$\"\"$ $\"\"$ $\"\"$
Go backward to SIMD Mesh Matrix Multiplication
Go up to Top
Go forward to SIMD Cube Matrix Multiplication

SIMD Mesh Matrix Multiplication

Problem

Processor array of fixed size ( $2$ ^d x2^d),
Matrix size arbitrary ( $2$ ⁿ x2ⁿ, n>d).

Solution

Circular mapping of matrix columns ( $A$ ) resp. rows ( $B$ ) to processors.

Processor Array

$A$ ₀₀ $A$ ₀₁ $A$ ₀₂ $A$ ₀₃

$A$ ₀₄ $A$ ₀₅ $A$ ₀₆ $A$ ₀₇

$A$ ₁₀ $A$ ₁₁ $A$ ₁₂ $A$ ₁₃

$A$ ₁₄ $A$ ₁₅ $A$ ₁₆ $A$ ₁₇

$A$ ₂₀ $A$ ₂₁ $A$ ₂₂ $A$ ₂₃

$A$ ₂₄ $A$ ₂₅ $A$ ₂₆ $A$ ₂₇

$A$ ₃₀ $A$ ₃₁ $A$ ₃₂ $A$ ₃₃

$A$ ₃₄ $A$ ₃₅ $A$ ₃₆ $A$ ₃₇

Analogous for matrix

B

Author: Wolfgang Schreiner
Last modification: November 15, 1996

Processor Array
$A$ ₀₀	$A$ ₀₁	$A$ ₀₂	$A$ ₀₃
$A$ ₀₄	$A$ ₀₅	$A$ ₀₆	$A$ ₀₇
$A$ ₁₀	$A$ ₁₁	$A$ ₁₂	$A$ ₁₃
$A$ ₁₄	$A$ ₁₅	$A$ ₁₆	$A$ ₁₇
$A$ ₂₀	$A$ ₂₁	$A$ ₂₂	$A$ ₂₃
$A$ ₂₄	$A$ ₂₅	$A$ ₂₆	$A$ ₂₇
$A$ ₃₀	$A$ ₃₁	$A$ ₃₂	$A$ ₃₃
$A$ ₃₄	$A$ ₃₅	$A$ ₃₆	$A$ ₃₇