Multi-precision math¶

The nature of the calculations involved in HJCFIT especially in the root finding means that the code is susceptible to issues related to the limited precision of the floating point numbers use to represent values within the code. To work around these issues the code is able to use GMP and MPFR to perform specific calculations at higher precision. As multi precision math is not implemented in hardware it comes with very significant run time overhead, typically orders of magnitude slower we have added support for multi-precision as a fall back mechanism. Currently there is only support for fallback in find_eigs_bound which is known to be problematic. The pattern that we follow is to do the calculations with regular precision floating point. If that fails we rerun the calculation with multi-precision. Currently only at 128 bits but that could easily be extended via an iterative process to arbitrary precision.

The code can be compilled with and without this feature. Currently CMake is setup to automatically download and build GMP and MPFR on OSX and linux if not found. However, this feature is not enabled on Windows by default. GMP is not supported on Windows but it should be possible to build and use MPIR as a drop-in replacement for GMP on windows which MPFR can be linked against. However, there is currently no support for building this automatically on windows. To control if this option should be enabled the flag DCPROGS_USE_MPFR can be set to on or off.