Related papers: OFP-Repair: Repairing Floating-point Errors via Or…
We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…
This paper provides a bound on the number of numeric operations (fixed or floating point) that can safely be performed before accuracy is lost. This work has important implications for control systems with safety-critical software, as these…
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…
With the rapid development and large-scale popularity of program software, modern society increasingly relies on software systems. However, the problems exposed by software have also come to the fore. Software defect has become an important…
Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…
Software debugging is tedious, time-consuming, and even error-prone by itself. So, various automated debugging techniques have been proposed in the literature to facilitate the debugging process. Automated Program Repair (APR) is one of the…
High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well…
Automated program repair (APR) techniques are effective in fixing inevitable defects in software, enhancing development efficiency and software robustness. However, due to the difficulty of generating precise specifications, existing APR…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of…
Various automated program repair (APR) techniques have been proposed to fix bugs automatically in the last decade. Although recent researches have made significant progress on the effectiveness and efficiency, it is still unclear how APR…
The amount of data generated and gathered in scientific simulations and data collection applications is continuously growing, putting mounting pressure on storage and bandwidth concerns. A means of reducing such issues is data compression;…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
Due to the promising future of Automated Program Repair (APR), researchers have proposed various APR techniques, including heuristic-based, template-based, and constraint-based techniques. Among such classic APR techniques, template-based…
Automated Program Repair (APR) aims to help developers automatically patch software bugs. However, current state-of-the-art traditional and learning-based APR techniques face the problem of limited patch variety, failing to fix complicated…
There is a growing interest in the use of reduced-precision arithmetic, exacerbated by the recent interest in artificial intelligence, especially with deep learning. Most architectures already provide reduced-precision capabilities (e.g.,…
We propose a new instruction (FPADDRE) that computes the round-off error in floating-point addition. We explain how this instruction benefits high-precision arithmetic operations in applications where double precision is not sufficient.…
In this article, we apply a new methodology for precision tuning to the N-body problem. Our technique, implemented in a tool named POP, makes it possible to optimize the numerical data types of a program performing floating-point…