Related papers: An efficient floating point multiplier design for …
Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…
Conversion between binary and decimal floating-point representations is ubiquitous. Floating-point radix conversion means converting both the exponent and the mantissa. We develop an atomic operation for FP radix conversion with simple…
The rapid adoption of low-precision arithmetic in artificial intelligence and edge computing has created a strong demand for energy-efficient and flexible floating-point multiply-accumulate (MAC) units. This paper presents a dual-precision…
We present two fast algorithms for matrix-vector multiplication $y=Ax$, where $A$ is a Hankel matrix. The current asymptotically fastest method is based on the Fast Fourier Transform (FFT), however in multiprecision arithmetics with very…
In modern low-power embedded platforms, floating-point (FP) operations emerge as a major contributor to the energy consumption of compute-intensive applications with large dynamic range. Experimental evidence shows that 50% of the energy…
In this work we present a new structure for multiplication in finite fields. This structure is based on a digit-level LFSR (Linear Feedback Shift Register) multiplier in which the area of digit-multipliers are reduced using the Karatsuba…
Electronic devices primarily aim to offer low power consumption, high speed, and a compact area. The performance of very large-scale integration (VLSI) devices is influenced by arithmetic operations, where multiplication is a crucial…
This paper presents a novel algorithm for the modulus operation for FPGA implementation. The proposed algorithm use only addition, subtraction, logical, and bit shift operations, avoiding the complexities and hardware costs associated with…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
In this work, approximate eight-bit floating-point operations performed using simple integer operations is discussed. For two-bit mantissa formats, faithful rounding can always be obtained for the considered operations. For all operations,…
This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…
Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…
We improve the space complexity of Karatsuba multiplication on a quantum computer from $O(n^{1.427})$ to $O(n)$ while maintaining $O(n^{\lg 3})$ gate complexity. We achieve this by ensuring recursive calls can add their outputs directly…
Securing communication channels is especially needed in wireless environments. But applying cipher mechanisms in software is limited by the calculation and energy resources of the mobile devices. If hardware is applied to realize…
In this paper, we report the results obtained from the acceleration of multi-binary64-type multiple precision matrix multiplication with AVX2. We target double-double (DD), triple-double (TD), and quad-double (QD) precision arithmetic…
Matrix multiplication is a fundamental kernel in large-scale artificial intelligence and scientific computing, but its performance on conventional electronic accelerators is increasingly constrained by memory bandwidth and energy…
The Multilevel Fast Multipole Algorithm (MLFMA) has known applications in scientific modeling in the fields of telecommunications, physics, mechanics, and chemistry. Accelerating calculation of far-field using GPUs and GPU clusters for…
The unprecedented demand for computing resources to train DNN models has led to a search for minimal numerical encoding. Recent state-of-the-art (SOTA) proposals advocate for multi-level scaled narrow bitwidth numerical formats. In this…
Multiplication is a core operation in modern neural network (NN) computations, contributing significantly to energy consumption. The linear-complexity multiplication (L-Mul) algorithm is specifically proposed as an approximate…
Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…