightSize" in step 1
       referred to the amount of data outstanding in step 1, when Fast
       Recovery was entered, while "FlightSize" in step 5 refers to the
       amount of data outstanding in step 5, when Fast Recovery is
       exited.) If the second option is selected, the implementation
       should take measures to avoid a possible burst of data, in case
       the amount of data outstanding in the network was much less than
       the new congestion window allows [HTH98].  Exit the Fast Recovery
       procedure.

       If this ACK does *not* acknowledge all of the data up to and
       including "recover", then this is a partial ACK.  In this case,
       retransmit the first unacknowledged segment.  Deflate the
       congestion window by the amount of new data acknowledged, then
       add back one MSS and send a new segment if permitted by the new
       value of cwnd.  This "partial window deflation" attempts to
       ensure that, when Fast Recovery eventually ends, approximately
       ssthresh amount of data will be outstanding in the network.  Do
       not exit the Fast Recovery procedure (i.e., if any duplicate ACKs
       subsequently arrive, execute Steps 3 and 4 above).


       For the first partial ACK that arrives during Fast Recovery, also
       reset the retransmit timer.

   Note that in Step 5, the congestion window is deflated when a partial
   acknowledgement is received.  The congestion window was likely to
   have been inflated considerably when the partial acknowledgement was
   received.  In addition, depending on the original pattern of packet
   losses, the partial acknowledgement might acknowledge nearly a window
   of data.  In this case, if the congestion window was not deflated,
   the data sender might be able to send nearly a window of data back-
   to-back.

   There are several possible variants to the simple response to partial



Floyd & Henderson             Experimental                      [Page 4]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   acknowledgements described above.  First, there is a question of when
   to reset the retransmit timer after a partial acknowledgement.  This
   is discussed further in Section 4 below.

   There is a related question of how many packets to retransmit after
   each partial acknowledgement.  The algorithm described above
   retransmits a single packet after each partial acknowledgement.  This
   is the most conservative alternative, in that it is the least likely
   to result in an unnecessarily-retransmitted packet.  A variant that
   would recover faster from a window with many packet drops would be to
   effectively Slow-Start, requiring less than N roundtrip times to
   recover from N losses [Hoe96].  With this slightly-more-aggressive
   response to partial acknowledgements, it would be advantageous to
   reset the retransmit timer after each retransmission.  Because we
   have not experimented with this variant in our simulator, we do not
   discuss this variant further in this document.

   A third question involves avoiding multiple Fast Retransmits caused
   by the retransmission of packets already received by the receiver.
   This is discussed in Section 5 below.  Avoiding multiple Fast
   Retransmits is particularly important if more aggressive responses to
   partial acknowledgements are implemented, because in this case the
   sender is more likely to retransmit packets already received by the
   receiver.

   As a final note, we would observe that in the absence of the SACK
   option, the data sender is working from limited information.  One
   could spend a great deal of time considering exactly which variant of
   Fast Recovery is optimal for which scenario in this case.  When the
   issue of recovery from multiple dropped packets from a single window
   of data is of particular importance, the best alternative would be to
   use the SACK option.

4. Resetting the retransmit timer.

   The algorithm in Section 3 resets the retransmit timer only after the
   first partial ACK.  In this case, if a large number of packets were
   dropped from a window of data, the TCP data sender's retransmit timer
   will ultimately expire, and the TCP data sender will invoke Slow-
   Start.  (This is illustrated on page 12 of [F98].)  We call this the
   Impatient variant of NewReno.

   In contrast, the NewReno simulations in [FF96] illustrate the
   algorithm described above, with the modification that the retransmit
   timer is reset after each partial acknowledgement.  We call this the
   Slow-but-Steady variant of NewReno.  In this case, for a window with
   a large number of packet drops, the TCP data sender retransmits at
   most one packet per roundtrip time.  (This behavior is illustrated in



Floyd & Henderson             Experimental                      [Page 5]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   the New-Reno TCP simulation of Figure 5 in [FF96], and on page 11 of
   [F98].)

   For TCP implementations where the Retransmission Timeout Value (RTO)
   is generally not much larger than the round-trip time (RTT), the
   Impatient variant can result in a retransmit timeout even in a
   scenario with a small number of packet drops.  For TCP
   implementations where the Retransmission Timeout Value (RTO) is
   usually considerably larger than the round-trip time (RTT), the Slow-
   but-Steady variant can remain in Fast Recovery for a long time when
   multiple packets have been dropped from a window of data.  Neither of
   these variants are optimal; one possibility for a more optimal
   algorithm might be one that recovered more quickly from multiple
   packet drops, and combined this with the Slow-but-Steady variant in
   terms of resetting the retransmit timers.  We note, however, that
   there is a limitation to the potential performance in this case in
   the absence of the SACK option.

5. Avoiding Multiple Fast Retransmits

   In the absence of the SACK option, a duplicate acknowledgement
   carries no information to identify the data packet or packets at the
   TCP data receiver that triggered that duplicate acknowledgement.  The
   TCP data sender is unable to distinguish between a duplicate
   acknowledgement that results from a lost or delayed data packet, and
   a duplicate acknowledgement that results from the sender's
   retransmission of a data packet that had already been received at the
   TCP data receiver.  Because of this, multiple segment losses from a
   single window of data can sometimes result in unnecessary multiple
   Fast Retransmits (and multiple reductions of the congestion window)
   [Flo94].

   With the Fast Retransmit and Fast Recovery algorithms in Reno or
   NewReno TCP, the performance problems caused by multiple Fast
   Retransmits are relatively minor (compared to the potential problems
   with Tahoe TCP, which does not implement Fast Recovery).
   Nevertheless, unnecessary Fast Retransmits can occur with Reno or
   NewReno TCP, particularly if a Retransmit Timeout occurs during Fast
   Recovery.  (This is illustrated for Reno on page 6 of [F98], and for
   NewReno on page 8 of [F98].)  With NewReno, the data sender remains
   in Fast Recovery until either a Retransmit Timeout, or until all of
   the data outstanding when Fast Retransmit was entered has been
   acknowledged.  Thus with NewReno, the problem of multiple Fast
   Retransmits from a single window of data can only occur after a
   Retransmit Timeout.

   The following modification to the algorithms in Section 3 eliminates
   the problem of multiple Fast Retransmits.  (This modification is



Floyd & Henderson             Experimental                      [Page 6]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   called "bugfix" in [F98], and is illustrated on pages 7 and 9.)  This
   modification uses a new variable "send_high", whose initial value is
   the initial send sequence number.  After each retransmit timeout, the
   highest sequence numbers transmitted so far is recorded in the
   variable "send_high".


   If, after a retransmit timeout, the TCP data sender retransmits three
   consecutive packets that have already been received by the data
   receiver, then the TCP data sender will receive three duplicate
   acknowledgements that do not acknowledge "send_high".  In this case,
   the duplicate acknowledgements are not an indication of a new
   instance of congestion.  They are simply an indication that the
   sender has unnecessarily retransmitted at least three packets.

   We note that if the TCP data sender receives three duplicate
   acknowledgements that do not acknowledge "send_high", the sender does
   not know whether these duplicate acknowledgements resulted from a new
   packet drop or not.  For a TCP that implements the bugfix described
   in this section for avoiding multiple fast retransmits, the sender
   does not infer a packet drop from duplicate acknowledgements in these
   circumstances.  As always, the retransmit timer is the backup
   mechanism for inferring packet loss in this case.

   The modification to Fast Retransmit for avoiding multiple Fast
   Retransmits replaces Step 1 in Section 3 with Step 1A below.  In
   addition, the modification adds Step 6 below:

   1A. When the third duplicate ACK is received and the sender is not
       already in the Fast Recovery procedure, check to see if those
       duplicate ACKs cover more than "send_high".  If they do, then set
       ssthresh to no more than the value given in equation 1, record
       the the highest sequence number transmitted in the variable
       "recover", and go to Step 2.  If the duplicate ACKs don't cover
       "send_high", then do nothing.  That is, do not enter the Fast
       Retransmit and Fast Recovery procedure, do not change ssthresh,
       do not go to Step 2 to retransmit the "lost" segment, and do not
       execute Step 3 upon subsequent duplicate ACKs.

   Steps 2-5 are the same as those steps in Section 3 above.

   6.  After a retransmit timeout, record the highest sequence number
       transmitted in the variable "send_high" and exit the Fast
       Recovery procedure if applicable.

   Step 1A above, in checking whether the duplicate ACKs cover *more*
   than "send_high", is the Careful variant of this algorithm.  Another
   possible variant would be to require simply that the three duplicate



Floyd & Henderson             Experimental                      [Page 7]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   acknowledgements *cover* "send_high" before initiating another Fast
   Retransmit.  We call this the Less Careful variant to Fast
   Retransmit.

   There are two separate scenarios in which the TCP sender could
   receive three duplicate acknowledgements acknowledging "send_high"
   but no more than "send_high".  One scenario would be that the data
   sender transmitted four packets with sequence numbers higher than
   "send_high", that the first packet was dropped in the network, and
   the following three packets triggered three duplicate
   acknowledgements acknowledging "send_high".  The second scenario
   would be that the sender unnecessarily retransmitted three packets
   below "send_high", and that these three packets triggered three
   duplicate acknowledgements acknowledging "send_high".  In the absence
   of SACK, the TCP sender in unable to distinguish between these two
   scenarios.

   For the Careful variant of Fast Retransmit, the data sender would
   have to wait for a retransmit timeout in the first scenario, but
   would not have an unnecessary Fast Retransmit in the second scenario.
   For the Less Careful variant to Fast Retransmit, the data sender
   would Fast Retransmit as desired in the first scenario, and would
   unnecessarily Fast Retransmit in the second scenario.  The NS
   simulator has implemented the Less Careful variant of NewReno, and
   the TCP implementation in Sun's Solaris 7 implements the Careful
   variant.  This document recommends the Careful variant given in Step
   1A above.

6. Implementation issues for the data receiver.

   [RFC2001] specifies that "Out-of-order data segments SHOULD be
   acknowledged immediately, in order to trigger the fast retransmit
   algorithm." Neal Cardwell has noted [C98] that some data receivers do
   not send an immediate acknowledgement when they send a partial
   acknowledgment, but instead wait first for their delayed
   acknowledgement timer to expire.  As [C98] notes, this severely
   limits the potential benefit from NewReno by delaying the receipt of
   the partial acknowledgement at the data sender.  Our recommendation
   is that the data receiver send an immediate acknowledgement for an
   out-of-order segment, even when that out-of-order segment fills a
   hole in the buffer.

7. Simulations

   Simulations with NewReno are illustrated with the validation test
   "tcl/test/test-all-newreno" in the NS simulator.  The command
   "../../ns test-suite-newreno.tcl reno" shows a simulation with Reno
   TCP, illustrating the data sender's lack of response to a partial



Floyd & Henderson             Experimental                      [Page 8]

RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


   acknowledgement.  In contrast, the command "../../ns test-suite-
   newreno.tcl newreno_B" shows a simulation with the same scenario
   using the NewReno algorithms described in this paper.

   The tests "../../ns test-suite-newreno.tcl newreno1_B0" and "../../ns
   test-suite-newreno.tcl newreno1_B" show the Slow-but-Steady and the
   Impatient variants of NewReno, respectively.

8. Conclusions

   Our recommendation is that TCP implementations include the NewReno
   modification to the Fast Recovery algorithm given in Section 3, along
   with the modification for avoiding multiple Fast Retransmits given in
   Section 5.  The NewReno modification given in Section 3 can be
   important even for TCP implementations that support the SACK option,
   because the SACK option can only be used for TCP connections when
   both TCP end-nodes support the SACK option.  The NewReno modification
   given in Section 3 implements the Impatient rather than the Slow-but-
   Steady variant of NewReno.

   While this document mentions several possible variations to the
   NewReno algorithm, we have not explored all of these possible
   variations, and therefore are unable to make recommendations about
   some of them.  Our belief is that the differences between any two
   variants of NewReno are small compared to the differences between
   Reno and NewReno.  That is, the important thing is to implement
   NewReno instead of Reno, for a TCP invocation without SACK; it is
   less important exactly which variant of NewReno is implemented.

9. Acknowledgements

   Many thanks to Anil Agarwal, Mark Allman, Vern Paxson, Kacheong Poon,
   and Bernie Volz for detailed feedback on this document.

10. References

   [C98]         Neal Cardwell, "delayed ACKs for retransmitted packets:
                 ouch!". November 1998.  Email to the tcpimpl mailing
                 list, Message-ID "Pine.LNX.4.02A.9811021421340.26785-
                 100000@sake.cs.washington.edu", archived at
                 "http://tcp-impl.lerc.nasa.gov/tcp-impl".

   [F98]         Sally Floyd.  Revisions to RFC 2001.  Presentation to
                 the TCPIMPL Working Group, August 1998.  URLs
                 "ftp://ftp.ee.lbl.gov/talks/sf-tcpimpl-aug98.ps" and
                 "ftp://ftp.ee.lbl.gov/talks/sf-tcpimpl-aug98.pdf".

   [FF96]        Kevin Fall and Sally Floyd.  Simulation-based



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RFC 2582      NewReno Modification to TCP's Fast Recovery     April 1999


                 Comparisons of Tahoe, Reno and SACK TCP.  Computer
                 Communication Review, July 1996.  URL
                 "ftp://ftp.ee.lbl.gov/papers/sacks.ps.Z".

   [Flo94]       S. Floyd, TCP and Successive Fast Retransmits.
                 Technical report, October 1994.  URL
                 "ftp://ftp.ee.lbl.gov/papers/fastretrans.ps".

   [Hen98]       Tom Henderson, Re: NewReno and the 2001 Revision.
                 September 1998.  Email to the tcpimpl mailing list,
                 Message ID "Pine.BSI.3.95.980923224136.26134A-
                 100000@raptor.CS.Berkeley.EDU", archived at
                 "http://tcp-impl.lerc.nasa.gov/tcp-impl".

   [Hoe95]       J. Hoe, Startup Dynamics of TCP's Congestion Control
                 and Avoidance Schemes. Master's Thesis, MIT, 1995.  URL
                 "http://ana-www.lcs.mit.edu/anaweb/ps-papers/hoe-
                 thesis.ps".

   [Hoe96]       J. Hoe, "Improving the Start-up Behavior of a
                 Congestion Control Scheme for TCP",  In ACM SIGCOMM,
                 August 1996.  URL
                 "http://www.acm.org/sigcomm/sigcomm96/program.html".


   [HTH98]       Hughes, A., Touch, J.  and J. Heidemann, "Issues in TCP
                 Slow-Start Restart After Idle", Work in Progress, March
                 1998.

   [LM97]        Dong Lin and Robert Morris, "Dynamics of Random Early
                 Detection", SIGCOMM 97, September 1997.  URL
                 "http://www.acm.org/sigcomm/sigcomm97/program.html".

   [MMFR96]      Mathis, M., Mahdavi, J., Floyd, S. and A. Romanow, "TCP
                 Selective Acknowledgement Options", RFC 2018, October
                 1996.

   [NS]          The UCB/LBNL/VINT Network Simulator (NS). URL
                 "http://www-mash.cs.berkeley.edu/ns/".

   [RFC2001]     Stevens, W., "TCP Slow Start, Congestion Avoidance,
                 Fast Retransmit, and Fast Recovery Algorithms", RFC
                 2001, January 1997.

   [RFC2581]     Stevens, W., Allman, M. and V. Paxson, "TCP Congestion
                 Control", RFC 2581, April 1999.





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11. Security Considerations

   RFC 2581 discusses general security considerations concerning TCP
   congestion control.  This document describes a specific algorithm
   that conforms with the congestion control requirements of RFC 2581,
   and so those considerations apply to this algorithm, too.  There are
   no known additional security concerns for this specific algorithm.

12. AUTHORS' ADDRESSES

   Sally Floyd
   AT&T Center for Internet Research at ICSI (ACIRI)

   Phone: +1 (510) 642-4274 x189
   EMail: floyd@acm.org
   URL:  http://www.aciri.org/floyd/


   Tom Henderson
   University of California at Berkeley

   Phone: +1 (510) 642-8919
   EMail: tomh@cs.berkeley.edu
   URL: http://www.cs.berkeley.edu/~tomh/



























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13.  Full Copyright Statement

   Copyright (C) The Internet Society (1999).  All Rights Reserved.

   This document and translations of it may be copied and furnished to
   others, and derivative works that comment on or otherwise explain it
   or assist in its implementation may be prepared, copied, published
   and distributed, in whole or in part, without restriction of any
   kind, provided that the above copyright notice and this paragraph are
   included on all such copies and derivative works.  However, this
   document itself may not be modified in any way, such as by removing
   the copyright notice or references to the Internet Society or other
   Internet organizations, except as needed for the purpose of
   developing Internet standards in which case the procedures for
   copyrights defined in the Internet Standards process must be
   followed, or as required to translate it into languages other than
   English.

   The limited permissions granted above are perpetual and will not be
   revoked by the Internet Society or its successors or assigns.

   This document and the information contained herein is provided on an
   "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
   TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
   BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
   HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
























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