Related papers: Computing Floating-Point Errors by Injecting Pertu…
Floating-point program errors can lead to severe consequences, particularly in critical domains such as military applications. Only a small subset of inputs may induce substantial floating-point errors, prompting researchers to develop…
Errors in floating-point programs can lead to severe consequences, particularly in critical domains such as military, aerospace, and financial systems, making their repair a crucial research problem. In practice, some errors can be fixed…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root…
The evolution of floating-point computation has been shaped by algorithmic advancements, architectural innovations, and the increasing computational demands of modern technologies, such as artificial intelligence (AI) and high-performance…
Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…
Current critical systems commonly use a lot of floating-point computations, and thus the testing or static analysis of programs containing floating-point operators has become a priority. However, correctly defining the semantics of common…
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…
Floating-point arithmetic is error-prone and unintuitive. Floating-point debuggers instrument programs to monitor floating-point arithmetic at run time and flag numerical issues. They estimate residues, i.e., the difference between actual…
Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…
In this paper, we use reduced precision checking (RPC) to detect errors in floating point arithmetic. Prior work explored RPC for addition and multiplication. In this work, we extend RPC to a complete floating point unit (FPU), including…
Floating-point accumulation networks (FPANs) are key building blocks used in many floating-point algorithms, including compensated summation and double-double arithmetic. FPANs are notoriously difficult to analyze, and algorithms using…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
In this work, we provide energy-efficient architectural support for floating point accuracy. Our goal is to provide accuracy that is far greater than that provided by the processor's hardware floating point unit (FPU). Specifically, for…
Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…
Errors due to hardware or low level software problems, if detected, can be fixed by various schemes, such as recomputation from a checkpoint. Silent errors are errors in application state that have escaped low-level error detection. At…