Is Your Model Susceptible to Floating-Point Errors?

This paper provides a framework that highlights the features of computer models that make them especially vulnerable to floating-point errors, and suggests ways in which the impact of such errors can be mitigated. We focus on small floating-point errors because these are most likely to occur, whilst still potentially having a major influence on the outcome of the model. The significance of small floating-point errors in computer models can often be reduced by applying a range of different techniques to different parts of the code. Which technique is most appropriate depends on the specifics of the particular numerical situation under investigation. We illustrate the framework by applying it to six example agent-based models in the literature.Floating Point Arithmetic, Floating Point Errors, Agent Based Modelling, Computer Modelling, Replication

Survey of Floating-Point Software Arithmetics and Basic Library Mathematical Functions

Abstract Not Provided

Statistical Tests, Tests of Significance, and Tests of a Hypothesis Using Excel

Microsoft’s spreadsheet program Excel has many statistical functions and routines. Over the years there have been criticisms about the inaccuracies of these functions and routines (see McCullough 1998, 1999). This article reviews some of these statistical methods used to test for differences between two samples. In practice, the analysis is done by a software program and often with the actual method used unknown. The user has to select the method and variations to be used, without full knowledge of just what calculations are used. Usually there is no convenient trace back to textbook explanations. This article describes the Excel algorithm and gives textbook related explanations to bolster Microsoft’s Help explanations

HDL IMPLEMENTATION AND ANALYSIS OF A RESIDUAL REGISTER FOR A FLOATING-POINT ARITHMETIC UNIT

Processors used in lower-end scientific applications like graphic cards and video game consoles have IEEE single precision floating-point hardware [23]. Double precision offers higher precision at higher implementation cost and lower performance. The need for high precision computations in these applications is not enough to justify the use double precision hardware and the extra hardware complexity needed [23]. Native-pair arithmetic offers an interesting and feasible solution to this problem. This technique invented by T. J. Dekker uses single-length floating-point numbers to represent higher precision floating-point numbers [3]. Native-pair arithmetic has been proposed by Dr. William R. Dieter and Dr. Henry G. Dietz to achieve better accuracy using standard IEEE single precision floating point hardware [1]. Native-pair arithmetic results in better accuracy however it decreases the performance by 11x and 17x for addition and multiplication respectively [2]. The proposed implementation uses a residual register to store the error residual term [2]. This addition is not only cost efficient but also results in acceptable accuracy with 10 times the performance of 64-bit hardware. This thesis demonstrates the implementation of a 32-bit floating-point unit with residual register and estimates the hardware cost and performance

Computing the Lambert W function in arbitrary-precision complex interval arithmetic

We describe an algorithm to evaluate all the complex branches of the Lambert W function with rigorous error bounds in interval arithmetic, which has been implemented in the Arb library. The classic 1996 paper on the Lambert W function by Corless et al. provides a thorough but partly heuristic numerical analysis which needs to be complemented with some explicit inequalities and practical observations about managing precision and branch cuts.Comment: 16 pages, 4 figure