Added 8-4 derivatives. Note only Diff_gv has been updated to use it. Diff_gf

has to be modified in other ways as well.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@9 f69c4107-0314-4c4f-9ad4-17e986b73f4a

4 files changed, 472 insertions, 2 deletions

diff --git a/param.ccl b/param.ccl
index b18495a..4881ebf 100644
--- a/param.ccl
+++ b/param.ccl
@@ -3,5 +3,5 @@
 
 INT order "Order of accuracy" STEERABLE=always
 {
-  2:6:2 :: ""
+  2:8:2 :: ""
 } 2
diff --git a/src/Derivatives_8_4.F90 b/src/Derivatives_8_4.F90
new file mode 100644
index 0000000..fb312f1
--- /dev/null
+++ b/src/Derivatives_8_4.F90
@@ -0,0 +1,457 @@
+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine deriv_gf_8_4 ( var, ni, nj, nk, dir, bb, gsize, delta, dvar )
+
+  implicit none
+
+  DECLARE_CCTK_FUNCTIONS
+  DECLARE_CCTK_PARAMETERS
+
+  CCTK_REAL, parameter :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  CCTK_INT, intent(IN) :: ni, nj, nk
+  CCTK_REAL, dimension(ni,nj,nk), intent(IN) :: var
+  CCTK_INT, intent(IN) :: dir
+  CCTK_INT, intent(IN) :: bb(2)
+  CCTK_INT, intent(IN) :: gsize
+  CCTK_REAL, intent(IN) :: delta
+  CCTK_REAL, dimension(ni,nj,nk), intent(OUT) :: dvar
+
+  CCTK_REAL, dimension(4), save :: a
+  CCTK_REAL, dimension(12,8), save :: q 
+  CCTK_REAL, parameter :: x1 = 0.541_wp, x2 = -0.0675_wp, x3 = 0.748_wp
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr, j, k
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    a(1) = 4.0_wp/5.0_wp; a(2) = -1.0_wp/5.0_wp
+    a(3) = 4.0_wp/105.0_wp; a(4) = -1.0_wp/280.0_wp
+
+    q(1,1) = -2540160.0_wp/1498139.0_wp
+    q(2,1) = 9.0_wp * ( 2257920.0_wp*x1 + 11289600.0_wp*x2 + &
+                        22579200.0_wp*x3 - 15849163.0_wp ) / 5992556.0_wp
+    q(3,1) = 3.0_wp * ( -33868800.0_wp*x1 - 162570240.0_wp*x2 - &
+                         304819200.0_wp*x3 + 235236677.0_wp ) / 5992556.0_wp
+    q(4,1) = ( 609638400.0_wp*x1 + 2743372800.0_wp*x2 + &
+               4572288000.0_wp * x3 - 3577778591.0_wp ) / 17977668.0_wp
+    q(5,1) = 3.0_wp * ( -16934400*x1 - 67737600.0_wp*x2 - &
+                         84672000.0_wp*x3 + 67906303.0_wp ) / 1498139.0_wp
+    q(6,1) = 105.0_wp * ( 967680.0_wp*x1 + 2903040.0_wp*x2 - &
+                          305821.0_wp ) / 5992556.0_wp
+    q(7,1) = 49.0_wp * ( -1244160.0_wp*x1 + 18662400.0_wp * x3 - &
+                          13322233.0_wp ) / 17977668.0_wp
+    q(8,1) = 3.0_wp * ( -6773760.0_wp*x2 - 33868800.0_wp*x3 + &
+                         24839327.0_wp ) / 5992556.0_wp
+    q(9,1) = zero; q(10,1) = zero; q(11,1) = zero; q(12,1) = zero
+
+    q(1,2) = 9.0_wp * ( -2257920.0_wp*x1 - 11289600.0_wp*x2 - &
+                         22579200.0_wp*x3 + 15849163.0_wp ) / 31004596.0_wp
+    q(2,2) = zero
+    q(3,2) = 3.0_wp * ( 7257600.0_wp*x1 + 33868800.0_wp*x2 + &
+                        60963840.0_wp*x3 - 47167457.0_wp ) / 2214614.0_wp
+    q(4,2) = 3.0_wp * ( -9676800.0_wp*x1 - 42336000.0_wp*x2 - &
+                         67737600.0_wp*x3 + 53224573.0_wp ) / 1107307.0_wp
+    q(5,2) = 7.0_wp * ( 55987200.0_wp*x1 + 217728000.0_wp*x2 + &
+                        261273600.0_wp*x3 - 211102099.0_wp ) / 13287684.0_wp
+    q(6,2) = 3.0_wp * ( -11612160.0_wp*x1 - 33868800.0_wp*x2 + &
+                         3884117.0_wp ) / 2214614.0_wp
+    q(7,2) = 150.0_wp * ( 24192.0_wp*x1 - 338688.0_wp*x3 + &
+                          240463.0_wp ) / 1107307.0_wp
+    q(8,2) = ( 152409600.0_wp*x2 + 731566080.0_wp*x3 - &
+               536324953.0_wp ) / 46506894.0_wp
+    q(9,2) = zero; q(10,2) = zero; q(11,2) = zero; q(12,2) = zero
+
+    q(1,3) = ( 33868800.0_wp*x1 + 162570240.0_wp*x2 + &
+               304819200.0_wp*x3 - 235236677.0_wp ) / 1743924.0_wp
+    q(2,3) = ( -7257600.0_wp*x1 - 33868800.0_wp*x2 - &
+                60963840.0_wp*x3 + 47167457.0_wp ) / 124566.0_wp
+    q(3,3) = zero
+    q(4,3) = ( 24192000.0_wp*x1 + 101606400.0_wp*x2 + &
+               152409600.0_wp*x3 - 120219461.0_wp ) / 124566.0_wp
+    q(5,3) = ( -72576000.0_wp*x1 - 270950400.0_wp*x2 - &
+                304819200.0_wp*x3 + 249289259.0_wp ) / 249132.0_wp
+    q(6,3) = 9.0_wp * ( 806400.0_wp*x1 + 2257920.0_wp*x2 - &
+                        290167.0_wp ) / 41522.0_wp
+    q(7,3) = 6.0_wp * ( -134400.0_wp*x1 + 1693440.0_wp*x3 - &
+                         1191611.0_wp ) / 20761.0_wp
+    q(8,3) = 5.0_wp * ( -2257920.0_wp*x2 - 10160640.0_wp*x3 + &
+                         7439833.0_wp ) / 290654.0_wp
+    q(9,3) = zero; q(10,3) = zero; q(11,3) = zero; q(12,3) = zero
+
+    q(1,4) = ( -609638400.0_wp*x1 - 2743372800.0_wp*x2 - &
+               4572288000.0_wp*x3 + 3577778591.0_wp ) / 109619916.0_wp
+    q(2,4) = 3.0_wp * ( 9676800.0_wp*x1 + 42336000.0_wp*x2 + &
+                        67737600.0_wp*x3 - 53224573.0_wp ) / 1304999.0_wp
+    q(3,4) = 3.0_wp * ( -24192000.0_wp*x1 - 101606400.0_wp*x2 - &
+                         152409600.0_wp*x3 + 120219461.0_wp ) / 2609998.0_wp
+    q(4,4) = zero
+    q(5,4) = 9.0_wp * ( 16128000.0_wp*x1 + 56448000.0_wp*x2 + &
+                        56448000.0_wp*x3 - 47206049.0_wp ) / 5219996.0_wp
+    q(6,4) = 3.0_wp * ( -19353600.0_wp*x1 - 50803200.0_wp*x2 + &
+                         7628371.0_wp ) / 2609998.0_wp
+    q(7,4) = 2.0_wp * ( 10886400.0_wp*x1 - 114307200.0_wp*x3 + &
+                        79048289.0_wp ) / 3914997.0_wp
+    q(8,4) = 75.0_wp * ( 1354752.0_wp*x2 + 5419008.0_wp*x3 - &
+                         3952831.0_wp ) / 18269986.0_wp
+    q(9,4) = zero; q(10,4) = zero; q(11,4) = zero; q(12,4) = zero
+
+    q(1,5) = 3.0_wp * ( 16934400.0_wp*x1 + 67737600.0_wp*x2 + &
+                        84672000.0_wp*x3 - 67906303.0_wp ) / 2096689.0_wp
+    q(2,5) = 7.0_wp * ( -55987200.0_wp*x1 - 217728000.0_wp*x2 - &
+                         261273600.0_wp*x3 + 211102099.0_wp ) / 3594324.0_wp
+    q(3,5) = 3.0_wp * ( 72576000.0_wp*x1 + 270950400.0_wp*x2 + &
+                        304819200.0_wp*x3 - 249289259.0_wp ) / 1198108.0_wp
+    q(4,5) = 9.0_wp * ( -16128000.0_wp*x1 - 56448000.0_wp*x2 - &
+                         56448000.0_wp*x3 + 47206049.0_wp ) / 1198108.0_wp
+    q(5,5) = zero
+    q(6,5) = 105.0_wp * ( 414720.0_wp*x1 + 967680.0_wp*x2 - &
+                          165527.0_wp ) / 1198108.0_wp
+    q(7,5) = 15.0_wp * ( -967680.0_wp*x1 + 6773760.0_wp*x3 - &
+                          4472029.0_wp ) / 1198108.0_wp
+    q(8,5) = ( -304819200.0_wp*x2 - 914457600.0_wp*x3 + &
+               657798011.0_wp ) / 25160268.0_wp
+    q(9,5) = -2592.0_wp/299527.0_wp; 
+    q(10,5) = zero; q(11,5) = zero; q(12,5) = zero
+
+    q(1,6) = 5.0_wp * ( -967680.0_wp*x1 - 2903040.0_wp*x2 + &
+                         305821.0_wp ) / 1237164.0_wp
+    q(2,6) = ( 11612160.0_wp*x1 + 33868800.0_wp*x2 - &
+               3884117.0_wp ) / 618582.0_wp
+    q(3,6) = 9.0_wp * ( -806400.0_wp*x1 - 2257920.0_wp*x2 + &
+                         290167.0_wp ) / 206194.0_wp
+    q(4,6) = ( 19353600.0_wp*x1 + 50803200.0_wp*x2 - &
+               7628371.0_wp ) / 618582.0_wp
+    q(5,6) = 35.0_wp * ( -414720.0_wp*x1 - 967680.0_wp*x2 + &
+                          165527.0_wp ) / 1237164.0_wp
+    q(6,6) = zero; q(7,6) = 80640.0_wp*x1 / 103097.0_wp
+    q(8,6) = 80640.0_wp*x2 / 103097.0_wp; q(9,6) = 3072.0_wp / 103097.0_wp
+    q(10,6) = -288.0_wp/103097.0_wp; q(11,6) = zero; q(12,6) = zero
+
+    q(1,7) = 7.0_wp * ( 1244160.0_wp*x1 - 18662400.0_wp*x3 + &
+                        13322233.0_wp ) / 8041092.0_wp
+    q(2,7) = 150.0_wp * ( -24192.0_wp*x1 + 338688.0_wp*x3 - &
+                           240463.0_wp ) / 670091.0_wp
+    q(3,7) = 54.0_wp * ( 134400.0_wp*x1 - 1693440.0_wp*x3 + &
+                         1191611.0_wp ) / 670091.0_wp
+    q(4,7) = 2.0_wp * ( -10886400.0_wp*x1 + 114307200.0_wp*x3 - &
+                         79048289.0_wp ) / 2010273.0_wp
+    q(5,7) = 15.0_wp * ( 967680.0_wp*x1 - 6773760.0_wp*x3 + &
+                         4472029.0_wp ) / 2680364.0_wp
+    q(6,7) = -725760.0_wp*x1 / 670091.0_wp; q(7,7) = zero
+    q(8,7) = 725760.0_wp*x3 / 670091.0_wp; q(9,7) = -145152.0_wp/670091.0_wp
+    q(10,7) = 27648.0_wp/670091.0_wp; q(11,7) = -2592.0_wp/670091.0_wp
+    q(12,7) = zero
+
+    q(1,8) = 3.0_wp * ( 6773760.0_wp*x2 + 33868800.0_wp*x3 - &
+                        24839327.0_wp ) / 20510956.0_wp
+    q(2,8) = ( -152409600.0_wp*x2 - 731566080.0_wp*x3 + &
+                536324953.0_wp ) / 30766434.0_wp
+    q(3,8) = 45.0_wp * ( 2257920.0_wp*x2 + 10160640.0_wp*x3 - &
+                         7439833.0_wp ) / 10255478.0_wp
+    q(4,8) = 75.0_wp * ( -1354752.0_wp*x2 - 5419008.0_wp*x3 + &
+                          3952831.0_wp ) / 10255478.0_wp
+    q(5,8) = ( 304819200.0_wp*x2 + 914457600.0_wp*x3 - &
+               657798011.0_wp ) / 61532868.0_wp
+    q(6,8) = -5080320.0_wp*x2 / 5127739.0_wp
+    q(7,8) = -5080320.0_wp*x3 / 5127739.0_wp; q(8,8) = zero
+    q(9,8) = 4064256.0_wp/5127739.0_wp; q(10,8) = -1016064.0_wp/5127739.0_wp
+    q(11,8) = 193536.0_wp/5127739.0_wp; q(12,8) = -18144.0_wp/5127739.0_wp
+
+    first = .false. 
+  end if
+
+  idel = 1.0_wp / delta
+
+  direction: select case (dir)
+  case (0) direction
+    if ( bb(1) == 0 ) then
+      il = 1 + gsize
+    else
+      dvar(1,:,:) = ( q(1,1) * var(1,:,:) + q(2,1) * var(2,:,:) + &
+                      q(3,1) * var(3,:,:) + q(4,1) * var(4,:,:) + &
+                      q(5,1) * var(5,:,:) + q(6,1) * var(6,:,:) + &
+                      q(7,1) * var(7,:,:) + q(8,1) * var(8,:,:) ) * idel
+      dvar(2,:,:) = ( q(1,2) * var(1,:,:) + q(3,2) * var(3,:,:) + &
+                      q(4,2) * var(4,:,:) + q(5,2) * var(5,:,:) + &
+                      q(6,2) * var(6,:,:) + q(7,2) * var(7,:,:) + &
+                      q(8,2) * var(8,:,:) ) * idel
+      dvar(3,:,:) = ( q(1,3) * var(1,:,:) + q(2,3) * var(2,:,:) + &
+                      q(4,3) * var(4,:,:) + q(5,3) * var(5,:,:) + &
+                      q(6,3) * var(6,:,:) + q(7,3) * var(7,:,:) + &
+                      q(8,3) * var(8,:,:) ) * idel
+      dvar(4,:,:) = ( q(1,4) * var(1,:,:) + q(2,4) * var(2,:,:) + &
+                      q(3,4) * var(3,:,:) + q(5,4) * var(5,:,:) + &
+                      q(6,4) * var(6,:,:) + q(7,4) * var(7,:,:) + &
+                      q(8,4) * var(8,:,:) ) * idel
+      dvar(5,:,:) = ( q(1,5) * var(1,:,:) + q(2,5) * var(2,:,:) + &
+                      q(3,5) * var(3,:,:) + q(4,5) * var(4,:,:) + &
+                      q(6,5) * var(6,:,:) + q(7,5) * var(7,:,:) + &
+                      q(8,5) * var(8,:,:) + q(9,5) * var(9,:,:) ) * idel
+      dvar(6,:,:) = ( q(1,6) * var(1,:,:) + q(2,6) * var(2,:,:) + &
+                      q(3,6) * var(3,:,:) + q(4,6) * var(4,:,:) + &
+                      q(5,6) * var(5,:,:) + q(7,6) * var(7,:,:) + &
+                      q(8,6) * var(8,:,:) + q(9,6) * var(9,:,:) + &
+                      q(10,6) * var(10,:,:) ) * idel
+      dvar(7,:,:) = ( q(1,7) * var(1,:,:) + q(2,7) * var(2,:,:) + &
+                      q(3,7) * var(3,:,:) + q(4,7) * var(4,:,:) + &
+                      q(5,7) * var(5,:,:) + q(6,7) * var(6,:,:) + &
+                      q(8,7) * var(8,:,:) + q(9,7) * var(9,:,:) + &
+                      q(10,7) * var(10,:,:) + q(11,7) * var(11,:,:) ) * idel
+      dvar(8,:,:) = ( q(1,8) * var(1,:,:) + q(2,8) * var(2,:,:) + &
+                      q(3,8) * var(3,:,:) + q(4,8) * var(4,:,:) + &
+                      q(5,8) * var(5,:,:) + q(6,8) * var(6,:,:) + &
+                      q(7,8) * var(7,:,:) + q(9,8) * var(9,:,:) + &
+                      q(10,8) * var(10,:,:) + q(11,8) * var(11,:,:) + &
+                      q(12,8) * var(12,:,:) ) * idel
+      il = 9
+    end if
+    if ( bb(2) == 0 ) then
+      ir = ni - gsize
+    else
+      dvar(ni,:,:) =   - ( q(1,1) * var(ni,:,:) + q(2,1) * var(ni-1,:,:) + &
+                           q(3,1) * var(ni-2,:,:) + q(4,1) * var(ni-3,:,:) + &
+                           q(5,1) * var(ni-4,:,:) + q(6,1) * var(ni-5,:,:) + &
+                           q(7,1) * var(ni-6,:,:) + &
+                           q(8,1) * var(ni-7,:,:) ) * idel
+      dvar(ni-1,:,:) = - ( q(1,2) * var(ni,:,:) + q(3,2) * var(ni-2,:,:) + &
+                           q(4,2) * var(ni-3,:,:) + q(5,2) * var(ni-4,:,:) + &
+                           q(6,2) * var(ni-5,:,:) + q(7,2) * var(ni-6,:,:) + &
+                           q(8,2) * var(ni-7,:,:) ) * idel
+      dvar(ni-2,:,:) = - ( q(1,3) * var(ni,:,:) + q(2,3) * var(ni-1,:,:) + &
+                           q(4,3) * var(ni-3,:,:) + q(5,3) * var(ni-4,:,:) + &
+                           q(6,3) * var(ni-5,:,:) + q(7,3) * var(ni-6,:,:) + &
+                           q(8,3) * var(ni-7,:,:) ) * idel
+      dvar(ni-3,:,:) = - ( q(1,4) * var(ni,:,:) + q(2,4) * var(ni-1,:,:) + &
+                           q(3,4) * var(ni-2,:,:) + q(5,4) * var(ni-4,:,:) + &
+                           q(6,4) * var(ni-5,:,:) + q(7,4) * var(ni-6,:,:) + &
+                           q(8,4) * var(ni-7,:,:) ) * idel
+      dvar(ni-4,:,:) = - ( q(1,5) * var(ni,:,:) + q(2,5) * var(ni-1,:,:) + &
+                           q(3,5) * var(ni-2,:,:) + q(4,5) * var(ni-3,:,:) + &
+                           q(6,5) * var(ni-5,:,:) + q(7,5) * var(ni-6,:,:) + &
+                           q(8,5) * var(ni-7,:,:) + &
+                           q(9,5) * var(ni-8,:,:) ) * idel
+      dvar(ni-5,:,:) = - ( q(1,6) * var(ni,:,:) + q(2,6) * var(ni-1,:,:) + &
+                           q(3,6) * var(ni-2,:,:) + q(4,6) * var(ni-3,:,:) + &
+                           q(5,6) * var(ni-4,:,:) + q(7,6) * var(ni-6,:,:) + &
+                           q(8,6) * var(ni-7,:,:) + q(9,6) * var(ni-8,:,:) + &
+                           q(10,6) * var(ni-9,:,:) ) * idel
+      dvar(ni-6,:,:) = - ( q(1,7) * var(ni,:,:) + q(2,7) * var(ni-1,:,:) + &
+                           q(3,7) * var(ni-2,:,:) + q(4,7) * var(ni-3,:,:) + &
+                           q(5,7) * var(ni-4,:,:) + q(6,7) * var(ni-5,:,:) + &
+                           q(8,7) * var(ni-7,:,:) + q(9,7) * var(ni-8,:,:) + &
+                           q(10,7) * var(ni-9,:,:) + &
+                           q(11,7) * var(ni-10,:,:) ) * idel
+      dvar(ni-7,:,:) = - ( q(1,8) * var(ni,:,:) + q(2,8) * var(ni-1,:,:) + &
+                           q(3,8) * var(ni-2,:,:) + q(4,8) * var(ni-3,:,:) + &
+                           q(5,8) * var(ni-4,:,:) + q(6,8) * var(ni-5,:,:) + &
+                           q(7,8) * var(ni-6,:,:) + q(9,8) * var(ni-8,:,:) + &
+                           q(10,8) * var(ni-9,:,:) + &
+                           q(11,8) * var(ni-10,:,:) + &
+                           q(12,8) * var(ni-11,:,:) ) * idel
+      ir = ni - 8
+    end if
+    dvar(il:ir,:,:) = ( a(1) * ( var(il+1:ir+1,:,:) - &
+                                 var(il-1:ir-1,:,:) ) + &
+                        a(2) * ( var(il+2:ir+2,:,:) - &
+                                 var(il-2:ir-2,:,:) ) + &
+                        a(3) * ( var(il+3:ir+3,:,:) - &
+                                 var(il-3:ir-3,:,:) ) + &
+                        a(4) * ( var(il+4:ir+4,:,:) - &
+                                 var(il-4:ir-4,:,:) ) ) * idel
+  case (1) direction
+    if ( bb(1) == 0 ) then
+      jl = 1 + gsize
+    else
+      dvar(:,1,:) = ( q(1,1) * var(:,1,:) + q(2,1) * var(:,2,:) + &
+                      q(3,1) * var(:,3,:) + q(4,1) * var(:,4,:) + &
+                      q(5,1) * var(:,5,:) + q(6,1) * var(:,6,:) + &
+                      q(7,1) * var(:,7,:) + q(8,1) * var(:,8,:) ) * idel
+      dvar(:,2,:) = ( q(1,2) * var(:,1,:) + q(3,2) * var(:,3,:) + &
+                      q(4,2) * var(:,4,:) + q(5,2) * var(:,5,:) + &
+                      q(6,2) * var(:,6,:) + q(7,2) * var(:,7,:) + &
+                      q(8,2) * var(:,8,:) ) * idel
+      dvar(:,3,:) = ( q(1,3) * var(:,1,:) + q(2,3) * var(:,2,:) + &
+                      q(4,3) * var(:,4,:) + q(5,3) * var(:,5,:) + &
+                      q(6,3) * var(:,6,:) + q(7,3) * var(:,7,:) + &
+                      q(8,3) * var(:,8,:) ) * idel
+      dvar(:,4,:) = ( q(1,4) * var(:,1,:) + q(2,4) * var(:,2,:) + &
+                      q(3,4) * var(:,3,:) + q(5,4) * var(:,5,:) + &
+                      q(6,4) * var(:,6,:) + q(7,4) * var(:,7,:) + &
+                      q(8,4) * var(:,8,:) ) * idel
+      dvar(:,5,:) = ( q(1,5) * var(:,1,:) + q(2,5) * var(:,2,:) + &
+                      q(3,5) * var(:,3,:) + q(4,5) * var(:,4,:) + &
+                      q(6,5) * var(:,6,:) + q(7,5) * var(:,7,:) + &
+                      q(8,5) * var(:,8,:) + q(9,5) * var(:,9,:) ) * idel
+      dvar(:,6,:) = ( q(1,6) * var(:,1,:) + q(2,6) * var(:,2,:) + &
+                      q(3,6) * var(:,3,:) + q(4,6) * var(:,4,:) + &
+                      q(5,6) * var(:,5,:) + q(7,6) * var(:,7,:) + &
+                      q(8,6) * var(:,8,:) + q(9,6) * var(:,9,:) + &
+                      q(10,6) * var(:,10,:) ) * idel
+      dvar(:,7,:) = ( q(1,7) * var(:,1,:) + q(2,7) * var(:,2,:) + &
+                      q(3,7) * var(:,3,:) + q(4,7) * var(:,4,:) + &
+                      q(5,7) * var(:,5,:) + q(6,7) * var(:,6,:) + &
+                      q(8,7) * var(:,8,:) + q(9,7) * var(:,9,:) + &
+                      q(10,7) * var(:,10,:) + q(11,7) * var(:,11,:) ) * idel
+      dvar(:,8,:) = ( q(1,8) * var(:,1,:) + q(2,8) * var(:,2,:) + &
+                      q(3,8) * var(:,3,:) + q(4,8) * var(:,4,:) + &
+                      q(5,8) * var(:,5,:) + q(6,8) * var(:,6,:) + &
+                      q(7,8) * var(:,7,:) + q(9,8) * var(:,9,:) + &
+                      q(10,8) * var(:,10,:) + q(11,8) * var(:,11,:) + &
+                      q(12,8) * var(:,12,:) ) * idel
+      jl = 9
+    end if
+    if ( bb(2) == 0 ) then
+      jr = nj - gsize
+    else
+      dvar(:,nj,:) =   - ( q(1,1) * var(:,nj,:) + q(2,1) * var(:,nj-1,:) + &
+                           q(3,1) * var(:,nj-2,:) + q(4,1) * var(:,nj-3,:) + &
+                           q(5,1) * var(:,nj-4,:) + q(6,1) * var(:,nj-5,:) + &
+                           q(7,1) * var(:,nj-6,:) + &
+                           q(8,1) * var(:,nj-7,:) ) * idel
+      dvar(:,nj-1,:) = - ( q(1,2) * var(:,nj,:) + q(3,2) * var(:,nj-2,:) + &
+                           q(4,2) * var(:,nj-3,:) + q(5,2) * var(:,nj-4,:) + &
+                           q(6,2) * var(:,nj-5,:) + q(7,2) * var(:,nj-6,:) + &
+                           q(8,2) * var(:,nj-7,:) ) * idel
+      dvar(:,nj-2,:) = - ( q(1,3) * var(:,nj,:) + q(2,3) * var(:,nj-1,:) + &
+                           q(4,3) * var(:,nj-3,:) + q(5,3) * var(:,nj-4,:) + &
+                           q(6,3) * var(:,nj-5,:) + q(7,3) * var(:,nj-6,:) + &
+                           q(8,3) * var(:,nj-7,:) ) * idel
+      dvar(:,nj-3,:) = - ( q(1,4) * var(:,nj,:) + q(2,4) * var(:,nj-1,:) + &
+                           q(3,4) * var(:,nj-2,:) + q(5,4) * var(:,nj-4,:) + &
+                           q(6,4) * var(:,nj-5,:) + q(7,4) * var(:,nj-6,:) + &
+                           q(8,4) * var(:,nj-7,:) ) * idel
+      dvar(:,nj-4,:) = - ( q(1,5) * var(:,nj,:) + q(2,5) * var(:,nj-1,:) + &
+                           q(3,5) * var(:,nj-2,:) + q(4,5) * var(:,nj-3,:) + &
+                           q(6,5) * var(:,nj-5,:) + q(7,5) * var(:,nj-6,:) + &
+                           q(8,5) * var(:,nj-7,:) + &
+                           q(9,5) * var(:,nj-8,:) ) * idel
+      dvar(:,nj-5,:) = - ( q(1,6) * var(:,nj,:) + q(2,6) * var(:,nj-1,:) + &
+                           q(3,6) * var(:,nj-2,:) + q(4,6) * var(:,nj-3,:) + &
+                           q(5,6) * var(:,nj-4,:) + q(7,6) * var(:,nj-6,:) + &
+                           q(8,6) * var(:,nj-7,:) + q(9,6) * var(:,nj-8,:) + &
+                           q(10,6) * var(:,nj-9,:) ) * idel
+      dvar(:,nj-6,:) = - ( q(1,7) * var(:,nj,:) + q(2,7) * var(:,nj-1,:) + &
+                           q(3,7) * var(:,nj-2,:) + q(4,7) * var(:,nj-3,:) + &
+                           q(5,7) * var(:,nj-4,:) + q(6,7) * var(:,nj-5,:) + &
+                           q(8,7) * var(:,nj-7,:) + q(9,7) * var(:,nj-8,:) + &
+                           q(10,7) * var(:,nj-9,:) + &
+                           q(11,7) * var(:,nj-10,:) ) * idel
+      dvar(:,nj-7,:) = - ( q(1,8) * var(:,nj,:) + q(2,8) * var(:,nj-1,:) + &
+                           q(3,8) * var(:,nj-2,:) + q(4,8) * var(:,nj-3,:) + &
+                           q(5,8) * var(:,nj-4,:) + q(6,8) * var(:,nj-5,:) + &
+                           q(7,8) * var(:,nj-6,:) + q(9,8) * var(:,nj-8,:) + &
+                           q(10,8) * var(:,nj-9,:) + &
+                           q(11,8) * var(:,nj-10,:) + &
+                           q(12,8) * var(:,nj-11,:) ) * idel
+      jr = nj - 8
+    end if
+    dvar(:,jl:jr,:) = ( a(1) * ( var(:,jl+1:jr+1,:) - &
+                                 var(:,jl-1:jr-1,:) ) + &
+                        a(2) * ( var(:,jl+2:jr+2,:) - &
+                                 var(:,jl-2:jr-2,:) ) + &
+                        a(3) * ( var(:,jl+3:jr+3,:) - &
+                                 var(:,jl-3:jr-3,:) ) + &
+                        a(4) * ( var(:,jl+4:jr+4,:) - &
+                                 var(:,jl-4:jr-4,:) ) ) * idel
+  case (2) direction
+    if ( bb(1) == 0 ) then
+      kl = 1 + gsize
+    else
+      dvar(:,:,1) = ( q(1,1) * var(:,:,1) + q(2,1) * var(:,:,2) + &
+                      q(3,1) * var(:,:,3) + q(4,1) * var(:,:,4) + &
+                      q(5,1) * var(:,:,5) + q(6,1) * var(:,:,6) + &
+                      q(7,1) * var(:,:,7) + q(8,1) * var(:,:,8) ) * idel
+      dvar(:,:,2) = ( q(1,2) * var(:,:,1) + q(3,2) * var(:,:,3) + &
+                      q(4,2) * var(:,:,4) + q(5,2) * var(:,:,5) + &
+                      q(6,2) * var(:,:,6) + q(7,2) * var(:,:,7) + &
+                      q(8,2) * var(:,:,8) ) * idel
+      dvar(:,:,3) = ( q(1,3) * var(:,:,1) + q(2,3) * var(:,:,2) + &
+                      q(4,3) * var(:,:,4) + q(5,3) * var(:,:,5) + &
+                      q(6,3) * var(:,:,6) + q(7,3) * var(:,:,7) + &
+                      q(8,3) * var(:,:,8) ) * idel
+      dvar(:,:,4) = ( q(1,4) * var(:,:,1) + q(2,4) * var(:,:,2) + &
+                      q(3,4) * var(:,:,3) + q(5,4) * var(:,:,5) + &
+                      q(6,4) * var(:,:,6) + q(7,4) * var(:,:,7) + &
+                      q(8,4) * var(:,:,8) ) * idel
+      dvar(:,:,5) = ( q(1,5) * var(:,:,1) + q(2,5) * var(:,:,2) + &
+                      q(3,5) * var(:,:,3) + q(4,5) * var(:,:,4) + &
+                      q(6,5) * var(:,:,6) + q(7,5) * var(:,:,7) + &
+                      q(8,5) * var(:,:,8) + q(9,5) * var(:,:,9) ) * idel
+      dvar(:,:,6) = ( q(1,6) * var(:,:,1) + q(2,6) * var(:,:,2) + &
+                      q(3,6) * var(:,:,3) + q(4,6) * var(:,:,4) + &
+                      q(5,6) * var(:,:,5) + q(7,6) * var(:,:,7) + &
+                      q(8,6) * var(:,:,8) + q(9,6) * var(:,:,9) + &
+                      q(10,6) * var(:,:,10) ) * idel
+      dvar(:,:,7) = ( q(1,7) * var(:,:,1) + q(2,7) * var(:,:,2) + &
+                      q(3,7) * var(:,:,3) + q(4,7) * var(:,:,4) + &
+                      q(5,7) * var(:,:,5) + q(6,7) * var(:,:,6) + &
+                      q(8,7) * var(:,:,8) + q(9,7) * var(:,:,9) + &
+                      q(10,7) * var(:,:,10) + q(11,7) * var(:,:,11) ) * idel
+      dvar(:,:,8) = ( q(1,8) * var(:,:,1) + q(2,8) * var(:,:,2) + &
+                      q(3,8) * var(:,:,3) + q(4,8) * var(:,:,4) + &
+                      q(5,8) * var(:,:,5) + q(6,8) * var(:,:,6) + &
+                      q(7,8) * var(:,:,7) + q(9,8) * var(:,:,9) + &
+                      q(10,8) * var(:,:,10) + q(11,8) * var(:,:,11) + &
+                      q(12,8) * var(:,:,12) ) * idel
+      kl = 9
+    end if
+    if ( bb(2) == 0 ) then
+      kr = nk - gsize
+    else 
+      dvar(:,:,nk) =   - ( q(1,1) * var(:,:,nk) + q(2,1) * var(:,:,nk-1) + &
+                           q(3,1) * var(:,:,nk-2) + q(4,1) * var(:,:,nk-3) + &
+                           q(5,1) * var(:,:,nk-4) + q(6,1) * var(:,:,nk-5) + &
+                           q(7,1) * var(:,:,nk-6) + &
+                           q(8,1) * var(:,:,nk-7) ) * idel
+      dvar(:,:,nk-1) = - ( q(1,2) * var(:,:,nk) + q(3,2) * var(:,:,nk-2) + &
+                           q(4,2) * var(:,:,nk-3) + q(5,2) * var(:,:,nk-4) + &
+                           q(6,2) * var(:,:,nk-5) + q(7,2) * var(:,:,nk-6) + &
+                           q(8,2) * var(:,:,nk-7) ) * idel
+      dvar(:,:,nk-2) = - ( q(1,3) * var(:,:,nk) + q(2,3) * var(:,:,nk-1) + &
+                           q(4,3) * var(:,:,nk-3) + q(5,3) * var(:,:,nk-4) + &
+                           q(6,3) * var(:,:,nk-5) + q(7,3) * var(:,:,nk-6) + &
+                           q(8,3) * var(:,:,nk-7) ) * idel
+      dvar(:,:,nk-3) = - ( q(1,4) * var(:,:,nk) + q(2,4) * var(:,:,nk-1) + &
+                           q(3,4) * var(:,:,nk-2) + q(5,4) * var(:,:,nk-4) + &
+                           q(6,4) * var(:,:,nk-5) + q(7,4) * var(:,:,nk-6) + &
+                           q(8,4) * var(:,:,nk-7) ) * idel
+      dvar(:,:,nk-4) = - ( q(1,5) * var(:,:,nk) + q(2,5) * var(:,:,nk-1) + &
+                           q(3,5) * var(:,:,nk-2) + q(4,5) * var(:,:,nk-3) + &
+                           q(6,5) * var(:,:,nk-5) + q(7,5) * var(:,:,nk-6) + &
+                           q(8,5) * var(:,:,nk-7) + &
+                           q(9,5) * var(:,:,nk-8) ) * idel
+      dvar(:,:,nk-5) = - ( q(1,6) * var(:,:,nk) + q(2,6) * var(:,:,nk-1) + &
+                           q(3,6) * var(:,:,nk-2) + q(4,6) * var(:,:,nk-3) + &
+                           q(5,6) * var(:,:,nk-4) + q(7,6) * var(:,:,nk-6) + &
+                           q(8,6) * var(:,:,nk-7) + q(9,6) * var(:,:,nk-8) + &
+                           q(10,6) * var(:,:,nk-9) ) * idel
+      dvar(:,:,nk-6) = - ( q(1,7) * var(:,:,nk) + q(2,7) * var(:,:,nk-1) + &
+                           q(3,7) * var(:,:,nk-2) + q(4,7) * var(:,:,nk-3) + &
+                           q(5,7) * var(:,:,nk-4) + q(6,7) * var(:,:,nk-5) + &
+                           q(8,7) * var(:,:,nk-7) + q(9,7) * var(:,:,nk-8) + &
+                           q(10,7) * var(:,:,nk-9) + &
+                           q(11,7) * var(:,:,nk-10) ) * idel
+      dvar(:,:,nk-7) = - ( q(1,8) * var(:,:,nk) + q(2,8) * var(:,:,nk-1) + &
+                           q(3,8) * var(:,:,nk-2) + q(4,8) * var(:,:,nk-3) + &
+                           q(5,8) * var(:,:,nk-4) + q(6,8) * var(:,:,nk-5) + &
+                           q(7,8) * var(:,:,nk-6) + q(9,8) * var(:,:,nk-8) + &
+                           q(10,8) * var(:,:,nk-9) + &
+                           q(11,8) * var(:,:,nk-10) + &
+                           q(12,8) * var(:,:,nk-11) ) * idel
+      kr = nk - 8
+    end if
+    dvar(:,:,kl:kr) = ( a(1) * ( var(:,:,kl+1:kr+1) - &
+                                 var(:,:,kl-1:kr-1) ) + &
+                        a(2) * ( var(:,:,kl+2:kr+2) - &
+                                 var(:,:,kl-2:kr-2) ) + &
+                        a(3) * ( var(:,:,kl+3:kr+3) - &
+                                 var(:,:,kl-3:kr-3) ) + &
+                        a(4) * ( var(:,:,kl+4:kr+4) - &
+                                 var(:,:,kl-4:kr-4) ) ) * idel
+  end select direction
+end subroutine deriv_gf_8_4
diff --git a/src/call_derivs.c b/src/call_derivs.c
index 30c280a..e8c051a 100644
--- a/src/call_derivs.c
+++ b/src/call_derivs.c
@@ -42,6 +42,15 @@ void DiffGv ( const CCTK_POINTER cctkGH_, const CCTK_INT dir,
                                        const CCTK_INT *gsize,
                                        const CCTK_REAL *delta,
                                        CCTK_REAL *dvar);
+  void CCTK_FCALL CCTK_FNAME(deriv_gf_8_4)(const CCTK_REAL *var,
+                                       const CCTK_INT *ni,
+                                       const CCTK_INT *nj,
+                                       const CCTK_INT *nk,
+                                       const CCTK_INT *dir,
+                                       const CCTK_INT *bb,
+                                       const CCTK_INT *gsize,
+                                       const CCTK_REAL *delta,
+                                       CCTK_REAL *dvar);
 
   
   ni = cctk_lsh[0]; nj = cctk_lsh[1]; nk = cctk_lsh[2];
@@ -82,6 +91,10 @@ void DiffGv ( const CCTK_POINTER cctkGH_, const CCTK_INT dir,
     CCTK_FNAME(deriv_gf_6_3)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar);
     break;
   }
+  case 8: {
+    CCTK_FNAME(deriv_gf_8_4)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar);
+    break;
+  }
   default:
     assert(0);
   }
diff --git a/src/make.code.defn b/src/make.code.defn
index 70a8873..a5db2d8 100644
--- a/src/make.code.defn
+++ b/src/make.code.defn
@@ -2,7 +2,7 @@
 # $Header$
 
 # Source files in this directory
-SRCS =  Derivatives_2_1.F90 Derivatives_4_2.F90 Derivatives_6_3.F90 call_derivs.c call_derivs_name.c
+SRCS =  Derivatives_2_1.F90 Derivatives_4_2.F90 Derivatives_6_3.F90 Derivatives_8_4.F90 call_derivs.c call_derivs_name.c
 
 # Subdirectories containing source files
 SUBDIRS =