DISPOSICIONES GENERALES SOBRE LAS RETENCIONES APLICABLES A LA COPARTICIPACION DE IMPUESTOS

I set the goal to partition main memory area between DRAM and NVM such that system- level execution time and energy are within 20% of their respective global minima and the area of the NVM partition is minimized. Due to the first-order nature of the models I regard speedups and energy savings below 1.5-2x as noise and dismiss them. Minimizing the area of the NVM partition keeps system cost and lifetime closest to those of the baseline, as motivated below. Replacing a DRAM DIMM with an NVM DIMM does not reduce main memory cost, since for one NVM DIMM to cost less than one DRAM DIMM, NVM must cost less per bit for at least as many times as it is denser than DRAM (which does not hold even for NAND Flash, which is 16x denser but only 10x less expensive per bit than DRAM). Since NVM such as PCM and NAND Flash suffer from lower write endurance than DRAM, the less NVM is employed, the better it is for system lifetime.

Figures 3.4 to 3.7 show selected partitioning results and the respective speedups and energy savings. Figures 3.4 to 3.7 have the same format, where the horizontal axis shows workloads W0-W8 composed from different program sets according to (3.9). The bottom vertical axis shows the best partitioning (i.e., partitioning that meets the above goal) as the ratio of the NVM area over the total main memory area. The normalized NVM area ranges from 0 to 75%, since main memory comprises four DIMMs in total, where one DIMM is always DRAM to implement a hybrid with two partitions. That is, the partitioning options are one to three NVM DIMMs plus the DRAM-only baseline. The best partitioning found for execution time as the target metric is shown by bars, and that for execution energy is

Figure 3.4 shows partitioning results for the hybrids with HDD and workloads from themcf/soplexset. For workloads W0-W1 and W3-W4 the hybrids employing NAND Flash (II-L and II-H) offer significant improvements (17-19x) vs. the respective DRAM- only baselines, but the hybrids employing PCM (I-L and I-H) do not. This is so because hybrids II-L and II-H provide enough main memory capacity to fit the entire working sets of these workloads, and the benefit of eliminating HDD accesses is greater than the overhead of accessing the NAND Flash partition. At the same time, the density of PCM is 4x lower than that of NAND Flash, which makes the capacities of hybrids I-L and I-H too small to eliminate HDD accesses even when the area of the PCM partition is maximized to 75%. As a result, for these workloads the overhead of accessing the PCM partition is greater than the benefit of reducing the number of HDD accesses, and so the normalized best PCM area is 0%.

For W2 in Figure 3.4 hybrid II-L offers no improvements, despite that it can provide enough main memory capacity to fit the entire working set of the workload. This is so because the LU DRA policy, employed by the hybrid, does not allocate enough DRAM to themcfinstances to fit their first plateaus (Figure 3.3). Instead,soplexwins the DRAM capacity, since it has a lower utility of it. This results in a great number of migrations between the DRAM and NAND Flash partitions initiated by the instances ofmcf. The execution-time and energy overhead of these migrations exceeds the benefit of eliminating HDD accesses. On the contrary, hybrid II-H attains significant improvements (7x) for this workload thanks to the HU DRA policy, that allocates enough DRAM to themcfinstances to fit their first plateaus. Note that hybrids II-L and II-H offer equal improvements for workloads W0-W1 and W3-W4, because the LU and HU DRA policies result in equal capacity distributions.

For W5-W7 in Figure 3.4 hybrids I-L and I-H attain great improvements (10-34x), because the benefit of eliminating HDD accesses is greater than the overhead of accessing the PCM partition for these workloads. For W5, the hybrids offer greater improvements than hybrids II-L and II-H, since PCM is faster and more energy efficient than NAND Flash. For W6-W7 hybrids II-L and II-H are worse than their respective DRAM-only baselines, because the overhead of accessing the NAND Flash partition is greater than the benefit of eliminating HDD accesses. For W8 all four hybrids make no sense, since the workload is in-memory w.r.t. the baseline DRAM-only capacity.

Figure 3.5 shows results for the hybrids with HDD and workloads from thelbm/sjeng program set. The results can be explained similarly to those in Figure 3.4. For W0- W5 the hybrids attain great improvements (above 14x), because they provide enough main memory capacity to fit the entire working sets of the workloads, and the benefit of

Figure 3.5: Results for hybrids with HDD andlbm/sjengworkloads

Figure 3.6: Results for hybrids III-L and III-H andlbm/sjengworkloads

eliminating HDD accesses is greater than the overhead of accessing the NVM partition. Hybrids I-L and I-H offer greater improvements for these workloads than hybrids II-L and II-H, since PCM is faster and more energy efficient than NAND Flash. For W6-W8 all four hybrids are worse than their respective baselines, since these workloads are in-memory w.r.t. the baseline DRAM-only capacity.

As for the systems with SSD backing store, I find that for the workloads containing mcf, hybrids with PCM (III-L and III-H) provide either no benefit or not enough benefit for the partitioning goal set in the beginning of this section. At the same time, hybrids IV-L and IV-H are never better than their respective baselines for all workloads considered, because the access latencies and dynamic energies of NAND Flash are too close to those

Figure 3.7: Results for hybrids with HDD andCG/sjengworkloads

of SSD, and the overhead of accessing the NAND Flash partition is greater than the benefit of eliminating SSD accesses.

Figure 3.6 shows results for the hybrids with PCM, SSD, and workloads from the lbm/sjengprogram set. The results resemble those for hybrids I-L and I-H in Figure 3.5: The improvements are significant for W0-W5 (4-8x) but smaller than those offered by hybrids I-L and I-H in Figure 3.5, since the access latency and dynamic energy gaps between DRAM and SSD are smaller than those between DRAM and HDD.

The results for workloads containingCGand respective workloads containinglbm are similar, becauseCGandlbmhave similar miss curves (recall Figure 3.3). For instance, compare Figure 3.7 and Figure 3.5: The best partitionings are the same, althoughCG affects the improvements by having a much smaller fraction of writes and almost double

TCP Ucompared to those oflbm(Table 3.3).

Intuitively, hybrid memory offers speedups and energy savings compared to equal- area DRAM-only memory if the benefit of reducing the number of disk accesses is greater than the overhead of migrations between the hybrid partitions. However, for specific workloads speedups and energy savings can be relatively small (e.g., below 1.5x) and can depend on DRA (e.g., the case of W2 in Figure 3.4). Crystal comes in handy in such situations and quickly identifies promising design points. For instance, Crystal shows how the density of NAND Flash enables hybrids that offer significant improvements for W0-W1 and W3-W4 in Figure 3.4, while the density of PCM is not high enough to offer any improvements for these workloads. The shorter access latencies and higher energy efficiency of PCM compared to NAND Flash bear no advantage is such cases.

Finally, I observe that for all the memory technologies, hybrids, and workloads considered in this chapter, hybrid configurations that satisfy the partitioning goal minimize execution time at the same time as they minimizing execution energy, and speedups are similar to energy savings for each given hybrid and workload. In other words, execution time and energy follow the same trend for the technologies. This is so because the NVM access latencies and dynamic energies are worse than those of DRAM but better than those of disk. Ultimately, partitioning can be done for execution time even if the actual target metric is energy, and this further simplifies the use of Crystal. In the next section I validate the best partitionings identified by Crystal.