Places with precision issues when compiling for float

[AlexanderSinn]

I made a branch of amrex where amrex::Real is replaced with a special type that checks for out-of-range and precision loss.

AMReX branch:
https://github.com/AlexanderSinn/amrex/tree/try_add_MockReal_attempt_1
HiPACE++ branch:
https://github.com/AlexanderSinn/hipace/tree/test_with_float_using_MockReal

Compile with NOACC, double precision, and in RelWithDebInfo mode.

The input parameter amrex.mock_real_crash_errno can be used to crash at a specific error location to generate a backtrace.

I then ran a standard blowout wake in SI units script at low resolution and took not of all the places with issues, while replacing them with amrex::Real::unchecked_add to remove them from the output.

• diagnostic: no need to have shape factor when grid is aligned with simulation grid

• shape factors: cancelation in xmid-xfloor

• gamma_psi-1._rt for plasma particles

• derivative shape factor

• AddRhoIons

• HPMG:
  both add and sub in: return rhs + acf*phi(i,j,0,n) - lap;
lap = facx * (phi(i-1,j,0,n) + phi(i+1,j,0,n));
  laplacian() opeprator+=
  restrict_nd

• Depos etc:
  const amrex::Real xmid = (xp - x_pos_offset) * dx_inv;
const amrex::Real ymid = (yp - y_pos_offset) * dy_inv;

• Beam pusher: ( uz * gammap_inv - clight )

• Beam pusher: ( uz_next * gamma_next_inv - clight );

• Beam deposition: wq*(1._rt-vz*clightinv);

• SolvePoissonPsiExmByEypBxEzBz: Bz source term, dy_jx +- dx_jy
  ExmBy calc:
  - (arr(i+1,j,Psi) - arr(i-1,j,Psi))*dx_inv;
- (arr(i,j+1,Psi) - arr(i,j-1,Psi))*dy_inv
  Bz source derivative_inner: (array(i+is_x_dir,j+is_y_dir) - array(i-is_x_dir,j-is_y_dir)) * dx_inv;

• doGatherShapeN: ExmByp += (shape_dx* shape_y) * slice_arr(i, j, psi_comp) * dx_inv;

• GetPosOffset: geom.ProbLo(dir) + geom.ProbHi(dir)

• InitParticles: plo[0] + (i + r[0] + x_offset)*dx[0];
plo[1] + (j + r[1] + y_offset)*dx[1];

• ExplicitDeposition both amrex::Gpu::Atomic::Add

• amrex::Geometry computeRoundoffDomain: auto idx = int(std::floor((x - plo)*dxinv));

• InitBeamFixedWeightPDF3D: m_get_momentum.m_u_std[2] = std::sqrt(avg_uz_sq/integral - (avg_uz/integral)*(avg_uz/integral))

• Diagnostic TrimIOBox const amrex::Real mid = (rbox_3d.lo(slice_dir) + rbox_3d.hi(slice_dir)) / 2.;

• AdvancePlasmaParticles: PlasmaMomentumPush and DualNumber operator+