I am developing some numerical software, whose performance, depends a lot on the numerical accuracy (i.e., floats, double etc.). I have noticed that the ARM NEON does not fully comply with the IEEE754 floating point standard. Is there a way to emulate NEON's floating point precision, on an x86 CPU ? For example a library that emulates the NEON SIMD floating point operations.
Probably.
I'm less familiar with SSE, but you can force many of the SSE modes to behave like NEON. This will depend on your compiler and available libraries, but see some Visual Studio FP unit control functions. This might be good enough for your requirements.
Furthermore, you can use the arm_neon.h header to ensure that you are using similar intrinsics to accomplish similar things.
Finally, if you really require achieving this precision at these boundary conditions, you are going to want a good test suite to verify that you are achieving your results as intended.
Finally finally, even with pure "C" code, which typically complies with IEEE-754, and uses the VFP on ARM as other commenters have mentioned, you will get different results because floating point is a highly... irregular process, subject to the whim of optimization and order of operations. It is challenging to get results to match across different compilers, let alone hardware architectures. For example, to get highly agreeable results on Intel with gcc it's often required to use the -ffloat-store flag, if you want to compare with /fp:precise on CL/MSVS.
In the end, you may need to accept some kind of non-zero error tolerance. Trying to get to zero may be difficult, but it would be awesome to hear your results if you get there. It seems possible... but difficult.