ARSep 1, 2022Code
Hermes: Accelerating Long-Latency Load Requests via Perceptron-Based Off-Chip Load PredictionRahul Bera, Konstantinos Kanellopoulos, Shankar Balachandran et al.
Long-latency load requests continue to limit the performance of high-performance processors. To increase the latency tolerance of a processor, architects have primarily relied on two key techniques: sophisticated data prefetchers and large on-chip caches. In this work, we show that: 1) even a sophisticated state-of-the-art prefetcher can only predict half of the off-chip load requests on average across a wide range of workloads, and 2) due to the increasing size and complexity of on-chip caches, a large fraction of the latency of an off-chip load request is spent accessing the on-chip cache hierarchy. The goal of this work is to accelerate off-chip load requests by removing the on-chip cache access latency from their critical path. To this end, we propose a new technique called Hermes, whose key idea is to: 1) accurately predict which load requests might go off-chip, and 2) speculatively fetch the data required by the predicted off-chip loads directly from the main memory, while also concurrently accessing the cache hierarchy for such loads. To enable Hermes, we develop a new lightweight, perceptron-based off-chip load prediction technique that learns to identify off-chip load requests using multiple program features (e.g., sequence of program counters). For every load request, the predictor observes a set of program features to predict whether or not the load would go off-chip. If the load is predicted to go off-chip, Hermes issues a speculative request directly to the memory controller once the load's physical address is generated. If the prediction is correct, the load eventually misses the cache hierarchy and waits for the ongoing speculative request to finish, thus hiding the on-chip cache hierarchy access latency from the critical path of the off-chip load. Our evaluation shows that Hermes significantly improves performance of a state-of-the-art baseline. We open-source Hermes.
GNDec 9, 2022Code
TargetCall: Eliminating the Wasted Computation in Basecalling via Pre-Basecalling FilteringMeryem Banu Cavlak, Gagandeep Singh, Mohammed Alser et al.
Basecalling is an essential step in nanopore sequencing analysis where the raw signals of nanopore sequencers are converted into nucleotide sequences, i.e., reads. State-of-the-art basecallers employ complex deep learning models to achieve high basecalling accuracy. This makes basecalling computationally inefficient and memory-hungry, bottlenecking the entire genome analysis pipeline. However, for many applications, the majority of reads do no match the reference genome of interest (i.e., target reference) and thus are discarded in later steps in the genomics pipeline, wasting the basecalling computation. To overcome this issue, we propose TargetCall, the first pre-basecalling filter to eliminate the wasted computation in basecalling. TargetCall's key idea is to discard reads that will not match the target reference (i.e., off-target reads) prior to basecalling. TargetCall consists of two main components: (1) LightCall, a lightweight neural network basecaller that produces noisy reads; and (2) Similarity Check, which labels each of these noisy reads as on-target or off-target by matching them to the target reference. Our thorough experimental evaluations show that TargetCall 1) improves the end-to-end basecalling runtime performance of the state-of-the-art basecaller by 3.31x while maintaining high (98.88%) recall in keeping on-target reads, 2) maintains high accuracy in downstream analysis, and 3) achieves better runtime performance, throughput, recall, precision, and generality compared to prior works. TargetCall is available at https://github.com/CMU-SAFARI/TargetCall.
MSApr 3, 2023Code
TransPimLib: A Library for Efficient Transcendental Functions on Processing-in-Memory SystemsMaurus Item, Juan Gómez-Luna, Yuxin Guo et al.
Processing-in-memory (PIM) promises to alleviate the data movement bottleneck in modern computing systems. However, current real-world PIM systems have the inherent disadvantage that their hardware is more constrained than in conventional processors (CPU, GPU), due to the difficulty and cost of building processing elements near or inside the memory. As a result, general-purpose PIM architectures support fairly limited instruction sets and struggle to execute complex operations such as transcendental functions and other hard-to-calculate operations (e.g., square root). These operations are particularly important for some modern workloads, e.g., activation functions in machine learning applications. In order to provide support for transcendental (and other hard-to-calculate) functions in general-purpose PIM systems, we present \emph{TransPimLib}, a library that provides CORDIC-based and LUT-based methods for trigonometric functions, hyperbolic functions, exponentiation, logarithm, square root, etc. We develop an implementation of TransPimLib for the UPMEM PIM architecture and perform a thorough evaluation of TransPimLib's methods in terms of performance and accuracy, using microbenchmarks and three full workloads (Blackscholes, Sigmoid, Softmax). We open-source all our code and datasets at~\url{https://github.com/CMU-SAFARI/transpimlib}.
GNFeb 4
Processing-in-memory for genomics workloadsWilliam Andrew Simon, Leonid Yavits, Konstantina Koliogeorgi et al.
Low-cost, high-throughput DNA and RNA sequencing (HTS) data is the backbone of the life sciences. Genome sequencing is now becoming a part of Predictive, Preventive, Personalized, and Participatory (termed 'P4') medicine. All genomic data are currently processed in energy-hungry computer clusters and centers, necessitating data transfer, consuming substantial energy, and wasting valuable time. Therefore, there is a need for fast, energy-efficient, and cost-efficient technologies that enable genomics research without requiring data centers and cloud platforms. We recently launched the BioPIM Project to leverage emerging processing-in-memory (PIM) technologies to enable energy- and cost-efficient analysis of bioinformatics workloads. The BioPIM Project focuses on co-designing algorithms and data structures commonly used in genomics with several PIM architectures to achieve the highest cost, energy, and time savings.
ARMar 20
Accelerating Triangle Counting with Real Processing-in-Memory SystemsLorenzo Asquini, Manos Frouzakis, Juan Gómez-Luna et al.
Triangle Counting (TC) is a procedure that involves enumerating the number of triangles within a graph. It has important applications in numerous fields, such as social or biological network analysis and network security. TC is a memory-bound workload that does not scale efficiently in conventional processor-centric systems due to several memory accesses across large memory regions and low data reuse. However, recent Processing-in-Memory (PIM) architectures present a promising solution to alleviate these bottlenecks. Our work presents the first TC algorithm that leverages the capabilities of the UPMEM system, the first commercially available PIM architecture, while at the same time addressing its limitations. We use a vertex coloring technique to avoid expensive communication between PIM cores and employ reservoir sampling to address the limited amount of memory available in the PIM cores' DRAM banks. In addition, our work makes use of the Misra-Gries summary to speed up counting triangles on graphs with high-degree nodes and uniform sampling of the graph edges for quicker approximate results. Our PIM implementation surpasses state-of-the-art CPU-based TC implementations when processing dynamic graphs in Coordinate List format, showcasing the effectiveness of the UPMEM architecture in addressing TC's memory-bound challenges.
ARApr 10, 2024Code
PIM-Opt: Demystifying Distributed Optimization Algorithms on a Real-World Processing-In-Memory SystemSteve Rhyner, Haocong Luo, Juan Gómez-Luna et al.
Modern Machine Learning (ML) training on large-scale datasets is a very time-consuming workload. It relies on the optimization algorithm Stochastic Gradient Descent (SGD) due to its effectiveness, simplicity, and generalization performance. Processor-centric architectures (e.g., CPUs, GPUs) commonly used for modern ML training workloads based on SGD are bottlenecked by data movement between the processor and memory units due to the poor data locality in accessing large datasets. As a result, processor-centric architectures suffer from low performance and high energy consumption while executing ML training workloads. Processing-In-Memory (PIM) is a promising solution to alleviate the data movement bottleneck by placing the computation mechanisms inside or near memory. Our goal is to understand the capabilities of popular distributed SGD algorithms on real-world PIM systems to accelerate data-intensive ML training workloads. To this end, we 1) implement several representative centralized parallel SGD algorithms on the real-world UPMEM PIM system, 2) rigorously evaluate these algorithms for ML training on large-scale datasets in terms of performance, accuracy, and scalability, 3) compare to conventional CPU and GPU baselines, and 4) discuss implications for future PIM hardware and highlight the need for a shift to an algorithm-hardware codesign. Our results demonstrate three major findings: 1) The UPMEM PIM system can be a viable alternative to state-of-the-art CPUs and GPUs for many memory-bound ML training workloads, especially when operations and datatypes are natively supported by PIM hardware, 2) it is important to carefully choose the optimization algorithms that best fit PIM, and 3) the UPMEM PIM system does not scale approximately linearly with the number of nodes for many data-intensive ML training workloads. We open source all our code to facilitate future research.
CRMay 19
Taking Cryptography Out of the Data Path via Near-Memory Processing in DRAMNicola Barcarolo, Brahmaiah Gandham, Mohammad Sadrosadati et al.
Cryptographic algorithms such as AES-128 and SHA-256 are fundamental to ensuring data security and integrity. Although these algorithms are computationally efficient, their performance is often constrained by the processor-centric architectures (e.g., CPUs, GPUs), primarily due to the memory bottleneck. This constraint leads to increased latency and higher energy consumption, particularly when handling large volumes of data. To overcome these challenges, Processing-in-Memory (PIM) has emerged as a promising architectural paradigm, allowing computation to occur directly within or near memory units. By minimizing data movement between the processor and memory units, PIM can significantly accelerate cryptographic algorithms while improving energy efficiency. Several pieces of prior work have demonstrated the effectiveness of PIM at fundamentally accelerating cryptographic algorithms. However, none of the prior works have extensively demonstrated the potential of a real-world PIM system. In this paper, we want to investigate the potential and limitations of real-world PIM in accelerating cryptographic algorithms. As part of our methodology, the UPMEM PIM architecture is used to assess the scalability of cryptographic algorithms. When these algorithms operate on a single rank, their performance remains below that of modern CPUs. However, distributing the computation across multiple ranks significantly enhances performance. When all available ranks are utilized, real-world PIM can accelerate cryptographic algorithms more effectively.
ARFeb 26, 2024Code
PyGim: An Efficient Graph Neural Network Library for Real Processing-In-Memory ArchitecturesChristina Giannoula, Peiming Yang, Ivan Fernandez et al.
Graph Neural Networks (GNNs) are emerging ML models to analyze graph-structure data. Graph Neural Network (GNN) execution involves both compute-intensive and memory-intensive kernels, the latter dominates the total time, being significantly bottlenecked by data movement between memory and processors. Processing-In-Memory (PIM) systems can alleviate this data movement bottleneck by placing simple processors near or inside to memory arrays. In this work, we introduce PyGim, an efficient ML library that accelerates GNNs on real PIM systems. We propose intelligent parallelization techniques for memory-intensive kernels of GNNs tailored for real PIM systems, and develop handy Python API for them. We provide hybrid GNN execution, in which the compute-intensive and memory-intensive kernels are executed in processor-centric and memory-centric computing systems, respectively. We extensively evaluate PyGim on a real-world PIM system with 1992 PIM cores using emerging GNN models, and demonstrate that it outperforms its state-of-the-art CPU counterpart on Intel Xeon by on average 3.04x, and achieves higher resource utilization than CPU and GPU systems. Our work provides useful recommendations for software, system and hardware designers. PyGim is publicly available at https://github.com/CMU-SAFARI/PyGim.
CRMay 13
HE-PIM: Demystifying Homomorphic Operations on a Real-world Processing-in-Memory SystemHarshita Gupta, Mayank Kabra, Jaewoo Park et al.
Homomorphic encryption (HE) enables computation over encrypted data, offering strong privacy guarantees for untrusted computing environments. Practical adoption remains limited by high computational complexity, large ciphertext sizes, and substantial data movement. Processor-centric architectures (CPUs, GPUs, ASICs) hit fundamental bottlenecks on HE workloads because ciphertexts are large, data locality is low, and primitives such as relinearization and bootstrapping repeatedly access large auxiliary metadata. Processing-In-Memory (PIM) is a promising mitigation by computing near or inside memory. Prior PIM proposals for HE either do not target real-world PIM systems or cover only a narrow set of operations. We comprehensively characterize HE operations on a real-world, general-purpose PIM system. We implement a complete set of HE kernels used by emerging applications (databases, machine learning) on the UPMEM PIM system, evaluate performance and scalability, compare against CPU and GPU baselines, and discuss implications for future PIM hardware. Our results demonstrate four major findings. (1) HE-based applications expose distinct bottlenecks across execution stages: some kernels are compute-bound due to modular arithmetic, while others are memory-bound due to large ciphertexts and intermediate data. These bottlenecks are exacerbated by limited per-core compute and per-bank capacity, which force frequent data movement. (2) The dominant compute bottleneck is the lack of native 64-bit modular integer multiplication, a key HE primitive. (3) Limited per-bank memory capacity is the second major bottleneck, since HE ciphertexts and auxiliary metadata do not fit and require inter-bank movement. (4) Despite these limits, PIM can be a viable alternative to state-of-the-art CPU and GPU systems for HE when equipped with native modular multiplication and efficient inter-PIM data movement.
ARMar 26, 2025Code
Harmonia: A Multi-Agent Reinforcement Learning Approach to Data Placement and Migration in Hybrid Storage SystemsRakesh Nadig, Vamanan Arulchelvan, Rahul Bera et al.
Hybrid storage systems (HSS) integrate multiple storage devices with diverse characteristics to deliver high performance and capacity at low cost. The performance of an HSS highly depends on the effectiveness of two key policies: (1) the data-placement policy, which determines the best-fit storage device for incoming data, and (2) the data-migration policy, which dynamically rearranges stored data (i.e., prefetches hot data and evicts cold data) across the devices to sustain high HSS performance. Prior works optimize either data placement or data migration in isolation, which leads to suboptimal HSS performance. Unfortunately, no prior work tries to optimize both policies together. Our goal is to design a holistic data-management technique that optimizes both data-placement and data-migration policies to fully exploit the potential of an HSS, and thus significantly improve system performance. We propose Harmonia, a multi-agent reinforcement learning (RL)-based data-management technique that employs two lightweight autonomous RL agents, a data-placement agent and a data-migration agent, that adapt their policies for the current workload and HSS configuration while coordinating with each other to improve overall HSS performance. We evaluate Harmonia on real HSS configurations with up to four heterogeneous storage devices and seventeen data-intensive workloads. On performance-optimized (cost-optimized) HSS with two storage devices, Harmonia outperforms the best-performing prior approach by 49.5% (31.7%) on average. On an HSS with three (four) devices, Harmonia outperforms the best-performing prior work by 37.0% (42.0%) on average. Harmonia's performance benefits come with low latency (240ns for inference) and storage overheads (206 KiB in DRAM for both RL agents combined). We will open-source Harmonia's implementation to aid future research on HSS.
LGMay 7, 2024
SwiftRL: Towards Efficient Reinforcement Learning on Real Processing-In-Memory SystemsKailash Gogineni, Sai Santosh Dayapule, Juan Gómez-Luna et al.
Reinforcement Learning (RL) trains agents to learn optimal behavior by maximizing reward signals from experience datasets. However, RL training often faces memory limitations, leading to execution latencies and prolonged training times. To overcome this, SwiftRL explores Processing-In-Memory (PIM) architectures to accelerate RL workloads. We achieve near-linear performance scaling by implementing RL algorithms like Tabular Q-learning and SARSA on UPMEM PIM systems and optimizing for hardware. Our experiments on OpenAI GYM environments using UPMEM hardware demonstrate superior performance compared to CPU and GPU implementations.
ARFeb 21, 2025
PAPI: Exploiting Dynamic Parallelism in Large Language Model Decoding with a Processing-In-Memory-Enabled Computing SystemYintao He, Haiyu Mao, Christina Giannoula et al.
Large language models (LLMs) are widely used for natural language understanding and text generation. An LLM model relies on a time-consuming step called LLM decoding to generate output tokens. Several prior works focus on improving the performance of LLM decoding using parallelism techniques, such as batching and speculative decoding. State-of-the-art LLM decoding has both compute-bound and memory-bound kernels. Some prior works statically identify and map these different kernels to a heterogeneous architecture consisting of both processing-in-memory (PIM) units and computation-centric accelerators. We observe that characteristics of LLM decoding kernels (e.g., whether or not a kernel is memory-bound) can change dynamically due to parameter changes to meet user and/or system demands, making (1) static kernel mapping to PIM units and computation-centric accelerators suboptimal, and (2) one-size-fits-all approach of designing PIM units inefficient due to a large degree of heterogeneity even in memory-bound kernels. In this paper, we aim to accelerate LLM decoding while considering the dynamically changing characteristics of the kernels involved. We propose PAPI (PArallel Decoding with PIM), a PIM-enabled heterogeneous architecture that exploits dynamic scheduling of compute-bound or memory-bound kernels to suitable hardware units. PAPI has two key mechanisms: (1) online kernel characterization to dynamically schedule kernels to the most suitable hardware units at runtime and (2) a PIM-enabled heterogeneous computing system that harmoniously orchestrates both computation-centric processing units and hybrid PIM units with different computing capabilities. Our experimental results on three broadly-used LLMs show that PAPI achieves 1.8$\times$ and 11.1$\times$ speedups over a state-of-the-art heterogeneous LLM accelerator and a state-of-the-art PIM-only LLM accelerator, respectively.
ARNov 19, 2025
A Tensor Compiler for Processing-In-Memory ArchitecturesPeiming Yang, Sankeerth Durvasula, Ivan Fernandez et al.
Processing-In-Memory (PIM) devices integrated with high-performance Host processors (e.g., GPUs) can accelerate memory-intensive kernels in Machine Learning (ML) models, including Large Language Models (LLMs), by leveraging high memory bandwidth at PIM cores. However, Host processors and PIM cores require different data layouts: Hosts need consecutive elements distributed across DRAM banks, while PIM cores need them within local banks. This necessitates data rearrangements in ML kernel execution that pose significant performance and programmability challenges, further exacerbated by the need to support diverse PIM backends. Current compilation approaches lack systematic optimization for diverse ML kernels across multiple PIM backends and may largely ignore data rearrangements during compute code optimization. We demonstrate that data rearrangements and compute code optimization are interdependent, and need to be jointly optimized during the tuning process. To address this, we design DCC, the first data-centric ML compiler for PIM systems that jointly co-optimizes data rearrangements and compute code in a unified tuning process. DCC integrates a multi-layer PIM abstraction that enables various data distribution and processing strategies on different PIM backends. DCC enables effective co-optimization by mapping data partitioning strategies to compute loop partitions, applying PIM-specific code optimizations and leveraging a fast and accurate performance prediction model to select optimal configurations. Our evaluations in various individual ML kernels demonstrate that DCC achieves up to 7.68x speedup (2.7x average) on HBM-PIM and up to 13.17x speedup (5.75x average) on AttAcc PIM backend over GPU-only execution. In end-to-end LLM inference, DCC on AttAcc accelerates GPT-3 and LLaMA-2 by up to 7.71x (4.88x average) over GPU.
CLJun 19, 2025
REIS: A High-Performance and Energy-Efficient Retrieval System with In-Storage ProcessingKangqi Chen, Andreas Kosmas Kakolyris, Rakesh Nadig et al.
Large Language Models (LLMs) face an inherent challenge: their knowledge is confined to the data that they have been trained on. To overcome this issue, Retrieval-Augmented Generation (RAG) complements the static training-derived knowledge of LLMs with an external knowledge repository. RAG consists of three stages: indexing, retrieval, and generation. The retrieval stage of RAG becomes a significant bottleneck in inference pipelines. In this stage, a user query is mapped to an embedding vector and an Approximate Nearest Neighbor Search (ANNS) algorithm searches for similar vectors in the database to identify relevant items. Due to the large database sizes, ANNS incurs significant data movement overheads between the host and the storage system. To alleviate these overheads, prior works propose In-Storage Processing (ISP) techniques that accelerate ANNS by performing computations inside storage. However, existing works that leverage ISP for ANNS (i) employ algorithms that are not tailored to ISP systems, (ii) do not accelerate data retrieval operations for data selected by ANNS, and (iii) introduce significant hardware modifications, limiting performance and hindering their adoption. We propose REIS, the first ISP system tailored for RAG that addresses these limitations with three key mechanisms. First, REIS employs a database layout that links database embedding vectors to their associated documents, enabling efficient retrieval. Second, it enables efficient ANNS by introducing an ISP-tailored data placement technique that distributes embeddings across the planes of the storage system and employs a lightweight Flash Translation Layer. Third, REIS leverages an ANNS engine that uses the existing computational resources inside the storage system. Compared to a server-grade system, REIS improves the performance (energy efficiency) of retrieval by an average of 13x (55x).
ARJun 10, 2021
CODIC: A Low-Cost Substrate for Enabling Custom In-DRAM Functionalities and OptimizationsLois Orosa, Yaohua Wang, Mohammad Sadrosadati et al.
DRAM is the dominant main memory technology used in modern computing systems. Computing systems implement a memory controller that interfaces with DRAM via DRAM commands. DRAM executes the given commands using internal components (e.g., access transistors, sense amplifiers) that are orchestrated by DRAM internal timings, which are fixed foreach DRAM command. Unfortunately, the use of fixed internal timings limits the types of operations that DRAM can perform and hinders the implementation of new functionalities and custom mechanisms that improve DRAM reliability, performance and energy. To overcome these limitations, we propose enabling programmable DRAM internal timings for controlling in-DRAM components. To this end, we design CODIC, a new low-cost DRAM substrate that enables fine-grained control over four previously fixed internal DRAM timings that are key to many DRAM operations. We implement CODIC with only minimal changes to the DRAM chip and the DDRx interface. To demonstrate the potential of CODIC, we propose two new CODIC-based security mechanisms that outperform state-of-the-art mechanisms in several ways: (1) a new DRAM Physical Unclonable Function (PUF) that is more robust and has significantly higher throughput than state-of-the-art DRAM PUFs, and (2) the first cold boot attack prevention mechanism that does not introduce any performance or energy overheads at runtime.
CRFeb 19, 2019
Dataplant: Enhancing System Security with Low-Cost In-DRAM Value Generation PrimitivesLois Orosa, Yaohua Wang, Ivan Puddu et al.
DRAM manufacturers have been prioritizing memory capacity, yield, and bandwidth for years, while trying to keep the design complexity as simple as possible. DRAM chips do not carry out any computation or other important functions, such as security. Processors implement most of the existing security mechanisms that protect the system against security threats, because 1) executing security mechanisms usually require non-trivial computational capabilities (e.g., encryption), and 2) commodity DRAM chips are not designed to perform computations or tasks other than data storage. In this work, we advocate for DRAM as a key component for providing security mechanisms to the system. To this end, we propose Dataplant, a new class of low-cost, high-performance, and reliable security primitives that can be integrated in commodity DRAM chips with minimal changes. The main idea of Dataplant is to slightly modify the internal DRAM timing signals to expose the inherent process variation found in all DRAM chips for generating unpredictable but reproducible values (e.g., keys) within DRAM. We use Dataplant to build two new security mechanisms. First, a new Dataplant-based physical unclonable function (PUF) with non-destructive read-out, low evaluation latency, robust responses, resiliency to temperature changes, and data-independent responses. Second, a new cold boot attack prevention mechanism that automatically destroys all data within DRAM on every power cycle with zero run-time energy and latency overheads. Using a combination of detailed simulations and experiments with 136 real commodity DRAM chips, we show that our Dataplant-based PUF has 1.8x higher throughput than the best state-of-the-art DRAM PUFs. We also demonstrate that our Dataplant-based cold boot attack protection mechanism is 19.5x faster and consumes 2.54x less energy when compared to existing mechanisms.
LGDec 30, 2018
ORIGAMI: A Heterogeneous Split Architecture for In-Memory Acceleration of LearningHajar Falahati, Pejman Lotfi-Kamran, Mohammad Sadrosadati et al.
Memory bandwidth bottleneck is a major challenges in processing machine learning (ML) algorithms. In-memory acceleration has potential to address this problem; however, it needs to address two challenges. First, in-memory accelerator should be general enough to support a large set of different ML algorithms. Second, it should be efficient enough to utilize bandwidth while meeting limited power and area budgets of logic layer of a 3D-stacked memory. We observe that previous work fails to simultaneously address both challenges. We propose ORIGAMI, a heterogeneous set of in-memory accelerators, to support compute demands of different ML algorithms, and also uses an off-the-shelf compute platform (e.g.,FPGA,GPU,TPU,etc.) to utilize bandwidth without violating strict area and power budgets. ORIGAMI offers a pattern-matching technique to identify similar computation patterns of ML algorithms and extracts a compute engine for each pattern. These compute engines constitute heterogeneous accelerators integrated on logic layer of a 3D-stacked memory. Combination of these compute engines can execute any type of ML algorithms. To utilize available bandwidth without violating area and power budgets of logic layer, ORIGAMI comes with a computation-splitting compiler that divides an ML algorithm between in-memory accelerators and an out-of-the-memory platform in a balanced way and with minimum inter-communications. Combination of pattern matching and split execution offers a new design point for acceleration of ML algorithms. Evaluation results across 12 popular ML algorithms show that ORIGAMI outperforms state-of-the-art accelerator with 3D-stacked memory in terms of performance and energy-delay product (EDP) by 1.5x and 29x (up to 1.6x and 31x), respectively. Furthermore, results are within a 1% margin of an ideal system that has unlimited compute resources on logic layer of a 3D-stacked memory.