Appendix G - Clemson University

G-20 ■ Appendix G Vector Processors
The value of T start is the sum of
■ The vector load start-up of 12 clock cycles
■ A 7-clock-cycle start-up for the multiply
■ A 12-clock-cycle start-up for the store
Thus, the value of T start is given by
So, the overall value becomes
T start = 12 + 7 + 12 = 31
T 200 = 660 + 4 × 31= 784
The execution time per element with all start-up costs is then 784/200 = 3.9,
compared with a chime approximation of three. In Section G.4, we will be more
ambitious—allowing overlapping of separate convoys.
Figure G.9 shows the overhead and effective rates per element for the previous
example (A = B × s) with various vector lengths. A chime counting model
would lead to 3 clock cycles per element, while the two sources of overhead add
0.9 clock cycles per element in the limit.
The next few sections introduce enhancements that reduce this time. We will
see how to reduce the number of convoys and hence the number of chimes using
a technique called chaining. The loop overhead can be reduced by further overlapping
the execution of vector and scalar instructions, allowing the scalar loop
overhead in one iteration to be executed while the vector instructions in the previous
instruction are completing. Finally, the vector start-up overhead can also be
eliminated, using a technique that allows overlap of vector instructions in separate
convoys.
Vector Stride
The second problem this section addresses is that the position in memory of adjacent
elements in a vector may not be sequential. Consider the straightforward
code for matrix multiply:
do 10 i = 1,100
do 10 j = 1,100
A(i,j) = 0.0
do 10 k = 1,100
10 A(i,j) = A(i,j)+B(i,k)*C(k,j)
At the statement labeled 10 we could vectorize the multiplication of each row of B
with each column of C and strip-mine the inner loop with k as the index variable.