While accelerators offer much-needed gains in serial performance and energy efficiency, their integration into heterogeneous systems is primarily physical and their logical integration is incomplete. Accelerators are connected in ad-hoc ways with a variety of processor-accelerator communication overheads. Meanwhile, application and system software must deal with cumbersome synchronization interfaces, dedicated memory regions, and specialized data formats.
This paper investigates a key aspect of logical integration: the unification of accelerators and CPUs in a shared virtual and physical address space. A unified address space makes data structures and pointers globally visible, obviates the need for expensive and error-prone data marshaling between CPUs and accelerators, and un-burdens CPUs from pinning accelerator data pages in fixed locations in main memory, improving memory efficiency . Recent work tries to reduce transfer times with smarter packing and unpacking schemes [6, 7, 8, 9]; similarly, recent CUDA releases permit limited CPU/GPU virtual address sharing . However, none of these approaches solve the problem as generally and as flexibly as unified address spaces. A unified address space, for example, is a key component of the Heterogeneous System Architecture  specification promoted by the likes of AMD, Intel, NVIDIA, Qualcomm, ARM, and Samsung.
With its heterogeneous uniform memory access (hUMA) technology , AMD’s recent Berlin processor committed fully to HSA, and the academic community has responded with memory management unit (MMU) designs for GPUs [16, 17], one of the more mature acceleration technologies currently available. Both studies have shown that address translation overheads in GPUs can be brought down to the levels traditionally deemed acceptable in the CPU world, 5-15% of runtime.
This work goes beyond the state of the art by considering the general design space of MMU hardware for any abstract accelerator, extracting general principles of how to achieve efficient virtual-to-physical address translation. First, we taxonomize the diverse population of accelerators, organizing it along four key dimensions (Section 2). Second, we use those dimensions to explore a design space of generic accelerators, extracting principles for heterogeneous MMU design (Section 3). Finally, we close with a set of recommendations and strategies for address translation in heterogeneous systems (Section 4).
2 Taxonomy of Accelerators
Reasoning about accelerators in a general way requires careful understanding of the space of possible accelerators. While previous accelerator taxonomies have focused on their programming models 
, we classify accelerators in a hardware-centric way that defines the coverage and bounds of the design space exploration that follows in Section3. There are four key dimensions in this feature space.
Offload kernel size.
Accelerators run the gamut in terms of the amount of work they accept per invocation, from large, application-like GPGPU kernels to fine-grain operations such as vector instructions or DCTs. A range of engines such as transcoders, checksums, compression blocks, and facial recognition engines cover the middle ground.
Kernel speedup over software. Depending on how an accelerator is imlemented and its degree of programmability, it will offer different speedups on the kernel relative to a software implementation.
Characteristic reference pattern. The acceleration target and accelerator microarchitecture combine to produce a characteristic memory reference pattern for each accelerator. Some, such as FFT or data analytics, will be streaming, whereas others, such as highly-multithreaded-GPUs, will produce essentially random accesses. The list of possible reference patterns is unbounded, but we will cover three broad classes in our design space exploration.
Distance from CPU. Lastly, some accelerators are tightly coupled with a CPU while others are more distant. This is driven not only by integration choices, but also by the desired degree of autonomy from the CPU and its state.
3 Design Space Exploration
In this MMU design space exploration we will explicitly reason about the impact of each of these four dimensions on MMU design, both for the accelerator and when taking the CPU and accelerator memory management together as a whole in a heterogeneous system MMU.
3.1 Experimental Methodology
Here we lay out the key features of our design space exploration methodology.
Benchmarks. To focus on acceleration rather than parallelization, we use eight single-threaded benchmarks from SPEC (applu, art, astar, bwaves, cactus, gems, mcf, and swim) and two scientific applications (graph500 and gups). For each application, we simulate a 250M instruction simpoint trace. As there are no workloads that map to abstract accelerators, we use these general workloads, isolating acceleration targets as described below.
Identification of hotspots. To identify regions of each benchmark that might typically be targeted by an accelerator, we select hotspots from each trace. For these experiments we consider an instruction “hot” if it executes more than 100K times. Our heterogeneous MMU simulator, described below, sends uninterrupted sequences of hot instructions longer than a hotspot size threshold to run on the accelerator, with all other instructions executed by the CPU.
We consider the range of hotspot size thresholds shown in Figure 1 to capture the range of offload sizes seen in modern accelerators. For example, we consider three versions of applu, one with hotspots larger than 100 dynamic instructions, another with hotspots larger 400, and a third with hotspots larger than 1000, resulting in acceleration of 78%, 69%, and 40% respectively of the application’s dynamic instructions. Note on the x-axis of Figure 1 that these hotspot sizes range over three orders of magnitude, from hundreds to tens of thousands of instructions.
Accelerator reference patterns. To understand the impact an accelerator’s memory access pattern has on the MMU, the simulator can apply a transformation to the accelerator’s reference stream. These transformations change only the order in which the addresses are accessed, not the addresses themselves. Matching the breadth of accelerators found in Section 2, we use three patterns: original program order, random order (i.e., minimal locality), and sorted order, mimicking a streaming accelerator with high locality.
Heterogeneous MMU simulator. Unfortunately detailed CPU simulators are too slow to run workloads large enough for virtual memory studies [1, 2], and the issue is compounded here by our need to conduct a broad hardware design space exploration. Thus, like in other recent work [1, 2, 14, 15], our simulator is detailed with respect to the dynamics of the MMU but, because the core and cache configurations are not part of the target design space, we calibrate and use a first-order model.
The detailed part of the simulator models a spectrum of MMU configurations ranging from no address translation support on the accelerator – requiring the accelerator to fetch all address translations from the CPU – to full accelerator-based translation with a multithreaded page table walker. As input, it takes the instruction trace described above.
Like recent work on GPU MMUs [16, 17], we focus on dTLB accesses, which affect the system far more than iTLB accesses. Similarly, we assume x86-style, four-level, radix-tree page tables, specifically focusing 4KB page sizes instead of larger (2MB and 1GB) pages. While large pages likely reduce TLB miss rates, they also incur overheads (special OS algorithms for large page promotion, increased page traffic, pinning restrictions [13, 15]) that would not be properly captured by our experimental methods. We also assume, like other recent MMU work [14, 15, 16], the absence of page faults moving data from backing store to main memory, as most systems have sufficient memory to eliminate page faults in the steady state .
Each TLB’s access time, energy, and area are derived from CACTI 6.5 , while the page table walker area and power is characterized from RTL by Synopsys Design Compiler. For page table walk time, the simulator accepts a parameter derived from real performance counter measurements. Like past work [1, 2], this is reasonable provided that the cache configuration, which is the primary determinant of page table walk time, does not change. As cache configuration is not part of our design space, it does not.
The simulator computes overall execution time as thes sum of four terms: The MMU times are calculated in detail via the simulated trace, while the non-MMU terms are computed analytically: . The term is a simulator parameter that calibrates this model with each application’s performance counter-derived CPI when not walking the page table. The rationale again is that the core configuration is not part of our design space and thus this component of performance is not subject to significant change across our design space. The accelerator’s computation time term is very similar to that of the CPU, but with a speedup applied.
Simulator calibration and validation.
We calibrate and validate the system model using an Intel Xeon CPU with Sandybridge cores and a 4MB last-level cache. Each core has a 64-entry and 512-entry L1 and L2 TLB. On the calibration side, this is the server on which we compute each application’s CPI and average page walk time as input parameters for the simulator. On the validation side, we configure the simulator to match this machine’s MMU and compare how well the simulator tracks real-system performance. Across all 10 benchmarks, the the coefficient of determination (R squared value) of estimated versus actual execution time of 0.955.
Experimental baseline and normalization. In the experiments that follow, much of the data will be normalized to the performance, MMU area, and MMU energy of the Sandybridge configuration. When relative performance is plotted, it is the performance of the whole application relative to unaccelerated software executing on the Sandybridge.
3.2 CPU-Managed Address Translation
We first examine the dynamics CPU-managed address translation. Here, accelerators invoke the CPU to help translate virtual addresses, so in all of these configurations the CPU is ultimately responsible for address translation. In the first category, the accelerator has no MMU and probes the CPU’s MMU on every reference. In the second, the accelerator maintains an L1 TLB, probing the CPU only on an L1 miss. In both cases, remote probes of the CPU’s MMU access the CPU’s L2 TLB, as L1 TLBs are tightly coupled with the CPU pipeline and would require costly arbitration logic to coordinate CPU accesses with remote accelerator accesses.
In the following experiments, we measure the application runtime if hotspots are offloaded to an accelerator that offers 10x speedup and the remainder of the code is run on the CPU with the baseline MMU configuration. Figure 2 plots the results, with each datapoint representing an average across 28 experiments – 10 applications with 2 or 3 hotspot sizes per application. For reference, we have highlighted two key points: the runtime of the unaccelerated, software-only application – 100% – and the lower bound on overall runtime given Amdahl’s law – 32%.
No accelerator MMU. We first consider scenarios where the accelerator has no MMU, and all accelerator memory references look up the CPU L2 TLB. Intuitively, paying a remote communication cost for every memory reference quickly swamps the accelerator’s original benefits, and this is borne out by the data in Figure 2 where we see that even with an aggressively low 1ns communication delay between the accelerator and the CPU, any acceleration benefits are more than outweighted by the address translation activity back and forth between accelerator and CPU.
One component of the cost of probing the CPU MMU is the overhead of handling L2 TLB misses, so there may be system-wide benefits to increasing CPU L2 TLB size, boosting the hit rate, and reducing average address translation time. The second data series in Figure 2 plots the average application runtime when the CPU L2 TLB capacity is quadrupled – from 256 to 1024 entries – and we see that this boost in resources has no impact on the runtimes, suggesting that communication costs dominate any benefits of acceleration when the accelerator has no MMU hardware of its own.
Accelerator with L1 TLB filter. Intuitively, an L1 TLB on the accelerator would filter communication between the accelerator and CPU. Figure 2 also plots the impact of a 64-entry, 4-way set-associative L1 TLB filter – the largest of four filters we tried. We found that such a filter does improve performance, yet despite achieving hit rates in excess of 96-98% this TLB is insufficient to eliminate communication-induced overheads. Even under optimistic delays of 1-10ns and reference patterns with maximal locality, address translation eats half to three quarters of the accelerator’s potential savings.
Overall, these two analyses signal strongly that the only feasible way to support a unified address space with realistic accelerator-CPU is to remove CPU-accelerator communication from the picture, by empowering an accelerator to walk the page table. The following experiments explore the tradeoffs in this space.
3.3 MMUs For Accelerators
There are many potential MMU implementations for accelerators, and understanding the relative importance of resources and topology (e.g., single-level or two-level) is critical for a resource-efficient design.
First, the right MMU design is highly application- and reference pattern-dependent, with a potential co-design opportunity between candidate accelerator microarchitectures and their corresponding MMUs. For example, is it preferable to have a smaller accelerator with little locality and a large MMU or a larger accelerator with better locality and a small MMU? The answer depends on the particulars of the application and accelerators and MMUs, suggesting that accelerator MMUs are best viewed as specialized, application-specific circuits, just like the accelerators they support.
Second, when given an MMU area budget, it is not at all obvious which components – L1 TLBs, L2 TLBs, or PTWs – are most critical to performance. The answer depends on the cost-benefit of the various components which is again application-dependent. Somewhat surprisingly, we find that PTW organization is sometimes more critical than the other components, a fact that is usually ignored by CPUs , which focus on improving TLB organization. This, in turn, suggests that there may be substantial value in exploring the design of novel page tables, page table locking and scalability .
Accelerator MMU design space. In this analysis, we evaluate 54 acclerator MMU configurations for each application. While we find that speedups and hotspots sizes influence the results slightly, the relative benefits and trends of various MMU organizations remain unaffected regardless of the exact accelerator speed or hotspot size. Therefore, we will present only acceleration factors of 10x on the middle hotspot size for each application.
The 54 MMU configurations are as follows.
First there are 6 page-table-walker (PTW) designs where the accelerator MMU has no TLBs or other caches, just a hardware page table walker. While a standard CPU PTW resolves TLB misses one at a time, recent work has shown the benefits of multithreaded PTWs that resolve multiple TLB misses together , so we examine PTWs that resolve 1, 2, 4, 8, 16, and 32 translations at a time.
Second, we assess the benefits of placing 32-entry (2-way), and 64-entry (4-way) L1 TLBs in tandem with PTWs of different multithreaded factors for a total of 12 L1 TLB plus PTW configurations.
Finally, we incorporate a second level into the TLB hierarchy with 256, 512, and 1024-entry TLBs – the sizes commercially available for CPUs  – for 36 three-level MMU hierarchies.
As additional reference points, we mark two values when presenting these designs in Figure 4, the minimum runtime as bounded by Amdahl’s law, and a slightly less optimistic scenario where every accelerator memory reference is met with a hit in our smallest, fastest L1 TLB (32-entry, 2-way associative).
Mind the gap. The most surprising takeaway from this design space exploration, as seen in Figure 4, is the often-substantial gap between the lower bound on accelerated runtime (Amdahl’s bound) and an ideal L1 TLB with 100% hits. This gap, as high as 40% in some cases, arises because even a perfect L1 TLB does have a hit time, and even that can become a bottleneck for the accelerator. Reclaiming this performance loss requires a fundamental rethink of address translation.
MMU structural analysis. Analyzing the area-performance tradeoffs of these 54 MMU configurations, we derive several general insights.
In limited circumstances, TLB-less MMUs with only a page table walker can be viable design options – i.e., the address translation time does not entirely negate the acceleration speedups. However, not only do PTWs have to be heavily multithreaded – e.g., bwaves requires a 32-way PTW – and thus fairly large, there are still many benchmarks – e.g., applu – where in the best case, the PTW-only MMU remains more than 20% away from the ideal acceleration. In fact, astar, cactus, and gups with 32-way parallelized PTWs outperform the idealized L1 TLB, with the parallel walks of well-cached page table entries beating many small L1 TLB hits. This suggests that PTW organization is crucial to overall performance, with multithreading being an important design variable.
Despite the cases described above, the addition of an L1 TLB typically improves performance beyond a bare PTW. For example, applu, art, and swim make such effective use of an L1 TLB that they achieve close to the ideal TLB ideal, even when paired with small serial PTWs. In other benchmarks, such as mcf, graph500, and cactus, the benefits are more gradual, with roughly a 50% performance improvement from the smallest to the largest L1 TLBs. Here, PTW multithreading remains important, particularly when the L1 TLB is small. Overall, these configurations indicate that L1 TLBs can often boost performance, but the gains quickly become incremental as the L1 TLB grows.
Finally, we see that L2 TLBs provide improved performance for little area. For example, the insertion of even a 256-entry L2 TLB into any hierarchy gives an automatic 5-10% performance boost. However, as with the L1, the benefits of growing the L2 are incremental, with a 1024-entry L2 TLB outperforming a 512-entry TLB by just 2-3%. Overall, for a given area budget, it appears more performance-effective to invest in PTW multithreading rather than growing beyond 512-entry L2 TLBs.
Impact of reference patterns. Finally, we assess the impact of memory reference pattern reordering on these results. Figure 4 picks four benchmarks (astar, cactus, gups, and mcf) which cover the range of observed behavior when access patterns change. In general, the streaming reference pattern offers the most benefit when total accelerator MMU area is small. This makes sense since larger MMUs attain higher reach and process page table walks more efficiently, making them less sensitive to reference pattern. At larger MMU sizes, the original program order and streaming orders tend to converge. However, random access remains noticeably worse for astar and mcf, with atleast a 10% performance gap in most cases. Overall, however, these experiments suggest that the lower the locality, the more valuable larger MMUs are.
3.4 System-level MMU Organization
In the final set of experiments, we explore area- and energy-efficient system-wide MMUs – i.e., MMUs that support both the CPU and an accelerator.
The results indicate that area and energy analysis of system-wide MMU resources is nuanced and must take into account not only MMU resources but interactions with other on-chip structures such as accelerators and caches. As in Section 3.3, we find that system-level MMU design hinges on the workloads, suggesting there are careful strategic decisions to be made as to which resources are private – e.g., L1 TLBs – and which are shared – e.g., a large, heavily multithreaded page table walker.
Furthermore, our analysis on the energy tradeoffs between additional address translation hardware versus the cache accesses they eliminate matches well-known observations that a large fraction of system energy on today’s chips is expended on data movement . We find that in cases like address translation, much of this data movement – i.e., page table walks – can be mitigated with TLBs.
Finally, although one might initially expect that MMU design choices would change depending on the speedup enjoyed by the accelerator, we found that the overall trends are in fact largely unchanged. Streaming references, as expected, can get away with smaller MMUs, expending lower energy, to achieve the same performance while randomized references are slightly worse on both metrics.
System-level design space. As in Section 3.3 we assume an acceleration speedup of 10x and focus on the medium sized hotspots. Figure 6 plots the area-performance trade-offs of 486 system-wide MMU configurations: the 54 accelerator MMUs explored in the previous section crossed with 9 different CPU MMU configurations. In this plot, we have highlighted the area-optimal designs, the energy-optimal designs, and the designs that are both energy- and area-optimal.
MMU structural analysis. As is Figure 6 shows, the energy- and area- Pareto optimal designs only rarely overlap. It turns out that the area and energy impacts of MMU components are very different. For example, adding even a small TLB for the accelerator dramatically reduces the number of page table walks, which significantly reduces the page table walk’s L1, L2, and last-level cache accesses. Since caches – particularly large multi-megabyte ones – expend more access energy than smaller 32-entry or 64-entry TLBs, the overall area increases with the addition of TLBs, but the overall energy decreases. Only when TLBs are so overprovisioned that they no longer conserve energy, do energy and area rise together.
CPU and accelerator resource split. Figure 6 reveals how total MMU area and energy for the optimal designs is split between the CPU and accelerator sides. We see little pattern in the split. Spending an increased share of system-wide MMU area on the accelerator side does not correlate with an increase in address translation energy on the accelerator side. For example, gems, which executes few of its instructions on the accelerator, devotes most of its energy to the CPU MMU, until the accelerator MMU gets very large, expending a lot of energy to improve performance just incrementally. This also reinforces the earlier observation that area and energy behave quite differently as resources.
4 General Strategies and
This design space exploration has yielded a number of insights into the dynamics of heterogeneous MMUs.
Relying on the CPU MMU to support a unified address space across accelerators of any granularity, but particularly small, is not a viable option. The overhead of even infrequent translations with 1ns accelerator-CPU communication will wipe out the benefits of using accelerator (Section 3.2).
For complete address translation on an accelerator, a page table walker alone, if sufficiently parallelized, can outperform hierarchies that include TLBs (Section 3.3)
Applications respond to MMUs on acclerators in very different ways, with each application prefering a different MMU configuration (Section 3.3). Moreover, even an ideal (100% hit rate) L1 TLB can be a performance bottleneck on an accelerator. To maximize performance, MMUs on accelerators are best designed as application-specific MMUs, as specialized to the application as the accelerator itself.
To achieve good performance with a system-wide MMU area budget, accelerator and CPU MMU configurations must be carefully chosen with an understanding of the interaction among various components – e.g. TLBs and page table walkers – across the CPU and accelerators (Section 3.4). Among area-optimal designs, accelerator MMUs consume a significant portion of the area.
While one may expect larger MMUs to expend more energy, this is usually not the case because large TLBs eliminate energy-intensive memory references from page table walks (Section 3.4). Therefore, energy-optimal MMU configurations are often different from area-optimal designs.
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