Check out the new USENIX Web site. next up previous
Next: 3.2 dgemm and block Up: 3. Some results Previous: 3. Some results

3.1 daxpy and ddot

daxpy and ddot are the two main level 1 BLAS, daxpy is a linear combination of vectors $y = \alpha . x + y$ and ddot is a dot product of the form $\alpha = x^T . y$ (the ``d'' before each name indicates that the BLAS use double precision floating point arithmetics).

Performances results for daxpy are presented figure [*] and acceleration is showed [*]. Observed results are typical for level 1 operations: we observe a peak when data fits into L1 cache and a smooth decrease when data does not fits in L1 but remains in L2. Performance from main memory is driven by memory bandwidth. Acceleration is quite good for large vectors especially when datas are in cache.

Figure: daxpy performances with 1 and 2 processors
\begin{figure} \begin{center} \epsfig{file=daxpy_ext2.eps,width=7cm} \end{center} \end{figure}

Figure: daxpy acceleration for 2 processors
\begin{figure} \begin{center} \epsfig{file=daxpy_ext2_acc.eps,width=7cm} \end{center} \end{figure}

Performance results for ddot are showed figure [*] and figure [*] for acceleration. Comments on performances results are the same as for daxpy but we observed that scaling is not as good as for daxpy: cache operation scaling is roughly 1.8 but remains good. On the other side memory operation scaling in poor ($\le 1.5$). To understand that we make some memory bandwidth measurements with very large vectors to not consider time spent in synchronization and the results are presented in table [*]: we see that single processor ddot use more than half of the theoretical peak memory bandwidth (the system uses pc100 SDRAM allowing 800e6 B/s memory bandwidth) and dual processor uses up to 75% of available bandwidth which seems very good for the test system.

Figure: ddot performances with 1 and 2 processors.
\begin{figure} \begin{center} \epsfig{file=ddot_ext.eps,width=7cm} \end{center} \end{figure}

Figure: ddot acceleration for 2 processors.
\begin{figure} \begin{center} \epsfig{file=ddot_ext_acc.eps,width=7cm} \end{center} \end{figure}


Table: memory bandwidth used by ddot with 1 and 2 processors.
nproc n memory bandwidth (1e6 B/s)
1 10000 440
1 100000 470
2 10000 590
2 100000 600

The daxpy and ddot BLAS show good acceleration with the blasth library when datas are present into cache memory, this behavior is in fact common to all level 1 operations since each component of vectors is used only one time in computation (no temporal locality). Operations on small vectors ($n \leq 1000$) will not scale due synchronization cost compared to the small number of floating point operations issued (n or 2.n for level 1 BLAS). The memory bandwidth is the key point for scalability when datas are out of cache which is always true for very large data sets.

next up previous
Next: 3.2 dgemm and block Up: 3. Some results Previous: 3. Some results
Thomas Guignon
2000-08-24