In order to measure DTLB performance, we collected sample data for Retired Instructions, Data Cache Accesses, L1 DTLB Miss and L2 DTLB Hit, and L1 DTLB and L2 DTLB Miss events. (See Section 6.5.1.)

  Event                Classic function  Improved function
  Abbreviation        multiply_matrices  multiply_matrices
  ------------------  -----------------  -----------------
  Ret_instructions               68,180             88,150 samples
  DC_accesses                   402,415            602,298 samples
  DTLB_L1M_L2H                   59,532                 53 samples
  DTLB_L1M_L2M                  157,529                175 samples

In their paper titled "On Reducing TLB Misses in Matrix Multiplication," Kazushige Goto and Robert van de Geijn assert that translation lookaside buffer misses are the limiting factor in fast matrix multiplication. The event data supports their claim.

Derived measurements were computed from the event data:

                       Classic function  Improved function
  Measurement         multiply_matrices  multiply_matrices
  ------------------  -----------------  -----------------
  Elapsed time                  13.2340             3.4370 seconds
  L1 DTLB req rate               0.5902             0.6833
  L1 DTLB miss rate              0.3184             0.0003
  L1 DTLB miss ratio             0.5394             0.0004
  L2 DTLB req rate               0.3184             0.0003
  L2 DTLB miss rate              0.2310             0.0002
  L2 DTLB miss ratio             0.7257             0.7675

The L1 DTLB request rate is higher for the improved version since it performs more memory access operations than the classic version. For the textbook program, an L1 DTLB miss occurs every 3.1 instructions and an L2 DTLB miss occurs every 4.3 instructions -- clearly unacceptable. The improved matrix multiplication program executes at least 3,300 instructions per DTLB miss.