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SIMD Hypercube Matrix Multiplication

• Hypercube of $n3=2d$ processors $=>d=3s$ (for some $s$).
• 64 processors $=>n=4,\; d=8,\; s=3$.

  $$

  Hypercube	d5 d4	d3 d2	d1 d0
  Cube	x	y	z

• Embedding algorithm
  • Cube indices in binary form ($s$ bits each)
  • Concatenate indices ($3s=d$ bits)
• Neighbor processors in cube remain neighbors in hypercube.
• Any cube algorithm can be executed with same efficiency on hypercube.