5 ms·
The dilemma is hypothetical (because we now know the exact precision requirement for those functions over all 64-bit doubles) but let's assume that we don't kno
by lifthrasiir 2mo ago
The dilemma is hypothetical (because we now know the exact precision requirement for those functions over all 64-bit doubles) but let's assume that we don't know that and also we happen to use decimals instead. What if, some f(x) is known to be, say, 123.4999...9997 with 1,000 fractional digits? You have to calculate at least 1,000 decimal digits of f(x) in order to correctly round, before that we only know it's between 123.4999...999 and 123.5000...001. There seems no mathematical theory that specially prevents this annoying possibility, hence the dilemma.
- dataflow 2mo ago> because we now know the exact precision requirement for those functions over all 64-bit doubles Do you have a link or something on this?
- lifthrasiir 2mo agoI'm on a mobile right now so I can't give the exact paper link but you can learn about the CORE-MATH project [1]. [1] https://core-math.gitlabpages.inria.fr/ https://core-math.gitlabpages.inria.fr/
- lioeters 2mo ago> CORE-MATH Mission: provide on-the-shelf high performance open-source mathematical functions with correct rounding that can be integrated into current mathematical libraries (GNU libc, Intel Math Library, AMD Libm, Newlib, OpenLibm, Musl, Apple Libm, llvm-libc, Microsoft libm, CUDA libm, ROCm) That's beautiful. Here's the Git repo with implementation. https://gitlab.inria.fr/core-math/core-math/-/blob/master/README.md https://gitlab.inria.fr/core-math/core-math/-/blob/master/RE...