In redundant arithmetic, which processes the MSB first, the carry will propagate for a few bits only. Here we define two latency models for bit-serial arithmetic.

Rebrasti lim za pokrivanje cena video. Many and require the serialization or enumeration of related entities. For example, a must know whether some packet comes 'before' or 'after' some other packet.

The () attempts to define 'Serial Number Arithmetic' for the purposes of manipulating and comparing these. This task is rather more complex than it might first appear, because most algorithms use fixed size () representations for sequence numbers. It is often important for the algorithm not to 'break down' when the numbers become so large that they are incremented one last time and 'wrap' around their maximum numeric ranges (go instantly from a large positive number to 0, or a large negative number). Unfortunately, some protocols choose to ignore these issues, and simply use very large integers for their counters, in the hope that the program will be replaced (or they will retire), before the problem occurs (see ).

Many communication protocols apply serial number arithmetic to packet sequence numbers in their implementation of a. Some versions of TCP use. PAWS applies the same serial number arithmetic to packet timestamps, using the timestamp as an extension of the high-order bits of the sequence number.

Contents • • • • • • • • Operations on sequence numbers [ ] Only addition of a small positive to a sequence number, and comparison of two sequence numbers are discussed. Only unsigned binary implementations are discussed, with an arbitrary size in bits noted throughout the RFC (and below) as 'SERIAL_BITS'. Addition [ ] Adding an integer to a sequence number is simple unsigned integer addition, followed by unsigned to bring the result back into range (usually implicit in the unsigned addition, on most architectures.) s' = (s + n) modulo (2 ^ SERIAL_BITS) Addition of a value outside the range [0. (2 ^(SERIAL_BITS - 1) - 1)] is undefined. Basically, adding values beyond this range will cause the resultant sequence number to 'wrap', and (often) result in a number that is considered 'less than' the original sequence number! Comparison [ ] A means of comparing two sequence numbers i1 and i2 (the unsigned integer representations of sequence numbers s1 and s2) is presented.

Equality is defined as simple numeric equality. The algorithm presented for comparison is very complex, having to take into account whether the first sequence number is close to the 'end' of its range of values, and thus a smaller 'wrapped' number may actually be considered 'greater' than the first sequence number. Thus i1 is considered less than i2, only if: (i1 i2 and i1 - i2 > 2^(SERIAL_BITS - 1)) Likewise, i1 is considered greater than i2, only if: (i1 2^(SERIAL_BITS - 1)) or (i1 > i2 and i1 - i2 (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. Thus, it is often difficult or impossible to avoid all 'undefined' comparisons of sequence numbers. However, a relatively simple solution is available. By mapping the unsigned sequence numbers onto signed arithmetic operations, every comparison of any sequence number is defined, and the comparison operation itself is dramatically simplified.

All comparisons specified by the RFC retain their original truth values; only the formerly 'undefined' comparisons are affected. General solution [ ] The algorithm specifies that, for N-bit sequence numbers, there are 2 (N−1)−1 values considered 'greater than', and 2 (N−1)−1 considered 'less than'.

Comparison against the remaining value (exactly 2 N−1 distant) is deemed to be 'undefined'. Most modern hardware implements signed binary arithmetic operations.