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Solution #5: Using registers for highly reused variables.

• C[i][j] is replaced with registers and write into memory at the final step. It effectively reduce the frequency of accessing memory.
• For example, (index is used to identify each chuck in a matrix)
  • C₀₀ = A₀₀*B₀₀ + A₀₁*B₁₀ + A₀₂*B₂₀ + A₀₃*B₃₀
    C₀₁ = A₀₀*B₀₁ + A₀₁*B₁₁ + A₀₂*B₂₁ + A₀₃*B₃₁
  • A and C are reused, thus can be replaced with registers. The following is the result.
  • R2 = A₀₀; R3 = A₀₁; R4 = A₀₂; R5 = A₀₃;
    R0 = R2*B₀₀ + R3*B₁₀ + R4*B₂₀ + R5*B₃₀
    R1 = R2*B₀₁ + R3*B₁₁ + R4*B₂₁ + R5*B₃₁
    C₀₀ = R0; C₀₁ = R1;
    
• When using registers instead of memory access, block size should be small because most systems have only a limited number of registers.
• Loop unrolling is useful technique to apply this optimization.