1. Chapter One Introduction to Pipelined Processors

2. Linear pipeline (Static & Unifunctional)
In a linear pipeline data flows from one stage to another and all stages are used once in a computation and it is for one functional evaluation.

3. Nonlinear Pipeline

4. Non-linear pipeline
In floating point adder, stage (2) and (4) needs a shift register.
We can use the same shift register and then there will be only 3 stages.
Then we should have a feedback from third stage to second stage.
Further the same pipeline can be used to perform fixed point addition.
A pipeline with feed-forward and/or feedback connections is called non-linear

5. Example: 3-stage nonlinear pipeline

6. 3 stage non-linear pipeline
Output A
Input
Output B Sa Sb Sc
It has 3 stages Sa, Sb and Sc and latches.
Multiplexers(cross circles) can take more than one input and pass one of the inputs to output
Output of stages has been tapped and used for feedback and feed-forward.

7. 3 stage non-linear pipeline
The above pipeline can perform a variety of functions.
Each functional evaluation can be represented by a particular sequence of usage of stages.
Some examples are:
Sa, Sb, Sc
Sa, Sb, Sc, Sb, Sc, Sa
Sa, Sc, Sb, Sa, Sb, Sc

8. Reservation Table
Each functional evaluation can be represented using a diagram called Reservation Table(rt).
It is the space-time diagram of a pipeline corresponding to one functional evaluation.
X axis – time units
Y axis – stages

9. Reservation Table
For first sequence Sa, Sb, Sc, Sb, Sc, Sa called function A , we have 1 2 3 4 5 Sa A Sb Sc

10. Reservation Table For second sequence Sa, Sc, Sb, Sa, Sb, Sc
called function B, we have 1 2 3 4 5 Sa B Sb Sc

11. 3 stage non-linear pipeline
Output A
Output B Sa Sb Sc
Input
Reservation Table
Time  1 2 3 4 5 Sa Sb Sc
Stage 

12. Function A

13. 3 stage pipeline : Sa, Sb, Sc, Sb, Sc, Sa
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa A Sb Sc
Stage 

14. 3 stage pipeline : Sa, Sb, Sc, Sb, Sc, Sa
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa A Sb Sc
Stage 

15. 3 stage pipeline : Sa, Sb, Sc, Sb, Sc, Sa
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa A Sb Sc
Stage 

16. 3 stage pipeline : Sa, Sb, Sc, Sb, Sc, Sa
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa A Sb Sc
Stage 

17. 3 stage pipeline : Sa, Sb, Sc, Sb, Sc, Sa
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa A Sb Sc
Stage 

18. 3 stage pipeline : Sa, Sb, Sc, Sb, Sc, Sa
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa A Sb Sc
Stage 

19. Function B

20. 3 stage pipeline: Sa, Sc, Sb, Sa, Sb, Sc
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa B Sb Sc
Stage 

21. 3 stage pipeline: Sa, Sc, Sb, Sa, Sb, Sc
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa B Sb Sc
Stage 

22. 3 stage pipeline: Sa, Sc, Sb, Sa, Sb, Sc
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa B Sb Sc
Stage 

23. 3 stage pipeline: Sa, Sc, Sb, Sa, Sb, Sc
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa B Sb Sc
Stage 

24. 3 stage pipeline: Sa, Sc, Sb, Sa, Sb, Sc
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa B Sb Sc
Stage 

25. 3 stage pipeline: Sa, Sc, Sb, Sa, Sb, Sc
Output A
Input
Output B Sa Sb Sc
Reservation Table
Time  1 2 3 4 5 Sa B Sb Sc
Stage 

26. Reservation Table
After starting a function, the stages need to be reserved in corresponding time units.
Each function supported by multifunction pipeline is represented by different RTs
Time taken for function evaluation in units of clock period is compute time.(For A & B, it is 6)

27. Reservation Table
Marking in same row => usage of stage more than once
Marking in same column => more than one stage at a time

28. Multifunction pipelines
Hardware of multifunction pipeline should be reconfigurable.
Multifunction pipeline can be static or dynamic

29. Multifunction pipelines
Static:
Initially configured for one functional evaluation.
For another function, pipeline need to be drained and reconfigured.
You cannot have two inputs of different function at the same time

30. Multifunction pipelines
Dynamic:
Can do different functional evaluation at a time.
It is difficult to control as we need to be sure that there is no conflict in usage of stages.