Obligatory reference to computable analysis: https://en.wikipedia.org/wiki/Computable_analysis https://en.wikipedia.org/wiki/Computable_analysis This shows tha

Obligatory reference to computable analysis: https://en.wikipedia.org/wiki/Computable_analysis https://en.wikipedia.org/wiki/Computable_analysis This shows that you can do exact real arithmetic without worrying about round-off errors. But it's expensive. If you want something more practical (but dodgy), you can use arbitrary-precision arithmetic instead of exact real arithmetic. To that end, there's the Decimal module in the Python standard lib. There's also the BC programming language which is part of POSIX. If you want to do matrix arithmetic, you can use mpmath for Python like they did in this blog post, or Eigen3 for C++ with an arbitrary-precision type. This is dodgy of course because the arithmetic remains inexact, albeit with smaller rounding errors than double-precision floats.