Optimization_1x4_9

Copy the contents of file MMult_1x4_8.c into a file named MMult_1x4_9.c and change the contents:

|| from || to || ||<^> -Include(HowToOptimizeGemm/Details/MMult_1x4_8)- ||<^> -Include(HowToOptimizeGemm/Details/MMult_1x4_9)- ||

Change the first lines in the makefile to {{{ OLD := MMult_1x4_8 NEW := MMult_1x4_9
}}}

• make run {{{ octave:3> PlotAll % this will create the plot }}}

This time the performance graph will look something like

ImageLink(http://www.cs.utexas.edu/users/rvdg/HowToOptimizeGemm/Graphs/compare_MMult-1x4-8_MMult-1x4-9.png,http://www.cs.utexas.edu/users/rvdg/HowToOptimizeGemm/Graphs/compare_MMult-1x4-8_MMult-1x4-9.png,width=40%)

We now use something called 'indirect addressing'. Notice, for example, the line {{{ c_00_reg += a_0p_reg * *(bp0_pntr+1); }}} Here

*a0p_reg holds the element A( 0, p+1 ) (yes, this is a bit confusing. A better name for the variable would be good...)

• We want to bp0_pntr' points to element B( p, 0 ). Hence bp0_pntr+1' addresses the element B( p+1, 0 ). There is a special machine instruction to then access the element at `bp0_pntr+1' that does not require the pointer to be updated.

• As a result, the pointers that address the elements in the columns of B only need to be updated once every fourth iteration of the loop.

Interestingly, it appears that the compiler did this optimization automatically, and hence we see no performance improvement...