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This paper presents a novel method for generating a single polynomialapproximation that produces correctly rounded results for all inputs of anelementary function for multiple representations. The generated polynomialapproximation has the nice property that the first few lower degree termsproduce correctly rounded results for specific representations of smallerbitwidths, which we call progressive performance. To generate such progressivepolynomial approximations, we approximate the correctly rounded result andformulate the computation of correctly rounded polynomial approximations as alinear program similar to our prior work on the RLibm project. To enable theuse of resulting polynomial approximations in mainstream libraries, we want toavoid piecewise polynomials with large lookup tables. We observe that theproblem of computing polynomial approximations for elementary functions is alinear programming problem in low dimensions, i.e., with a small number ofunknowns. We design a fast randomized algorithm for computing polynomialapproximations with progressive performance. Our method produces correct andfast polynomials that require a small amount of storage. A few polynomialapproximations from our prototype have already been incorporated into LLVM'smath library.

RLIBM-PROG: Progressive Polynomial Approximations for Fast Correctly Rounded Math Libraries