Jacobian matrices can be accumulated using either the forward or reverse mode of Automatic Di erentiation. Alternatively, derivative code can be generated to compute the Jacobian directly at the current argument. The minimisation of the corresponding number of arithmetic operations leads to a computationally hard combinatorial optimisation problem. A method for its approximate solution by dynam...

Can we assure math computations by automatic verifying floating-point accuracy? We define fast arithmetic (based on Dekker [1]) over twofold approximations z ≈ z0 + z1, such that z0 is standard result and z1 assesses inaccuracy ∆z0 = z − z0. We propose on-fly tracking z1, detecting if ∆z0 appears too high. We believe permanent tracking is worth its cost. C++ test code for Intel AVX available vi...

I describe a C++ program for computing the smallest enclosing ball of a point set in d-dimensional space, using floating-point arithmetic only. The program is very fast for d ≤ 20, robust and simple (about 300 lines of code, excluding prototype definitions). Its new features are a pivoting approach resembling the simplex method for linear programming, and a robust update scheme for intermediate...

Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the solution will be computed using many cores. In this paper we describe our multithreaded implementation to track one solution path defined by a polynomial homotopy. Limiting quality to accuracy and confusing accuracy with...

This article is about twofold arithmetic [1, 2]. Here I introduce algorithms and experimental code for twofold variant of C/C++ standard functions exp() and log(), and expm1() and log1p(). Twofold function y0 + y1 ≈ f(x0 + x1) is nearly 2x-precise so can assess accuracy of standard one. Performance allows assessing on-fly: twofold texp() over double is ~10x times faster than expq() by GNU quadm...

In this paper, an approach to synthesize correct programs from specifications is presented. The idea is to extract code from definitions appearing in statements which have been mechanically proved with the help of a proof assistant. This approach has been found when proving the correctness of certain Computer Algebra programs (for Algebraic Topology) by using the Isabelle proof assistant. To ea...

This directory contains the Neuron code for the CA1 pyramidal cell model and the experiments described in: 1. Poirazi, P. Brannon, T. & Mel, B.W. Arithmetic of Subthreshold Synaptic Summation in a Model CA1 Pyramidal Cell. In Press, Neuron , February 2003. 2. Poirazi, P. Brannon, T. & Mel, B.W. Online Supplement: About the Model. In Press, Neuron , February 2003. 3. Poirazi, P. Brannon, T. & Me...

Due to the ever complexity of digital systems, there is a noticeable need for more abstract and structural mechanisms as well as design methodologies that systematically and formally derive low level concrete designs from high level abstract ones. To this aim, we present a methodological design approach that automatically generates a functional HDL code from SysML diagrams modeling hardware des...

A hybrid lossy/lossless audio coding is presented in this paper. The lossy coding part is based on code excitation approach where the excitation gain is adapted in a sample-by-sample fashion. Two short term predictors are used to cope with rapid time-varying nature of audio signals. The error signal between the input and the synthetic signal is sent to the decoder after arithmetic coding to ach...

The class of completely regular codes includes not only some of the most important error-correcting codes, such as perfect codes and uniformly packed codes, but also a number of substructures fundamental to the study of distance-regular graphs themselves. In a companion paper, we study products of completely regular codes and codes whose parameters form arithmetic progressions. This family of c...