Implicite typecast in differential probability

[szabo137]

Problem statement

In the cross-section interface, there is an implicit typecasting for momenta with element types not equal to Float64. Consider, for instance, the test implementation introduced in #146:

using Random
using QEDbase

include("test_implementation/TestImplementation.jl")
using .TestImplementation

RNG = MersenneTwister(1)

MOM_TYPE = TestMomentum{Float32}

TESTPROC = TestProcess(2,2)
TESTMODEL = TestModel()
TESTPSDEF = TestPhaseSpaceDefinition{MOM_TYPE}()
P_IN = MOM_TYPE.(eachcol(rand(RNG,4,2)))
P_OUT = MOM_TYPE.(eachcol(rand(RNG,4,2)))
PS_POINT = TestPhaseSpacePoint(
                        TESTPROC, TESTMODEL, TESTPSDEF, P_IN, P_OUT
                    )
prop_on_psp = differential_probability(PS_POINT)

typeof(prop) # returns Float64, expected Float32

I guess the reason for this behavior is the implementation of averaging_norm, which returns the inverse of the number of spin configurations, which is the inverse of an integer, which is, per default, a Float64. This is then propagated to the top level, i.e. the differential_probability.

Similar behavior is found for differential_cross_section, probably caused by the same reason.

Suggested solution

Rewrite the parts involving the averaging_norm in such a way that the division with the number of spin combinations happens at a stage where the element type is known, e.g., directly in the calculation of differential_probability.