Math: User-Controlled Fast Math

[ax3l]

In PIConGPU we discussed the influence of fast math for important functions such a trigonometric functions in ComputationalRadiationPhysics/picongpu#1489. The main problem is, that some restrictions like

cosf == __cosf(x):

For x in [-π,π], the maximum absolute error is 2^-21.19, and larger otherwise.

are only know to the implementer writing that cosine (since he/she knows the definition range of the input). The cleanest way would be to expose that to the user without using the shotgun approach of compiler flags could be:

An additional template argument for math functions like sqrt and sin to explicitly enable fast-math if the range of the argument's range and expected value range is 100% satisfying the reduced precision: default PMacc::math::sin<T_FastMath=False>().

Of course, the individual, absolute hardware specific fast-math errors are hardware dependent, but usually follow at least a similar scheme (such as expected input range).