Task: Implement WT_Standing.cc for McLachlan/ML_WaveToy thorn

thorn_name: McLachlan/ML_WaveToy
src_filename: WT_Standing.cc
interface: # File produced by Kranc

implements: ML_WaveToy

inherits:   Boundary GenericFD Grid



USES INCLUDE: loopcontrol.h
USES INCLUDE: Symmetry.h
USES INCLUDE: vectors.h
USES INCLUDE: Boundary.h

CCTK_INT FUNCTION MoLRegisterEvolved(CCTK_INT IN EvolvedIndex, CCTK_INT IN RHSIndex)
USES FUNCTION MoLRegisterEvolved

SUBROUTINE Diff_coeff(CCTK_POINTER_TO_CONST IN cctkGH, CCTK_INT IN dir, CCTK_INT IN nsize, CCTK_INT OUT ARRAY imin, CCTK_INT OUT ARRAY imax, CCTK_REAL OUT ARRAY q, CCTK_INT IN table_handle)
USES FUNCTION Diff_coeff

CCTK_INT FUNCTION MultiPatch_GetMap(CCTK_POINTER_TO_CONST IN cctkGH)
USES FUNCTION MultiPatch_GetMap

CCTK_INT FUNCTION MultiPatch_GetBbox(CCTK_POINTER_TO_CONST IN cctkGH, CCTK_INT IN size, CCTK_INT OUT ARRAY bbox)
USES FUNCTION MultiPatch_GetBbox

CCTK_INT FUNCTION GetBoundarySpecification(CCTK_INT IN size, CCTK_INT OUT ARRAY nboundaryzones, CCTK_INT OUT ARRAY is_internal, CCTK_INT OUT ARRAY is_staggered, CCTK_INT OUT ARRAY shiftout)
USES FUNCTION GetBoundarySpecification

CCTK_INT FUNCTION MultiPatch_GetBoundarySpecification(CCTK_INT IN map, CCTK_INT IN size, CCTK_INT OUT ARRAY nboundaryzones, CCTK_INT OUT ARRAY is_internal, CCTK_INT OUT ARRAY is_staggered, CCTK_INT OUT ARRAY shiftout)
USES FUNCTION MultiPatch_GetBoundarySpecification

CCTK_INT FUNCTION SymmetryTableHandleForGrid(CCTK_POINTER_TO_CONST IN cctkGH)
USES FUNCTION SymmetryTableHandleForGrid

CCTK_INT FUNCTION Boundary_SelectGroupForBC(CCTK_POINTER_TO_CONST IN GH, CCTK_INT IN faces, CCTK_INT IN boundary_width, CCTK_INT IN table_handle, CCTK_STRING IN group_name, CCTK_STRING IN bc_name)
USES FUNCTION Boundary_SelectGroupForBC

CCTK_INT FUNCTION Boundary_SelectVarForBC(CCTK_POINTER_TO_CONST IN GH, CCTK_INT IN faces, CCTK_INT IN boundary_width, CCTK_INT IN table_handle, CCTK_STRING IN var_name, CCTK_STRING IN bc_name)
USES FUNCTION Boundary_SelectVarForBC

public:
CCTK_REAL WT_u type=GF timelevels=4 tags='tensortypealias="Scalar" tensorweight=0'
{
  u
} "WT_u"

public:
CCTK_REAL WT_rho type=GF timelevels=4 tags='tensortypealias="Scalar" tensorweight=0'
{
  rho
} "WT_rho"

public:
CCTK_REAL WT_eps type=GF timelevels=1 tags='tensortypealias="Scalar" tensorweight=0 Prolongation="None"'
{
  eps
} "WT_eps"

public:
CCTK_REAL WT_rhorhs type=GF timelevels=4 tags='tensortypealias="Scalar" tensorweight=0 Prolongation="None"'
{
  rhorhs
} "WT_rhorhs"

public:
CCTK_REAL WT_urhs type=GF timelevels=4 tags='tensortypealias="Scalar" tensorweight=0 Prolongation="None"'
{
  urhs
} "WT_urhs"

schedule: # File produced by Kranc

STORAGE: WT_u[timelevels]

STORAGE: WT_rho[timelevels]

STORAGE: WT_eps[other_timelevels]

STORAGE: WT_rhorhs[rhs_timelevels]

STORAGE: WT_urhs[rhs_timelevels]
schedule ML_WaveToy_Startup at STARTUP
{
  LANG: C
  OPTIONS: meta
} "create banner"

schedule ML_WaveToy_RegisterSymmetries in SymmetryRegister
{
  LANG: C
  OPTIONS: meta
} "register symmetries"

if (CCTK_EQUALS(initial_data, "Gaussian"))
{
  schedule WT_Gaussian AT initial
  {
    LANG: C
    READS: grid::r(Everywhere)
    WRITES: ML_WaveToy::rho(Everywhere)
    WRITES: ML_WaveToy::u(Everywhere)
  } "WT_Gaussian"
}

if (CCTK_EQUALS(initial_data, "Standing"))
{
  schedule WT_Standing AT initial
  {
    LANG: C
    READS: grid::x(Everywhere)
    READS: grid::y(Everywhere)
    READS: grid::z(Everywhere)
    WRITES: ML_WaveToy::rho(Everywhere)
    WRITES: ML_WaveToy::u(Everywhere)
  } "WT_Standing"
}

schedule WT_RHS IN MoL_CalcRHS
{
  LANG: C
  READS: ML_WaveToy::rho(Everywhere)
  READS: ML_WaveToy::u(Everywhere)
  WRITES: ML_WaveToy::rhorhs(Interior)
  WRITES: ML_WaveToy::urhs(Interior)
} "WT_RHS"

schedule WT_Dirichlet IN MoL_CalcRHS
{
  LANG: C
  WRITES: ML_WaveToy::rhorhs(Boundary)
  WRITES: ML_WaveToy::urhs(Boundary)
} "WT_Dirichlet"

schedule WT_Dirichlet AT analysis
{
  LANG: C
  SYNC: WT_rhorhs
  SYNC: WT_urhs
  WRITES: ML_WaveToy::rhorhs(Boundary)
  WRITES: ML_WaveToy::urhs(Boundary)
} "WT_Dirichlet"

schedule WT_Energy AT analysis
{
  LANG: C
  SYNC: WT_eps
  READS: ML_WaveToy::rho(Everywhere)
  READS: ML_WaveToy::u(Everywhere)
  WRITES: ML_WaveToy::eps(Interior)
} "WT_Energy"

schedule WT_EnergyBoundary AT analysis
{
  LANG: C
  SYNC: WT_eps
  WRITES: ML_WaveToy::eps(Boundary)
} "WT_EnergyBoundary"

schedule ML_WaveToy_SelectBoundConds in MoL_PostStep
{
  LANG: C
  OPTIONS: level
  SYNC: WT_u
  SYNC: WT_rho
} "select boundary conditions"

schedule ML_WaveToy_CheckBoundaries at BASEGRID
{
  LANG: C
  OPTIONS: meta
} "check boundaries treatment"

schedule ML_WaveToy_RegisterVars in MoL_Register
{
  LANG: C
  OPTIONS: meta
} "Register Variables for MoL"
schedule group ApplyBCs as ML_WaveToy_ApplyBCs in MoL_PostStep after ML_WaveToy_SelectBoundConds
{
} "Apply boundary conditions controlled by thorn Boundary"

param: # File produced by Kranc


shares: GenericFD

USES CCTK_INT assume_stress_energy_state


shares: MethodOfLines

USES CCTK_INT MoL_Num_Evolved_Vars
USES CCTK_INT MoL_Num_ArrayEvolved_Vars

restricted:
CCTK_INT verbose "verbose" STEERABLE=ALWAYS
{
  *:* :: ""
} 0

restricted:
CCTK_INT other_timelevels "Number of active timelevels for non-evolved grid functions" STEERABLE=RECOVER
{
  0:4 :: ""
} 1

restricted:
CCTK_REAL amplitude "Amplitude of initial Gaussian"
{
  *:* :: ""
} 1

restricted:
CCTK_REAL width "Width of initial Gaussian"
{
  *:* :: ""
} 1

restricted:
CCTK_INT tile_size "Loop tile size"
{
  *:* :: ""
} -1

private:
CCTK_KEYWORD initial_data "initial_data"
{
  "Gaussian" :: ""
  "Standing" :: ""
} "Gaussian"

restricted:
CCTK_INT ML_WaveToy_MaxNumEvolvedVars "Number of evolved variables used by this thorn" ACCUMULATOR-BASE=MethodofLines::MoL_Num_Evolved_Vars STEERABLE=RECOVER
{
  2:2 :: "Number of evolved variables used by this thorn"
} 2

restricted:
CCTK_INT ML_WaveToy_MaxNumArrayEvolvedVars "Number of Array evolved variables used by this thorn" ACCUMULATOR-BASE=MethodofLines::MoL_Num_ArrayEvolved_Vars STEERABLE=RECOVER
{
  0:0 :: "Number of Array evolved variables used by this thorn"
} 0

restricted:
CCTK_INT timelevels "Number of active timelevels" STEERABLE=RECOVER
{
  0:4 :: ""
} 4

restricted:
CCTK_INT rhs_timelevels "Number of active RHS timelevels" STEERABLE=RECOVER
{
  0:4 :: ""
} 1

restricted:
CCTK_INT WT_Gaussian_calc_every "WT_Gaussian_calc_every" STEERABLE=ALWAYS
{
  *:* :: ""
} 1

restricted:
CCTK_INT WT_Standing_calc_every "WT_Standing_calc_every" STEERABLE=ALWAYS
{
  *:* :: ""
} 1

restricted:
CCTK_INT WT_RHS_calc_every "WT_RHS_calc_every" STEERABLE=ALWAYS
{
  *:* :: ""
} 1

restricted:
CCTK_INT WT_Dirichlet_calc_every "WT_Dirichlet_calc_every" STEERABLE=ALWAYS
{
  *:* :: ""
} 1

restricted:
CCTK_INT WT_Energy_calc_every "WT_Energy_calc_every" STEERABLE=ALWAYS
{
  *:* :: ""
} 1

restricted:
CCTK_INT WT_EnergyBoundary_calc_every "WT_EnergyBoundary_calc_every" STEERABLE=ALWAYS
{
  *:* :: ""
} 1

restricted:
CCTK_INT WT_Gaussian_calc_offset "WT_Gaussian_calc_offset" STEERABLE=ALWAYS
{
  *:* :: ""
} 0

restricted:
CCTK_INT WT_Standing_calc_offset "WT_Standing_calc_offset" STEERABLE=ALWAYS
{
  *:* :: ""
} 0

restricted:
CCTK_INT WT_RHS_calc_offset "WT_RHS_calc_offset" STEERABLE=ALWAYS
{
  *:* :: ""
} 0

restricted:
CCTK_INT WT_Dirichlet_calc_offset "WT_Dirichlet_calc_offset" STEERABLE=ALWAYS
{
  *:* :: ""
} 0

restricted:
CCTK_INT WT_Energy_calc_offset "WT_Energy_calc_offset" STEERABLE=ALWAYS
{
  *:* :: ""
} 0

restricted:
CCTK_INT WT_EnergyBoundary_calc_offset "WT_EnergyBoundary_calc_offset" STEERABLE=ALWAYS
{
  *:* :: ""
} 0

private:
CCTK_KEYWORD u_bound "Boundary condition to implement" STEERABLE=ALWAYS
{
  "flat" :: "Flat boundary condition"
  "none" :: "No boundary condition"
  "static" :: "Boundaries held fixed"
  "radiative" :: "Radiation boundary condition"
  "scalar" :: "Dirichlet boundary condition"
  "newrad" :: "Improved radiative boundary condition"
  "skip" :: "skip boundary condition code"
} "skip"

private:
CCTK_KEYWORD rho_bound "Boundary condition to implement" STEERABLE=ALWAYS
{
  "flat" :: "Flat boundary condition"
  "none" :: "No boundary condition"
  "static" :: "Boundaries held fixed"
  "radiative" :: "Radiation boundary condition"
  "scalar" :: "Dirichlet boundary condition"
  "newrad" :: "Improved radiative boundary condition"
  "skip" :: "skip boundary condition code"
} "skip"

private:
CCTK_KEYWORD WT_u_bound "Boundary condition to implement" STEERABLE=ALWAYS
{
  "flat" :: "Flat boundary condition"
  "none" :: "No boundary condition"
  "static" :: "Boundaries held fixed"
  "radiative" :: "Radiation boundary condition"
  "scalar" :: "Dirichlet boundary condition"
  "newrad" :: "Improved radiative boundary condition"
  "skip" :: "skip boundary condition code"
} "none"

private:
CCTK_KEYWORD WT_rho_bound "Boundary condition to implement" STEERABLE=ALWAYS
{
  "flat" :: "Flat boundary condition"
  "none" :: "No boundary condition"
  "static" :: "Boundaries held fixed"
  "radiative" :: "Radiation boundary condition"
  "scalar" :: "Dirichlet boundary condition"
  "newrad" :: "Improved radiative boundary condition"
  "skip" :: "skip boundary condition code"
} "none"

private:
CCTK_REAL u_bound_speed "characteristic speed at boundary" STEERABLE=ALWAYS
{
  0:* :: "outgoing characteristic speed > 0"
} 1.

private:
CCTK_REAL rho_bound_speed "characteristic speed at boundary" STEERABLE=ALWAYS
{
  0:* :: "outgoing characteristic speed > 0"
} 1.

private:
CCTK_REAL WT_u_bound_speed "characteristic speed at boundary" STEERABLE=ALWAYS
{
  0:* :: "outgoing characteristic speed > 0"
} 1.

private:
CCTK_REAL WT_rho_bound_speed "characteristic speed at boundary" STEERABLE=ALWAYS
{
  0:* :: "outgoing characteristic speed > 0"
} 1.

private:
CCTK_REAL u_bound_limit "limit value for r -> infinity" STEERABLE=ALWAYS
{
  *:* :: "value of limit value is unrestricted"
} 0.

private:
CCTK_REAL rho_bound_limit "limit value for r -> infinity" STEERABLE=ALWAYS
{
  *:* :: "value of limit value is unrestricted"
} 0.

private:
CCTK_REAL WT_u_bound_limit "limit value for r -> infinity" STEERABLE=ALWAYS
{
  *:* :: "value of limit value is unrestricted"
} 0.

private:
CCTK_REAL WT_rho_bound_limit "limit value for r -> infinity" STEERABLE=ALWAYS
{
  *:* :: "value of limit value is unrestricted"
} 0.

private:
CCTK_REAL u_bound_scalar "Dirichlet boundary value" STEERABLE=ALWAYS
{
  *:* :: "unrestricted"
} 0.

private:
CCTK_REAL rho_bound_scalar "Dirichlet boundary value" STEERABLE=ALWAYS
{
  *:* :: "unrestricted"
} 0.

private:
CCTK_REAL WT_u_bound_scalar "Dirichlet boundary value" STEERABLE=ALWAYS
{
  *:* :: "unrestricted"
} 0.

private:
CCTK_REAL WT_rho_bound_scalar "Dirichlet boundary value" STEERABLE=ALWAYS
{
  *:* :: "unrestricted"
} 0.


configuration: # File produced by Kranc

REQUIRES GenericFD
REQUIRES LoopControl
REQUIRES Vectors

context: WT_RHS.cc:
```
/*  File produced by Kranc */

#define KRANC_C

#include <algorithm>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Kranc.hh"
#include "Differencing.h"
#include "loopcontrol.h"
#include "vectors.h"

namespace ML_WaveToy {

extern "C" void WT_RHS_SelectBCs(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (cctk_iteration % WT_RHS_calc_every != WT_RHS_calc_offset)
    return;
  CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
  ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_WaveToy::WT_rhorhs","flat");
  if (ierr < 0)
    CCTK_WARN(CCTK_WARN_ALERT, "Failed to register flat BC for ML_WaveToy::WT_rhorhs.");
  ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_WaveToy::WT_urhs","flat");
  if (ierr < 0)
    CCTK_WARN(CCTK_WARN_ALERT, "Failed to register flat BC for ML_WaveToy::WT_urhs.");
  return;
}

static void WT_RHS_Body(const cGH* restrict const cctkGH, const int dir, const int face, const CCTK_REAL normal[3], const CCTK_REAL tangentA[3], const CCTK_REAL tangentB[3], const int imin[3], const int imax[3], const int n_subblock_gfs, CCTK_REAL* restrict const subblock_gfs[])
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  /* Include user-supplied include files */
  /* Initialise finite differencing variables */
  const ptrdiff_t di CCTK_ATTRIBUTE_UNUSED = 1;
  const ptrdiff_t dj CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t dk CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * di;
  const ptrdiff_t cdj CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dj;
  const ptrdiff_t cdk CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dk;
  const ptrdiff_t cctkLbnd1 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[0];
  const ptrdiff_t cctkLbnd2 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[1];
  const ptrdiff_t cctkLbnd3 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[2];
  const CCTK_REAL_VEC t CCTK_ATTRIBUTE_UNUSED = ToReal(cctk_time);
  const CCTK_REAL_VEC cctkOriginSpace1 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(0));
  const CCTK_REAL_VEC cctkOriginSpace2 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(1));
  const CCTK_REAL_VEC cctkOriginSpace3 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(2));
  const CCTK_REAL_VEC dt CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_TIME);
  const CCTK_REAL_VEC dx CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(0));
  const CCTK_REAL_VEC dy CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(1));
  const CCTK_REAL_VEC dz CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(2));
  const CCTK_REAL_VEC dxi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dx);
  const CCTK_REAL_VEC dyi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dy);
  const CCTK_REAL_VEC dzi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dz);
  const CCTK_REAL_VEC khalf CCTK_ATTRIBUTE_UNUSED = ToReal(0.5);
  const CCTK_REAL_VEC kthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.333333333333333333333333333333);
  const CCTK_REAL_VEC ktwothird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.666666666666666666666666666667);
  const CCTK_REAL_VEC kfourthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(1.33333333333333333333333333333);
  const CCTK_REAL_VEC hdxi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dxi,ToReal(0.5));
  const CCTK_REAL_VEC hdyi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dyi,ToReal(0.5));
  const CCTK_REAL_VEC hdzi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dzi,ToReal(0.5));
  /* Initialize predefined quantities */
  const CCTK_REAL_VEC p1o12dx CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dx);
  const CCTK_REAL_VEC p1o12dy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dy);
  const CCTK_REAL_VEC p1o12dz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dz);
  const CCTK_REAL_VEC p1o144dxdy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dy));
  const CCTK_REAL_VEC p1o144dxdz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dz));
  const CCTK_REAL_VEC p1o144dydz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dy,dz));
  const CCTK_REAL_VEC pm1o12dx2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dx,dx));
  const CCTK_REAL_VEC pm1o12dy2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dy,dy));
  const CCTK_REAL_VEC pm1o12dz2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dz,dz));
  /* Assign local copies of arrays functions */
  
  
  /* Calculate temporaries and arrays functions */
  /* Copy local copies back to grid functions */
  /* Loop over the grid points */
  const int imin0=imin[0];
  const int imin1=imin[1];
  const int imin2=imin[2];
  const int imax0=imax[0];
  const int imax1=imax[1];
  const int imax2=imax[2];
  #pragma omp parallel
  CCTK_LOOP3STR(WT_RHS,
    i,j,k, imin0,imin1,imin2, imax0,imax1,imax2,
    cctk_ash[0],cctk_ash[1],cctk_ash[2],
    vecimin,vecimax, CCTK_REAL_VEC_SIZE)
  {
    const ptrdiff_t index CCTK_ATTRIBUTE_UNUSED = di*i + dj*j + dk*k;
    /* Assign local copies of grid functions */
    
    CCTK_REAL_VEC rhoL CCTK_ATTRIBUTE_UNUSED = vec_load(rho[index]);
    CCTK_REAL_VEC uL CCTK_ATTRIBUTE_UNUSED = vec_load(u[index]);
    
    /* Include user supplied include files */
    /* Precompute derivatives */
    const CCTK_REAL_VEC PDstandardNth11u CCTK_ATTRIBUTE_UNUSED = PDstandardNth11(&u[index]);
    const CCTK_REAL_VEC PDstandardNth22u CCTK_ATTRIBUTE_UNUSED = PDstandardNth22(&u[index]);
    const CCTK_REAL_VEC PDstandardNth33u CCTK_ATTRIBUTE_UNUSED = PDstandardNth33(&u[index]);
    /* Calculate temporaries and grid functions */
    CCTK_REAL_VEC urhsL CCTK_ATTRIBUTE_UNUSED = rhoL;
    
    CCTK_REAL_VEC rhorhsL CCTK_ATTRIBUTE_UNUSED = 
      kadd(PDstandardNth11u,kadd(PDstandardNth22u,PDstandardNth33u));
    /* Copy local copies back to grid functions */
    vec_store_partial_prepare(i,vecimin,vecimax);
    vec_store_nta_partial(rhorhs[index],rhorhsL);
    vec_store_nta_partial(urhs[index],urhsL);
  }
  CCTK_ENDLOOP3STR(WT_RHS);
}
extern "C" void WT_RHS(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Entering WT_RHS_Body");
  }
  if (cctk_iteration % WT_RHS_calc_every != WT_RHS_calc_offset)
  {
    return;
  }
  
  const char* const groups[] = {
    "ML_WaveToy::WT_rho",
    "ML_WaveToy::WT_rhorhs",
    "ML_WaveToy::WT_u",
    "ML_WaveToy::WT_urhs"};
  AssertGroupStorage(cctkGH, "WT_RHS", 4, groups);
  
  EnsureStencilFits(cctkGH, "WT_RHS", 2, 2, 2);
  
  LoopOverInterior(cctkGH, WT_RHS_Body);
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Leaving WT_RHS_Body");
  }
}

} // namespace ML_WaveToy

```

WT_Energy.cc:
```
/*  File produced by Kranc */

#define KRANC_C

#include <algorithm>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Kranc.hh"
#include "Differencing.h"
#include "loopcontrol.h"
#include "vectors.h"

namespace ML_WaveToy {

extern "C" void WT_Energy_SelectBCs(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (cctk_iteration % WT_Energy_calc_every != WT_Energy_calc_offset)
    return;
  CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
  ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_WaveToy::WT_eps","flat");
  if (ierr < 0)
    CCTK_WARN(CCTK_WARN_ALERT, "Failed to register flat BC for ML_WaveToy::WT_eps.");
  return;
}

static void WT_Energy_Body(const cGH* restrict const cctkGH, const int dir, const int face, const CCTK_REAL normal[3], const CCTK_REAL tangentA[3], const CCTK_REAL tangentB[3], const int imin[3], const int imax[3], const int n_subblock_gfs, CCTK_REAL* restrict const subblock_gfs[])
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  /* Include user-supplied include files */
  /* Initialise finite differencing variables */
  const ptrdiff_t di CCTK_ATTRIBUTE_UNUSED = 1;
  const ptrdiff_t dj CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t dk CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * di;
  const ptrdiff_t cdj CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dj;
  const ptrdiff_t cdk CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dk;
  const ptrdiff_t cctkLbnd1 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[0];
  const ptrdiff_t cctkLbnd2 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[1];
  const ptrdiff_t cctkLbnd3 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[2];
  const CCTK_REAL_VEC t CCTK_ATTRIBUTE_UNUSED = ToReal(cctk_time);
  const CCTK_REAL_VEC cctkOriginSpace1 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(0));
  const CCTK_REAL_VEC cctkOriginSpace2 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(1));
  const CCTK_REAL_VEC cctkOriginSpace3 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(2));
  const CCTK_REAL_VEC dt CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_TIME);
  const CCTK_REAL_VEC dx CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(0));
  const CCTK_REAL_VEC dy CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(1));
  const CCTK_REAL_VEC dz CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(2));
  const CCTK_REAL_VEC dxi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dx);
  const CCTK_REAL_VEC dyi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dy);
  const CCTK_REAL_VEC dzi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dz);
  const CCTK_REAL_VEC khalf CCTK_ATTRIBUTE_UNUSED = ToReal(0.5);
  const CCTK_REAL_VEC kthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.333333333333333333333333333333);
  const CCTK_REAL_VEC ktwothird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.666666666666666666666666666667);
  const CCTK_REAL_VEC kfourthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(1.33333333333333333333333333333);
  const CCTK_REAL_VEC hdxi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dxi,ToReal(0.5));
  const CCTK_REAL_VEC hdyi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dyi,ToReal(0.5));
  const CCTK_REAL_VEC hdzi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dzi,ToReal(0.5));
  /* Initialize predefined quantities */
  const CCTK_REAL_VEC p1o12dx CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dx);
  const CCTK_REAL_VEC p1o12dy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dy);
  const CCTK_REAL_VEC p1o12dz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dz);
  const CCTK_REAL_VEC p1o144dxdy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dy));
  const CCTK_REAL_VEC p1o144dxdz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dz));
  const CCTK_REAL_VEC p1o144dydz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dy,dz));
  const CCTK_REAL_VEC pm1o12dx2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dx,dx));
  const CCTK_REAL_VEC pm1o12dy2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dy,dy));
  const CCTK_REAL_VEC pm1o12dz2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dz,dz));
  /* Assign local copies of arrays functions */
  
  
  /* Calculate temporaries and arrays functions */
  /* Copy local copies back to grid functions */
  /* Loop over the grid points */
  const int imin0=imin[0];
  const int imin1=imin[1];
  const int imin2=imin[2];
  const int imax0=imax[0];
  const int imax1=imax[1];
  const int imax2=imax[2];
  #pragma omp parallel
  CCTK_LOOP3STR(WT_Energy,
    i,j,k, imin0,imin1,imin2, imax0,imax1,imax2,
    cctk_ash[0],cctk_ash[1],cctk_ash[2],
    vecimin,vecimax, CCTK_REAL_VEC_SIZE)
  {
    const ptrdiff_t index CCTK_ATTRIBUTE_UNUSED = di*i + dj*j + dk*k;
    /* Assign local copies of grid functions */
    
    CCTK_REAL_VEC rhoL CCTK_ATTRIBUTE_UNUSED = vec_load(rho[index]);
    CCTK_REAL_VEC uL CCTK_ATTRIBUTE_UNUSED = vec_load(u[index]);
    
    /* Include user supplied include files */
    /* Precompute derivatives */
    const CCTK_REAL_VEC PDstandardNth1u CCTK_ATTRIBUTE_UNUSED = PDstandardNth1(&u[index]);
    const CCTK_REAL_VEC PDstandardNth2u CCTK_ATTRIBUTE_UNUSED = PDstandardNth2(&u[index]);
    const CCTK_REAL_VEC PDstandardNth3u CCTK_ATTRIBUTE_UNUSED = PDstandardNth3(&u[index]);
    /* Calculate temporaries and grid functions */
    CCTK_REAL_VEC epsL CCTK_ATTRIBUTE_UNUSED = 
      kmul(kmadd(rhoL,rhoL,kmadd(PDstandardNth1u,PDstandardNth1u,kmadd(PDstandardNth2u,PDstandardNth2u,kmul(PDstandardNth3u,PDstandardNth3u)))),ToReal(0.5));
    /* Copy local copies back to grid functions */
    vec_store_partial_prepare(i,vecimin,vecimax);
    vec_store_nta_partial(eps[index],epsL);
  }
  CCTK_ENDLOOP3STR(WT_Energy);
}
extern "C" void WT_Energy(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Entering WT_Energy_Body");
  }
  if (cctk_iteration % WT_Energy_calc_every != WT_Energy_calc_offset)
  {
    return;
  }
  
  const char* const groups[] = {
    "ML_WaveToy::WT_eps",
    "ML_WaveToy::WT_rho",
    "ML_WaveToy::WT_u"};
  AssertGroupStorage(cctkGH, "WT_Energy", 3, groups);
  
  EnsureStencilFits(cctkGH, "WT_Energy", 2, 2, 2);
  
  LoopOverInterior(cctkGH, WT_Energy_Body);
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Leaving WT_Energy_Body");
  }
}

} // namespace ML_WaveToy

```

Kranc.cc:
```

/*  Copyright 2014 Ian Hinder

    This file is part of Kranc.

    Kranc is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    Kranc is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with Kranc; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*/
                                             
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

#include <cctk.h>
#include <cctk_Arguments.h>
#include <cctk_Parameters.h>
#include <util_Table.h>

#include <Symmetry.h>
            
#include "Kranc.hh"

namespace ML_WaveToy {

/*********************************************************************
 * GetBoundaryWidths
 *********************************************************************/

void GetBoundaryWidths(cGH const * restrict const cctkGH, CCTK_INT nboundaryzones[6])
{
  CCTK_INT is_internal[6];
  CCTK_INT is_staggered[6];
  CCTK_INT shiftout[6];
  int ierr = -1;

  if (CCTK_IsFunctionAliased ("MultiPatch_GetBoundarySpecification")) {
    int const map = MultiPatch_GetMap (cctkGH);
    /* This doesn't make sense in level mode */
    if (map < 0)
    {
      static int have_warned = 0;
      if (!have_warned)
      {
        CCTK_WARN(1, "GetBoundaryWidths: Could not determine current map (can be caused by calling in LEVEL mode)");
        have_warned = 1;
      }
      for (int i = 0; i < 6; i++)
        nboundaryzones[i] = 0;
      return;
    }
    ierr = MultiPatch_GetBoundarySpecification
      (map, 6, nboundaryzones, is_internal, is_staggered, shiftout);
    if (ierr != 0)
      CCTK_WARN(0, "Could not obtain boundary specification");
  } else if (CCTK_IsFunctionAliased ("GetBoundarySpecification")) {
    ierr = GetBoundarySpecification
      (6, nboundaryzones, is_internal, is_staggered, shiftout);
    if (ierr != 0)
      CCTK_WARN(0, "Could not obtain boundary specification");
  } else {
    CCTK_WARN(0, "Could not obtain boundary specification");
  }
}

/*********************************************************************
 * GetBoundaryWidth
 *********************************************************************/

int GetBoundaryWidth(cGH const * restrict const cctkGH)
{
  CCTK_INT nboundaryzones[6];
  GetBoundaryWidths(cctkGH, nboundaryzones);

  int bw = nboundaryzones[0];

  for (int i = 1; i < 6; i++)
    if (nboundaryzones[i] != bw)
    CCTK_WARN(0, "Number of boundary points is different on different faces");

  return bw;
}

/*********************************************************************
 * GetBoundaryInfo
 *********************************************************************/

/* Return the array indices in imin and imax for looping over the
   interior of the grid. imin is the index of the first grid point.
   imax is the index of the last grid point plus 1.  So a loop over
   the interior of the grid would be

   for (i = imin; i < imax; i++)

   The indexing is C-style. Also return whether the boundary is a
   symmetry, physical or interprocessor boundary.  Carpet refinement
   boundaries are treated as interprocessor boundaries.
*/
void GetBoundaryInfo(cGH const * restrict const cctkGH,
                               int const * restrict const cctk_ash,
                               int const * restrict const cctk_lsh,
                               int const * restrict const cctk_bbox,
			       int const * restrict const cctk_nghostzones,
                               int * restrict const imin, 
			       int * restrict const imax,
                               int * restrict const is_symbnd, 
			       int * restrict const is_physbnd,
                               int * restrict const is_ipbnd)
{
  CCTK_INT bbox[6];
  CCTK_INT nboundaryzones[6];
  CCTK_INT is_internal[6];
  CCTK_INT is_staggered[6];
  CCTK_INT shiftout[6];
  CCTK_INT symbnd[6];

  int symtable = 0;
  int dir = 0;
  int face = 0;
  int npoints = 0;
  int iret = 0;
  int ierr = 0;

  if (CCTK_IsFunctionAliased ("MultiPatch_GetBbox")) {
    ierr = MultiPatch_GetBbox (cctkGH, 6, bbox);
    if (ierr != 0)
      CCTK_WARN(0, "Could not obtain bbox specification");
  } else {
    for (dir = 0; dir < 6; dir++)
    {
      bbox[dir] = 0;
    }
  }

  if (CCTK_IsFunctionAliased ("MultiPatch_GetBoundarySpecification")) {
    int const map = MultiPatch_GetMap (cctkGH);
    if (map < 0)
      CCTK_WARN(0, "Could not obtain boundary specification");
    ierr = MultiPatch_GetBoundarySpecification
      (map, 6, nboundaryzones, is_internal, is_staggered, shiftout);
    if (ierr != 0)
      CCTK_WARN(0, "Could not obtain boundary specification");
  } else if (CCTK_IsFunctionAliased ("GetBoundarySpecification")) {
    ierr = GetBoundarySpecification
      (6, nboundaryzones, is_internal, is_staggered, shiftout);
    if (ierr != 0)
      CCTK_WARN(0, "Could not obtain boundary specification");
  } else {
    CCTK_WARN(0, "Could not obtain boundary specification");
  }

  symtable = SymmetryTableHandleForGrid(cctkGH);
  if (symtable < 0) 
  {
    CCTK_WARN(0, "Could not obtain symmetry table");
  }  
  
  iret = Util_TableGetIntArray(symtable, 6, symbnd, "symmetry_handle");
  if (iret != 6) CCTK_WARN (0, "Could not obtain symmetry information");

  for (dir = 0; dir < 6; dir++)
  {
    is_ipbnd[dir] = (!cctk_bbox[dir]);
    is_symbnd[dir] = (!is_ipbnd[dir] && symbnd[dir] >= 0 && !bbox[dir]);
    is_physbnd[dir] = (!is_ipbnd[dir] && !is_symbnd[dir]);
  }

  for (dir = 0; dir < 3; dir++)
  {
    for (face = 0; face < 2; face++)
    {
      int index = dir*2 + face;
      if (is_ipbnd[index])
      {
	/* Inter-processor boundary */
	npoints = cctk_nghostzones[dir];
      }
      else
      {
	/* Symmetry or physical boundary */
	npoints = nboundaryzones[index];
             
	if (is_symbnd[index])
	{
	  /* Ensure that the number of symmetry zones is the same
	     as the number of ghost zones */
	  if (npoints != cctk_nghostzones[dir])
	  {
	    CCTK_WARN (1, "The number of symmetry points is different from the number of ghost points; this is probably an error");
	  }
	}
      }

      switch(face)
      {
      case 0: /* Lower boundary */
	imin[dir] = npoints;
	break;
      case 1: /* Upper boundary */
	imax[dir] = cctk_lsh[dir] - npoints;
	break;
      default:
	CCTK_WARN(0, "internal error");
      }
    }
  }
}

/*********************************************************************
 * LoopOverEverything
 *********************************************************************/

void LoopOverEverything(cGH const * restrict const cctkGH, Kranc_Calculation const calc)
{
  DECLARE_CCTK_ARGUMENTS

  int   dir = 0;
  int   face = 0;
  CCTK_REAL  normal[] = {0,0,0};
  CCTK_REAL  tangentA[] = {0,0,0};
  CCTK_REAL  tangentB[] = {0,0,0};
  int   bmin[] = {0,0,0};
  int   bmax[] = {cctk_lsh[0],cctk_lsh[1],cctk_lsh[2]};

  calc(cctkGH, dir, face, normal, tangentA, tangentB, bmin, bmax, 0, NULL);
  return;
}

/*********************************************************************
 * LoopOverBoundary
 *********************************************************************/

void LoopOverBoundary(cGH const * restrict const cctkGH, Kranc_Calculation const calc)
{
  DECLARE_CCTK_ARGUMENTS

  int   dir1, dir2, dir3;
  int   dir[3];
  CCTK_REAL  normal[3];
  CCTK_REAL  tangentA[3];
  CCTK_REAL  tangentB[3];
  int   bmin[3];
  int   bmax[3];
  int   have_bnd;
  int   all_physbnd;
  int   d;

  int   is_symbnd[6], is_physbnd[6], is_ipbnd[6];
  int   imin[3], imax[3];
  int        old_dir = 0;
  int        old_face = 0;

  GetBoundaryInfo(cctkGH, cctk_ash, cctk_lsh, cctk_bbox,
                  cctk_nghostzones, 
                  imin, imax, is_symbnd, is_physbnd, is_ipbnd);

 /* Loop over all faces */
  for (dir3 = -1; dir3 <= +1; dir3++)
  {
    for (dir2 = -1; dir2 <= +1; dir2++)
    {
      for (dir1 = -1; dir1 <= +1; dir1++)
      {
        dir[0] = dir1;
        dir[1] = dir2;
        dir[2] = dir3;

        have_bnd = 0;          /* one of the faces is a boundary */
        all_physbnd = 1;       /* all boundary faces are physical
                                  boundaries */

        for (d = 0; d < 3; d++)
        {
          switch(dir[d])
          {
          case -1:
            bmin[d] = 0;
            bmax[d] = imin[d];
            have_bnd = 1;
            all_physbnd = all_physbnd && is_physbnd[2*d+0];
            break;
          case 0:
            bmin[d] = imin[d];
            bmax[d] = imax[d];
            break;
          case +1:
            bmin[d] = imax[d];
            bmax[d] = cctk_lsh[d];
            have_bnd = 1;
            all_physbnd = all_physbnd && is_physbnd[2*d+1];
            break;
          }

          /* Choose a basis */
          normal[d] = dir[d];
          tangentA[d] = dir[(d+1)%3];
          tangentB[d] = dir[(d+2)%3];
        }

        if (have_bnd && all_physbnd)
        {
#if 0
          CCTK_REAL normal_norm = 0.0;
          for (d = 0; d < 3; d++)
          {
            normal_norm += pow(normal[d], 2);
          }
          normal_norm = sqrt(normal_norm);
          for (d = 0; d < 3; d++)
          {
            normal[d] /= normal_norm;
          }
#endif
          
          calc(cctkGH, old_dir, old_face, normal, tangentA, tangentB, bmin, bmax, 0, NULL);
        }

      }
    }
  }
  
  return;
}

/*********************************************************************
 * LoopOverBoundaryWithGhosts
 *********************************************************************/

void LoopOverBoundaryWithGhosts(cGH const * restrict const cctkGH, Kranc_Calculation const calc)
{
  DECLARE_CCTK_ARGUMENTS

  int   dir1, dir2, dir3;
  int   dir[3];
  CCTK_REAL  normal[3];
  CCTK_REAL  tangentA[3];
  CCTK_REAL  tangentB[3];
  int   bmin[3];
  int   bmax[3];
  int   have_bnd;
  int   have_physbnd;
  int   d;

  int   is_symbnd[6], is_physbnd[6], is_ipbnd[6];
  int   imin[3], imax[3];
  int        old_dir = 0;
  int        old_face = 0;

  GetBoundaryInfo(cctkGH, cctk_ash, cctk_lsh, cctk_bbox,
                  cctk_nghostzones, 
                  imin, imax, is_symbnd, is_physbnd, is_ipbnd);

 /* Loop over all faces */
  for (dir3 = -1; dir3 <= +1; dir3++)
  {
    for (dir2 = -1; dir2 <= +1; dir2++)
    {
      for (dir1 = -1; dir1 <= +1; dir1++)
      {
        dir[0] = dir1;
        dir[1] = dir2;
        dir[2] = dir3;

        have_bnd = 0;          /* one of the faces is a boundary */
        have_physbnd = 0;      /* one of the boundary faces is a physical
                                  boundary */

        for (d = 0; d < 3; d++)
        {
          switch(dir[d])
          {
          case -1:
            bmin[d] = 0;
            bmax[d] = imin[d];
            have_bnd = 1;
            have_physbnd = have_physbnd || is_physbnd[2*d+0];
            break;
          case 0:
            bmin[d] = imin[d];
            bmax[d] = imax[d];
            break;
          case +1:
            bmin[d] = imax[d];
            bmax[d] = cctk_lsh[d];
            have_bnd = 1;
            have_physbnd = have_physbnd || is_physbnd[2*d+1];
            break;
          }

          /* Choose a basis */
          normal[d] = dir[d];
          tangentA[d] = dir[(d+1)%3];
          tangentB[d] = dir[(d+2)%3];
        }

        if (have_bnd && have_physbnd)
        {
#if 0
          CCTK_REAL normal_norm = 0.0;
          for (d = 0; d < 3; d++)
          {
            normal_norm += pow(normal[d], 2);
          }
          normal_norm = sqrt(normal_norm);
          for (d = 0; d < 3; d++)
          {
            normal[d] /= normal_norm;
          }
#endif
          
          calc(cctkGH, old_dir, old_face, normal, tangentA, tangentB, bmin, bmax, 0, NULL);
        }

      }
    }
  }
  
  return;
}

/*********************************************************************
 * LoopOverInterior
 *********************************************************************/

void LoopOverInterior(cGH const * restrict const cctkGH, Kranc_Calculation const calc)
{
  DECLARE_CCTK_ARGUMENTS

  CCTK_REAL  normal[] = {0,0,0};
  CCTK_REAL  tangentA[] = {0,0,0};
  CCTK_REAL  tangentB[] = {0,0,0};

  int   is_symbnd[6], is_physbnd[6], is_ipbnd[6];
  int   imin[3], imax[3];
  int        dir = 0;
  int        face = 0;

  GetBoundaryInfo(cctkGH, cctk_ash, cctk_lsh, cctk_bbox,
                            cctk_nghostzones, 
                            imin, imax, is_symbnd, is_physbnd, is_ipbnd);

  calc(cctkGH, dir, face, normal, tangentA, tangentB, imin, imax, 0, NULL);
  
  return;
}

/*********************************************************************
 * AssertGroupStorage
 *********************************************************************/

void AssertGroupStorage(cGH const * restrict const cctkGH, const char *calc,
                                  int ngroups, const char *const group_names[])
{
  for (int i = 0; i < ngroups; i++)
  {
    int result = CCTK_QueryGroupStorage(cctkGH, group_names[i]);
    if (result == 0)
    {
      CCTK_VWarn(CCTK_WARN_ABORT, __LINE__, __FILE__, CCTK_THORNSTRING,
                 "Error in %s: Group \"%s\" does not have storage", calc, group_names[i]);
    }
    else if (result < 0)
    {
      CCTK_VWarn(CCTK_WARN_ABORT, __LINE__, __FILE__, CCTK_THORNSTRING,
                 "Error in %s: Invalid group name \"%s\"", calc, group_names[i]);
    }
  }
}

/*********************************************************************
 * GroupDataPointers
 *********************************************************************/

/* Return a list of pointers to the members of a named group */
void GroupDataPointers(cGH const * restrict const cctkGH, const char *group_name,
                                 int nvars, CCTK_REAL const *restrict *ptrs)
{
  int group_index, status;
  cGroup  group_info;

  group_index = CCTK_GroupIndex(group_name);
  if (group_index < 0)
    CCTK_VWarn(CCTK_WARN_ABORT,   __LINE__, __FILE__, CCTK_THORNSTRING,
               "Error return %d trying to get group index for group \'%s\'",
               group_index,
               group_name);

  status = CCTK_GroupData(group_index, &group_info);
  if (status < 0)
    CCTK_VWarn(CCTK_WARN_ABORT,   __LINE__, __FILE__, CCTK_THORNSTRING,
               "Error return %d trying to get info for group \'%s\'",
               status,
               group_name);

  if (group_info.numvars != nvars)
  {
    CCTK_VWarn(CCTK_WARN_ABORT,   __LINE__, __FILE__, CCTK_THORNSTRING,
               "Group \'%s\' has %d variables but %d were expected",
               group_name, group_info.numvars, nvars);
  }

  int v1 = CCTK_FirstVarIndex(group_name);

  for (int v = 0; v < nvars; v++)
  {
    ptrs[v] = (CCTK_REAL const *) CCTK_VarDataPtrI(cctkGH, 0 /* timelevel */, v1+v);
  }
}

/*********************************************************************
 * EnsureStencilFits
 *********************************************************************/

void EnsureStencilFits(cGH const * restrict const cctkGH, const char *calc, int ni, int nj, int nk)
{
  DECLARE_CCTK_ARGUMENTS

  CCTK_INT bws[6];
  GetBoundaryWidths(cctkGH, bws);

  int ns[] = {ni, nj, nk};
  const char *dirs[] = {"x", "y", "z"};
  const char *faces[] = {"lower", "upper"};
  int abort = 0;

  for (int dir = 0; dir < 3; dir++)
  {
    for (int face = 0; face < 2; face++)
    {
      int bw = bws[2*dir+face];
      if (bw < ns[dir])
      {
        CCTK_VInfo(CCTK_THORNSTRING,
                   "The stencil for %s requires %d points, but the %s %s boundary has only %d points.",
                   calc, ns[dir], faces[face], dirs[dir], bw);
        abort = 1;
      }
    }
    int gz = cctk_nghostzones[dir];
    if (gz < ns[dir])
    {
      CCTK_VInfo(CCTK_THORNSTRING,
                 "The stencil for %s requires %d points, but there are only %d ghost zones in the %s direction.",
                 calc, ns[dir], gz, dirs[dir]);
      abort = 1;
    }
  }

  if (abort)
  {
    CCTK_VWarn(CCTK_WARN_ABORT, __LINE__, __FILE__, CCTK_THORNSTRING,
               "Insufficient ghost or boundary points for %s", calc);
  }
}

/*********************************************************************
 * idiv
 *********************************************************************/

// Divide, rounding to minus infinity
static int idiv(int x, int y)
{
  // round down manually if the result is negative
  return (x^y) >= 0 ? x/y : (x-y+1)/y;
}

/*********************************************************************
 * imod
 *********************************************************************/

// // Modulo, rounding to minus infinity
// static int imod(int x, int y)
// {
//   return (x^y) >= 0 ? x%y : (x-y+1)%y + y-1;
// }

/*********************************************************************
 * ialign
 *********************************************************************/

// Align x to a multiple of y
static int ialign(int x, int y)
{
  return idiv(x, y) * y;
}

/*********************************************************************
 * TiledLoop
 *********************************************************************/

void TiledLoop(
  cGH const * restrict const cctkGH,
  const KrancData & restrict kd_coarse,
  void (calc)(const cGH* restrict const cctkGH,
              const KrancData & restrict kd))
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;

  // Interior region
  int imin[3], imax[3];
  // Boundary types
  int is_symbnd[6], is_physbnd[6], is_ipbnd[6];

  GetBoundaryInfo(cctkGH, cctk_ash, cctk_lsh, cctk_bbox,
                            cctk_nghostzones, 
                            imin, imax, is_symbnd, is_physbnd, is_ipbnd);

  // Tile size
  int tile_size_l[3];
  // Loop bounds covered by tiles (may be larger)
  int tiled_imin[3];
  int tiled_imax[3];

  if (tile_size == -1)
  {
    for (int d = 0; d < 3; d++)
    {
      // Loop in a single tile
      tiled_imin[d] = kd_coarse.imin[d];
      tiled_imax[d] = kd_coarse.imax[d];
      tile_size_l[d] = tiled_imax[d] - tiled_imin[d];
    }
  }
  else
  {
    for (int d = 0; d < 3; d++)
    {
      tile_size_l[d] = tile_size;
      // Align with beginning of interior of domain
      tiled_imin[d] =
        imin[d] + ialign(kd_coarse.imin[d] - imin[d], tile_size_l[d]);
      tiled_imax[d] = kd_coarse.imax[d];
    }
  }

  const int dti = tile_size_l[0];
  const int dtj = tile_size_l[1];
  const int dtk = tile_size_l[2];
#pragma omp parallel for collapse(3)
  for (int tk = tiled_imin[2]; tk < tiled_imax[2]; tk += dtk)
  {
    for (int tj = tiled_imin[1]; tj < tiled_imax[1]; tj += dtj)
    {
      for (int ti = tiled_imin[0]; ti < tiled_imax[0]; ti += dti)
      {
        KrancData kd = kd_coarse;

        kd.dir = 0;
        kd.face = 0;
        // TODO: initialise the rest, or use a constructor

        kd.tile_imin[0] = ti;
        kd.tile_imax[0] = ti + dti;
        kd.tile_imin[1] = tj;
        kd.tile_imax[1] = tj + dtj;
        kd.tile_imin[2] = tk;
        kd.tile_imax[2] = tk + dtk;

        calc(cctkGH, kd);
      }
    }
  }
}

/*********************************************************************
 * TiledLoopOverEverything
 *********************************************************************/

void TiledLoopOverEverything(
  cGH const * restrict const cctkGH,
  void (calc)(const cGH* restrict const cctkGH,
              const KrancData & restrict kd))
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;

  KrancData kd_coarse;

  for (int d = 0; d < 3; d++)
  {
    kd_coarse.imin[d] = 0;
    kd_coarse.imax[d] = cctk_lsh[d];
  }

  TiledLoop(cctkGH, kd_coarse, calc);
}

/*********************************************************************
 * TiledLoopOverInterior
 *********************************************************************/

void TiledLoopOverInterior(
  cGH const * restrict const cctkGH,
  void (calc)(const cGH* restrict const cctkGH,
              const KrancData & restrict kd))
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;

  // Interior region
  int imin[3], imax[3];
  // Boundary types
  int is_symbnd[6], is_physbnd[6], is_ipbnd[6];

  GetBoundaryInfo(cctkGH, cctk_ash, cctk_lsh, cctk_bbox,
                            cctk_nghostzones, 
                            imin, imax, is_symbnd, is_physbnd, is_ipbnd);

  KrancData kd_coarse;

  for (int d = 0; d < 3; d++)
  {
    kd_coarse.imin[d] = imin[d];
    kd_coarse.imax[d] = imax[d];
  }

  TiledLoop(cctkGH, kd_coarse, calc);
}

} // namespace ML_WaveToy
```

WT_Dirichlet.cc:
```
/*  File produced by Kranc */

#define KRANC_C

#include <algorithm>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Kranc.hh"
#include "Differencing.h"
#include "loopcontrol.h"
#include "vectors.h"

namespace ML_WaveToy {

extern "C" void WT_Dirichlet_SelectBCs(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (cctk_iteration % WT_Dirichlet_calc_every != WT_Dirichlet_calc_offset)
    return;
  CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
  ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_WaveToy::WT_rhorhs","flat");
  if (ierr < 0)
    CCTK_WARN(CCTK_WARN_ALERT, "Failed to register flat BC for ML_WaveToy::WT_rhorhs.");
  ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_WaveToy::WT_urhs","flat");
  if (ierr < 0)
    CCTK_WARN(CCTK_WARN_ALERT, "Failed to register flat BC for ML_WaveToy::WT_urhs.");
  return;
}

static void WT_Dirichlet_Body(const cGH* restrict const cctkGH, const int dir, const int face, const CCTK_REAL normal[3], const CCTK_REAL tangentA[3], const CCTK_REAL tangentB[3], const int imin[3], const int imax[3], const int n_subblock_gfs, CCTK_REAL* restrict const subblock_gfs[])
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  /* Include user-supplied include files */
  /* Initialise finite differencing variables */
  const ptrdiff_t di CCTK_ATTRIBUTE_UNUSED = 1;
  const ptrdiff_t dj CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t dk CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * di;
  const ptrdiff_t cdj CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dj;
  const ptrdiff_t cdk CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dk;
  const ptrdiff_t cctkLbnd1 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[0];
  const ptrdiff_t cctkLbnd2 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[1];
  const ptrdiff_t cctkLbnd3 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[2];
  const CCTK_REAL_VEC t CCTK_ATTRIBUTE_UNUSED = ToReal(cctk_time);
  const CCTK_REAL_VEC cctkOriginSpace1 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(0));
  const CCTK_REAL_VEC cctkOriginSpace2 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(1));
  const CCTK_REAL_VEC cctkOriginSpace3 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(2));
  const CCTK_REAL_VEC dt CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_TIME);
  const CCTK_REAL_VEC dx CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(0));
  const CCTK_REAL_VEC dy CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(1));
  const CCTK_REAL_VEC dz CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(2));
  const CCTK_REAL_VEC dxi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dx);
  const CCTK_REAL_VEC dyi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dy);
  const CCTK_REAL_VEC dzi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dz);
  const CCTK_REAL_VEC khalf CCTK_ATTRIBUTE_UNUSED = ToReal(0.5);
  const CCTK_REAL_VEC kthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.333333333333333333333333333333);
  const CCTK_REAL_VEC ktwothird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.666666666666666666666666666667);
  const CCTK_REAL_VEC kfourthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(1.33333333333333333333333333333);
  const CCTK_REAL_VEC hdxi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dxi,ToReal(0.5));
  const CCTK_REAL_VEC hdyi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dyi,ToReal(0.5));
  const CCTK_REAL_VEC hdzi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dzi,ToReal(0.5));
  /* Initialize predefined quantities */
  const CCTK_REAL_VEC p1o12dx CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dx);
  const CCTK_REAL_VEC p1o12dy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dy);
  const CCTK_REAL_VEC p1o12dz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dz);
  const CCTK_REAL_VEC p1o144dxdy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dy));
  const CCTK_REAL_VEC p1o144dxdz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dz));
  const CCTK_REAL_VEC p1o144dydz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dy,dz));
  const CCTK_REAL_VEC pm1o12dx2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dx,dx));
  const CCTK_REAL_VEC pm1o12dy2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dy,dy));
  const CCTK_REAL_VEC pm1o12dz2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dz,dz));
  /* Assign local copies of arrays functions */
  
  
  /* Calculate temporaries and arrays functions */
  /* Copy local copies back to grid functions */
  /* Loop over the grid points */
  const int imin0=imin[0];
  const int imin1=imin[1];
  const int imin2=imin[2];
  const int imax0=imax[0];
  const int imax1=imax[1];
  const int imax2=imax[2];
  #pragma omp parallel
  CCTK_LOOP3STR(WT_Dirichlet,
    i,j,k, imin0,imin1,imin2, imax0,imax1,imax2,
    cctk_ash[0],cctk_ash[1],cctk_ash[2],
    vecimin,vecimax, CCTK_REAL_VEC_SIZE)
  {
    const ptrdiff_t index CCTK_ATTRIBUTE_UNUSED = di*i + dj*j + dk*k;
    /* Assign local copies of grid functions */
    
    
    /* Include user supplied include files */
    /* Precompute derivatives */
    /* Calculate temporaries and grid functions */
    CCTK_REAL_VEC urhsL CCTK_ATTRIBUTE_UNUSED = ToReal(0);
    
    CCTK_REAL_VEC rhorhsL CCTK_ATTRIBUTE_UNUSED = ToReal(0);
    /* Copy local copies back to grid functions */
    vec_store_partial_prepare(i,vecimin,vecimax);
    vec_store_nta_partial(rhorhs[index],rhorhsL);
    vec_store_nta_partial(urhs[index],urhsL);
  }
  CCTK_ENDLOOP3STR(WT_Dirichlet);
}
extern "C" void WT_Dirichlet(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Entering WT_Dirichlet_Body");
  }
  if (cctk_iteration % WT_Dirichlet_calc_every != WT_Dirichlet_calc_offset)
  {
    return;
  }
  
  const char* const groups[] = {
    "ML_WaveToy::WT_rhorhs",
    "ML_WaveToy::WT_urhs"};
  AssertGroupStorage(cctkGH, "WT_Dirichlet", 2, groups);
  
  
  LoopOverBoundary(cctkGH, WT_Dirichlet_Body);
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Leaving WT_Dirichlet_Body");
  }
}

} // namespace ML_WaveToy

```

Kranc.hh:
```
#ifndef KRANC_HH
#define KRANC_HH

#include <cmath>
#include <math.h>
#include <sys/time.h>

#include <cctk.h>

namespace ML_WaveToy {

/*********************************************************************
 * Types
 *********************************************************************/

struct KrancData
{
  // Actual loop bounds
  int imin[3];
  int imax[3];
  // Region covered by this tile
  int tile_imin[3];
  int tile_imax[3];
  // Boundary information
  int dir;
  int face;
  CCTK_REAL normal[3];
  CCTK_REAL tangentA[3];
  CCTK_REAL tangentB[3];
};

typedef void(*Kranc_Calculation)(cGH const * restrict cctkGH,
                                 int eir,
                                 int face,
                                 CCTK_REAL const normal[3],
                                 CCTK_REAL const tangentA[3],
                                 CCTK_REAL const tangentB[3],
                                 int const min[3],
                                 int const max[3], 
                                 int n_subblock_gfs, 
                                 CCTK_REAL * restrict const subblock_gfs[]);

/*********************************************************************
 * Function declarations
 *********************************************************************/

// Boundary information

int GetBoundaryWidth(cGH const * restrict const cctkGH);

void GetBoundaryInfo(cGH const * restrict cctkGH,
                                  int const * restrict cctk_ash,
                                  int const * restrict cctk_lsh,
                                  int const * restrict cctk_bbox,
                                  int const * restrict cctk_nghostzones,
                                  int * restrict imin, 
                                  int * restrict imax,
                                  int * restrict is_symbnd, 
                                  int * restrict is_physbnd,
                                  int * restrict is_ipbnd);

// Looping

void LoopOverEverything(cGH const * restrict cctkGH,
                                     Kranc_Calculation calc);
void LoopOverBoundary(cGH const * restrict cctkGH,
                                   Kranc_Calculation calc);
void LoopOverBoundaryWithGhosts(cGH const * restrict cctkGH,
                                             Kranc_Calculation calc);
void LoopOverInterior(cGH const * restrict cctkGH,
                                   Kranc_Calculation calc);

// Tiled looping

void TiledLoop(
  cGH const * restrict const cctkGH,
  const KrancData & restrict kd_coarse,
  void (calc)(const cGH* restrict const cctkGH,
              const KrancData & restrict kd));

void TiledLoopOverEverything(
  cGH const * restrict const cctkGH,
  void (calc)(const cGH* restrict const cctkGH,
              const KrancData & restrict kd));

void TiledLoopOverInterior(
  cGH const * restrict const cctkGH,
  void (calc)(const cGH* restrict const cctkGH,
              const KrancData & restrict kd));

// void TiledLoopOverBoundary(
//   cGH const * restrict const cctkGH,
//   void (calc)(const cGH* restrict const cctkGH,
//               const KrancData & restrict kd));

// Runtime checks

void EnsureStencilFits(cGH const * restrict const cctkGH,
                                    const char *calc, int ni, int nj, int nk);
void GroupDataPointers(cGH const * restrict const cctkGH,
                                    const char *group_name, int nvars,
                                    CCTK_REAL const *restrict *ptrs);
void AssertGroupStorage(cGH const * restrict const cctkGH,
                                     const char *calc, int ngroups,
                                     const char *const group_names[]);


/*********************************************************************
 * Gridfunction access macros
 *********************************************************************/

  /* Grid function access */
  /* var is a pointer to a grid point, i,j,k are offsets with respect
     to that point.
     For example: KRANC_GFINDEX3D_OFFSET(&u[ind3d],-1,-1,0) */
  /* simple implementation */
  /* #define KRANC_GFOFFSET3D(var,i,j,k) ((var)[di*(i)+dj*(j)+dk*(k)]) */
  /* more efficient implementation for some compilers */
#define KRANC_GFOFFSET3D(var,i,j,k)                                     \
  (*(CCTK_REAL const*)&((char const*)(var))[cdi*(i)+cdj*(j)+cdk*(k)])

#define GFOffset(u,di,dj,dk) KRANC_GFOFFSET3D(&(u)[index],di,dj,dk)

/*********************************************************************
 * Macros used in Kranc expressions
 *********************************************************************/

#define IfThen(x,y,z) ((x) ? (y) : (z))
#define MinMod(x, y)  ((x) * (y) < 0 ? 0 : (fabs((x)) < fabs((y)) ? (x) : (y)))
#define VanLeer(x, y)  ((x) * (y) < 0 ? 0 : (Min3(2*fabs(x),2*fabs(y),0.5*(fabs(x)+fabs(y)))*Sign((x)+(y))))
#define StepFunction(x) ((x)>0)

/*********************************************************************
 * Numerical constants not defined in C++
 *********************************************************************/

#define E           M_E
#define Pi          M_PI

/*********************************************************************
 * Declare functions on the device if compiled for CUDA
 *********************************************************************/

#ifdef __CUDACC__
#define KRANC_WHERE __device__
#else
#define KRANC_WHERE
#endif

/*********************************************************************
 * Implement the signum function, used for Mathematica's Sign function
 *********************************************************************/

KRANC_WHERE static inline CCTK_REAL sgn(CCTK_REAL x)
{
#ifdef __cplusplus
  using namespace std;
#endif
  return x==(CCTK_REAL)0.0 ? (CCTK_REAL)0.0 : copysign((CCTK_REAL)1.0, x);
}

KRANC_WHERE static inline int isgn(CCTK_REAL x)
{
  if (x == (CCTK_REAL)0.0) return 0;
#ifdef __cplusplus
  using namespace std;
  int s = signbit(x);
#else
  int s = signbit(x);
#endif
  return s ? -1 : +1;
}

} // namespace ML_WaveToy

#endif  // #ifndef KRANC_HH
```

Differencing.h:
```
#include <assert.h>
#include "vectors.h"

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth1(u) (kmul(p1o12dx,kmadd(ToReal(-8),KRANC_GFOFFSET3D(u,-1,0,0),kmadd(ToReal(8),KRANC_GFOFFSET3D(u,1,0,0),ksub(KRANC_GFOFFSET3D(u,-2,0,0),KRANC_GFOFFSET3D(u,2,0,0))))))
#else
#  define PDstandardNth1(u) (PDstandardNth1_impl(u,p1o12dx,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth1_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o12dx, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth1_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o12dx, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return kmul(p1o12dx,kmadd(ToReal(-8),KRANC_GFOFFSET3D(u,-1,0,0),kmadd(ToReal(8),KRANC_GFOFFSET3D(u,1,0,0),ksub(KRANC_GFOFFSET3D(u,-2,0,0),KRANC_GFOFFSET3D(u,2,0,0)))));
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth2(u) (kmul(p1o12dy,kmadd(ToReal(-8),KRANC_GFOFFSET3D(u,0,-1,0),kmadd(ToReal(8),KRANC_GFOFFSET3D(u,0,1,0),ksub(KRANC_GFOFFSET3D(u,0,-2,0),KRANC_GFOFFSET3D(u,0,2,0))))))
#else
#  define PDstandardNth2(u) (PDstandardNth2_impl(u,p1o12dy,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth2_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o12dy, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth2_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o12dy, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return kmul(p1o12dy,kmadd(ToReal(-8),KRANC_GFOFFSET3D(u,0,-1,0),kmadd(ToReal(8),KRANC_GFOFFSET3D(u,0,1,0),ksub(KRANC_GFOFFSET3D(u,0,-2,0),KRANC_GFOFFSET3D(u,0,2,0)))));
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth3(u) (kmul(p1o12dz,kmadd(ToReal(-8),KRANC_GFOFFSET3D(u,0,0,-1),kmadd(ToReal(8),KRANC_GFOFFSET3D(u,0,0,1),ksub(KRANC_GFOFFSET3D(u,0,0,-2),KRANC_GFOFFSET3D(u,0,0,2))))))
#else
#  define PDstandardNth3(u) (PDstandardNth3_impl(u,p1o12dz,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth3_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o12dz, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth3_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o12dz, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return PDstandardNth2_impl(u, p1o12dz, cdk, cdj);
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth11(u) (kmul(pm1o12dx2,kmadd(ToReal(30),KRANC_GFOFFSET3D(u,0,0,0),kmadd(ToReal(-16),kadd(KRANC_GFOFFSET3D(u,-1,0,0),KRANC_GFOFFSET3D(u,1,0,0)),kadd(KRANC_GFOFFSET3D(u,-2,0,0),KRANC_GFOFFSET3D(u,2,0,0))))))
#else
#  define PDstandardNth11(u) (PDstandardNth11_impl(u,pm1o12dx2,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth11_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC pm1o12dx2, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth11_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC pm1o12dx2, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return kmul(pm1o12dx2,kmadd(ToReal(30),KRANC_GFOFFSET3D(u,0,0,0),kmadd(ToReal(-16),kadd(KRANC_GFOFFSET3D(u,-1,0,0),KRANC_GFOFFSET3D(u,1,0,0)),kadd(KRANC_GFOFFSET3D(u,-2,0,0),KRANC_GFOFFSET3D(u,2,0,0)))));
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth22(u) (kmul(pm1o12dy2,kmadd(ToReal(30),KRANC_GFOFFSET3D(u,0,0,0),kmadd(ToReal(-16),kadd(KRANC_GFOFFSET3D(u,0,-1,0),KRANC_GFOFFSET3D(u,0,1,0)),kadd(KRANC_GFOFFSET3D(u,0,-2,0),KRANC_GFOFFSET3D(u,0,2,0))))))
#else
#  define PDstandardNth22(u) (PDstandardNth22_impl(u,pm1o12dy2,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth22_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC pm1o12dy2, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth22_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC pm1o12dy2, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return kmul(pm1o12dy2,kmadd(ToReal(30),KRANC_GFOFFSET3D(u,0,0,0),kmadd(ToReal(-16),kadd(KRANC_GFOFFSET3D(u,0,-1,0),KRANC_GFOFFSET3D(u,0,1,0)),kadd(KRANC_GFOFFSET3D(u,0,-2,0),KRANC_GFOFFSET3D(u,0,2,0)))));
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth33(u) (kmul(pm1o12dz2,kmadd(ToReal(30),KRANC_GFOFFSET3D(u,0,0,0),kmadd(ToReal(-16),kadd(KRANC_GFOFFSET3D(u,0,0,-1),KRANC_GFOFFSET3D(u,0,0,1)),kadd(KRANC_GFOFFSET3D(u,0,0,-2),KRANC_GFOFFSET3D(u,0,0,2))))))
#else
#  define PDstandardNth33(u) (PDstandardNth33_impl(u,pm1o12dz2,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth33_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC pm1o12dz2, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth33_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC pm1o12dz2, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return PDstandardNth22_impl(u, pm1o12dz2, cdk, cdj);
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth12(u) (kmul(p1o144dxdy,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,-1,1,0),KRANC_GFOFFSET3D(u,1,-1,0)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,-1,-1,0),KRANC_GFOFFSET3D(u,1,1,0)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,-1,2,0),kadd(KRANC_GFOFFSET3D(u,1,-2,0),kadd(KRANC_GFOFFSET3D(u,-2,1,0),KRANC_GFOFFSET3D(u,2,-1,0)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,-1,-2,0),kadd(KRANC_GFOFFSET3D(u,1,2,0),kadd(KRANC_GFOFFSET3D(u,-2,-1,0),KRANC_GFOFFSET3D(u,2,1,0)))),kadd(KRANC_GFOFFSET3D(u,-2,-2,0),ksub(ksub(KRANC_GFOFFSET3D(u,2,2,0),KRANC_GFOFFSET3D(u,2,-2,0)),KRANC_GFOFFSET3D(u,-2,2,0)))))))))
#else
#  define PDstandardNth12(u) (PDstandardNth12_impl(u,p1o144dxdy,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth12_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdy, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth12_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdy, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return kmul(p1o144dxdy,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,-1,1,0),KRANC_GFOFFSET3D(u,1,-1,0)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,-1,-1,0),KRANC_GFOFFSET3D(u,1,1,0)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,-1,2,0),kadd(KRANC_GFOFFSET3D(u,1,-2,0),kadd(KRANC_GFOFFSET3D(u,-2,1,0),KRANC_GFOFFSET3D(u,2,-1,0)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,-1,-2,0),kadd(KRANC_GFOFFSET3D(u,1,2,0),kadd(KRANC_GFOFFSET3D(u,-2,-1,0),KRANC_GFOFFSET3D(u,2,1,0)))),kadd(KRANC_GFOFFSET3D(u,-2,-2,0),ksub(ksub(KRANC_GFOFFSET3D(u,2,2,0),KRANC_GFOFFSET3D(u,2,-2,0)),KRANC_GFOFFSET3D(u,-2,2,0))))))));
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth13(u) (kmul(p1o144dxdz,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,-1,0,1),KRANC_GFOFFSET3D(u,1,0,-1)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,-1,0,-1),KRANC_GFOFFSET3D(u,1,0,1)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,-1,0,2),kadd(KRANC_GFOFFSET3D(u,1,0,-2),kadd(KRANC_GFOFFSET3D(u,-2,0,1),KRANC_GFOFFSET3D(u,2,0,-1)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,-1,0,-2),kadd(KRANC_GFOFFSET3D(u,1,0,2),kadd(KRANC_GFOFFSET3D(u,-2,0,-1),KRANC_GFOFFSET3D(u,2,0,1)))),kadd(KRANC_GFOFFSET3D(u,-2,0,-2),ksub(ksub(KRANC_GFOFFSET3D(u,2,0,2),KRANC_GFOFFSET3D(u,2,0,-2)),KRANC_GFOFFSET3D(u,-2,0,2)))))))))
#else
#  define PDstandardNth13(u) (PDstandardNth13_impl(u,p1o144dxdz,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth13_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdz, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth13_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdz, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return PDstandardNth12_impl(u, p1o144dxdz, cdk, cdj);
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth21(u) (kmul(p1o144dxdy,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,-1,1,0),KRANC_GFOFFSET3D(u,1,-1,0)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,-1,-1,0),KRANC_GFOFFSET3D(u,1,1,0)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,-1,2,0),kadd(KRANC_GFOFFSET3D(u,1,-2,0),kadd(KRANC_GFOFFSET3D(u,-2,1,0),KRANC_GFOFFSET3D(u,2,-1,0)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,-1,-2,0),kadd(KRANC_GFOFFSET3D(u,1,2,0),kadd(KRANC_GFOFFSET3D(u,-2,-1,0),KRANC_GFOFFSET3D(u,2,1,0)))),kadd(KRANC_GFOFFSET3D(u,-2,-2,0),ksub(ksub(KRANC_GFOFFSET3D(u,2,2,0),KRANC_GFOFFSET3D(u,2,-2,0)),KRANC_GFOFFSET3D(u,-2,2,0)))))))))
#else
#  define PDstandardNth21(u) (PDstandardNth21_impl(u,p1o144dxdy,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth21_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdy, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth21_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdy, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return PDstandardNth12_impl(u, p1o144dxdy, cdj, cdk);
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth23(u) (kmul(p1o144dydz,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,0,-1,1),KRANC_GFOFFSET3D(u,0,1,-1)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,0,-1,-1),KRANC_GFOFFSET3D(u,0,1,1)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,0,-1,2),kadd(KRANC_GFOFFSET3D(u,0,1,-2),kadd(KRANC_GFOFFSET3D(u,0,-2,1),KRANC_GFOFFSET3D(u,0,2,-1)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,0,-1,-2),kadd(KRANC_GFOFFSET3D(u,0,1,2),kadd(KRANC_GFOFFSET3D(u,0,-2,-1),KRANC_GFOFFSET3D(u,0,2,1)))),kadd(KRANC_GFOFFSET3D(u,0,-2,-2),ksub(ksub(KRANC_GFOFFSET3D(u,0,2,2),KRANC_GFOFFSET3D(u,0,2,-2)),KRANC_GFOFFSET3D(u,0,-2,2)))))))))
#else
#  define PDstandardNth23(u) (PDstandardNth23_impl(u,p1o144dydz,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth23_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dydz, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth23_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dydz, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return kmul(p1o144dydz,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,0,-1,1),KRANC_GFOFFSET3D(u,0,1,-1)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,0,-1,-1),KRANC_GFOFFSET3D(u,0,1,1)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,0,-1,2),kadd(KRANC_GFOFFSET3D(u,0,1,-2),kadd(KRANC_GFOFFSET3D(u,0,-2,1),KRANC_GFOFFSET3D(u,0,2,-1)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,0,-1,-2),kadd(KRANC_GFOFFSET3D(u,0,1,2),kadd(KRANC_GFOFFSET3D(u,0,-2,-1),KRANC_GFOFFSET3D(u,0,2,1)))),kadd(KRANC_GFOFFSET3D(u,0,-2,-2),ksub(ksub(KRANC_GFOFFSET3D(u,0,2,2),KRANC_GFOFFSET3D(u,0,2,-2)),KRANC_GFOFFSET3D(u,0,-2,2))))))));
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth31(u) (kmul(p1o144dxdz,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,-1,0,1),KRANC_GFOFFSET3D(u,1,0,-1)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,-1,0,-1),KRANC_GFOFFSET3D(u,1,0,1)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,-1,0,2),kadd(KRANC_GFOFFSET3D(u,1,0,-2),kadd(KRANC_GFOFFSET3D(u,-2,0,1),KRANC_GFOFFSET3D(u,2,0,-1)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,-1,0,-2),kadd(KRANC_GFOFFSET3D(u,1,0,2),kadd(KRANC_GFOFFSET3D(u,-2,0,-1),KRANC_GFOFFSET3D(u,2,0,1)))),kadd(KRANC_GFOFFSET3D(u,-2,0,-2),ksub(ksub(KRANC_GFOFFSET3D(u,2,0,2),KRANC_GFOFFSET3D(u,2,0,-2)),KRANC_GFOFFSET3D(u,-2,0,2)))))))))
#else
#  define PDstandardNth31(u) (PDstandardNth31_impl(u,p1o144dxdz,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth31_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdz, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth31_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dxdz, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return PDstandardNth12_impl(u, p1o144dxdz, cdk, cdj);
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth32(u) (kmul(p1o144dydz,kmadd(ToReal(-64),kadd(KRANC_GFOFFSET3D(u,0,-1,1),KRANC_GFOFFSET3D(u,0,1,-1)),kmadd(ToReal(64),kadd(KRANC_GFOFFSET3D(u,0,-1,-1),KRANC_GFOFFSET3D(u,0,1,1)),kmadd(ToReal(8),kadd(KRANC_GFOFFSET3D(u,0,-1,2),kadd(KRANC_GFOFFSET3D(u,0,1,-2),kadd(KRANC_GFOFFSET3D(u,0,-2,1),KRANC_GFOFFSET3D(u,0,2,-1)))),kmadd(ToReal(-8),kadd(KRANC_GFOFFSET3D(u,0,-1,-2),kadd(KRANC_GFOFFSET3D(u,0,1,2),kadd(KRANC_GFOFFSET3D(u,0,-2,-1),KRANC_GFOFFSET3D(u,0,2,1)))),kadd(KRANC_GFOFFSET3D(u,0,-2,-2),ksub(ksub(KRANC_GFOFFSET3D(u,0,2,2),KRANC_GFOFFSET3D(u,0,2,-2)),KRANC_GFOFFSET3D(u,0,-2,2)))))))))
#else
#  define PDstandardNth32(u) (PDstandardNth32_impl(u,p1o144dydz,cdj,cdk))
static CCTK_REAL_VEC PDstandardNth32_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dydz, const ptrdiff_t cdj, const ptrdiff_t cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL_VEC PDstandardNth32_impl(const CCTK_REAL* restrict const u, const CCTK_REAL_VEC p1o144dydz, const ptrdiff_t cdj, const ptrdiff_t cdk)
{
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL);
  return PDstandardNth23_impl(u, p1o144dydz, cdj, cdk);
}
#endif


```

WT_Gaussian.cc:
```
/*  File produced by Kranc */

#define KRANC_C

#include <algorithm>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Kranc.hh"
#include "Differencing.h"
#include "loopcontrol.h"
#include "vectors.h"

namespace ML_WaveToy {


static void WT_Gaussian_Body(const cGH* restrict const cctkGH, const int dir, const int face, const CCTK_REAL normal[3], const CCTK_REAL tangentA[3], const CCTK_REAL tangentB[3], const int imin[3], const int imax[3], const int n_subblock_gfs, CCTK_REAL* restrict const subblock_gfs[])
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  /* Include user-supplied include files */
  /* Initialise finite differencing variables */
  const ptrdiff_t di CCTK_ATTRIBUTE_UNUSED = 1;
  const ptrdiff_t dj CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t dk CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * di;
  const ptrdiff_t cdj CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dj;
  const ptrdiff_t cdk CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dk;
  const ptrdiff_t cctkLbnd1 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[0];
  const ptrdiff_t cctkLbnd2 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[1];
  const ptrdiff_t cctkLbnd3 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[2];
  const CCTK_REAL_VEC t CCTK_ATTRIBUTE_UNUSED = ToReal(cctk_time);
  const CCTK_REAL_VEC cctkOriginSpace1 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(0));
  const CCTK_REAL_VEC cctkOriginSpace2 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(1));
  const CCTK_REAL_VEC cctkOriginSpace3 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(2));
  const CCTK_REAL_VEC dt CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_TIME);
  const CCTK_REAL_VEC dx CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(0));
  const CCTK_REAL_VEC dy CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(1));
  const CCTK_REAL_VEC dz CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(2));
  const CCTK_REAL_VEC dxi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dx);
  const CCTK_REAL_VEC dyi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dy);
  const CCTK_REAL_VEC dzi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dz);
  const CCTK_REAL_VEC khalf CCTK_ATTRIBUTE_UNUSED = ToReal(0.5);
  const CCTK_REAL_VEC kthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.333333333333333333333333333333);
  const CCTK_REAL_VEC ktwothird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.666666666666666666666666666667);
  const CCTK_REAL_VEC kfourthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(1.33333333333333333333333333333);
  const CCTK_REAL_VEC hdxi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dxi,ToReal(0.5));
  const CCTK_REAL_VEC hdyi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dyi,ToReal(0.5));
  const CCTK_REAL_VEC hdzi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dzi,ToReal(0.5));
  /* Initialize predefined quantities */
  const CCTK_REAL_VEC p1o12dx CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dx);
  const CCTK_REAL_VEC p1o12dy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dy);
  const CCTK_REAL_VEC p1o12dz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dz);
  const CCTK_REAL_VEC p1o144dxdy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dy));
  const CCTK_REAL_VEC p1o144dxdz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dz));
  const CCTK_REAL_VEC p1o144dydz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dy,dz));
  const CCTK_REAL_VEC pm1o12dx2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dx,dx));
  const CCTK_REAL_VEC pm1o12dy2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dy,dy));
  const CCTK_REAL_VEC pm1o12dz2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dz,dz));
  /* Assign local copies of arrays functions */
  
  
  /* Calculate temporaries and arrays functions */
  /* Copy local copies back to grid functions */
  /* Loop over the grid points */
  const int imin0=imin[0];
  const int imin1=imin[1];
  const int imin2=imin[2];
  const int imax0=imax[0];
  const int imax1=imax[1];
  const int imax2=imax[2];
  #pragma omp parallel
  CCTK_LOOP3STR(WT_Gaussian,
    i,j,k, imin0,imin1,imin2, imax0,imax1,imax2,
    cctk_ash[0],cctk_ash[1],cctk_ash[2],
    vecimin,vecimax, CCTK_REAL_VEC_SIZE)
  {
    const ptrdiff_t index CCTK_ATTRIBUTE_UNUSED = di*i + dj*j + dk*k;
    /* Assign local copies of grid functions */
    
    CCTK_REAL_VEC rL CCTK_ATTRIBUTE_UNUSED = vec_load(r[index]);
    
    /* Include user supplied include files */
    /* Precompute derivatives */
    /* Calculate temporaries and grid functions */
    CCTK_REAL_VEC uL CCTK_ATTRIBUTE_UNUSED = 
      kmul(kexp(kmul(ToReal(pow(width,-2)),kmul(ToReal(-0.5),kmul(rL,rL)))),ToReal(amplitude));
    
    CCTK_REAL_VEC rhoL CCTK_ATTRIBUTE_UNUSED = ToReal(0);
    /* Copy local copies back to grid functions */
    vec_store_partial_prepare(i,vecimin,vecimax);
    vec_store_nta_partial(rho[index],rhoL);
    vec_store_nta_partial(u[index],uL);
  }
  CCTK_ENDLOOP3STR(WT_Gaussian);
}
extern "C" void WT_Gaussian(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Entering WT_Gaussian_Body");
  }
  if (cctk_iteration % WT_Gaussian_calc_every != WT_Gaussian_calc_offset)
  {
    return;
  }
  
  const char* const groups[] = {
    "grid::coordinates",
    "ML_WaveToy::WT_rho",
    "ML_WaveToy::WT_u"};
  AssertGroupStorage(cctkGH, "WT_Gaussian", 3, groups);
  
  
  LoopOverEverything(cctkGH, WT_Gaussian_Body);
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Leaving WT_Gaussian_Body");
  }
}

} // namespace ML_WaveToy

```

RegisterMoL.cc:
```
/*  File produced by Kranc */

#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"

extern "C" void ML_WaveToy_RegisterVars(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
  /* Register all the evolved grid functions with MoL */
  ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_WaveToy::rho"),  CCTK_VarIndex("ML_WaveToy::rhorhs"));
  ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_WaveToy::u"),  CCTK_VarIndex("ML_WaveToy::urhs"));
  /* Register all the evolved Array functions with MoL */
  return;
}

```

make.code.defn:
```
# File produced by Kranc

SRCS = Boundaries.cc Kranc.cc RegisterMoL.cc RegisterSymmetries.cc Startup.cc WT_Dirichlet.cc WT_EnergyBoundary.cc WT_Energy.cc WT_Gaussian.cc WT_RHS.cc WT_Standing.cc 

```

WT_EnergyBoundary.cc:
```
/*  File produced by Kranc */

#define KRANC_C

#include <algorithm>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Kranc.hh"
#include "Differencing.h"
#include "loopcontrol.h"
#include "vectors.h"

namespace ML_WaveToy {

extern "C" void WT_EnergyBoundary_SelectBCs(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (cctk_iteration % WT_EnergyBoundary_calc_every != WT_EnergyBoundary_calc_offset)
    return;
  CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
  ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_WaveToy::WT_eps","flat");
  if (ierr < 0)
    CCTK_WARN(CCTK_WARN_ALERT, "Failed to register flat BC for ML_WaveToy::WT_eps.");
  return;
}

static void WT_EnergyBoundary_Body(const cGH* restrict const cctkGH, const int dir, const int face, const CCTK_REAL normal[3], const CCTK_REAL tangentA[3], const CCTK_REAL tangentB[3], const int imin[3], const int imax[3], const int n_subblock_gfs, CCTK_REAL* restrict const subblock_gfs[])
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  /* Include user-supplied include files */
  /* Initialise finite differencing variables */
  const ptrdiff_t di CCTK_ATTRIBUTE_UNUSED = 1;
  const ptrdiff_t dj CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t dk CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * di;
  const ptrdiff_t cdj CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dj;
  const ptrdiff_t cdk CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dk;
  const ptrdiff_t cctkLbnd1 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[0];
  const ptrdiff_t cctkLbnd2 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[1];
  const ptrdiff_t cctkLbnd3 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[2];
  const CCTK_REAL_VEC t CCTK_ATTRIBUTE_UNUSED = ToReal(cctk_time);
  const CCTK_REAL_VEC cctkOriginSpace1 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(0));
  const CCTK_REAL_VEC cctkOriginSpace2 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(1));
  const CCTK_REAL_VEC cctkOriginSpace3 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(2));
  const CCTK_REAL_VEC dt CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_TIME);
  const CCTK_REAL_VEC dx CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(0));
  const CCTK_REAL_VEC dy CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(1));
  const CCTK_REAL_VEC dz CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(2));
  const CCTK_REAL_VEC dxi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dx);
  const CCTK_REAL_VEC dyi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dy);
  const CCTK_REAL_VEC dzi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dz);
  const CCTK_REAL_VEC khalf CCTK_ATTRIBUTE_UNUSED = ToReal(0.5);
  const CCTK_REAL_VEC kthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.333333333333333333333333333333);
  const CCTK_REAL_VEC ktwothird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.666666666666666666666666666667);
  const CCTK_REAL_VEC kfourthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(1.33333333333333333333333333333);
  const CCTK_REAL_VEC hdxi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dxi,ToReal(0.5));
  const CCTK_REAL_VEC hdyi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dyi,ToReal(0.5));
  const CCTK_REAL_VEC hdzi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dzi,ToReal(0.5));
  /* Initialize predefined quantities */
  const CCTK_REAL_VEC p1o12dx CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dx);
  const CCTK_REAL_VEC p1o12dy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dy);
  const CCTK_REAL_VEC p1o12dz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dz);
  const CCTK_REAL_VEC p1o144dxdy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dy));
  const CCTK_REAL_VEC p1o144dxdz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dz));
  const CCTK_REAL_VEC p1o144dydz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dy,dz));
  const CCTK_REAL_VEC pm1o12dx2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dx,dx));
  const CCTK_REAL_VEC pm1o12dy2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dy,dy));
  const CCTK_REAL_VEC pm1o12dz2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dz,dz));
  /* Assign local copies of arrays functions */
  
  
  /* Calculate temporaries and arrays functions */
  /* Copy local copies back to grid functions */
  /* Loop over the grid points */
  const int imin0=imin[0];
  const int imin1=imin[1];
  const int imin2=imin[2];
  const int imax0=imax[0];
  const int imax1=imax[1];
  const int imax2=imax[2];
  #pragma omp parallel
  CCTK_LOOP3STR(WT_EnergyBoundary,
    i,j,k, imin0,imin1,imin2, imax0,imax1,imax2,
    cctk_ash[0],cctk_ash[1],cctk_ash[2],
    vecimin,vecimax, CCTK_REAL_VEC_SIZE)
  {
    const ptrdiff_t index CCTK_ATTRIBUTE_UNUSED = di*i + dj*j + dk*k;
    /* Assign local copies of grid functions */
    
    
    /* Include user supplied include files */
    /* Precompute derivatives */
    /* Calculate temporaries and grid functions */
    CCTK_REAL_VEC epsL CCTK_ATTRIBUTE_UNUSED = ToReal(0);
    /* Copy local copies back to grid functions */
    vec_store_partial_prepare(i,vecimin,vecimax);
    vec_store_nta_partial(eps[index],epsL);
  }
  CCTK_ENDLOOP3STR(WT_EnergyBoundary);
}
extern "C" void WT_EnergyBoundary(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Entering WT_EnergyBoundary_Body");
  }
  if (cctk_iteration % WT_EnergyBoundary_calc_every != WT_EnergyBoundary_calc_offset)
  {
    return;
  }
  
  const char* const groups[] = {
    "ML_WaveToy::WT_eps"};
  AssertGroupStorage(cctkGH, "WT_EnergyBoundary", 1, groups);
  
  
  LoopOverBoundary(cctkGH, WT_EnergyBoundary_Body);
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Leaving WT_EnergyBoundary_Body");
  }
}

} // namespace ML_WaveToy

```

RegisterSymmetries.cc:
```
/*  File produced by Kranc */

#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Symmetry.h"

extern "C" void ML_WaveToy_RegisterSymmetries(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  /* array holding symmetry definitions */
  int sym[3];
  
  /* Register symmetries of grid functions */
  sym[0] = 1;
  sym[1] = 1;
  sym[2] = 1;
  SetCartSymVN(cctkGH, sym, "ML_WaveToy::u");
  
  sym[0] = 1;
  sym[1] = 1;
  sym[2] = 1;
  SetCartSymVN(cctkGH, sym, "ML_WaveToy::rho");
  
  sym[0] = 1;
  sym[1] = 1;
  sym[2] = 1;
  SetCartSymVN(cctkGH, sym, "ML_WaveToy::eps");
  
}

```

Startup.cc:
```
/*  File produced by Kranc */

#include "cctk.h"

extern "C" int ML_WaveToy_Startup(void)
{
  const char* banner CCTK_ATTRIBUTE_UNUSED = "ML_WaveToy";
  CCTK_RegisterBanner(banner);
  return 0;
}

```

Boundaries.cc:
```
/*  File produced by Kranc */

#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "cctk_Faces.h"
#include "util_Table.h"
#include "Symmetry.h"


/* the boundary treatment is split into 3 steps:    */
/* 1. excision                                      */
/* 2. symmetries                                    */
/* 3. "other" boundary conditions, e.g. radiative */

/* to simplify scheduling and testing, the 3 steps  */
/* are currently applied in separate functions      */


extern "C" void ML_WaveToy_CheckBoundaries(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  return;
}

extern "C" void ML_WaveToy_SelectBoundConds(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  CCTK_INT ierr CCTK_ATTRIBUTE_UNUSED = 0;
  
  if (CCTK_EQUALS(WT_u_bound, "none"  ) ||
      CCTK_EQUALS(WT_u_bound, "static") ||
      CCTK_EQUALS(WT_u_bound, "flat"  ) ||
      CCTK_EQUALS(WT_u_bound, "zero"  ) )
  {
    ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, 1, -1,
                      "ML_WaveToy::WT_u", WT_u_bound);
    if (ierr < 0)
       CCTK_ERROR("Failed to register WT_u_bound BC for ML_WaveToy::WT_u!");
  }
  
  if (CCTK_EQUALS(WT_rho_bound, "none"  ) ||
      CCTK_EQUALS(WT_rho_bound, "static") ||
      CCTK_EQUALS(WT_rho_bound, "flat"  ) ||
      CCTK_EQUALS(WT_rho_bound, "zero"  ) )
  {
    ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, 1, -1,
                      "ML_WaveToy::WT_rho", WT_rho_bound);
    if (ierr < 0)
       CCTK_ERROR("Failed to register WT_rho_bound BC for ML_WaveToy::WT_rho!");
  }
  
  if (CCTK_EQUALS(u_bound, "none"  ) ||
      CCTK_EQUALS(u_bound, "static") ||
      CCTK_EQUALS(u_bound, "flat"  ) ||
      CCTK_EQUALS(u_bound, "zero"  ) )
  {
    ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1,
                      "ML_WaveToy::u", u_bound);
    if (ierr < 0)
       CCTK_ERROR("Failed to register u_bound BC for ML_WaveToy::u!");
  }
  
  if (CCTK_EQUALS(rho_bound, "none"  ) ||
      CCTK_EQUALS(rho_bound, "static") ||
      CCTK_EQUALS(rho_bound, "flat"  ) ||
      CCTK_EQUALS(rho_bound, "zero"  ) )
  {
    ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1,
                      "ML_WaveToy::rho", rho_bound);
    if (ierr < 0)
       CCTK_ERROR("Failed to register rho_bound BC for ML_WaveToy::rho!");
  }
  
  if (CCTK_EQUALS(WT_u_bound, "radiative"))
  {
   /* select radiation boundary condition */
    static CCTK_INT handle_WT_u_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_WT_u_bound < 0) handle_WT_u_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_WT_u_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_WT_u_bound , WT_u_bound_limit, "LIMIT") < 0)
       CCTK_ERROR("could not set LIMIT value in table!");
    if (Util_TableSetReal(handle_WT_u_bound ,WT_u_bound_speed, "SPEED") < 0)
       CCTK_ERROR("could not set SPEED value in table!");
  
    ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, 1, handle_WT_u_bound, 
                      "ML_WaveToy::WT_u", "Radiation");
  
    if (ierr < 0)
       CCTK_ERROR("Failed to register Radiation BC for ML_WaveToy::WT_u!");
  
  }
  
  if (CCTK_EQUALS(WT_rho_bound, "radiative"))
  {
   /* select radiation boundary condition */
    static CCTK_INT handle_WT_rho_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_WT_rho_bound < 0) handle_WT_rho_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_WT_rho_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_WT_rho_bound , WT_rho_bound_limit, "LIMIT") < 0)
       CCTK_ERROR("could not set LIMIT value in table!");
    if (Util_TableSetReal(handle_WT_rho_bound ,WT_rho_bound_speed, "SPEED") < 0)
       CCTK_ERROR("could not set SPEED value in table!");
  
    ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, 1, handle_WT_rho_bound, 
                      "ML_WaveToy::WT_rho", "Radiation");
  
    if (ierr < 0)
       CCTK_ERROR("Failed to register Radiation BC for ML_WaveToy::WT_rho!");
  
  }
  
  if (CCTK_EQUALS(u_bound, "radiative"))
  {
   /* select radiation boundary condition */
    static CCTK_INT handle_u_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_u_bound < 0) handle_u_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_u_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_u_bound , u_bound_limit, "LIMIT") < 0)
       CCTK_ERROR("could not set LIMIT value in table!");
    if (Util_TableSetReal(handle_u_bound ,u_bound_speed, "SPEED") < 0)
        CCTK_ERROR("could not set SPEED value in table!");
  
    ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_u_bound, 
                      "ML_WaveToy::u", "Radiation");
  
    if (ierr < 0)
       CCTK_ERROR("Failed to register Radiation BC for ML_WaveToy::u!");
  
  }
  
  if (CCTK_EQUALS(rho_bound, "radiative"))
  {
   /* select radiation boundary condition */
    static CCTK_INT handle_rho_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_rho_bound < 0) handle_rho_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_rho_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_rho_bound , rho_bound_limit, "LIMIT") < 0)
       CCTK_ERROR("could not set LIMIT value in table!");
    if (Util_TableSetReal(handle_rho_bound ,rho_bound_speed, "SPEED") < 0)
        CCTK_ERROR("could not set SPEED value in table!");
  
    ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_rho_bound, 
                      "ML_WaveToy::rho", "Radiation");
  
    if (ierr < 0)
       CCTK_ERROR("Failed to register Radiation BC for ML_WaveToy::rho!");
  
  }
  
  if (CCTK_EQUALS(WT_u_bound, "scalar"))
  {
   /* select scalar boundary condition */
    static CCTK_INT handle_WT_u_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_WT_u_bound < 0) handle_WT_u_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_WT_u_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_WT_u_bound ,WT_u_bound_scalar, "SCALAR") < 0)
        CCTK_ERROR("could not set SCALAR value in table!");
  
    ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, 1, handle_WT_u_bound, 
                      "ML_WaveToy::WT_u", "scalar");
  
    if (ierr < 0)
       CCTK_ERROR("Failed to register Scalar BC for ML_WaveToy::WT_u!");
  
  }
  
  if (CCTK_EQUALS(WT_rho_bound, "scalar"))
  {
   /* select scalar boundary condition */
    static CCTK_INT handle_WT_rho_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_WT_rho_bound < 0) handle_WT_rho_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_WT_rho_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_WT_rho_bound ,WT_rho_bound_scalar, "SCALAR") < 0)
        CCTK_ERROR("could not set SCALAR value in table!");
  
    ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, 1, handle_WT_rho_bound, 
                      "ML_WaveToy::WT_rho", "scalar");
  
    if (ierr < 0)
       CCTK_ERROR("Failed to register Scalar BC for ML_WaveToy::WT_rho!");
  
  }
  
  if (CCTK_EQUALS(u_bound, "scalar"))
  {
   /* select scalar boundary condition */
    static CCTK_INT handle_u_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_u_bound < 0) handle_u_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_u_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_u_bound ,u_bound_scalar, "SCALAR") < 0)
      CCTK_ERROR("could not set SCALAR value in table!");
  
    ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_u_bound, 
                      "ML_WaveToy::u", "scalar");
  
    if (ierr < 0)
       CCTK_ERROR("Error in registering Scalar BC for ML_WaveToy::u!");
  
  }
  
  if (CCTK_EQUALS(rho_bound, "scalar"))
  {
   /* select scalar boundary condition */
    static CCTK_INT handle_rho_bound CCTK_ATTRIBUTE_UNUSED = -1;
    if (handle_rho_bound < 0) handle_rho_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE);
    if (handle_rho_bound < 0) CCTK_ERROR("could not create table!");
    if (Util_TableSetReal(handle_rho_bound ,rho_bound_scalar, "SCALAR") < 0)
      CCTK_ERROR("could not set SCALAR value in table!");
  
    ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_rho_bound, 
                      "ML_WaveToy::rho", "scalar");
  
    if (ierr < 0)
       CCTK_ERROR("Error in registering Scalar BC for ML_WaveToy::rho!");
  
  }
  return;
}



/* template for entries in parameter file:
#$bound$#ML_WaveToy::WT_u_bound       = "skip"
#$bound$#ML_WaveToy::WT_u_bound_speed = 1.0
#$bound$#ML_WaveToy::WT_u_bound_limit = 0.0
#$bound$#ML_WaveToy::WT_u_bound_scalar = 0.0

#$bound$#ML_WaveToy::WT_rho_bound       = "skip"
#$bound$#ML_WaveToy::WT_rho_bound_speed = 1.0
#$bound$#ML_WaveToy::WT_rho_bound_limit = 0.0
#$bound$#ML_WaveToy::WT_rho_bound_scalar = 0.0

#$bound$#ML_WaveToy::u_bound       = "skip"
#$bound$#ML_WaveToy::u_bound_speed = 1.0
#$bound$#ML_WaveToy::u_bound_limit = 0.0
#$bound$#ML_WaveToy::u_bound_scalar = 0.0

#$bound$#ML_WaveToy::rho_bound       = "skip"
#$bound$#ML_WaveToy::rho_bound_speed = 1.0
#$bound$#ML_WaveToy::rho_bound_limit = 0.0
#$bound$#ML_WaveToy::rho_bound_scalar = 0.0

*/


```



Reference solution:
src_code: /*  File produced by Kranc */

#define KRANC_C

#include <algorithm>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "Kranc.hh"
#include "Differencing.h"
#include "loopcontrol.h"
#include "vectors.h"

namespace ML_WaveToy {


static void WT_Standing_Body(const cGH* restrict const cctkGH, const int dir, const int face, const CCTK_REAL normal[3], const CCTK_REAL tangentA[3], const CCTK_REAL tangentB[3], const int imin[3], const int imax[3], const int n_subblock_gfs, CCTK_REAL* restrict const subblock_gfs[])
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  /* Include user-supplied include files */
  /* Initialise finite differencing variables */
  const ptrdiff_t di CCTK_ATTRIBUTE_UNUSED = 1;
  const ptrdiff_t dj CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t dk CCTK_ATTRIBUTE_UNUSED = 
    CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0);
  const ptrdiff_t cdi CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * di;
  const ptrdiff_t cdj CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dj;
  const ptrdiff_t cdk CCTK_ATTRIBUTE_UNUSED = sizeof(CCTK_REAL) * dk;
  const ptrdiff_t cctkLbnd1 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[0];
  const ptrdiff_t cctkLbnd2 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[1];
  const ptrdiff_t cctkLbnd3 CCTK_ATTRIBUTE_UNUSED = cctk_lbnd[2];
  const CCTK_REAL_VEC t CCTK_ATTRIBUTE_UNUSED = ToReal(cctk_time);
  const CCTK_REAL_VEC cctkOriginSpace1 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(0));
  const CCTK_REAL_VEC cctkOriginSpace2 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(1));
  const CCTK_REAL_VEC cctkOriginSpace3 CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_ORIGIN_SPACE(2));
  const CCTK_REAL_VEC dt CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_TIME);
  const CCTK_REAL_VEC dx CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(0));
  const CCTK_REAL_VEC dy CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(1));
  const CCTK_REAL_VEC dz CCTK_ATTRIBUTE_UNUSED = 
    ToReal(CCTK_DELTA_SPACE(2));
  const CCTK_REAL_VEC dxi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dx);
  const CCTK_REAL_VEC dyi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dy);
  const CCTK_REAL_VEC dzi CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(1),dz);
  const CCTK_REAL_VEC khalf CCTK_ATTRIBUTE_UNUSED = ToReal(0.5);
  const CCTK_REAL_VEC kthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.333333333333333333333333333333);
  const CCTK_REAL_VEC ktwothird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(0.666666666666666666666666666667);
  const CCTK_REAL_VEC kfourthird CCTK_ATTRIBUTE_UNUSED = 
    ToReal(1.33333333333333333333333333333);
  const CCTK_REAL_VEC hdxi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dxi,ToReal(0.5));
  const CCTK_REAL_VEC hdyi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dyi,ToReal(0.5));
  const CCTK_REAL_VEC hdzi CCTK_ATTRIBUTE_UNUSED = 
    kmul(dzi,ToReal(0.5));
  /* Initialize predefined quantities */
  const CCTK_REAL_VEC p1o12dx CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dx);
  const CCTK_REAL_VEC p1o12dy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dy);
  const CCTK_REAL_VEC p1o12dz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.0833333333333333333333333333333),dz);
  const CCTK_REAL_VEC p1o144dxdy CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dy));
  const CCTK_REAL_VEC p1o144dxdz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dx,dz));
  const CCTK_REAL_VEC p1o144dydz CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(0.00694444444444444444444444444444),kmul(dy,dz));
  const CCTK_REAL_VEC pm1o12dx2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dx,dx));
  const CCTK_REAL_VEC pm1o12dy2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dy,dy));
  const CCTK_REAL_VEC pm1o12dz2 CCTK_ATTRIBUTE_UNUSED = kdiv(ToReal(-0.0833333333333333333333333333333),kmul(dz,dz));
  /* Assign local copies of arrays functions */
  
  
  /* Calculate temporaries and arrays functions */
  /* Copy local copies back to grid functions */
  /* Loop over the grid points */
  const int imin0=imin[0];
  const int imin1=imin[1];
  const int imin2=imin[2];
  const int imax0=imax[0];
  const int imax1=imax[1];
  const int imax2=imax[2];
  #pragma omp parallel
  CCTK_LOOP3STR(WT_Standing,
    i,j,k, imin0,imin1,imin2, imax0,imax1,imax2,
    cctk_ash[0],cctk_ash[1],cctk_ash[2],
    vecimin,vecimax, CCTK_REAL_VEC_SIZE)
  {
    const ptrdiff_t index CCTK_ATTRIBUTE_UNUSED = di*i + dj*j + dk*k;
    /* Assign local copies of grid functions */
    
    CCTK_REAL_VEC xL CCTK_ATTRIBUTE_UNUSED = vec_load(x[index]);
    CCTK_REAL_VEC yL CCTK_ATTRIBUTE_UNUSED = vec_load(y[index]);
    CCTK_REAL_VEC zL CCTK_ATTRIBUTE_UNUSED = vec_load(z[index]);
    
    /* Include user supplied include files */
    /* Precompute derivatives */
    /* Calculate temporaries and grid functions */
    CCTK_REAL_VEC kvec CCTK_ATTRIBUTE_UNUSED = 
      ToReal(3.14159265358979323846264338328*pow(width,-1));
    
    CCTK_REAL_VEC omega CCTK_ATTRIBUTE_UNUSED = 
      kmul(kpow(kmul(kvec,kvec),0.5),ToReal(1.73205080756887729352744634151));
    
    CCTK_REAL_VEC uL CCTK_ATTRIBUTE_UNUSED = 
      kmul(kmul(kcos(kmul(xL,kvec)),kmul(kcos(kmul(yL,kvec)),kmul(kcos(kmul(zL,kvec)),kcos(kmul(omega,t))))),ToReal(amplitude));
    
    CCTK_REAL_VEC rhoL CCTK_ATTRIBUTE_UNUSED = 
      kneg(kmul(kmul(omega,kmul(kcos(kmul(xL,kvec)),kmul(kcos(kmul(yL,kvec)),kmul(kcos(kmul(zL,kvec)),ksin(kmul(omega,t)))))),ToReal(amplitude)));
    /* Copy local copies back to grid functions */
    vec_store_partial_prepare(i,vecimin,vecimax);
    vec_store_nta_partial(rho[index],rhoL);
    vec_store_nta_partial(u[index],uL);
  }
  CCTK_ENDLOOP3STR(WT_Standing);
}
extern "C" void WT_Standing(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;
  
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Entering WT_Standing_Body");
  }
  if (cctk_iteration % WT_Standing_calc_every != WT_Standing_calc_offset)
  {
    return;
  }
  
  const char* const groups[] = {
    "grid::coordinates",
    "ML_WaveToy::WT_rho",
    "ML_WaveToy::WT_u"};
  AssertGroupStorage(cctkGH, "WT_Standing", 3, groups);
  
  
  LoopOverEverything(cctkGH, WT_Standing_Body);
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Leaving WT_Standing_Body");
  }
}

} // namespace ML_WaveToy