Numerical Validation with the Discrete Stochastic Arithmetic on New Architectures

Abstract

Now Scientists are facing up to a new age. Power of computer enables us to perform experiences in silicio . Modelisations are enough accurate to obtain results closed to reality, although they sometimes fail. Several reasons can be given: the modelisation is not close enough to reality, the model is unstable, etc. One reason is often forgotten: errors coming from computers. Indeed, numerical computations are based on floating point number representation which is only an approximation of real numbers. Each operation generates a very small error that can propagate and cause the computed result to become completely different than the expected one. Several methods are well known to study the round-off errors propagation. The talk will focus on the DSA (discrete stochastic arithmetic) and its implementation: the CADNA software. The DSA allows us to study the round-off error propagation in all codes written in Fortran, C or C++ with few code modifications. This method is powerful but a bottleneck is the increase of the over-cost in computation time. Explanations and a solution will be given. In a second part, an overview of the CADNA implementation on multicore, distributed systems and GPU will be developed. ...