Related papers: Efficient Modular Arithmetic for SIMD Devices
Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their…
The prefix sum operation is a useful primitive with a broad range of applications. For database systems, it is a building block of many important operators including join, sort and filter queries. In this paper, we study different methods…
This paper will describe a simulator developed by the authors to explore the design of Fourier transform based multiplication using optics. Then it will demonstrate an application to the problem of constructing an all-optical modular…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
Matrix multiplication consumes a large fraction of the time taken in many machine-learning algorithms. Thus, accelerator chips that perform matrix multiplication faster than conventional processors or even GPU's are of increasing interest.…
This paper presents a low-latency hardware accelerator for modular polynomial multiplication for lattice-based post-quantum cryptography and homomorphic encryption applications. The proposed novel modular polynomial multiplier exploits the…
Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
We address the challenges associated with deploying neural networks on CPUs, with a particular focus on minimizing inference time while maintaining accuracy. Our novel approach is to use the dataflow (i.e., computation order) of a neural…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
The embedded DRAM (eDRAM) is more and more used in System On Chip (SOC). The integration of the DRAM capacitor process into a logic process is challenging to get satisfactory yields. The specific process of DRAM capacitor and the low…
As programmers turn to software-defined hardware (SDH) to maintain a high level of productivity while programming hardware to run complex algorithms, heavy-lifting must be done by the compiler to automatically partition on-chip arrays. In…
Particle-In-Cell (PIC) codes are broadly applied to the kinetic simulation of plasmas, from laser-matter interaction to astrophysics. Their heavy simulation cost can be mitigated by using the Single Instruction Multiple Data (SIMD)…
In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…
Modular and networked quantum architectures can scale beyond the qubit count of a single device, but executing a circuit across modules requires implementing non-local two-qubit gates using shared entanglement (ebits) and classical…
Digital MemComputing machines (DMMs), which employ nonlinear dynamical systems with memory (time non-locality), have proven to be a robust and scalable unconventional computing approach for solving a wide variety of combinatorial…
An efficient method is described to handle mesh indexes in multidimensional problems like numerical integration of partial differential equations, lattice model simulations, and determination of atomic neighbor lists. By creating an…
The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such…
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms in large and medium characteristic fields (e.g., {GF}$(p^2)$, {GF}$(p^{12})$) are the Number Field Sieve and its variants (special,…