Blitz++ Benchmarks: Acoustic3D

This benchmark solves the 3-D acoustic wave equation using a finite difference approximation. The grid size is 112x112x112.

The benchmark problem models the propagation of pressure waves through a cube. Each half of the cube is made of a different material, and each half has a hollow cavity (the cavity on the left doesn't show up very well). This image shows the pressure distribution in a two-dimensional slice over time. The ratio of time steps to frames is 25:1 (in the MPEG, it's 5:1).

Timing results

The Mflops rates are quite low because each iteration requires 21.4 Mb of data to be shipped through the CPU; this is far larger than the cache size. It's theoretically possible to get better performance through an iteration-space tiling, but this is beyond the scope of Blitz++ for now.

Optimizations

• Interlacing: It turns out that for this problem interlacing the arrays worsens performance, so this optimization wasn't used.
  
  
• Avoiding array copies: A lot of time in the untuned versions is wasted copying arrays to advance a time step. In the tuned versions, copying is replaced by either cycling the arrays (Blitz++) or by putting the stencil operation in a subroutine and manually cycling the array arguments (Fortran). A side effect of this optimization is that the number of time steps has to be divisible by three.
  
  
• Cache reuse: The tuned Fortran 77 version uses 8x8x8 tiles to achieve a higher L1 cache hit rate. Instead of tiling, the Blitz++ version uses a traversal based on the Hilbert space-filling curve. The library automatically detects the 3D stencil expression and generates the Hilbert-based traversal. Both approaches (tiling and the Hilbert curve) have the effect of increasing the L1 cache hit rate. The 8x8x8 tiles appear to be better in this situation.

Initial conditions setup