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Optimize BSSN RHS and finite difference calculations

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- Integrate Intel oneMKL VML for efficient Gauge calculation in bssn_rhs.f90
- Refactor fderivs in diff_new.f90 to separate bulk/boundary loops for better vectorization
- Add optimization report in docs/optimization_report.md
This commit is contained in:
CGH0S7
2026-01-19 10:49:14 +08:00
parent 039dce4d65
commit 3914659ebb
3 changed files with 827 additions and 106 deletions
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146
AMSS_NCKU_source/diff_new.f90
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@@ -962,6 +962,7 @@
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
integer :: ib_s, ib_e, jb_s, jb_e, kb_s, kb_e
real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -1001,109 +1002,66 @@
fy = ZEO
fz = ZEO
ib_s = max(1, imin + 2)
ib_e = min(ex(1)-1, imax - 2)
jb_s = max(1, jmin + 2)
jb_e = min(ex(2)-1, jmax - 2)
kb_s = max(1, kmin + 2)
kb_e = min(ex(3)-1, kmax - 2)
! Intel compiler directives for aggressive vectorization
!DIR$ SIMD
!DIR$ IVDEP
do k=1,ex(3)-1
do j=1,ex(2)-1
!DIR$ SIMD
do i=1,ex(1)-1
#if 0
! x direction
if(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
! Check if (j, k) are within the safe 4th-order range
if (k >= kb_s .and. k <= kb_e .and. j >= jb_s .and. j <= jb_e) then
! 1. Left Boundary Peel
do i=1, min(ex(1)-1, ib_s-1)
if(i+1 <= imax .and. i-1 >= imin .and. &
j+1 <= jmax .and. j-1 >= jmin .and. &
k+1 <= kmax .and. k-1 >= kmin) then
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
endif
enddo
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! 2. BULK CORE (No branches, full SIMD)
!DIR$ SIMD
do i=ib_s, ib_e
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
enddo
! set imax and imin 0
! 3. Right Boundary Peel
do i=max(1, ib_e+1), ex(1)-1
if(i+1 <= imax .and. i-1 >= imin .and. &
j+1 <= jmax .and. j-1 >= jmin .and. &
k+1 <= kmax .and. k-1 >= kmin) then
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
endif
enddo
else
! We are in a boundary slab (j or k is near edge)
! Fallback to standard loop with checks (max 2nd order possible here)
do i=1,ex(1)-1
if(i+1 <= imax .and. i-1 >= imin .and. &
j+1 <= jmax .and. j-1 >= jmin .and. &
k+1 <= kmax .and. k-1 >= kmin) then
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
endif
enddo
endif
! y direction
if(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
! z direction
if(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
#elif 0
! x direction
if(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+3 <= imax .and. i-1 >= imin)then
fx(i,j,k)=d12dx*(-3.d0*fh(i-1,j,k)-1.d1*fh(i,j,k)+1.8d1*fh(i+1,j,k)-6.d0*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+1 <= imax .and. i-3 >= imin)then
fx(i,j,k)=d12dx*( 3.d0*fh(i+1,j,k)+1.d1*fh(i,j,k)-1.8d1*fh(i-1,j,k)+6.d0*fh(i-2,j,k)-fh(i-3,j,k))
! set imax and imin 0
endif
! y direction
if(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+3 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d12dy*(-3.d0*fh(i,j-1,k)-1.d1*fh(i,j,k)+1.8d1*fh(i,j+1,k)-6.d0*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+1 <= jmax .and. j-3 >= jmin)then
fy(i,j,k)=d12dy*( 3.d0*fh(i,j+1,k)+1.d1*fh(i,j,k)-1.8d1*fh(i,j-1,k)+6.d0*fh(i,j-2,k)-fh(i,j-3,k))
! set jmax and jmin 0
endif
! z direction
if(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+3 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d12dz*(-3.d0*fh(i,j,k-1)-1.d1*fh(i,j,k)+1.8d1*fh(i,j,k+1)-6.d0*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+1 <= kmax .and. k-3 >= kmin)then
fz(i,j,k)=d12dz*( 3.d0*fh(i,j,k+1)+1.d1*fh(i,j,k)-1.8d1*fh(i,j,k-1)+6.d0*fh(i,j,k-2)-fh(i,j,k-3))
! set kmax and kmin 0
endif
#else
! for bam comparison
if(i+2 <= imax .and. i-2 >= imin .and. &
j+2 <= jmax .and. j-2 >= jmin .and. &
k+2 <= kmax .and. k-2 >= kmin) then
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(i+1 <= imax .and. i-1 >= imin .and. &
j+1 <= jmax .and. j-1 >= jmin .and. &
k+1 <= kmax .and. k-1 >= kmin) then
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
endif
#endif
enddo
enddo
enddo