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Abstract (partial) "An investigation of common techniques for approximating the Normal distribution Quantile function is presented. The high-precision arithmetic and rational approximation packages built in to Mathematica are used for this investigation, but we also present a benchmark easily used in other languages, based on the power series representation of the Normal Quantile developed recently by Steinbrecher, and using a simple non-linear recursive definition of its coefficients to provide a benchmark. Within an arbitrary precision environment this can be used to provide as much precision as is needed, … A simple version in C-style C++ is provided for benchmarking/education purposes … Using this benchmark with Mathematica's MiniMaxApproximation functions allows rational functions of diverse complexity to be constructed with relatively little effort. In this version of the note we explore the Beasley-Springer-Moro (BSM), Wichura "AS241" (1988) and Acklam algorithms, paying particular attention to the main rational approximations employed within a central region …"

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