Daisy - Framework for Analysis and Optimization of Numerical Programs (Tool Paper)

Abstract

Abstract. Automated techniques for analysis and optimization of finite-precision computations have recently garnered significant interest. Most of these were, however, developed independently. As a consequence, reuse and combination of the techniques is challenging and much of the underlying building blocks have been re-implemented several times, including in our own tools. This paper presents a new framework, called Daisy, which provides in a single tool the main building blocks for accuracy analysis of floating-point and fixed-point computations which have emerged from recent related work. Together with its modular structure and optimization methods, Daisy allows developers to easily recombine, explore and develop new techniques. Daisy's input language, a subset of Scala, and its limited dependencies make it furthermore user-friendly and portable.

A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4

“…FloVer's range and error validators perform dataflow roundoff error analysis and for this follow the same approach for computing absolute error bounds as Rosa [10], Fluctuat [17], Gappa [13] and Daisy [12].…”

“…We use Daisy [12] to generate certificates for our evaluation. During this, we found a subtle bug in the tool's static analysis of the division operator.…”

“…Certificates checked by FloVer encode only the minimal static analysis result, and thus using FloVer does not require formal verification expertise. Separately from FloVer, we implement fully automated certificate generation in the static analysis tool Daisy [12], demonstrating our envisioned tool-chain.…”

A Probabilistic Approach to Floating-Point Arithmetic

“…Moreover, since the output of such a program might very well turn out to be the input of another program doing arithmetic, one should also consider non-deterministic inputs. This is precisely what happens in practice with tools for numerical analysis like the recent [12], Daisy [4] or FPTaylor [15] which require for each variable of the program a range of possible values in order to perform a worst-case analysis.…”

Combining Tools for Optimization and Analysis of Floating-Point Computations

“…In this paper we report on our experience implementing the first combination of two complementary floating-point analysis tools using FPBench: Herbie [16] and Daisy [7]. Herbie optimizes the accuracy of straight-line floating-point expressions, but employs a dynamic roundoff error analysis and thus cannot provide sound guarantees on the results.…”