Compiler-level and hot-path optimizations for GW150914

- makefile.inc: add -ipo (interprocedural optimization) and
  -align array64byte (64-byte array alignment for vectorization)
- fmisc.f90: remove redundant funcc=0.d0 zeroing from symmetry_bd,
  symmetry_tbd, symmetry_stbd (~328+ full-array memsets eliminated
  per timestep)
- enforce_algebra.f90: rewrite enforce_ag and enforce_ga as point-wise
  loops, replacing 12 stack-allocated 3D temporary arrays with scalar
  locals for better cache locality

All changes are mathematically equivalent — no algorithmic modifications.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

AMSS_NCKU_source/enforce_algebra.f90

@@ -18,49 +18,61 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> Local variable:
-  
+
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA,detg
+  integer :: i,j,k
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8 :: lgxx,lgyy,lgzz,ldetg
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA,lscale
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  gxx = dxx + ONE
+  do k=1,ex(3)
-  gyy = dyy + ONE
+  do j=1,ex(2)
-  gzz = dzz + ONE
+  do i=1,ex(1)
 
-  detg =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+    lgxx = dxx(i,j,k) + ONE
-          gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
+    lgyy = dyy(i,j,k) + ONE
-  gupxx =   ( gyy * gzz - gyz * gyz ) / detg
+    lgzz = dzz(i,j,k) + ONE
-  gupxy = - ( gxy * gzz - gyz * gxz ) / detg
-  gupxz =   ( gxy * gyz - gyy * gxz ) / detg
-  gupyy =   ( gxx * gzz - gxz * gxz ) / detg
-  gupyz = - ( gxx * gyz - gxy * gxz ) / detg
-  gupzz =   ( gxx * gyy - gxy * gxy ) / detg
 
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+    ldetg =  lgxx * lgyy * lgzz &
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+           + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) &
+           + gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) &
+           - gxz(i,j,k) * lgyy * gxz(i,j,k) &
+           - gxy(i,j,k) * gxy(i,j,k) * lgzz &
+           - lgxx * gyz(i,j,k) * gyz(i,j,k)
 
-  Axx = Axx - F1o3 * gxx * trA
+    lgupxx =   ( lgyy * lgzz - gyz(i,j,k) * gyz(i,j,k) ) / ldetg
-  Axy = Axy - F1o3 * gxy * trA
+    lgupxy = - ( gxy(i,j,k) * lgzz - gyz(i,j,k) * gxz(i,j,k) ) / ldetg
-  Axz = Axz - F1o3 * gxz * trA
+    lgupxz =   ( gxy(i,j,k) * gyz(i,j,k) - lgyy * gxz(i,j,k) ) / ldetg
-  Ayy = Ayy - F1o3 * gyy * trA
+    lgupyy =   ( lgxx * lgzz - gxz(i,j,k) * gxz(i,j,k) ) / ldetg
-  Ayz = Ayz - F1o3 * gyz * trA
+    lgupyz = - ( lgxx * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / ldetg
-  Azz = Azz - F1o3 * gzz * trA
+    lgupzz =   ( lgxx * lgyy - gxy(i,j,k) * gxy(i,j,k) ) / ldetg
 
-  detg = ONE / ( detg ** F1o3 ) 
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
-  
+                 + lgupzz * Azz(i,j,k) &
-  gxx = gxx * detg
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
-  gxy = gxy * detg
+                 + lgupyz * Ayz(i,j,k))
-  gxz = gxz * detg
-  gyy = gyy * detg
-  gyz = gyz * detg
-  gzz = gzz * detg
 
-  dxx = gxx - ONE
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
-  dyy = gyy - ONE
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
-  dzz = gzz - ONE
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+    lscale = ONE / ( ldetg ** F1o3 )
+
+    dxx(i,j,k) = lgxx * lscale - ONE
+    gxy(i,j,k) = gxy(i,j,k) * lscale
+    gxz(i,j,k) = gxz(i,j,k) * lscale
+    dyy(i,j,k) = lgyy * lscale - ONE
+    gyz(i,j,k) = gyz(i,j,k) * lscale
+    dzz(i,j,k) = lgzz * lscale - ONE
+
+  enddo
+  enddo
+  enddo
 
   return
 
@@ -82,51 +94,71 @@
   real*8, dimension(ex(1),ex(2),ex(3)), intent(inout) :: Ayy,Ayz,Azz
 
 !~~~~~~~> Local variable:
-  
+
-  real*8, dimension(ex(1),ex(2),ex(3)) :: trA
+  integer :: i,j,k
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
+  real*8 :: lgxx,lgyy,lgzz,lscale
-  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
+  real*8 :: lgxy,lgxz,lgyz
+  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8 :: ltrA
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  gxx = dxx + ONE
+  do k=1,ex(3)
-  gyy = dyy + ONE
+  do j=1,ex(2)
-  gzz = dzz + ONE
+  do i=1,ex(1)
-! for g
-  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
 
-  gupzz = ONE / ( gupzz ** F1o3 ) 
+! for g: normalize determinant first
-  
+    lgxx = dxx(i,j,k) + ONE
-  gxx = gxx * gupzz
+    lgyy = dyy(i,j,k) + ONE
-  gxy = gxy * gupzz
+    lgzz = dzz(i,j,k) + ONE
-  gxz = gxz * gupzz
+    lgxy = gxy(i,j,k)
-  gyy = gyy * gupzz
+    lgxz = gxz(i,j,k)
-  gyz = gyz * gupzz
+    lgyz = gyz(i,j,k)
-  gzz = gzz * gupzz
 
-  dxx = gxx - ONE
+    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
-  dyy = gyy - ONE
+            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
-  dzz = gzz - ONE
+            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
-! for A  
 
-  gupxx =   ( gyy * gzz - gyz * gyz )
+    lscale = ONE / ( lscale ** F1o3 )
-  gupxy = - ( gxy * gzz - gyz * gxz )
-  gupxz =   ( gxy * gyz - gyy * gxz )
-  gupyy =   ( gxx * gzz - gxz * gxz )
-  gupyz = - ( gxx * gyz - gxy * gxz )
-  gupzz =   ( gxx * gyy - gxy * gxy )
 
-  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
+    lgxx = lgxx * lscale
-       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
+    lgxy = lgxy * lscale
+    lgxz = lgxz * lscale
+    lgyy = lgyy * lscale
+    lgyz = lgyz * lscale
+    lgzz = lgzz * lscale
 
-  Axx = Axx - F1o3 * gxx * trA
+    dxx(i,j,k) = lgxx - ONE
-  Axy = Axy - F1o3 * gxy * trA
+    gxy(i,j,k) = lgxy
-  Axz = Axz - F1o3 * gxz * trA
+    gxz(i,j,k) = lgxz
-  Ayy = Ayy - F1o3 * gyy * trA
+    dyy(i,j,k) = lgyy - ONE
-  Ayz = Ayz - F1o3 * gyz * trA
+    gyz(i,j,k) = lgyz
-  Azz = Azz - F1o3 * gzz * trA
+    dzz(i,j,k) = lgzz - ONE
+
+! for A: trace-free using normalized metric (det=1, no division needed)
+    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
+    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
+    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
+    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
+    lgupyz = - ( lgxx * lgyz - lgxy * lgxz )
+    lgupzz =   ( lgxx * lgyy - lgxy * lgxy )
+
+    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+                 + lgupzz * Azz(i,j,k) &
+         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
+                 + lgupyz * Ayz(i,j,k))
+
+    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+    Axy(i,j,k) = Axy(i,j,k) - F1o3 * lgxy * ltrA
+    Axz(i,j,k) = Axz(i,j,k) - F1o3 * lgxz * ltrA
+    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * lgyz * ltrA
+    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+
+  enddo
+  enddo
+  enddo
 
   return
 

AMSS_NCKU_source/fmisc.f90

@@ -324,7 +324,6 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -350,7 +349,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -379,7 +377,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -886,7 +883,6 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -912,7 +908,6 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -941,7 +936,6 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)

AMSS_NCKU_source/makefile.inc

@@ -16,10 +16,10 @@ LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore
 ## -fp-model fast=2: Aggressive floating-point optimizations
 ## -fma: Enable fused multiply-add instructions
 ## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
-CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma \
+CXXAPPFLAGS  = -O3 -xHost -fp-model fast=2 -fma -ipo \
                -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags  = -O3 -xHost -fp-model fast=2 -fma \
+f90appflags  = -O3 -xHost -fp-model fast=2 -fma -ipo \
-               -fpp -I${MKLROOT}/include
+               -align array64byte -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx