perf(polint): add switchable barycentric ordn=6 path

AMSS_NCKU_source/fmisc.f90

@@ -1115,6 +1115,9 @@ end subroutine d2dump
 !------------------------------------------------------------------------------
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
+#ifndef POLINT6_USE_BARYCENTRIC
+#define POLINT6_USE_BARYCENTRIC 1
+#endif
 
 !DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
   subroutine polint6_neville(xa, ya, x, y, dy)
@@ -1177,6 +1180,56 @@ end subroutine d2dump
   return
   end subroutine polint6_neville
 
+!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
+  subroutine polint6_barycentric(xa, ya, x, y, dy)
+  implicit none
+
+  real*8, dimension(6), intent(in) :: xa, ya
+  real*8, intent(in) :: x
+  real*8, intent(out) :: y, dy
+
+  integer :: i, j
+  real*8, dimension(6) :: lambda
+  real*8 :: dx, den_i, term, num, den
+
+  do i = 1, 6
+    if (x == xa(i)) then
+      y = ya(i)
+      dy = 0.d0
+      return
+    end if
+  end do
+
+  do i = 1, 6
+    den_i = 1.d0
+    do j = 1, 6
+      if (j /= i) then
+        dx = xa(i) - xa(j)
+        if (dx == 0.0d0) then
+          write(*,*) 'failure in polint for point',x
+          write(*,*) 'with input points: ',xa
+          stop
+        end if
+        den_i = den_i * dx
+      end if
+    end do
+    lambda(i) = 1.d0 / den_i
+  end do
+
+  num = 0.d0
+  den = 0.d0
+  do i = 1, 6
+    term = lambda(i) / (x - xa(i))
+    num = num + term * ya(i)
+    den = den + term
+  end do
+
+  y = num / den
+  dy = 0.d0
+
+  return
+  end subroutine polint6_barycentric
+
 !DIR$ ATTRIBUTES FORCEINLINE :: polint
   subroutine polint(xa, ya, x, y, dy, ordn)
   implicit none
@@ -1191,7 +1244,11 @@ end subroutine d2dump
   real*8 :: dif, dift, hp, h, den_val
 
   if (ordn == 6) then
+#if POLINT6_USE_BARYCENTRIC
+    call polint6_barycentric(xa, ya, x, y, dy)
+#else
     call polint6_neville(xa, ya, x, y, dy)
+#endif
     return
   end if
 

AMSS_NCKU_source/makefile

@@ -2,6 +2,12 @@
 
 include makefile.inc
 
+## polint(ordn=6) kernel selector:
+##   1 (default): barycentric fast path
+##   0          : fallback to Neville path
+POLINT6_USE_BARY ?= 1
+POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
+
 ## ABE build flags selected by PGO_MODE (set in makefile.inc, default: opt)
 ##   make                        -> opt  (PGO-guided, maximum performance)
 ##   make PGO_MODE=instrument    -> instrument (Phase 1: collect fresh profile data)
@@ -12,13 +18,13 @@ ifeq ($(PGO_MODE),instrument)
 CXXAPPFLAGS = -O3 -xHost -fma -fprofile-instr-generate -ipo \
               -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fma -fprofile-instr-generate -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 else
 ## opt (default): maximum performance with PGO profile data
 CXXAPPFLAGS = -O3 -xHost -fp-model fast=2 -fma -ipo \
               -Dfortran3 -Dnewc -I${MKLROOT}/include $(INTERP_LB_FLAGS)
 f90appflags = -O3 -xHost -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include
+              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
 endif
 
 .SUFFIXES: .o .f90 .C .for .cu