Related papers: On Approximate 8-bit Floating-Point Operations Usi…
Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the…
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…
Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
The effective use of computer vision and machine learning for on-orbit applications has been hampered by limited computing capabilities, and therefore limited performance. While embedded systems utilizing ARM processors have been shown to…
Floating point arithmetic is costly on FPGA platforms due to wide datapaths, normalization, and carry propagation, motivating alternative numerical representations that improve throughput and efficiency. This paper presents the Hybrid…
Half precision (FP16) promises to double FFT throughput on GPUs, but the prevailing view is that its 10-bit mantissa makes it unsuitable for radar-grade signal processing. We show this framing is wrong on Apple Silicon: the binding…
Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any…
As the demand for AI computation rapidly increases, more hardware is being developed to efficiently perform the low-precision matrix multiplications required by such workloads. However, these operations are generally not directly applicable…
The advent of switches with programmable dataplanes has enabled the rapid development of new network functionality, as well as providing a platform for acceleration of a broad range of application-level functionality. However, existing…
Floating-point operations can significantly impact the accuracy and performance of scientific applications on large-scale parallel systems. Recently, an emerging floating-point format called Posit has attracted attention as an alternative…
There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…
This article is concerned with the efficient computation of modular matrix multiplication C=AB mod p, a key kernel in computer algebra. We focus on floating-point arithmetic, which allows for using efficient matrix multiplication libraries.…
The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…
Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT),…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of $B$ bits of resolution, i.e. it might support only $2^B$ possible…
Modern transformer-based deep neural networks present unique technical challenges for effective acceleration in real-world applications. Apart from the vast amount of linear operations needed due to their sizes, modern transformer models…
Our RLibm project generates a single implementation for an elementary function that produces correctly rounded results for multiple rounding modes and representations with up to 32-bits. They are appealing for developing fast reference…
Transformer-based models, such as BERT, have been widely applied in a wide range of natural language processing tasks. However, one inevitable side effect is that they require massive memory storage and inference cost when deployed in…