Ensuring Numerical Quality in Grid Computing

Certain numerically intensive applications executed within a grid computing environment crucially depend on the properties of floating-point arithmetic implemented on the respective platform. Differences in these properties may have drastic effects. This paper identifies the central problems related to this situation. We propose an approach which gives the user valuable information on the various platforms available in a grid computing environment in order to assess the numerical quality of an algorithm run on each of these platforms. In this manner, the user will at least have very strong hints whether a program will perform reliably in a grid before actually executing it. Our approach extends the existing IeeeCC754 test suite by two "grid-enabled" modes: The first mode calculates a "numerical checksum" on a specific grid host and executes the job only if the checksum is identical to a locally generated one. The second mode provides the user with information on the reliability and IEEE 754-conformity of the underlying floating-point implementation of various platforms. Furthermore, it can help to find a set of compiler options to optimize the application\´s performance while retaining numerical stability.