Finding root causes of floating point error

Abstract

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 causes, which is difficult because floating-point errors are generally non-local, non-compositional, and non-uniform.This paper presents Herbgrind, a tool to help developers identify and address root causes in numerical code written in low-level languages like C/C++ and Fortran. Herbgrind dynamically tracks dependencies between operations and program outputs to avoid false positives and abstracts erroneous computations to simplified program fragments whose improvement can reduce output error. We perform several case studies applying Herbgrind to large, expert-crafted numerical programs and show that it scales to applications spanning hundreds of thousands of lines, correctly handling the low-level details of modern floating point hardware and mathematical libraries and tracking error across function boundaries and through the heap.CCS Concepts • Software and its engineering → Software maintenance tools;

Efficient automated repair of high floating-point errors in numerical libraries

“…Moreover, we also investigate the change of the maximum floating-point error and the average floating-point error over the input interval I err after repairing. Comparing with state-of-the-art tools To compare with state-of-the-art methods, we build a connection between two state-of-the-art tools Herbgrind [Sanchez-Stern et al 2018] and Herbie [Panchekha et al 2015] to construct a new tool HBG. The work flow of HBG is shown in Fig.…”

“…Based on FpDebug, Zou et al [2015] proposed a detection approach called LSGA to search for input that can trigger possible maximum floating-point error in a numerical program. Recently, Herbgrind, which is a similar tool of FpDebug, is developed by Sanchez-Stern et al [2018]. Besides supporting similar functionalities of FpDebug, Herbgrind can find the root cause of floating-point error and extract the corresponding floating-point expressions.…”

“…Like Salsa, Herbie uses mathematical rewriting to improving accuracy. To apply Herbie to numerical programs, the same authors of Herbie develop the tool Herbgrind [Sanchez-Stern et al 2018] to find root cause of floating-point error and extract the corresponding floating-point expressions that can be analyzed by Herbie. The combination of Herbie and Herbgrind is called HBG in our paper and its detailed implementation is introduced in ğ5.2.…”

Bit Manipulation: Conditional Statement using Bit-wise operators with C++

“…The source code of program can be read and understood by humans in the form of C ++ language. In order for the machine to understand it, the source program is translated into low-level machine language sequences [5].…”

Combining Tools for Optimization and Analysis of Floating-Point Computations

“…Other such tools use dynamic techniques to find inputs that suffer from large rounding errors [3,22]. Yet other tools perform rewriting-based optimization [4,16,19,7] and mixed-precision tuning [2,6] to improve the accuracy and performance of floating-point programs.…”