–1–
CSC/ECE 506: Architecture of Parallel Computers
Problem Set 4
Due Friday, August 2, 2002
Problems 1 and 4 will be graded. There are 40 points on these problems
. Note: You must do all
the problems, even the non-graded ones
. If you do not do some of them, half as many points as
they are worth will be subtracted from your score on the graded problems.
he following question is about sequential consistency, total store ordering and
partial store ordering.
Problem 1 .
(20 points)
Consider the following code running on a two-CPU system:
P
1
P
2
1a.
A
= 1; 2a.
C
= 1;
1b.
B
= 1; 2b.
Y
=
A
;
1c.
X
=
C
; 2c.
Z
=
B
;
(a)
(10 points)
Assuming that the initial values of
A
,
B
and
C
are 0, and that the machine is
sequentially consistent, list all the possible outcomes for final values of
X
,
Y
and
Z
in the
form of triplets (
X
,
Y
,
Z
).
Note that
dependencies
1a → 1b, 1b → 1c, 2a → 2b, and 2b → 2c are implicit in the code. That is,
1a must precede 1b, etc. Each of the possible outcomes occurs iff certain additional orderings
(e.g., 1c → 2a, 1b → 2c) hold. For each possible outcome, list the additional orderings that are
needed to produce it and also give at least one of the total orderings of statements 1a, 1b, 1c, 2a,
2b, and 2c that would produce it.
(b)
(3 points)
Total store ordering (TSO) allows reads to bypass writes. Give an example of a value
triplet that is possible with TSO but not with sequential consistency. Describe the ordering of
events that would lead to these results.
(c)
(4 points)
Partial store ordering (PSO) allows writes to bypass previous writes. What is the
minimum number of memory fences (synchronization operations, such as membar instructions)
that would have to be inserted in order to achieve the same behavior as a sequentially consistent
machine? Show the modified code.
(d)
(3 points)
In what situation would weak ordering lead to improved performance compared with
PSO? Mention also any other assumptions you have to make about the machine.
Problem 2
(15 points)
Consider a 4 node CC-NUMA DSM machine using a memory-based
directory protocol with average network transaction time between nodes of 20 µsec. Compute
the remote memory-access time and draw a network transaction diagram for a write miss on node 1
to a remote remote memory block on node 2, which is dirty on node 3 for the following directory
protocol optimizations:
(a) Strict request-response
(b) Intervention forwarding
(c) Reply forwarding
