#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth1(u) ((-KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1o2dx)
#else
#  define PDstandardNth1(u) (PDstandardNth1_impl(u,p1o2dx,cdj,cdk))
static CCTK_REAL PDstandardNth1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o2dx, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o2dx, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1o2dx;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth2(u) ((-KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1o2dy)
#else
#  define PDstandardNth2(u) (PDstandardNth2_impl(u,p1o2dy,cdj,cdk))
static CCTK_REAL PDstandardNth2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o2dy, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o2dy, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1o2dy;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth3(u) ((-KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1))*p1o2dz)
#else
#  define PDstandardNth3(u) (PDstandardNth3_impl(u,p1o2dz,cdj,cdk))
static CCTK_REAL PDstandardNth3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o2dz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o2dz, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1))*p1o2dz;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth11(u) ((-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1odx2)
#else
#  define PDstandardNth11(u) (PDstandardNth11_impl(u,p1odx2,cdj,cdk))
static CCTK_REAL PDstandardNth11_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx2, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth11_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx2, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1odx2;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth22(u) ((-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1ody2)
#else
#  define PDstandardNth22(u) (PDstandardNth22_impl(u,p1ody2,cdj,cdk))
static CCTK_REAL PDstandardNth22_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody2, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth22_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody2, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1ody2;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth33(u) ((-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1))*p1odz2)
#else
#  define PDstandardNth33(u) (PDstandardNth33_impl(u,p1odz2,cdj,cdk))
static CCTK_REAL PDstandardNth33_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz2, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth33_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz2, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1))*p1odz2;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth12(u) ((KRANC_GFOFFSET3D(u,-1,-1,0) - KRANC_GFOFFSET3D(u,-1,1,0) - KRANC_GFOFFSET3D(u,1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0))*p1o4dxdy)
#else
#  define PDstandardNth12(u) (PDstandardNth12_impl(u,p1o4dxdy,cdj,cdk))
static CCTK_REAL PDstandardNth12_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth12_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (KRANC_GFOFFSET3D(u,-1,-1,0) - KRANC_GFOFFSET3D(u,-1,1,0) - KRANC_GFOFFSET3D(u,1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0))*p1o4dxdy;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth13(u) ((KRANC_GFOFFSET3D(u,-1,0,-1) - KRANC_GFOFFSET3D(u,-1,0,1) - KRANC_GFOFFSET3D(u,1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1))*p1o4dxdz)
#else
#  define PDstandardNth13(u) (PDstandardNth13_impl(u,p1o4dxdz,cdj,cdk))
static CCTK_REAL PDstandardNth13_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth13_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (KRANC_GFOFFSET3D(u,-1,0,-1) - KRANC_GFOFFSET3D(u,-1,0,1) - KRANC_GFOFFSET3D(u,1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1))*p1o4dxdz;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth21(u) ((KRANC_GFOFFSET3D(u,-1,-1,0) - KRANC_GFOFFSET3D(u,-1,1,0) - KRANC_GFOFFSET3D(u,1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0))*p1o4dxdy)
#else
#  define PDstandardNth21(u) (PDstandardNth21_impl(u,p1o4dxdy,cdj,cdk))
static CCTK_REAL PDstandardNth21_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth21_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (KRANC_GFOFFSET3D(u,-1,-1,0) - KRANC_GFOFFSET3D(u,-1,1,0) - KRANC_GFOFFSET3D(u,1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0))*p1o4dxdy;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth23(u) ((KRANC_GFOFFSET3D(u,0,-1,-1) - KRANC_GFOFFSET3D(u,0,-1,1) - KRANC_GFOFFSET3D(u,0,1,-1) + KRANC_GFOFFSET3D(u,0,1,1))*p1o4dydz)
#else
#  define PDstandardNth23(u) (PDstandardNth23_impl(u,p1o4dydz,cdj,cdk))
static CCTK_REAL PDstandardNth23_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dydz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth23_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dydz, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (KRANC_GFOFFSET3D(u,0,-1,-1) - KRANC_GFOFFSET3D(u,0,-1,1) - KRANC_GFOFFSET3D(u,0,1,-1) + KRANC_GFOFFSET3D(u,0,1,1))*p1o4dydz;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth31(u) ((KRANC_GFOFFSET3D(u,-1,0,-1) - KRANC_GFOFFSET3D(u,-1,0,1) - KRANC_GFOFFSET3D(u,1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1))*p1o4dxdz)
#else
#  define PDstandardNth31(u) (PDstandardNth31_impl(u,p1o4dxdz,cdj,cdk))
static CCTK_REAL PDstandardNth31_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth31_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (KRANC_GFOFFSET3D(u,-1,0,-1) - KRANC_GFOFFSET3D(u,-1,0,1) - KRANC_GFOFFSET3D(u,1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1))*p1o4dxdz;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDstandardNth32(u) ((KRANC_GFOFFSET3D(u,0,-1,-1) - KRANC_GFOFFSET3D(u,0,-1,1) - KRANC_GFOFFSET3D(u,0,1,-1) + KRANC_GFOFFSET3D(u,0,1,1))*p1o4dydz)
#else
#  define PDstandardNth32(u) (PDstandardNth32_impl(u,p1o4dydz,cdj,cdk))
static CCTK_REAL PDstandardNth32_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dydz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDstandardNth32_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o4dydz, ptrdiff_t const cdj, ptrdiff_t const cdk)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (KRANC_GFOFFSET3D(u,0,-1,-1) - KRANC_GFOFFSET3D(u,0,-1,1) - KRANC_GFOFFSET3D(u,0,1,-1) + KRANC_GFOFFSET3D(u,0,1,1))*p1o4dydz;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDupwindNth1(u) ((3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,2*dir1,0,0) - 4*KRANC_GFOFFSET3D(u,dir1,0,0))*pm1o2dx*dir1)
#else
#  define PDupwindNth1(u) (PDupwindNth1_impl(u,pm1o2dx,cdj,cdk,dir1,dir2,dir3))
static CCTK_REAL PDupwindNth1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dx, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDupwindNth1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dx, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,2*dir1,0,0) - 4*KRANC_GFOFFSET3D(u,dir1,0,0))*pm1o2dx*dir1;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDupwindNth2(u) ((3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,2*dir2,0) - 4*KRANC_GFOFFSET3D(u,0,dir2,0))*pm1o2dy*dir2)
#else
#  define PDupwindNth2(u) (PDupwindNth2_impl(u,pm1o2dy,cdj,cdk,dir1,dir2,dir3))
static CCTK_REAL PDupwindNth2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dy, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDupwindNth2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dy, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,2*dir2,0) - 4*KRANC_GFOFFSET3D(u,0,dir2,0))*pm1o2dy*dir2;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDupwindNth3(u) ((3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,2*dir3) - 4*KRANC_GFOFFSET3D(u,0,0,dir3))*pm1o2dz*dir3)
#else
#  define PDupwindNth3(u) (PDupwindNth3_impl(u,pm1o2dz,cdj,cdk,dir1,dir2,dir3))
static CCTK_REAL PDupwindNth3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dz, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDupwindNth3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dz, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,2*dir3) - 4*KRANC_GFOFFSET3D(u,0,0,dir3))*pm1o2dz*dir3;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDonesided1(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,dir1,0,0))*p1odx*dir1)
#else
#  define PDonesided1(u) (PDonesided1_impl(u,p1odx,cdj,cdk,dir1,dir2,dir3))
static CCTK_REAL PDonesided1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDonesided1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,dir1,0,0))*p1odx*dir1;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDonesided2(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,dir2,0))*p1ody*dir2)
#else
#  define PDonesided2(u) (PDonesided2_impl(u,p1ody,cdj,cdk,dir1,dir2,dir3))
static CCTK_REAL PDonesided2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDonesided2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,dir2,0))*p1ody*dir2;
}
#endif

#ifndef KRANC_DIFF_FUNCTIONS
#  define PDonesided3(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,dir3))*p1odz*dir3)
#else
#  define PDonesided3(u) (PDonesided3_impl(u,p1odz,cdj,cdk,dir1,dir2,dir3))
static CCTK_REAL PDonesided3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
static CCTK_REAL PDonesided3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz, ptrdiff_t const cdj, ptrdiff_t const cdk, ptrdiff_t const dir1, ptrdiff_t const dir2, ptrdiff_t const dir3)
{
  ptrdiff_t const cdi=sizeof(CCTK_REAL);
  return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,dir3))*p1odz*dir3;
}
#endif