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CSC/ECE 506: Architecture of Parallel Computers
Problem Set 4
Due Thursday, May 2, 2002
Problems 1, 3, and 4 will be graded. There are 60 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.
Problem 1.
(20 points)
Assume a two-processor system executing the following code on CPUs
P
1 and
P
2 respectively.
P
1
P
2
1a
i
= 1 2a
k
= 1
1b
j
= 1 2b
Y
=
i
1c
X
=
k
2c
Z
=
j
Suppose that the initial value of every variable is 0.
(a) Assuming that the memory is sequentially consistent (see Lecture 13), list all possible (X, Y, Z)
triples at the end of execution of the above code by the respective processors on the two-
processor machine.
(b) Total store ordering (TSO) allows reads to bypass writes. What output triples (
X
,
Y
,
Z
) are
possible with TSO but not with sequential consistency? Explain briefly why these triples are
possible with TSO but not with Sequential Consistency for the above code.
(c) What is the minimum number of
membar
instructions (memory barrier, or fence; see VBEE
Lecture 21, on-campus Lecture 24) that need to be inserted into the TSO model for the above
code in order to guarantee sequential consistency? Show the resulting code.
(d) Partial store ordering (PSO, see Culler, Singh, and Gupta; p.689) not only allows reads to
bypass writes, but also allows writes to bypass writes. According to the original code (without the
membar instructions), what output triples (
X
,
Y
,
Z
) are possible with PSO but not with sequential
consistency? Explain why.
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
