As per Relevance of the word addition, we have this rfc below:
Network Working Group R.
Request for Comments: 1982 University of
Updates: 1034, 1035 R.
Category: Standards Track RGnet, Inc
August 1996
Serial Number
Status of this
This document specifies an Internet standards track protocol for
Internet community, and requests discussion and suggestions
improvements. Please refer to the current edition of the "
Official Protocol Standards" (STD 1) for the standardization
and status of this protocol. Distribution of this memo is unlimited
This memo defines serial number arithmetic, as used in the
Name System. The DNS has long relied upon serial number arithmetic
a concept which has never really been defined, certainly not in
IETF document, though which has been widely understood. This
supplies the missing definition. It is intended to update RFC1034
and RFC1035.
1.
The serial number field of the SOA resource record is defined
RFC1035
SERIAL The unsigned 32 bit version number of the original copy
the zone. Zone transfers preserve this value. This
wraps and should be compared using sequence
arithmetic
RFC1034 uses the same terminology when defining secondary server
consistency procedures
Unfortunately the term "sequence space arithmetic" is not defined
either RFC1034 or RFC1035, nor do any of their references
further information
This phrase seems to have been intending to specify arithmetic
used in TCP sequence numbers [RFC793], and defined in [IEN-74].
Unfortunately, the arithmetic defined in [IEN-74] is not adequate
the purposes of the DNS, as no general comparison operator
Elz & Bush Standards Track [Page 1]
RFC 1982 Serial Number Arithmetic August 1996
defined
To avoid further problems with this simple field, this
defines the field and the operations available upon it.
definition is intended merely to clarify the intent of RFC1034
RFC1035, and is believed to generally agree with
implementations. However, older, superseded, implementations
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
requirement that the value wraps. Nothing can be done with
implementations, beyond extermination
2. Serial Number
Serial numbers are formed from non-negative integers from a
subset of the range of all integer values. The lowest integer
every subset used for this purpose is zero, the maximum is always
less than a power of two
When considered as serial numbers however no value has any
significance, there is no minimum or maximum serial number,
value has a successor and predecessor
To define a serial number to be used in this way, the size of
serial number space must be given. This value, called "SERIAL_BITS",
gives the power of two which results in one larger than the
integer corresponding to a serial number value. This also
the number of bits required to hold every possible value of a
number of the defined type. The operations permitted upon
numbers are defined in the following section
3. Operations upon the serial
Only two operations are defined upon serial numbers, addition of
positive integer of limited range, and comparison with another
number
3.1.
Serial numbers may be incremented by the addition of a
integer n, where n is taken from the range of
[0 .. (2^(SERIAL_BITS - 1) - 1)]. For a sequence number s,
result of such an addition, s', is defined
s' = (s + n) modulo (2 ^ SERIAL_BITS
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RFC 1982 Serial Number Arithmetic August 1996
where the addition and modulus operations here act upon values
are non-negative values of unbounded size in the usual ways
integer arithmetic
Addition of a value outside the
[0 .. (2^(SERIAL_BITS - 1) - 1)] is undefined
3.2.
Any two serial numbers, s1 and s2, may be compared. The
of the result of this comparison is as follows
For the purposes of this definition, consider two integers, i1
i2, from the unbounded set of non-negative integers, such that i1
s1 have the same numeric value, as do i2 and s2. Arithmetic
comparisons applied to i1 and i2 use ordinary unbounded
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,
(i1 < i2 and i2 - i1 < 2^(SERIAL_BITS - 1))
(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
s2,
(i1 < i2 and i2 - i1 > 2^(SERIAL_BITS - 1))
(i1 > i2 and i1 - i2 < 2^(SERIAL_BITS - 1))
Note that there are some pairs of values s1 and s2 for which s1
not equal to s2, but for which s1 is neither greater than, nor
than, s2. An attempt to use these ordering operators on such
of values produces an undefined result
The reason for this is that those pairs of values are such that
simple definition that were to define s1 to be less than s2
(s1, s2) is such a pair, would also usually cause s2 to be less
s1, when the pair is (s2, s1). This would mean that the
order selected for a test could cause the result to differ,
to unpredictable implementations
While it would be possible to define the test in such a way that
inequality would not have this surprising property, while
defined for all pairs of values, such a definition would
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RFC 1982 Serial Number Arithmetic August 1996
unnecessarily burdensome to implement, and difficult to understand
and would still allow cases
s1 < s2 and (s1 + 1) > (s2 + 1)
which is just as non-intuitive
Thus the problem case is left undefined, implementations are free
return either result, or to flag an error, and users must take
not to depend on any particular outcome. Usually this will
avoiding allowing those particular pairs of numbers to co-exist
The relationships greater than or equal to, and less than or
to, follow in the natural way from the above definitions
4.
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
to s is well defined, (s + n) >= s. Further (s + n) == s only
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
number s, and m is another integer from the range defined as able
be added to a sequence number, and s" is the result of adding m
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
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
to sequence number s would produce a defined result, then corollary 1
applies, and s" is known to be greater than s
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RFC 1982 Serial Number Arithmetic August 1996
5.
5.1. A trivial
The simplest meaningful serial number space has SERIAL_BITS == 2.
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
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
2 > 0 or 0 > 2, and whether 1 > 3 or 3 > 1.
5.2. A slightly larger
Consider the case where SERIAL_BITS == 8. In this space the
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
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.
a serial number can cause it to become "smaller". Of course
incrementing by a smaller number will allow many more increments
be made before this occurs. However this is always something to
aware of, it can cause surprising errors, or be useful as it is
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
255 are not equal, but in each pair, neither number is defined
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
definitions, as mentioned above. However note that that would
255 > 127, while (255 + 1) < (127 + 1), as 0 < 128. Such
definition, apart from being arbitrary, would also be more costly
implement
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RFC 1982 Serial Number Arithmetic August 1996
6.
As this defined arithmetic may be useful for purposes other than
the DNS serial number, it may be referenced as Serial
Arithmetic from RFC1982. Any such reference shall be taken
implying that the rules of sections 2 to 5 of this document apply
the stated values
7. The DNS SOA serial
The serial number in the DNS SOA Resource Record is a Serial
as defined above, with SERIAL_BITS being 32. That is, the
number is a non negative integer with values taken from the
[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,
one or more steps, by more than this maximum within the period
by the value of SOA.expire. Doing so may leave some
servers with out of date copies of the zone, but with a serial
"greater" than that of the primary server. Of course,
circumstances may require this rule be set aside, for example,
the serial number needs to be set lower for some reason. If
must be done, then take special care to verify that ALL servers
correctly succeeded in following the primary server's serial
changes, at each step
Note that each, and every, increment to the serial number must
treated as the start of a new sequence of increments for
purpose, as well as being the continuation of all previous
started within the period specified by SOA.expire
Caution should also be exercised before causing the serial number
be set to the value zero. While this value is not in any way
in serial number arithmetic, or to the DNS SOA serial number,
DNS implementations have incorrectly treated zero as a special case
with special properties, and unusual behaviour may be expected
zero is used as a DNS SOA serial number
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RFC 1982 Serial Number Arithmetic August 1996
8. Document
RFC1034 and RFC1035 are to be treated as if the references
"sequence space arithmetic" therein are replaced by references
serial number arithmetic, as defined in this document
9. Security
This document does not consider security
It is not believed that anything in this document adds to
security issues that may exist with the DNS, nor does it do
to lessen them
[RFC1034] Domain Names - Concepts and Facilities
P. Mockapetris, STD 13, ISI, November 1987.
[RFC1035] Domain Names - Implementation and
P. Mockapetris, STD 13, ISI, November 1987
[RFC793] Transmission Control
Information Sciences Institute, STD 7, USC, September 1981
[IEN-74] Sequence Number
William W. Plummer, BB&N Inc, September 1978
Thanks to Rob Austein for suggesting clarification of the
comparison operators, and to Michael Patton for attempting to
another reference for this procedure. Thanks also to members of
IETF DNSIND working group of 1995-6, in particular, Paul Mockapetris
Authors'
Robert Elz Randy
Computer Science RGnet, Inc
University of Melbourne 10361 NE Sasquatch
Parkville, Vic, 3052 Bainbridge Island, Washington, 98110
Australia. United States
EMail: kre@munnari.OZ.AU EMail: randy@psg.
Elz & Bush Standards Track [Page 7]
if you see any problems within the linking, don't worry be happy,
this is version 0.1 of the Relevance System and you gotta expect some crappy subroutines sometimes,
just be content we did not write this in Java, which would have made this "bigger and better" HAHAHHA.
RFC documents can be found at I.E.T.F.
Relevance System Copyright © 2002 Spectrum WorldResearch
other technical nosh by ServerMasters Corporation
collaboration of BobX
