Which table for a dynamic pipeline becomes more interesting when a non-linear…

Concept — A reservation table is the stage-versus-time chart of a pipeline. Each row is a pipeline stage, each column is one clock cycle counted from the moment a task enters, and a mark at row S, column t means one task holds stage S during cycle t. In a static (linear) pipeline every task walks the stages once in order, so each row carries a single mark and the chart says nothing the stage list did not already say. A dynamic pipeline lets a task re-enter a stage, so one row can carry several marks: that multi-mark, non-linear pattern is precisely what the chart has to record.

Applying it here — Once a row holds two or more marks, two tasks launched a few cycles apart can demand the same stage in the same cycle. The differences between the marked cycle numbers inside a row are exactly the launch gaps that would cause such a collision. A three-stage dynamic pipeline whose task re-enters its first stage looks like this:

The S1 row is marked at cycles 1 and 4, a difference of 3, so a second task launched 3 cycles behind the first would meet it inside S1. Latency 3 is therefore forbidden. From that reading the whole schedule follows:

1. Collect, for every row, the differences between its marked cycles — this is the set of forbidden latencies.

2. Write the collision vector: one bit per latency, set to 1 wherever a latency is forbidden.

3. For each permissible latency p, shift the current state right by p and combine the result with the initial collision vector using a bitwise OR — that gives the next state, and branching over every permissible latency from every state grows the whole state diagram.

4. Enumerate the cycles of the state diagram, greedy cycles included, and take the smallest average latency (the MAL) as the best sustainable initiation rate.

Cross-check — the other tables named here:

• Confusion table (confusion matrix): a predicted-class against actual-class grid of counts used to score a classifier. Its axes are class labels, so it carries no clock-cycle information and no latency can be read from it.

• Inverted table (inverted index or inverted file): maps every attribute value or term to the list of records that carry it, so a search jumps straight to matching records. It indexes content, not time.

• Greedy table: not a named structure in this theory. "Greedy" enters one step later, as the greedy cycle of the state diagram — the cycle obtained by always taking the smallest permissible latency — which is derived from a reservation table rather than replacing it.

Result — the reservation table is the structure that becomes richer, and genuinely more interesting, for a dynamic pipeline following a non-linear pattern: the forbidden latencies, the collision vector, the state diagram and the minimum average latency all come out of it.