perf(polint): add ordn=6 specialized neville path

AMSS_NCKU_source/fmisc.f90

@@ -1112,26 +1112,92 @@ end subroutine d2dump
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 ! common code for cell and vertex
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-! Lagrangian polynomial interpolation
+! Lagrangian polynomial interpolation
-!------------------------------------------------------------------------------
+!------------------------------------------------------------------------------
-
+
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
-  subroutine polint(xa, ya, x, y, dy, ordn)
+  subroutine polint6_neville(xa, ya, x, y, dy)
-  implicit none
+  implicit none
-
+
-  integer, intent(in) :: ordn
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, m, ns, n_m
+  real*8, dimension(6) :: c, d, ho
+  real*8 :: dif, dift, hp, h, den_val
+
+  c = ya
+  d = ya
+  ho = xa - x
+
+  ns = 1
+  dif = abs(x - xa(1))
+
+  do i = 2, 6
+    dift = abs(x - xa(i))
+    if (dift < dif) then
+      ns = i
+      dif = dift
+    end if
+  end do
+
+  y = ya(ns)
+  ns = ns - 1
+
+  do m = 1, 5
+    n_m = 6 - m
+    do i = 1, n_m
+      hp = ho(i)
+      h  = ho(i+m)
+      den_val = hp - h
+
+      if (den_val == 0.0d0) then
+        write(*,*) 'failure in polint for point',x
+        write(*,*) 'with input points: ',xa
+        stop
+      end if
+
+      den_val = (c(i+1) - d(i)) / den_val
+
+      d(i) = h * den_val
+      c(i) = hp * den_val
+    end do
+
+    if (2 * ns < n_m) then
+      dy = c(ns + 1)
+    else
+      dy = d(ns)
+      ns = ns - 1
+    end if
+    y = y + dy
+  end do
+
+  return
+  end subroutine polint6_neville
+
+!DIR$ ATTRIBUTES FORCEINLINE :: polint
+  subroutine polint(xa, ya, x, y, dy, ordn)
+  implicit none
+
+  integer, intent(in) :: ordn
   real*8, dimension(ordn), intent(in) :: xa, ya
   real*8, intent(in) :: x
   real*8, intent(out) :: y, dy
 
-  integer :: i, m, ns, n_m
+  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
+  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
+  real*8 :: dif, dift, hp, h, den_val
-
+
-  c = ya
+  if (ordn == 6) then
-  d = ya
+    call polint6_neville(xa, ya, x, y, dy)
-  ho = xa - x
+    return
+  end if
+
+  c = ya
+  d = ya
+  ho = xa - x
 
   ns = 1
   dif = abs(x - xa(1))