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SIMD Hypercube Matrix Multiplication

Mapping of cube with dimension n to hypercube with dimension d.

• Hypercube of n³=2^d processors =>d=3s (for some s).
• 64 processors =>n=4, d=6, 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.