One Polynomial Approximation to Produce Correctly Rounded Results for Multiple Representations and Rounding Modes
To create a single polynomial approximation that produces correct results for multiple representations and rounding modes, we propose to generate a polynomial that generates the correctly rounded result of f(x) using the non-standard round-to-odd rounding mode with 2 additional precision bits compared to the largest floating point representation that we wish to support. We provide a proof that this method produces correctly rounded results for multiple representations and for all the standard rounding modes. More detailed explanation of our approach can be found in our POPL 2022 distinguished paper.
