Related papers: OFP-Repair: Repairing Floating-point Errors via Or…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
We study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to…
We investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…
Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
Automated Program Repair (APR) has evolved significantly with the advent of Large Language Models (LLMs). Fine-tuning LLMs for program repair is a recent avenue of research, with many dimensions which have not been explored. Existing work…
The Fast Fourier Transform (FFT), as a core computation in a wide range of scientific applications, is increasingly threatened by reliability issues. In this paper, we introduce TurboFFT, a high-performance FFT implementation equipped with…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
Motivated by the increasing interest in the posit numeric format, in this paper we evaluate the accuracy and efficiency of posit arithmetic in contrast to the traditional IEEE 754 32-bit floating-point (FP32) arithmetic. We first design and…
Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary to the validation of critical software. This problem is even more challenging when…
Users around the world rely on software-intensive systems in their day-to-day activities. These systems regularly contain bugs and security vulnerabilities. To facilitate bug fixing, data-driven models of automatic program repair use pairs…
Automated program repair (APR) has attracted widespread attention in recent years with substantial techniques being proposed. Meanwhile, a number of benchmarks have been established for evaluating the performances of APR techniques, among…
Neural operators, such as Fourier Neural Operators (FNO), form a principled approach for learning solution operators for PDEs and other mappings between function spaces. However, many real-world problems require high-resolution training…
Mixing precisions for performance has been an ongoing trend as the modern hardware accelerators started including new, and mostly lower-precision, data formats. The advantage of using them is a great potential of performance gain and energy…
Fault localization is a crucial step of automated program repair, because accurately identifying program locations that are most closely implicated with a fault greatly affects the effectiveness of the patching process. An ideal fault…
Fixed-Point-Oriented Programming (FPOP) is an emerging paradigm designed to streamline the implementation of problems involving self-referential computations. These include graph algorithms, static analysis, parsing, and distributed…
In recent years, Automated Program Repair (APR) has been extensively studied in academia and even drawn wide attention from industry. However, APR techniques can be extremely time consuming since (1) a large number of patches can be…
Analog mixed-signal (AMS) devices promise faster, more energy-efficient deep neural network (DNN) inference than their digital counterparts. However, recent studies show that DNNs on AMS devices with fixed-point numbers can incur an…
The output-error method is a mainstay of aircraft system identification from flight-test data. It is the method of choice for a wide range of applications, from the estimation of stability and control derivatives for aerodynamic database…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…