Matrix multiplication on worsktations
                        Preliminary test 96/06/27
                            Updated 97/10/30
		       (see also: bench_bm_mm.txt)



TABLE 1.  Matrix multiplication using program p25.f, compiling as
f77 -On ..., i.e., using defaults.  p25.f uses simple do-loops, the row 
index loop (vectorizable loop) being inside (locality). The MFLOPS entry
is defined as 2 N**3 / (CPU time).
========================================================================
Machine             Opt. level     ND       N        CPU (sec)   MFLOPS
------------------------------------------------------------------------
HP 710 32 MB           1          400     200            8          2
  (ur)                                    400           63          2
                       2, 3       400     200            2          8
                                          400           17          8
------------------------------------------------------------------------
SGI Indy R4600/133 SC  1          400     200            4          4
  64 MB (atlas)                           400           37          4
                       2          400     200            1          
                                          400           13         10
                       3          400     200            1
                                          400           13         10
------------------------------------------------------------------------
HP 715/75 64 MB        1          400     200            5          3
  (jupiter)                               400           39          3
                       2, 3       400     200            1         
                                          400           12         11
------------------------------------------------------------------------
SGI Indy R5000/150 SC  1          400     200            3.5        5
  64 MB (uranus)                          400           30          4
                       2          400     200            0.7       
                                          400            8         16
                       3          400     200            0.7
                                          400            8         16
------------------------------------------------------------------------
HP B132 32 MB          1          400     200            2          8
  (phobos)                                400           16          8
  *1                   2, 3       400     200            0.6       27
                                          400            4.5       28
------------------------------------------------------------------------
Pentium Pro P6/200     1          400     200            1         16
  64 MB (f9pc00)                          400            6         21
                       2, 3       400     200            0.6       27
                                          400            4.6       28
========================================================================
*1 Compiled on ur (HP-UX 9, HP 710), run on HP-UX 10 (no f77 yet on 
   phobos).

Increase of the CPU time if we put the summation loop to be innermost:
    SGI Indy R4600/133 SC:    times 2
    SGI Indy R5000/150 SC:    times 2.6
    HP 715/75:                times 3.5





TABLE 2.  As Table 1, but for program p25v.f, which calls DGEMM instead
of using DO loops. Default f77 options; using precompiled system 
libraries where available (not compiling dgemm.f explicitly).
========================================================================
Machine             Opt. level     ND       N        CPU (sec)   MFLOPS
------------------------------------------------------------------------
Pentium Pro P6/200     all        400     200            1.6       10 ?
  64 MB (f9pc00) *1                       400           12.6       10 ?
------------------------------------------------------------------------
SGI Indy R4600/100 PC  all        400     200         
  32 MB (old atlas) *                     400                      19
------------------------------------------------------------------------
SGI Indy R4600/133 SC  all        400     200            0.6       27
  64 MB (atlas) *                         400            4.2       30
                                  400     200            
                                          401            4.1       30
------------------------------------------------------------------------
SGI Indy R5000/150 SC  all        400     200            0.32      50
  64 MB (uranus) *                        400            2.64      48
========================================================================
*  Non-interleaved memory.
** Compilation on R5000: 
       f77 -O3 -n32 -mips4 ... /usr/lib32/mips4/libblas.a.
*1 f77 ... -lblas.