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-Network Working Group R. Elz
-Request for Comments: 1982 University of Melbourne
-Updates: 1034, 1035 R. Bush
-Category: Standards Track RGnet, Inc.
- August 1996
-
-
- Serial Number Arithmetic
-
-Status of this Memo
-
- This document specifies an Internet standards track protocol for the
- Internet community, and requests discussion and suggestions for
- improvements. Please refer to the current edition of the "Internet
- Official Protocol Standards" (STD 1) for the standardization state
- and status of this protocol. Distribution of this memo is unlimited.
-
-Abstract
-
- This memo defines serial number arithmetic, as used in the Domain
- Name System. The DNS has long relied upon serial number arithmetic,
- a concept which has never really been defined, certainly not in an
- IETF document, though which has been widely understood. This memo
- supplies the missing definition. It is intended to update RFC1034
- and RFC1035.
-
-1. Introduction
-
- The serial number field of the SOA resource record is defined in
- RFC1035 as
-
- SERIAL The unsigned 32 bit version number of the original copy of
- the zone. Zone transfers preserve this value. This value
- wraps and should be compared using sequence space
- arithmetic.
-
- RFC1034 uses the same terminology when defining secondary server zone
- consistency procedures.
-
- Unfortunately the term "sequence space arithmetic" is not defined in
- either RFC1034 or RFC1035, nor do any of their references provide
- further information.
-
- This phrase seems to have been intending to specify arithmetic as
- used in TCP sequence numbers [RFC793], and defined in [IEN-74].
-
- Unfortunately, the arithmetic defined in [IEN-74] is not adequate for
- the purposes of the DNS, as no general comparison operator is
-
-
-
-Elz & Bush Standards Track [Page 1]
-
-RFC 1982 Serial Number Arithmetic August 1996
-
-
- defined.
-
- To avoid further problems with this simple field, this document
- defines the field and the operations available upon it. This
- definition is intended merely to clarify the intent of RFC1034 and
- RFC1035, and is believed to generally agree with current
- implementations. However, older, superseded, implementations are
- known to have treated the serial number as a simple unsigned integer,
- with no attempt to implement any kind of "sequence space arithmetic",
- however that may have been interpreted, and further, ignoring the
- requirement that the value wraps. Nothing can be done with these
- implementations, beyond extermination.
-
-2. Serial Number Arithmetic
-
- Serial numbers are formed from non-negative integers from a finite
- subset of the range of all integer values. The lowest integer in
- every subset used for this purpose is zero, the maximum is always one
- less than a power of two.
-
- When considered as serial numbers however no value has any particular
- significance, there is no minimum or maximum serial number, every
- value has a successor and predecessor.
-
- To define a serial number to be used in this way, the size of the
- serial number space must be given. This value, called "SERIAL_BITS",
- gives the power of two which results in one larger than the largest
- integer corresponding to a serial number value. This also specifies
- the number of bits required to hold every possible value of a serial
- number of the defined type. The operations permitted upon serial
- numbers are defined in the following section.
-
-3. Operations upon the serial number
-
- Only two operations are defined upon serial numbers, addition of a
- positive integer of limited range, and comparison with another serial
- number.
-
-3.1. Addition
-
- Serial numbers may be incremented by the addition of a positive
- integer n, where n is taken from the range of integers
- [0 .. (2^(SERIAL_BITS - 1) - 1)]. For a sequence number s, the
- result of such an addition, s', is defined as
-
- s' = (s + n) modulo (2 ^ SERIAL_BITS)
-
-
-
-
-
-Elz & Bush Standards Track [Page 2]
-
-RFC 1982 Serial Number Arithmetic August 1996
-
-
- where the addition and modulus operations here act upon values that
- are non-negative values of unbounded size in the usual ways of
- integer arithmetic.
-
- Addition of a value outside the range
- [0 .. (2^(SERIAL_BITS - 1) - 1)] is undefined.
-
-3.2. Comparison
-
- Any two serial numbers, s1 and s2, may be compared. The definition
- of the result of this comparison is as follows.
-
- For the purposes of this definition, consider two integers, i1 and
- i2, from the unbounded set of non-negative integers, such that i1 and
- s1 have the same numeric value, as do i2 and s2. Arithmetic and
- comparisons applied to i1 and i2 use ordinary unbounded integer
- arithmetic.
-
- Then, s1 is said to be equal to s2 if and only if i1 is equal to i2,
- in all other cases, s1 is not equal to s2.
-
- s1 is said to be less than s2 if, and only if, s1 is not equal to s2,
- and
-
- (i1 < i2 and i2 - i1 < 2^(SERIAL_BITS - 1)) or
- (i1 > i2 and i1 - i2 > 2^(SERIAL_BITS - 1))
-
- s1 is said to be greater than s2 if, and only if, s1 is not equal to
- s2, and
-
- (i1 < i2 and i2 - i1 > 2^(SERIAL_BITS - 1)) or
- (i1 > i2 and i1 - i2 < 2^(SERIAL_BITS - 1))
-
- Note that there are some pairs of values s1 and s2 for which s1 is
- not equal to s2, but for which s1 is neither greater than, nor less
- than, s2. An attempt to use these ordering operators on such pairs
- of values produces an undefined result.
-
- The reason for this is that those pairs of values are such that any
- simple definition that were to define s1 to be less than s2 where
- (s1, s2) is such a pair, would also usually cause s2 to be less than
- s1, when the pair is (s2, s1). This would mean that the particular
- order selected for a test could cause the result to differ, leading
- to unpredictable implementations.
-
- While it would be possible to define the test in such a way that the
- inequality would not have this surprising property, while being
- defined for all pairs of values, such a definition would be
-
-
-
-Elz & Bush Standards Track [Page 3]
-
-RFC 1982 Serial Number Arithmetic August 1996
-
-
- unnecessarily burdensome to implement, and difficult to understand,
- and would still allow cases where
-
- s1 < s2 and (s1 + 1) > (s2 + 1)
-
- which is just as non-intuitive.
-
- Thus the problem case is left undefined, implementations are free to
- return either result, or to flag an error, and users must take care
- not to depend on any particular outcome. Usually this will mean
- avoiding allowing those particular pairs of numbers to co-exist.
-
- The relationships greater than or equal to, and less than or equal
- to, follow in the natural way from the above definitions.
-
-4. Corollaries
-
- These definitions give rise to some results of note.
-
-4.1. Corollary 1
-
- For any sequence number s and any integer n such that addition of n
- to s is well defined, (s + n) >= s. Further (s + n) == s only when
- n == 0, in all other defined cases, (s + n) > s.
-
-4.2. Corollary 2
-
- If s' is the result of adding the non-zero integer n to the sequence
- number s, and m is another integer from the range defined as able to
- be added to a sequence number, and s" is the result of adding m to
- s', then it is undefined whether s" is greater than, or less than s,
- though it is known that s" is not equal to s.
-
-4.3. Corollary 3
-
- If s" from the previous corollary is further incremented, then there
- is no longer any known relationship between the result and s.
-
-4.4. Corollary 4
-
- If in corollary 2 the value (n + m) is such that addition of the sum
- to sequence number s would produce a defined result, then corollary 1
- applies, and s" is known to be greater than s.
-
-
-
-
-
-
-
-
-Elz & Bush Standards Track [Page 4]
-
-RFC 1982 Serial Number Arithmetic August 1996
-
-
-5. Examples
-
-5.1. A trivial example
-
- The simplest meaningful serial number space has SERIAL_BITS == 2. In
- this space, the integers that make up the serial number space are 0,
- 1, 2, and 3. That is, 3 == 2^SERIAL_BITS - 1.
-
- In this space, the largest integer that it is meaningful to add to a
- sequence number is 2^(SERIAL_BITS - 1) - 1, or 1.
-
- Then, as defined 0+1 == 1, 1+1 == 2, 2+1 == 3, and 3+1 == 0.
- Further, 1 > 0, 2 > 1, 3 > 2, and 0 > 3. It is undefined whether
- 2 > 0 or 0 > 2, and whether 1 > 3 or 3 > 1.
-
-5.2. A slightly larger example
-
- Consider the case where SERIAL_BITS == 8. In this space the integers
- that make up the serial number space are 0, 1, 2, ... 254, 255.
- 255 == 2^SERIAL_BITS - 1.
-
- In this space, the largest integer that it is meaningful to add to a
- sequence number is 2^(SERIAL_BITS - 1) - 1, or 127.
-
- Addition is as expected in this space, for example: 255+1 == 0,
- 100+100 == 200, and 200+100 == 44.
-
- Comparison is more interesting, 1 > 0, 44 > 0, 100 > 0, 100 > 44,
- 200 > 100, 255 > 200, 0 > 255, 100 > 255, 0 > 200, and 44 > 200.
-
- Note that 100+100 > 100, but that (100+100)+100 < 100. Incrementing
- a serial number can cause it to become "smaller". Of course,
- incrementing by a smaller number will allow many more increments to
- be made before this occurs. However this is always something to be
- aware of, it can cause surprising errors, or be useful as it is the
- only defined way to actually cause a serial number to decrease.
-
- The pairs of values 0 and 128, 1 and 129, 2 and 130, etc, to 127 and
- 255 are not equal, but in each pair, neither number is defined as
- being greater than, or less than, the other.
-
- It could be defined (arbitrarily) that 128 > 0, 129 > 1,
- 130 > 2, ..., 255 > 127, by changing the comparison operator
- definitions, as mentioned above. However note that that would cause
- 255 > 127, while (255 + 1) < (127 + 1), as 0 < 128. Such a
- definition, apart from being arbitrary, would also be more costly to
- implement.
-
-
-
-
-Elz & Bush Standards Track [Page 5]
-
-RFC 1982 Serial Number Arithmetic August 1996
-
-
-6. Citation
-
- As this defined arithmetic may be useful for purposes other than for
- the DNS serial number, it may be referenced as Serial Number
- Arithmetic from RFC1982. Any such reference shall be taken as
- implying that the rules of sections 2 to 5 of this document apply to
- the stated values.
-
-7. The DNS SOA serial number
-
- The serial number in the DNS SOA Resource Record is a Serial Number
- as defined above, with SERIAL_BITS being 32. That is, the serial
- number is a non negative integer with values taken from the range
- [0 .. 4294967295]. That is, a 32 bit unsigned integer.
-
- The maximum defined increment is 2147483647 (2^31 - 1).
-
- Care should be taken that the serial number not be incremented, in
- one or more steps, by more than this maximum within the period given
- by the value of SOA.expire. Doing so may leave some secondary
- servers with out of date copies of the zone, but with a serial number
- "greater" than that of the primary server. Of course, special
- circumstances may require this rule be set aside, for example, when
- the serial number needs to be set lower for some reason. If this
- must be done, then take special care to verify that ALL servers have
- correctly succeeded in following the primary server's serial number
- changes, at each step.
-
- Note that each, and every, increment to the serial number must be
- treated as the start of a new sequence of increments for this
- purpose, as well as being the continuation of all previous sequences
- started within the period specified by SOA.expire.
-
- Caution should also be exercised before causing the serial number to
- be set to the value zero. While this value is not in any way special
- in serial number arithmetic, or to the DNS SOA serial number, many
- DNS implementations have incorrectly treated zero as a special case,
- with special properties, and unusual behaviour may be expected if
- zero is used as a DNS SOA serial number.
-
-
-
-
-
-
-
-
-
-
-
-
-Elz & Bush Standards Track [Page 6]
-
-RFC 1982 Serial Number Arithmetic August 1996
-
-
-8. Document Updates
-
- RFC1034 and RFC1035 are to be treated as if the references to
- "sequence space arithmetic" therein are replaced by references to
- serial number arithmetic, as defined in this document.
-
-9. Security Considerations
-
- This document does not consider security.
-
- It is not believed that anything in this document adds to any
- security issues that may exist with the DNS, nor does it do anything
- to lessen them.
-
-References
-
- [RFC1034] Domain Names - Concepts and Facilities,
- P. Mockapetris, STD 13, ISI, November 1987.
-
- [RFC1035] Domain Names - Implementation and Specification
- P. Mockapetris, STD 13, ISI, November 1987
-
- [RFC793] Transmission Control protocol
- Information Sciences Institute, STD 7, USC, September 1981
-
- [IEN-74] Sequence Number Arithmetic
- William W. Plummer, BB&N Inc, September 1978
-
-Acknowledgements
-
- Thanks to Rob Austein for suggesting clarification of the undefined
- comparison operators, and to Michael Patton for attempting to locate
- another reference for this procedure. Thanks also to members of the
- IETF DNSIND working group of 1995-6, in particular, Paul Mockapetris.
-
-Authors' Addresses
-
- Robert Elz Randy Bush
- Computer Science RGnet, Inc.
- University of Melbourne 10361 NE Sasquatch Lane
- Parkville, Vic, 3052 Bainbridge Island, Washington, 98110
- Australia. United States.
-
- EMail: kre@munnari.OZ.AU EMail: randy@psg.com
-
-
-
-
-
-
-
-Elz & Bush Standards Track [Page 7]
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