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-rw-r--r--Examples/Euler/src/Differencing.h504
1 files changed, 504 insertions, 0 deletions
diff --git a/Examples/Euler/src/Differencing.h b/Examples/Euler/src/Differencing.h
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+++ b/Examples/Euler/src/Differencing.h
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+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard2nd1(u) ((-KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1o2dx)
+#else
+# define PDstandard2nd1(u) (PDstandard2nd1_impl(u,p1o2dx,cdj,cdk))
+static CCTK_REAL PDstandard2nd1_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 PDstandard2nd1_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 PDstandard2nd2(u) ((-KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1o2dy)
+#else
+# define PDstandard2nd2(u) (PDstandard2nd2_impl(u,p1o2dy,cdj,cdk))
+static CCTK_REAL PDstandard2nd2_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 PDstandard2nd2_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 PDstandard2nd3(u) ((-KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1))*p1o2dz)
+#else
+# define PDstandard2nd3(u) (PDstandard2nd3_impl(u,p1o2dz,cdj,cdk))
+static CCTK_REAL PDstandard2nd3_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 PDstandard2nd3_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 PDstandard2nd11(u) ((-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1odx2)
+#else
+# define PDstandard2nd11(u) (PDstandard2nd11_impl(u,p1odx2,cdj,cdk))
+static CCTK_REAL PDstandard2nd11_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 PDstandard2nd11_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 PDstandard2nd22(u) ((-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1ody2)
+#else
+# define PDstandard2nd22(u) (PDstandard2nd22_impl(u,p1ody2,cdj,cdk))
+static CCTK_REAL PDstandard2nd22_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 PDstandard2nd22_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 PDstandard2nd33(u) ((-2*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1))*p1odz2)
+#else
+# define PDstandard2nd33(u) (PDstandard2nd33_impl(u,p1odz2,cdj,cdk))
+static CCTK_REAL PDstandard2nd33_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 PDstandard2nd33_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 PDstandard2nd12(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 PDstandard2nd12(u) (PDstandard2nd12_impl(u,p1o4dxdy,cdj,cdk))
+static CCTK_REAL PDstandard2nd12_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 PDstandard2nd12_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 PDstandard2nd13(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 PDstandard2nd13(u) (PDstandard2nd13_impl(u,p1o4dxdz,cdj,cdk))
+static CCTK_REAL PDstandard2nd13_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 PDstandard2nd13_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 PDstandard2nd21(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 PDstandard2nd21(u) (PDstandard2nd21_impl(u,p1o4dxdy,cdj,cdk))
+static CCTK_REAL PDstandard2nd21_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 PDstandard2nd21_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 PDstandard2nd23(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 PDstandard2nd23(u) (PDstandard2nd23_impl(u,p1o4dydz,cdj,cdk))
+static CCTK_REAL PDstandard2nd23_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 PDstandard2nd23_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 PDstandard2nd31(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 PDstandard2nd31(u) (PDstandard2nd31_impl(u,p1o4dxdz,cdj,cdk))
+static CCTK_REAL PDstandard2nd31_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 PDstandard2nd31_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 PDstandard2nd32(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 PDstandard2nd32(u) (PDstandard2nd32_impl(u,p1o4dydz,cdj,cdk))
+static CCTK_REAL PDstandard2nd32_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 PDstandard2nd32_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 PDstandard4th1(u) ((-8*KRANC_GFOFFSET3D(u,-1,0,0) + 8*KRANC_GFOFFSET3D(u,1,0,0) + KRANC_GFOFFSET3D(u,-2,0,0) - KRANC_GFOFFSET3D(u,2,0,0))*p1o12dx)
+#else
+# define PDstandard4th1(u) (PDstandard4th1_impl(u,p1o12dx,cdj,cdk))
+static CCTK_REAL PDstandard4th1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o12dx, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o12dx, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-8*KRANC_GFOFFSET3D(u,-1,0,0) + 8*KRANC_GFOFFSET3D(u,1,0,0) + KRANC_GFOFFSET3D(u,-2,0,0) - KRANC_GFOFFSET3D(u,2,0,0))*p1o12dx;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th2(u) ((-8*KRANC_GFOFFSET3D(u,0,-1,0) + 8*KRANC_GFOFFSET3D(u,0,1,0) + KRANC_GFOFFSET3D(u,0,-2,0) - KRANC_GFOFFSET3D(u,0,2,0))*p1o12dy)
+#else
+# define PDstandard4th2(u) (PDstandard4th2_impl(u,p1o12dy,cdj,cdk))
+static CCTK_REAL PDstandard4th2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o12dy, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o12dy, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-8*KRANC_GFOFFSET3D(u,0,-1,0) + 8*KRANC_GFOFFSET3D(u,0,1,0) + KRANC_GFOFFSET3D(u,0,-2,0) - KRANC_GFOFFSET3D(u,0,2,0))*p1o12dy;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th3(u) ((-8*KRANC_GFOFFSET3D(u,0,0,-1) + 8*KRANC_GFOFFSET3D(u,0,0,1) + KRANC_GFOFFSET3D(u,0,0,-2) - KRANC_GFOFFSET3D(u,0,0,2))*p1o12dz)
+#else
+# define PDstandard4th3(u) (PDstandard4th3_impl(u,p1o12dz,cdj,cdk))
+static CCTK_REAL PDstandard4th3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o12dz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o12dz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-8*KRANC_GFOFFSET3D(u,0,0,-1) + 8*KRANC_GFOFFSET3D(u,0,0,1) + KRANC_GFOFFSET3D(u,0,0,-2) - KRANC_GFOFFSET3D(u,0,0,2))*p1o12dz;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th11(u) ((30*KRANC_GFOFFSET3D(u,0,0,0) - 16*(KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0)) + KRANC_GFOFFSET3D(u,-2,0,0) + KRANC_GFOFFSET3D(u,2,0,0))*pm1o12dx2)
+#else
+# define PDstandard4th11(u) (PDstandard4th11_impl(u,pm1o12dx2,cdj,cdk))
+static CCTK_REAL PDstandard4th11_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o12dx2, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th11_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o12dx2, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (30*KRANC_GFOFFSET3D(u,0,0,0) - 16*(KRANC_GFOFFSET3D(u,-1,0,0) + KRANC_GFOFFSET3D(u,1,0,0)) + KRANC_GFOFFSET3D(u,-2,0,0) + KRANC_GFOFFSET3D(u,2,0,0))*pm1o12dx2;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th22(u) ((30*KRANC_GFOFFSET3D(u,0,0,0) - 16*(KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0)) + KRANC_GFOFFSET3D(u,0,-2,0) + KRANC_GFOFFSET3D(u,0,2,0))*pm1o12dy2)
+#else
+# define PDstandard4th22(u) (PDstandard4th22_impl(u,pm1o12dy2,cdj,cdk))
+static CCTK_REAL PDstandard4th22_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o12dy2, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th22_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o12dy2, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (30*KRANC_GFOFFSET3D(u,0,0,0) - 16*(KRANC_GFOFFSET3D(u,0,-1,0) + KRANC_GFOFFSET3D(u,0,1,0)) + KRANC_GFOFFSET3D(u,0,-2,0) + KRANC_GFOFFSET3D(u,0,2,0))*pm1o12dy2;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th33(u) ((30*KRANC_GFOFFSET3D(u,0,0,0) - 16*(KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1)) + KRANC_GFOFFSET3D(u,0,0,-2) + KRANC_GFOFFSET3D(u,0,0,2))*pm1o12dz2)
+#else
+# define PDstandard4th33(u) (PDstandard4th33_impl(u,pm1o12dz2,cdj,cdk))
+static CCTK_REAL PDstandard4th33_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o12dz2, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th33_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o12dz2, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (30*KRANC_GFOFFSET3D(u,0,0,0) - 16*(KRANC_GFOFFSET3D(u,0,0,-1) + KRANC_GFOFFSET3D(u,0,0,1)) + KRANC_GFOFFSET3D(u,0,0,-2) + KRANC_GFOFFSET3D(u,0,0,2))*pm1o12dz2;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th12(u) ((-64*(KRANC_GFOFFSET3D(u,-1,1,0) + KRANC_GFOFFSET3D(u,1,-1,0)) + 64*(KRANC_GFOFFSET3D(u,-1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0)) + 8*(KRANC_GFOFFSET3D(u,-1,2,0) + KRANC_GFOFFSET3D(u,1,-2,0) + KRANC_GFOFFSET3D(u,-2,1,0) + KRANC_GFOFFSET3D(u,2,-1,0)) - 8*(KRANC_GFOFFSET3D(u,-1,-2,0) + KRANC_GFOFFSET3D(u,1,2,0) + KRANC_GFOFFSET3D(u,-2,-1,0) + KRANC_GFOFFSET3D(u,2,1,0)) + KRANC_GFOFFSET3D(u,-2,-2,0) - KRANC_GFOFFSET3D(u,-2,2,0) - KRANC_GFOFFSET3D(u,2,-2,0) + KRANC_GFOFFSET3D(u,2,2,0))*p1o144dxdy)
+#else
+# define PDstandard4th12(u) (PDstandard4th12_impl(u,p1o144dxdy,cdj,cdk))
+static CCTK_REAL PDstandard4th12_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th12_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-64*(KRANC_GFOFFSET3D(u,-1,1,0) + KRANC_GFOFFSET3D(u,1,-1,0)) + 64*(KRANC_GFOFFSET3D(u,-1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0)) + 8*(KRANC_GFOFFSET3D(u,-1,2,0) + KRANC_GFOFFSET3D(u,1,-2,0) + KRANC_GFOFFSET3D(u,-2,1,0) + KRANC_GFOFFSET3D(u,2,-1,0)) - 8*(KRANC_GFOFFSET3D(u,-1,-2,0) + KRANC_GFOFFSET3D(u,1,2,0) + KRANC_GFOFFSET3D(u,-2,-1,0) + KRANC_GFOFFSET3D(u,2,1,0)) + KRANC_GFOFFSET3D(u,-2,-2,0) - KRANC_GFOFFSET3D(u,-2,2,0) - KRANC_GFOFFSET3D(u,2,-2,0) + KRANC_GFOFFSET3D(u,2,2,0))*p1o144dxdy;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th13(u) ((-64*(KRANC_GFOFFSET3D(u,-1,0,1) + KRANC_GFOFFSET3D(u,1,0,-1)) + 64*(KRANC_GFOFFSET3D(u,-1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1)) + 8*(KRANC_GFOFFSET3D(u,-1,0,2) + KRANC_GFOFFSET3D(u,1,0,-2) + KRANC_GFOFFSET3D(u,-2,0,1) + KRANC_GFOFFSET3D(u,2,0,-1)) - 8*(KRANC_GFOFFSET3D(u,-1,0,-2) + KRANC_GFOFFSET3D(u,1,0,2) + KRANC_GFOFFSET3D(u,-2,0,-1) + KRANC_GFOFFSET3D(u,2,0,1)) + KRANC_GFOFFSET3D(u,-2,0,-2) - KRANC_GFOFFSET3D(u,-2,0,2) - KRANC_GFOFFSET3D(u,2,0,-2) + KRANC_GFOFFSET3D(u,2,0,2))*p1o144dxdz)
+#else
+# define PDstandard4th13(u) (PDstandard4th13_impl(u,p1o144dxdz,cdj,cdk))
+static CCTK_REAL PDstandard4th13_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th13_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-64*(KRANC_GFOFFSET3D(u,-1,0,1) + KRANC_GFOFFSET3D(u,1,0,-1)) + 64*(KRANC_GFOFFSET3D(u,-1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1)) + 8*(KRANC_GFOFFSET3D(u,-1,0,2) + KRANC_GFOFFSET3D(u,1,0,-2) + KRANC_GFOFFSET3D(u,-2,0,1) + KRANC_GFOFFSET3D(u,2,0,-1)) - 8*(KRANC_GFOFFSET3D(u,-1,0,-2) + KRANC_GFOFFSET3D(u,1,0,2) + KRANC_GFOFFSET3D(u,-2,0,-1) + KRANC_GFOFFSET3D(u,2,0,1)) + KRANC_GFOFFSET3D(u,-2,0,-2) - KRANC_GFOFFSET3D(u,-2,0,2) - KRANC_GFOFFSET3D(u,2,0,-2) + KRANC_GFOFFSET3D(u,2,0,2))*p1o144dxdz;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th21(u) ((-64*(KRANC_GFOFFSET3D(u,-1,1,0) + KRANC_GFOFFSET3D(u,1,-1,0)) + 64*(KRANC_GFOFFSET3D(u,-1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0)) + 8*(KRANC_GFOFFSET3D(u,-1,2,0) + KRANC_GFOFFSET3D(u,1,-2,0) + KRANC_GFOFFSET3D(u,-2,1,0) + KRANC_GFOFFSET3D(u,2,-1,0)) - 8*(KRANC_GFOFFSET3D(u,-1,-2,0) + KRANC_GFOFFSET3D(u,1,2,0) + KRANC_GFOFFSET3D(u,-2,-1,0) + KRANC_GFOFFSET3D(u,2,1,0)) + KRANC_GFOFFSET3D(u,-2,-2,0) - KRANC_GFOFFSET3D(u,-2,2,0) - KRANC_GFOFFSET3D(u,2,-2,0) + KRANC_GFOFFSET3D(u,2,2,0))*p1o144dxdy)
+#else
+# define PDstandard4th21(u) (PDstandard4th21_impl(u,p1o144dxdy,cdj,cdk))
+static CCTK_REAL PDstandard4th21_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th21_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdy, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-64*(KRANC_GFOFFSET3D(u,-1,1,0) + KRANC_GFOFFSET3D(u,1,-1,0)) + 64*(KRANC_GFOFFSET3D(u,-1,-1,0) + KRANC_GFOFFSET3D(u,1,1,0)) + 8*(KRANC_GFOFFSET3D(u,-1,2,0) + KRANC_GFOFFSET3D(u,1,-2,0) + KRANC_GFOFFSET3D(u,-2,1,0) + KRANC_GFOFFSET3D(u,2,-1,0)) - 8*(KRANC_GFOFFSET3D(u,-1,-2,0) + KRANC_GFOFFSET3D(u,1,2,0) + KRANC_GFOFFSET3D(u,-2,-1,0) + KRANC_GFOFFSET3D(u,2,1,0)) + KRANC_GFOFFSET3D(u,-2,-2,0) - KRANC_GFOFFSET3D(u,-2,2,0) - KRANC_GFOFFSET3D(u,2,-2,0) + KRANC_GFOFFSET3D(u,2,2,0))*p1o144dxdy;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th23(u) ((-64*(KRANC_GFOFFSET3D(u,0,-1,1) + KRANC_GFOFFSET3D(u,0,1,-1)) + 64*(KRANC_GFOFFSET3D(u,0,-1,-1) + KRANC_GFOFFSET3D(u,0,1,1)) + 8*(KRANC_GFOFFSET3D(u,0,-1,2) + KRANC_GFOFFSET3D(u,0,1,-2) + KRANC_GFOFFSET3D(u,0,-2,1) + KRANC_GFOFFSET3D(u,0,2,-1)) - 8*(KRANC_GFOFFSET3D(u,0,-1,-2) + KRANC_GFOFFSET3D(u,0,1,2) + KRANC_GFOFFSET3D(u,0,-2,-1) + KRANC_GFOFFSET3D(u,0,2,1)) + KRANC_GFOFFSET3D(u,0,-2,-2) - KRANC_GFOFFSET3D(u,0,-2,2) - KRANC_GFOFFSET3D(u,0,2,-2) + KRANC_GFOFFSET3D(u,0,2,2))*p1o144dydz)
+#else
+# define PDstandard4th23(u) (PDstandard4th23_impl(u,p1o144dydz,cdj,cdk))
+static CCTK_REAL PDstandard4th23_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dydz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th23_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dydz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-64*(KRANC_GFOFFSET3D(u,0,-1,1) + KRANC_GFOFFSET3D(u,0,1,-1)) + 64*(KRANC_GFOFFSET3D(u,0,-1,-1) + KRANC_GFOFFSET3D(u,0,1,1)) + 8*(KRANC_GFOFFSET3D(u,0,-1,2) + KRANC_GFOFFSET3D(u,0,1,-2) + KRANC_GFOFFSET3D(u,0,-2,1) + KRANC_GFOFFSET3D(u,0,2,-1)) - 8*(KRANC_GFOFFSET3D(u,0,-1,-2) + KRANC_GFOFFSET3D(u,0,1,2) + KRANC_GFOFFSET3D(u,0,-2,-1) + KRANC_GFOFFSET3D(u,0,2,1)) + KRANC_GFOFFSET3D(u,0,-2,-2) - KRANC_GFOFFSET3D(u,0,-2,2) - KRANC_GFOFFSET3D(u,0,2,-2) + KRANC_GFOFFSET3D(u,0,2,2))*p1o144dydz;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th31(u) ((-64*(KRANC_GFOFFSET3D(u,-1,0,1) + KRANC_GFOFFSET3D(u,1,0,-1)) + 64*(KRANC_GFOFFSET3D(u,-1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1)) + 8*(KRANC_GFOFFSET3D(u,-1,0,2) + KRANC_GFOFFSET3D(u,1,0,-2) + KRANC_GFOFFSET3D(u,-2,0,1) + KRANC_GFOFFSET3D(u,2,0,-1)) - 8*(KRANC_GFOFFSET3D(u,-1,0,-2) + KRANC_GFOFFSET3D(u,1,0,2) + KRANC_GFOFFSET3D(u,-2,0,-1) + KRANC_GFOFFSET3D(u,2,0,1)) + KRANC_GFOFFSET3D(u,-2,0,-2) - KRANC_GFOFFSET3D(u,-2,0,2) - KRANC_GFOFFSET3D(u,2,0,-2) + KRANC_GFOFFSET3D(u,2,0,2))*p1o144dxdz)
+#else
+# define PDstandard4th31(u) (PDstandard4th31_impl(u,p1o144dxdz,cdj,cdk))
+static CCTK_REAL PDstandard4th31_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th31_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dxdz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-64*(KRANC_GFOFFSET3D(u,-1,0,1) + KRANC_GFOFFSET3D(u,1,0,-1)) + 64*(KRANC_GFOFFSET3D(u,-1,0,-1) + KRANC_GFOFFSET3D(u,1,0,1)) + 8*(KRANC_GFOFFSET3D(u,-1,0,2) + KRANC_GFOFFSET3D(u,1,0,-2) + KRANC_GFOFFSET3D(u,-2,0,1) + KRANC_GFOFFSET3D(u,2,0,-1)) - 8*(KRANC_GFOFFSET3D(u,-1,0,-2) + KRANC_GFOFFSET3D(u,1,0,2) + KRANC_GFOFFSET3D(u,-2,0,-1) + KRANC_GFOFFSET3D(u,2,0,1)) + KRANC_GFOFFSET3D(u,-2,0,-2) - KRANC_GFOFFSET3D(u,-2,0,2) - KRANC_GFOFFSET3D(u,2,0,-2) + KRANC_GFOFFSET3D(u,2,0,2))*p1o144dxdz;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDstandard4th32(u) ((-64*(KRANC_GFOFFSET3D(u,0,-1,1) + KRANC_GFOFFSET3D(u,0,1,-1)) + 64*(KRANC_GFOFFSET3D(u,0,-1,-1) + KRANC_GFOFFSET3D(u,0,1,1)) + 8*(KRANC_GFOFFSET3D(u,0,-1,2) + KRANC_GFOFFSET3D(u,0,1,-2) + KRANC_GFOFFSET3D(u,0,-2,1) + KRANC_GFOFFSET3D(u,0,2,-1)) - 8*(KRANC_GFOFFSET3D(u,0,-1,-2) + KRANC_GFOFFSET3D(u,0,1,2) + KRANC_GFOFFSET3D(u,0,-2,-1) + KRANC_GFOFFSET3D(u,0,2,1)) + KRANC_GFOFFSET3D(u,0,-2,-2) - KRANC_GFOFFSET3D(u,0,-2,2) - KRANC_GFOFFSET3D(u,0,2,-2) + KRANC_GFOFFSET3D(u,0,2,2))*p1o144dydz)
+#else
+# define PDstandard4th32(u) (PDstandard4th32_impl(u,p1o144dydz,cdj,cdk))
+static CCTK_REAL PDstandard4th32_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dydz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDstandard4th32_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o144dydz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-64*(KRANC_GFOFFSET3D(u,0,-1,1) + KRANC_GFOFFSET3D(u,0,1,-1)) + 64*(KRANC_GFOFFSET3D(u,0,-1,-1) + KRANC_GFOFFSET3D(u,0,1,1)) + 8*(KRANC_GFOFFSET3D(u,0,-1,2) + KRANC_GFOFFSET3D(u,0,1,-2) + KRANC_GFOFFSET3D(u,0,-2,1) + KRANC_GFOFFSET3D(u,0,2,-1)) - 8*(KRANC_GFOFFSET3D(u,0,-1,-2) + KRANC_GFOFFSET3D(u,0,1,2) + KRANC_GFOFFSET3D(u,0,-2,-1) + KRANC_GFOFFSET3D(u,0,2,1)) + KRANC_GFOFFSET3D(u,0,-2,-2) - KRANC_GFOFFSET3D(u,0,-2,2) - KRANC_GFOFFSET3D(u,0,2,-2) + KRANC_GFOFFSET3D(u,0,2,2))*p1o144dydz;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDonesided2nd1(u) ((3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,2*dir(1),0,0) - 4*KRANC_GFOFFSET3D(u,dir(1),0,0))*pm1o2dx*dir(1))
+#else
+# define PDonesided2nd1(u) (PDonesided2nd1_impl(u,pm1o2dx,cdj,cdk))
+static CCTK_REAL PDonesided2nd1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dx, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDonesided2nd1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dx, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,2*dir(1),0,0) - 4*KRANC_GFOFFSET3D(u,dir(1),0,0))*pm1o2dx*dir(1);
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDonesided2nd2(u) ((3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,2*dir(2),0) - 4*KRANC_GFOFFSET3D(u,0,dir(2),0))*pm1o2dy*dir(2))
+#else
+# define PDonesided2nd2(u) (PDonesided2nd2_impl(u,pm1o2dy,cdj,cdk))
+static CCTK_REAL PDonesided2nd2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dy, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDonesided2nd2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dy, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,2*dir(2),0) - 4*KRANC_GFOFFSET3D(u,0,dir(2),0))*pm1o2dy*dir(2);
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDonesided2nd3(u) ((3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,2*dir(3)) - 4*KRANC_GFOFFSET3D(u,0,0,dir(3)))*pm1o2dz*dir(3))
+#else
+# define PDonesided2nd3(u) (PDonesided2nd3_impl(u,pm1o2dz,cdj,cdk))
+static CCTK_REAL PDonesided2nd3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDonesided2nd3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const pm1o2dz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (3*KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,2*dir(3)) - 4*KRANC_GFOFFSET3D(u,0,0,dir(3)))*pm1o2dz*dir(3);
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDplus1(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1odx)
+#else
+# define PDplus1(u) (PDplus1_impl(u,p1odx,cdj,cdk))
+static CCTK_REAL PDplus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDplus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1odx;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDplus2(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1ody)
+#else
+# define PDplus2(u) (PDplus2_impl(u,p1ody,cdj,cdk))
+static CCTK_REAL PDplus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDplus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1ody;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDplus3(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,1))*p1odz)
+#else
+# define PDplus3(u) (PDplus3_impl(u,p1odz,cdj,cdk))
+static CCTK_REAL PDplus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDplus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,1))*p1odz;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDminus1(u) ((KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,-1,0,0))*p1odx)
+#else
+# define PDminus1(u) (PDminus1_impl(u,p1odx,cdj,cdk))
+static CCTK_REAL PDminus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDminus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odx, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,-1,0,0))*p1odx;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDminus2(u) ((KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,-1,0))*p1ody)
+#else
+# define PDminus2(u) (PDminus2_impl(u,p1ody,cdj,cdk))
+static CCTK_REAL PDminus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDminus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1ody, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,-1,0))*p1ody;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define PDminus3(u) ((KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,0,-1))*p1odz)
+#else
+# define PDminus3(u) (PDminus3_impl(u,p1odz,cdj,cdk))
+static CCTK_REAL PDminus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL PDminus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1odz, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,0,-1))*p1odz;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define DiffPlus1(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1o1)
+#else
+# define DiffPlus1(u) (DiffPlus1_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL DiffPlus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL DiffPlus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,1,0,0))*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define DiffPlus2(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1o1)
+#else
+# define DiffPlus2(u) (DiffPlus2_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL DiffPlus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL DiffPlus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,1,0))*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define DiffPlus3(u) ((-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,1))*p1o1)
+#else
+# define DiffPlus3(u) (DiffPlus3_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL DiffPlus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL DiffPlus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (-KRANC_GFOFFSET3D(u,0,0,0) + KRANC_GFOFFSET3D(u,0,0,1))*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define DiffMinus1(u) ((KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,-1,0,0))*p1o1)
+#else
+# define DiffMinus1(u) (DiffMinus1_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL DiffMinus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL DiffMinus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,-1,0,0))*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define DiffMinus2(u) ((KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,-1,0))*p1o1)
+#else
+# define DiffMinus2(u) (DiffMinus2_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL DiffMinus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL DiffMinus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,-1,0))*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define DiffMinus3(u) ((KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,0,-1))*p1o1)
+#else
+# define DiffMinus3(u) (DiffMinus3_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL DiffMinus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL DiffMinus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return (KRANC_GFOFFSET3D(u,0,0,0) - KRANC_GFOFFSET3D(u,0,0,-1))*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define ShiftMinus1(u) (KRANC_GFOFFSET3D(u,-1,0,0)*p1o1)
+#else
+# define ShiftMinus1(u) (ShiftMinus1_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL ShiftMinus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL ShiftMinus1_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return KRANC_GFOFFSET3D(u,-1,0,0)*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define ShiftMinus2(u) (KRANC_GFOFFSET3D(u,0,-1,0)*p1o1)
+#else
+# define ShiftMinus2(u) (ShiftMinus2_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL ShiftMinus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL ShiftMinus2_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return KRANC_GFOFFSET3D(u,0,-1,0)*p1o1;
+}
+#endif
+
+#ifndef KRANC_DIFF_FUNCTIONS
+# define ShiftMinus3(u) (KRANC_GFOFFSET3D(u,0,0,-1)*p1o1)
+#else
+# define ShiftMinus3(u) (ShiftMinus3_impl(u,p1o1,cdj,cdk))
+static CCTK_REAL ShiftMinus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk) CCTK_ATTRIBUTE_NOINLINE CCTK_ATTRIBUTE_UNUSED;
+static CCTK_REAL ShiftMinus3_impl(CCTK_REAL const* restrict const u, CCTK_REAL const p1o1, ptrdiff_t const cdj, ptrdiff_t const cdk)
+{
+ ptrdiff_t const cdi=sizeof(CCTK_REAL);
+ return KRANC_GFOFFSET3D(u,0,0,-1)*p1o1;
+}
+#endif
+