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We present algorithms to numerically evaluate Daubechies wavelets and scalingfunctions to high relative accuracy. These algorithms refine the suggestion ofDaubechies and Lagarias to evaluate functions defined by two-scale differenceequations using splines; carefully choosing amongst a family of rapidlyconvergent interpolators which effectively capture all the smoothness presentin the function and whose error term admits a small asymptotic constant. We arealso able to efficiently compute derivatives, though with a smoothness-inducedreduction in accuracy. An implementation is provided in the Boost SoftwareLibrary.

Towards 1ULP evaluation of Daubechies Wavelets