Intel ITANIUM ARCHITECTURE - SOFTWARE DEVELOPERS VOLUME 3 REV 2.3, Manual

Page: 217 / 1898

1:206 Volume 1, Part 2: Floating-point Applications
6.2.2 Execution Bandwidth
When sufficient ILP exists and can be exploited, the performance limitation is the
availability of the execution resources – or the execution bandwidth of the machine.
Consider the dense matrix multiply kernel from the BLAS3 library.
DO 1 i = 1, N
DO 1 j = 1, P
DO 1 k = 1, M
1 C[i,j] = C[i,j] + A[i,k]*B[k,j]
Common techniques of loop interchange, loop unrolling, and unroll-and-jam, can be
used to increase the available ILP in the inner loop. When this is done, the inner loop
contains an abundance of independent floating-point computations with a relatively
small number of memory operations. The performance constraint is then largely the
floating-point execution bandwidth of the machine (assuming sufficient registers are
available to hold the accumulators –
C[i,j]
and the intermediate computations).
6.2.3 Memory Latency
While cycle time disparity between the processor and memory creates a general
memory latency problem for most codes, there are a few special conditions in
floating-point codes that exacerbate its impact.
One such condition is the use of indirect addressing. Gather/scatter codes in general
and sparse matrix vector multiply code (below) in particular are good examples.
DO 1 ROW = 1, N
R[ROW] = 0.0d0
DO 1 I = ROWEND(ROW-1)+1, ROWEND(ROW)
1 R[ROW] = R[ROW] + A[I] * X[COL[I]]
The memory latency of the access of
COL[I]
is exposed, since it is used to index into
the vector
X
. The access of the element of
X
, the computation of the product, and the
summation of the product on
R[ROW]
are all dependent on the memory latency of the
access of
COL[I]
.
Another common condition in floating-point codes where memory latency impact is
exacerbated is the presence of ambiguous memory dependencies. Consider the
incomplete Cholesky conjugate gradient excerpt kernel, again from the Livermore
Fortran Kernel suite.
II = n
IPNTP = 0
222 IPNT = IPNTP
IPNTP = IPNTP + II
II =
II/2
I = IPNTP + 1
cdir$ ivdep
DO 2 K = IPNT+2, IPNTP, 2
I = I+1
2 X[I] = X[K] - V[K] * X[K-1] - V[K-1] * X[K+1]
IF (II .GT. 1) GO TO 222