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SIMD Hypercube Matrix Multiplication

Tree summation in hypercube.

Processors 000 001 010 011 100 101 110 111

Step 1 $r$ ₀ $s$ ₀ $r$ ₁ $s$ ₁ $r$ ₂ $s$ ₂ $r$ ₃ $s$ ₃

Step 2 $r$ ₀ $s$ ₀ $r$ ₁ $s$ ₁

Step 3 $r$ ₀ $s$ ₀

Each processor receives value from neighboring processors only.
Only short-distance communication is required.

Cube algorithm can be more efficient on hypercube!

Author: Wolfgang Schreiner
Last modification: November 15, 1996

Processors	000	001	010	011	100	101	110	111
Step 1	$r$ ₀	$s$ ₀	$r$ ₁	$s$ ₁	$r$ ₂	$s$ ₂	$r$ ₃	$s$ ₃
Step 2	$r$ ₀		$s$ ₀		$r$ ₁		$s$ ₁
Step 3	$r$ ₀				$s$ ₀