Polyhedron benchmark on Opteron

[Dominique Dhumieres]

> By fixing those silly loops where the last value is set to the next to
> last value inside the loop, rather than afterwards, gfortran can chop off
> 0.30 seconds, 

You are probably speaking of:

      DO N = 0, NP1
	  BAREA(N) = AREA(RBOUND(N))
	  IF (N == NP1) BAREA(N) = BAREA(N-1)
      END DO

and

      DO N = 1, NP1
	  CAREA(N) = AREA(RADIUS(N))
	  IF (N == NP1) CAREA(N) = CAREA(N-1)
      END DO

I did not see much gain by hand optimizing these loops (within the timing 
noise).

> leaving the monster array assignment with vector sqrt in
> eos as the one performance differentiation.

If you are speaking of

      VOL(:NP1) = DX(:NP1)/3.0*(BAREA(:NP1-1)+SQRT(BAREA(:NP1-1)*BAREA(1&
	   &    :NP1))+BAREA(1:NP1))

I did not see any improvement by replacing it by

      do n = 1, np1
         vol(n) = dx(n)*(barea(n-1)+sqrt(barea(n-1)*barea(n))+barea(n))/3.0
      end do

However replacing

          TEMP(:NODES) = IENER(:NODES)/SHEAT
          PRES(:NODES) = (CGAMMA - 1.0)*DENS(:NODES)*IENER(:NODES)
	  GAMMA(:NODES) = CGAMMA
          CS(:NODES) = SQRT(CGAMMA*PRES(:NODES)/DENS(:NODES))

by

	  GAMMA(:NODES) = CGAMMA
	  const = (CGAMMA - 1.0)*CGAMMA
	  RSHEAT = 1.0/SHEAT
	  do n = 1, nodes
	      TEMP(n) = IENER(n)*RSHEAT
	      PRES(n) = (CGAMMA - 1.0)*DENS(n)*IENER(n)
	      CS(n) = SQRT(const*IENER(n))
	  end do

gave me an important saving: from ~17" to ~13".  I did not try to split the
saving between the "loop fusion" (which should be detected by "good"
compilers) and the removal of unnecessary division (I am not sure that this
optimization could be done by (is allowed to) any compiler).

Dominique