Quadrature using 64-bit IEEE arithmetic for integrands over [0,1] with a singularity at 1

AbstractWe present a detailed study of some problems encountered when quadrature over [0,1] is attempted with integrands that have a singularity at 1. Methods designed to increase the accuracy of such quadratures, for example, the application of periodising transformations, are examined in the context of the representational limitations of 64-bit IEEE arithmetic near 1 in [0,1]. A heuristic is proposed for the forecasting of a lower bound on the irremovable error due to these limitations. We conclude by affirming the commonly accepted procedure that where possible, integrals should be symbolically transformed so that any remaining singularity occurs at 0