(LONG!) 64-bit Livermore Fortran Kernels Benchmark Results

John D. McCalpin mccalpin at perelandra.cms.udel.edu
Sun Nov 11 23:51:36 AEST 1990


This message contains the complete output for the Livermore Fortran
Kernels benchmark test running on an IBM RS/6000 Model 320 in DOUBLE
precision (64-bit).

The preceding note contains the same results for single-precision
arithmetic (32-bit). 

Comments:
---------
(1) The subroutine called "SIGNAL" supplied with the test must be
renamed since its name conflicts with an IBM system library (causing
the code to dump core).

(2) The tests were run with the "MULTI" parameter set to 50 (instead
of the default of 10) in order to get a long enough run to time
accurately. 

(3) The function SECOND() was defined as:
	REAL FUNCTION SECOND(OLDSEC)
	SECOND=MCLOCK()*0.01-OLDSEC
	RETURN
	END
    Note that the value of 0.01 (100 ticks per second) is correct.
    The value of 60 ticks per second given in the IBM documentation
    is incorrect.

(4) The column labeled "OK" in the output gives the number of
significant figures of accuracy of the checksum for each test.
IGNORE THIS COLUMN!!!! It is based on results for MULTI=10 and so is
not correct for the case I ran (MULTI=50).

(5) I did run the single and double-precision cases with MULTI=10 to
check the checksums and got results in agreement with another IEEE
machine (A Silicon Graphics 4D series box).  For 32-bit arithmetic the
checksums had typically 7-8 decimal digits of accuracy.

Note that there are some obscure bugs (?) in the code that prevent the
calculation of the checksum from being 64-bit accurate on a 32-bit machine
when everything is declared double-precision. I assume that this is
due to some implicit typecasts that I have not been able to find.  In
any case, I have verified that the code is correct by running it with
the "-r8" flag on the Silicon Graphics machine, which sets default
REAL precision to 64-bits in a fully consistent way.  This gave
accuracies of about 16 decimal digits.  Since IBM does not currently
provide an "auto-double" option on the xlf compiler, I was unable to
reproduce these results on the RS/6000.

(6) The code was compiled with the following command:
	xlf -O loops.f
Some minor performance improvements may be obtainable through the use
of other compiler options --- I have not tested these.

(7) PLEASE NOTE that all of these tests are effectively cache-
containable.  Unless *your* applications are also cache-containable
(or at least cache-friendly), you will not see the >20 MFLOPS
performance levels shown here.  On the other hand, certain carefully-
coded subroutines (such as DGEMM in IBM's libblas.a) can run
at over 30 MFLOPS on the Model 320 even for arrays much larger than
cache.

(8) Finally, here are the 64-bit results:
----------------------------------------------------------------------
        verify adequate loop size versus cpu clock accuracy
        -----     -------     -------    -------   --------
        extra     maximum     digital    dynamic   relative
        loop      cputime     clock      clock     timing  
        size      seconds     error      error     error   
        -----     -------     -------    -------   --------
            1   .0000E+00     100.00%    100.00%    100.00%
            2   .0000E+00     100.00%    100.00%    100.00%
            4   .1000E-01        .00%    264.57%   1888.35%
            8   .0000E+00     100.00%    100.00%    100.00%
           16   .1000E-01        .00%    264.57%    397.09%
           32   .0000E+00     100.00%    100.00%    100.00%
           64   .1000E-01        .00%    264.57%     24.27%
          128   .1000E-01        .00%    173.21%     24.27%
          256   .1000E-01        .00%    100.00%     24.27%
          512   .1000E-01        .00%     57.74%      6.80%
         1024   .2000E-01        .00%     29.79%       .97%
         2048   .4000E-01        .00%     13.32%       .97%
         4096   .7000E-01        .00%      7.69%       .97%
         6800              current run:   multi=   50.000
        -----     -------     -------    -------   --------

         approximate serial job time=    .4E+02 sec.    ( nruns= 7 runs)

 trial=      1      chksum=  421      pass=      0      fail=      0
 trial=      2      chksum=  421      pass=      1      fail=      0
 trial=      3      chksum=  421      pass=      2      fail=      0
 trial=      4      chksum=  421      pass=      3      fail=      0
 trial=      5      chksum=  421      pass=      4      fail=      0
 trial=      6      chksum=  421      pass=      5      fail=      0
 trial=      7      chksum=  421      pass=      6      fail=      0
1


 cpu clock overhead (t err): 

      run        average        standev        minimum        maximum
 tick   1    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   2    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   3    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   4    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   5    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   6    .100000E-01    .000000E+00    .100000E-01    .100000E-01
 tick   7    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 data   7    .999866E-01    .543323E-06    .999856E-01    .999877E-01
 data   7    .999860E-01    .917423E-06    .999843E-01    .999877E-01
 tick   7    .142857E-02    .349927E-02    .000000E+00    .100000E-01


 the experimental timing errors for all  7 runs
 --  ---------  ---------  --------- -----  -----   ---
  k   t min      t avg      t max    t err   tick   p-f
 --  ---------  ---------  --------- -----  -----   ---
  1  .1000E+00  .1057E+00  .1100E+00  4.68%  1.30%     0
  2  .1100E+00  .1157E+00  .1200E+00  4.28%  1.19%     0
  3  .4000E-01  .4286E-01  .5000E-01 10.54%  2.86%     0
  4  .4000E-01  .4714E-01  .5000E-01  9.58%  2.86%     0
  5  .9000E-01  .1000E+00  .1100E+00  5.35%  1.43%     0
  6  .4000E-01  .5000E-01  .6000E-01 10.69%  2.86%     0
  7  .1300E+00  .1400E+00  .1500E+00  3.82%  1.02%     0
  8  .1300E+00  .1471E+00  .1500E+00  4.76%  1.02%     0
  9  .1700E+00  .1771E+00  .2000E+00  5.82%   .79%     0
 10  .3600E+00  .3786E+00  .3900E+00  2.20%   .39%     0
 11  .7000E-01  .8286E-01  .9000E-01  8.45%  1.79%     0
 12  .8000E-01  .9000E-01  .1000E+00  5.94%  1.59%     0
 13  .7100E+00  .7229E+00  .7300E+00   .97%   .20%     0
 14  .5800E+00  .5900E+00  .6000E+00   .91%   .24%     0
 15  .2700E+00  .2786E+00  .2800E+00  1.26%   .51%     0
 16  .1700E+00  .1800E+00  .1900E+00  4.20%   .79%     0
 17  .2300E+00  .2386E+00  .2400E+00  1.47%   .60%     0
 18  .2100E+00  .2186E+00  .2200E+00  1.60%   .65%     0
 19  .1100E+00  .1200E+00  .1300E+00  4.45%  1.19%     0
 20  .2700E+00  .2786E+00  .2800E+00  1.26%   .51%     0
 21  .1680E+01  .1689E+01  .1710E+01   .59%   .08%     0
 22  .2600E+00  .2714E+00  .2800E+00  2.35%   .51%     0
 23  .1700E+00  .1771E+00  .1800E+00  2.55%   .79%     0
 24  .1600E+00  .1657E+00  .1700E+00  2.99%   .84%     0
 --  ---------  ---------  --------- -----  -----   ---


 net cpu timing variance (t err);  a few % is ok: 

                 average        standev        minimum        maximum
     terr          4.19%          2.99%           .59%         10.69%












1
 ********************************************
 the livermore  fortran kernels:  m f l o p s
 ********************************************

              computer : IBM RS/6000 Model 320   
              system   : AIX 3.1, 64-bit, 20 MHz 
              compiler : xlf -O (v1.1) 32kB cache
              date     : 11/02/90                
         mean do span  =   471

         when the computer performance range is very large   
         the net mflops rate of many fortran programs and    
         workloads will be in the sub-range between the equi-
         weighted harmonic and arithmetic means depending    
         on the degree of code parallelism and optimization. 
         the least biased central measure is the geometric 
         mean of 72 rates,  quoted +- a standard deviation.

 kernel  flops   microsec   mflop/sec span weight  check-sums             ok
 ------  -----   --------   --------- ---- ------  ---------------------- --
  1  .1752E+07  .1057E+06     16.5706 1001   1.00   .3580257008721524E+06  7
  2  .1300E+07  .1157E+06     11.2328  101   1.00   .3605241763137281E+04  8
  3  .9009E+06  .4286E+05     21.0210 1001   1.00   .7005200179428446E+02  8
  4  .8400E+06  .4714E+05     17.8182 1001   1.00   .4199475392699242E+01  8
  5  .1000E+07  .1000E+06     10.0000 1001   1.00   .3184210149404855E+05  8
  6  .5952E+06  .5000E+05     11.9040   64   1.00   .2288741318728983E+26  0
  7  .3184E+07  .1400E+06     22.7429  995   1.00   .4272975754667242E+06  8
  8  .3564E+07  .1471E+06     24.2214  100   1.00   .1050887604075329E+07  8
  9  .3091E+07  .1771E+06     17.4469  101   1.00   .8326105274034671E+06  8
 10  .1545E+07  .3786E+06      4.0819  101   1.00   .5117258847672790E+06  8
 11  .5500E+06  .8286E+05      6.6379 1001   1.00   .2340037680671110E+09  8
 12  .6000E+06  .9000E+05      6.6667 1000   1.00   .2126321196556091E-03  1
 13  .8064E+06  .7229E+06      1.1156   64   1.00   .1552259922630282E+12  0
 14  .1101E+07  .5900E+06      1.8663 1001   1.00   .2087503090558357E+11  4
 15  .8250E+06  .2786E+06      2.9615  101   1.00   .2760671680302306E+06  8
 16  .6625E+06  .1800E+06      3.6806   75   1.00   .9892820000000000E+06  0
 17  .1591E+07  .2386E+06      6.6678  101   1.00   .7802492407439027E+04  8
 18  .2178E+07  .2186E+06      9.9647  100   1.00   .4342684487413166E+06  1
 19  .1182E+07  .1200E+06      9.8475  101   1.00   .3795271869848748E+04  8
 20  .1300E+07  .2786E+06      4.6667 1000   1.00   .2128450971917007E+09  8
 21  .6312E+07  .1689E+07      3.7384  101   1.00   .2812029997465708E+09  0
 22  .9444E+06  .2714E+06      3.4792  101   1.00   .2057023067602647E+04  8
 23  .2178E+07  .1771E+06     12.2952  100   1.00   .2484930351216168E+06  5
 24  .2500E+06  .1657E+06      1.5086 1001   1.00   .3500000000000000E+04  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 24  .3825E+08  .6407E+07      5.9702  471                               122

         mflops    range:             report all range statistics:
         maximum   rate =     24.2214 mega-flops/sec.
         quartile  q3   =     14.4329 mega-flops/sec.
         average   rate =      9.6723 mega-flops/sec.
         geometric mean =      7.0671 mega-flops/sec.
         median    q2   =      8.2577 mega-flops/sec.
         harmonic  mean =      4.7693 mega-flops/sec.
         quartile  q1   =      3.7095 mega-flops/sec.
         minimum   rate =      1.1156 mega-flops/sec.


         standard  dev. =      6.8893 mega-flops/sec.
         geom.mean dev. =      7.3654 mega-flops/sec.
         mean precision =      5.08   decimal digits
1






                    sensitivity analysis


         the sensitivity of the harmonic mean rate (mflops)  
         to various weightings is shown in the table below.  
         seven work distributions are generated by assigning 
         two distinct weights to ranked kernels by quartiles.
         forty nine possible cpu workloads are then evaluated
         using seven sets of values for the total weights:   


             ------ ------ ------ ------ ------ ------ ------
   1st qt:       o      o      o      o      o      x      x
   2nd qt:       o      o      o      x      x      x      o
   3rd qt:       o      x      x      x      o      o      o
   4th qt:       x      x      o      o      o      o      o
             ------ ------ ------ ------ ------ ------ ------
   total
   weights                    net mflops:
    x    o
  ---- ----

  1.00  .00    2.01   2.88   5.10   6.92  10.79  13.91  19.57

   .95  .05    2.09   3.00   5.07   6.62   9.95  11.67  16.21

   .90  .10    2.17   3.13   5.05   6.35   9.23  10.05  13.84

   .80  .20    2.37   3.42   5.00   5.86   8.07   7.87  10.71

   .70  .30    2.61   3.78   4.96   5.45   7.17   6.47   8.73

   .60  .40    2.90   4.22   4.92   5.09   6.45   5.49   7.37

   .50  .50    3.27   4.77   4.87   4.77   5.86   4.77   6.38
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






 sensitivity of net mflops rate to use of optimal fortran code(sisd/simd model)

    2.88   3.47   4.37   5.89   7.14    9.06   12.39   15.17   19.57

     .00    .20    .40    .60    .70     .80     .90     .95    1.00
    fraction of operations run at optimal fortran rates


1


 cpu clock overhead (t err): 

      run        average        standev        minimum        maximum
 tick   1    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   2    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   3    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   4    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   5    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   6    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   7    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 data   7    .999866E-01    .543323E-06    .999856E-01    .999877E-01
 data   7    .999860E-01    .917423E-06    .999843E-01    .999877E-01
 tick   7    .000000E+00    .000000E+00    .000000E+00    .000000E+00


 the experimental timing errors for all  7 runs
 --  ---------  ---------  --------- -----  -----   ---
  k   t min      t avg      t max    t err   tick   p-f
 --  ---------  ---------  --------- -----  -----   ---
  1  .1200E+00  .1243E+00  .1300E+00  3.98%   .00%     0
  2  .1400E+00  .1414E+00  .1500E+00  2.47%   .00%     0
  3  .6000E-01  .6000E-01  .6000E-01   .00%   .00%     0
  4  .8000E-01  .8143E-01  .9000E-01  4.30%   .00%     0
  5  .1100E+00  .1143E+00  .1200E+00  4.33%   .00%     0
  6  .6000E-01  .6571E-01  .7000E-01  7.53%   .00%     0
  7  .1600E+00  .1600E+00  .1600E+00   .00%   .00%     0
  8  .1700E+00  .1786E+00  .1800E+00  1.96%   .00%     0
  9  .2000E+00  .2071E+00  .2200E+00  3.38%   .00%     0
 10  .4200E+00  .4271E+00  .4300E+00  1.06%   .00%     0
 11  .1000E+00  .1000E+00  .1000E+00   .00%   .00%     0
 12  .1000E+00  .1057E+00  .1100E+00  4.68%   .00%     0
 13  .8200E+00  .8257E+00  .8300E+00   .60%   .00%     0
 14  .5100E+00  .5157E+00  .5200E+00   .96%   .00%     0
 15  .5500E+00  .5571E+00  .5600E+00   .81%   .00%     0
 16  .2100E+00  .2157E+00  .2200E+00  2.29%   .00%     0
 17  .2700E+00  .2714E+00  .2800E+00  1.29%   .00%     0
 18  .2200E+00  .2200E+00  .2200E+00   .00%   .00%     0
 19  .1400E+00  .1414E+00  .1500E+00  2.47%   .00%     0
 20  .4300E+00  .4386E+00  .4400E+00   .80%   .00%     0
 21  .5000E+00  .5086E+00  .5100E+00   .69%   .00%     0
 22  .3400E+00  .3471E+00  .3500E+00  1.30%   .00%     0
 23  .2200E+00  .2243E+00  .2300E+00  2.21%   .00%     0
 24  .2000E+00  .2057E+00  .2100E+00  2.41%   .00%     0
 --  ---------  ---------  --------- -----  -----   ---


 net cpu timing variance (t err);  a few % is ok: 

                 average        standev        minimum        maximum
     terr          2.06%          1.83%           .00%          7.53%












1
 ********************************************
 the livermore  fortran kernels:  m f l o p s
 ********************************************

              computer : IBM RS/6000 Model 320   
              system   : AIX 3.1, 64-bit, 20 MHz 
              compiler : xlf -O (v1.1) 32kB cache
              date     : 11/02/90                
         mean do span  =    90

         when the computer performance range is very large   
         the net mflops rate of many fortran programs and    
         workloads will be in the sub-range between the equi-
         weighted harmonic and arithmetic means depending    
         on the degree of code parallelism and optimization. 
         the least biased central measure is the geometric 
         mean of 72 rates,  quoted +- a standard deviation.

 kernel  flops   microsec   mflop/sec span weight  check-sums             ok
 ------  -----   --------   --------- ---- ------  ---------------------- --
  1  .2020E+07  .1243E+06     16.2529  101   2.00   .3677341471833584E+04  7
  2  .1552E+07  .1414E+06     10.9737  101   2.00   .3605241763137281E+04  8
  3  .1071E+07  .6000E+05     17.8433  101   2.00   .7068190058985076E+01  8
  4  .8400E+06  .8143E+05     10.3158  101   2.00   .4199475392699242E+01  8
  5  .1100E+07  .1143E+06      9.6250  101   2.00   .3212322355798968E+03  8
  6  .6720E+06  .6571E+05     10.2261   32   2.00   .1960856598681209E+30  0
  7  .3555E+07  .1600E+06     22.2200  101   2.00   .4441910425224146E+04  8
  8  .4277E+07  .1786E+06     23.9501  100   2.00   .1050887604075329E+07  8
  9  .3606E+07  .2071E+06     17.4068  101   2.00   .8326105274034671E+06  8
 10  .1727E+07  .4271E+06      4.0434  101   2.00   .5117258847672790E+06  8
 11  .6400E+06  .1000E+06      6.4000  101   2.00   .2403492284702882E+06  8
 12  .6800E+06  .1057E+06      6.4324  100   2.00   .4923343658447266E-04  2
 13  .9184E+06  .8257E+06      1.1122   32   2.00   .1001353007004402E+12  0
 14  .1111E+07  .5157E+06      2.1543  101   2.00   .2139450190318256E+09  2
 15  .1650E+07  .5571E+06      2.9615  101   2.00   .2760671680302306E+06  8
 16  .7560E+06  .2157E+06      3.5046   40   2.00   .1134287000000000E+07  0
 17  .1818E+07  .2714E+06      6.6979  101   2.00   .7802492407439027E+04  8
 18  .2178E+07  .2200E+06      9.9000  100   2.00   .4342684487413166E+06  1
 19  .1394E+07  .1414E+06      9.8552  101   2.00   .3795271869848748E+04  8
 20  .2080E+07  .4386E+06      4.7427  100   2.00   .2188343542345499E+06  7
 21  .6250E+07  .5086E+06     12.2893   50   2.00   .1373396176759844E+09  0
 22  .1202E+07  .3471E+06      3.4623  101   2.00   .2057023067602647E+04  8
 23  .2722E+07  .2243E+06     12.1385  100   2.00   .2484930351216168E+06  6
 24  .3100E+06  .2057E+06      1.5069  101   2.00   .3500000000000000E+03  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 24  .4413E+08  .6237E+07      7.0752   90                               121

         mflops    range:             report all range statistics:
         maximum   rate =     23.9501 mega-flops/sec.
         quartile  q3   =     12.2139 mega-flops/sec.
         average   rate =      9.4173 mega-flops/sec.
         geometric mean =      7.1309 mega-flops/sec.
         median    q2   =      9.7401 mega-flops/sec.
         harmonic  mean =      4.9224 mega-flops/sec.
         quartile  q1   =      3.7740 mega-flops/sec.
         minimum   rate =      1.1122 mega-flops/sec.


         standard  dev. =      6.2889 mega-flops/sec.
         geom.mean dev. =      6.6916 mega-flops/sec.
         mean precision =      5.04   decimal digits
1






                    sensitivity analysis


         the sensitivity of the harmonic mean rate (mflops)  
         to various weightings is shown in the table below.  
         seven work distributions are generated by assigning 
         two distinct weights to ranked kernels by quartiles.
         forty nine possible cpu workloads are then evaluated
         using seven sets of values for the total weights:   


             ------ ------ ------ ------ ------ ------ ------
   1st qt:       o      o      o      o      o      x      x
   2nd qt:       o      o      o      x      x      x      o
   3rd qt:       o      x      x      x      o      o      o
   4th qt:       x      x      o      o      o      o      o
             ------ ------ ------ ------ ------ ------ ------
   total
   weights                    net mflops:
    x    o
  ---- ----

  1.00  .00    2.04   3.03   5.86   7.53  10.51  13.13  17.49

   .95  .05    2.12   3.15   5.79   7.15   9.77  11.25  14.94

   .90  .10    2.21   3.28   5.72   6.81   9.13   9.85  13.05

   .80  .20    2.42   3.58   5.58   6.21   8.07   7.88  10.40

   .70  .30    2.67   3.94   5.45   5.71   7.23   6.56   8.65

   .60  .40    2.97   4.38   5.32   5.29   6.55   5.63   7.41

   .50  .50    3.35   4.92   5.20   4.92   5.98   4.92   6.47
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






 sensitivity of net mflops rate to use of optimal fortran code(sisd/simd model)

    3.03   3.63   4.53   6.01   7.19    8.95   11.84   14.12   17.49

     .00    .20    .40    .60    .70     .80     .90     .95    1.00
    fraction of operations run at optimal fortran rates


1


 cpu clock overhead (t err): 

      run        average        standev        minimum        maximum
 tick   1    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   2    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   3    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   4    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   5    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   6    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   7    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 data   7    .999866E-01    .543323E-06    .999856E-01    .999877E-01
 data   7    .999860E-01    .917423E-06    .999843E-01    .999877E-01
 tick   7    .000000E+00    .000000E+00    .000000E+00    .000000E+00


 the experimental timing errors for all  7 runs
 --  ---------  ---------  --------- -----  -----   ---
  k   t min      t avg      t max    t err   tick   p-f
 --  ---------  ---------  --------- -----  -----   ---
  1  .9000E-01  .9429E-01  .1000E+00  5.25%   .00%     0
  2  .1100E+00  .1171E+00  .1200E+00  3.86%   .00%     0
  3  .4000E-01  .4857E-01  .5000E-01  7.20%   .00%     0
  4  .1000E+00  .1071E+00  .1100E+00  4.22%   .00%     0
  5  .8000E-01  .8286E-01  .9000E-01  5.45%   .00%     0
  6  .7000E-01  .7429E-01  .8000E-01  6.66%   .00%     0
  7  .1200E+00  .1229E+00  .1300E+00  3.68%   .00%     0
  8  .1300E+00  .1414E+00  .1500E+00  4.52%   .00%     0
  9  .1500E+00  .1514E+00  .1600E+00  2.31%   .00%     0
 10  .2200E+00  .2257E+00  .2300E+00  2.19%   .00%     0
 11  .8000E-01  .8143E-01  .9000E-01  4.30%   .00%     0
 12  .8000E-01  .8286E-01  .9000E-01  5.45%   .00%     0
 13  .6200E+00  .6271E+00  .6300E+00   .72%   .00%     0
 14  .3900E+00  .3914E+00  .4000E+00   .89%   .00%     0
 15  .2900E+00  .2986E+00  .3000E+00  1.17%   .00%     0
 16  .1600E+00  .1657E+00  .1700E+00  2.99%   .00%     0
 17  .1900E+00  .2014E+00  .2100E+00  3.17%   .00%     0
 18  .2100E+00  .2171E+00  .2200E+00  2.08%   .00%     0
 19  .1100E+00  .1100E+00  .1100E+00   .00%   .00%     0
 20  .3700E+00  .3857E+00  .3900E+00  1.89%   .00%     0
 21  .8600E+00  .8757E+00  .8800E+00   .83%   .00%     0
 22  .2300E+00  .2371E+00  .2400E+00  1.90%   .00%     0
 23  .1600E+00  .1614E+00  .1700E+00  2.17%   .00%     0
 24  .1600E+00  .1600E+00  .1600E+00   .00%   .00%     0
 --  ---------  ---------  --------- -----  -----   ---


 net cpu timing variance (t err);  a few % is ok: 

                 average        standev        minimum        maximum
     terr          3.04%          2.00%           .00%          7.20%












1
 ********************************************
 the livermore  fortran kernels:  m f l o p s
 ********************************************

              computer : IBM RS/6000 Model 320   
              system   : AIX 3.1, 64-bit, 20 MHz 
              compiler : xlf -O (v1.1) 32kB cache
              date     : 11/02/90                
         mean do span  =    19

         when the computer performance range is very large   
         the net mflops rate of many fortran programs and    
         workloads will be in the sub-range between the equi-
         weighted harmonic and arithmetic means depending    
         on the degree of code parallelism and optimization. 
         the least biased central measure is the geometric 
         mean of 72 rates,  quoted +- a standard deviation.

 kernel  flops   microsec   mflop/sec span weight  check-sums             ok
 ------  -----   --------   --------- ---- ------  ---------------------- --
  1  .1512E+07  .9429E+05     16.0364   27   1.00   .2698573244316686E+03  7
  2  .8096E+06  .1171E+06      6.9112   15   1.00   .8398933282494545E+02  8
  3  .7992E+06  .4857E+05     16.4541   27   1.00   .1889516363539674E+01  8
  4  .4560E+06  .1071E+06      4.2560   27   1.00   .4199475392699242E+01  8
  5  .8320E+06  .8286E+05     10.0414   27   1.00   .2227830674507612E+02  8
  6  .4032E+06  .7429E+05      5.4277    8   1.00   .3503988743573140E+18  0
  7  .2688E+07  .1229E+06     21.8791   21   1.00   .1992004156003820E+03  8
  8  .3370E+07  .1414E+06     23.8255   14   1.00   .2072380565635115E+05  8
  9  .2652E+07  .1514E+06     17.5132   15   1.00   .1836777921157486E+05  8
 10  .1350E+07  .2257E+06      5.9810   15   1.00   .1155903858502209E+05  8
 11  .4784E+06  .8143E+05      5.8751   27   1.00   .4585812909752131E+04  8
 12  .4992E+06  .8286E+05      6.0248   26   1.00   .1356005668640137E-04  2
 13  .6944E+06  .6271E+06      1.1072    8   1.00   .2729559141139016E+11  0
 14  .9504E+06  .3914E+06      2.4280   27   1.00   .1851535164869094E+08  1
 15  .9240E+06  .2986E+06      3.0947   15   1.00   .7762980993917696E+04  8
 16  .6160E+06  .1657E+06      3.7172   15   1.00   .9017120000000000E+06  0
 17  .1404E+07  .2014E+06      6.9702   15   1.00   .2063158045128956E+03  8
 18  .2288E+07  .2171E+06     10.5368   14   1.00   .6790452381066978E+04  8
 19  .1008E+07  .1100E+06      9.1636   15   1.00   .8877614968312321E+02  8
 20  .1893E+07  .3857E+06      4.9073   26   1.00   .4191399189884072E+04  8
 21  .1000E+08  .8757E+06     11.4192   20   1.00   .8773979719923909E+08  0
 22  .8160E+06  .2371E+06      3.4410   15   1.00   .4276978164173358E+02  8
 23  .2002E+07  .1614E+06     12.4018   14   1.00   .3395238412030041E+04  8
 24  .2392E+06  .1600E+06      1.4950   27   1.00   .9100000000000000E+02  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 24  .3868E+08  .5161E+07      7.4948   19                               130

         mflops    range:             report all range statistics:
         maximum   rate =     23.8255 mega-flops/sec.
         quartile  q3   =     11.9105 mega-flops/sec.
         average   rate =      8.7878 mega-flops/sec.
         geometric mean =      6.6733 mega-flops/sec.
         median    q2   =      6.4680 mega-flops/sec.
         harmonic  mean =      4.7800 mega-flops/sec.
         quartile  q1   =      3.9866 mega-flops/sec.
         minimum   rate =      1.1072 mega-flops/sec.


         standard  dev. =      6.2141 mega-flops/sec.
         geom.mean dev. =      6.5640 mega-flops/sec.
         mean precision =      5.42   decimal digits
1






                    sensitivity analysis


         the sensitivity of the harmonic mean rate (mflops)  
         to various weightings is shown in the table below.  
         seven work distributions are generated by assigning 
         two distinct weights to ranked kernels by quartiles.
         forty nine possible cpu workloads are then evaluated
         using seven sets of values for the total weights:   


             ------ ------ ------ ------ ------ ------ ------
   1st qt:       o      o      o      o      o      x      x
   2nd qt:       o      o      o      x      x      x      o
   3rd qt:       o      x      x      x      o      o      o
   4th qt:       x      x      o      o      o      o      o
             ------ ------ ------ ------ ------ ------ ------
   total
   weights                    net mflops:
    x    o
  ---- ----

  1.00  .00    2.09   3.01   5.33   6.65   8.83  11.67  17.21

   .95  .05    2.17   3.12   5.29   6.40   8.36  10.20  14.67

   .90  .10    2.26   3.25   5.25   6.16   7.94   9.06  12.78

   .80  .20    2.46   3.53   5.17   5.75   7.20   7.40  10.16

   .70  .30    2.70   3.87   5.09   5.38   6.60   6.26   8.44

   .60  .40    2.99   4.28   5.02   5.06   6.08   5.42   7.21

   .50  .50    3.35   4.78   4.95   4.78   5.64   4.78   6.30
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






 sensitivity of net mflops rate to use of optimal fortran code(sisd/simd model)

    3.01   3.60   4.49   5.95   7.12    8.85   11.69   13.92   17.21

     .00    .20    .40    .60    .70     .80     .90     .95    1.00
    fraction of operations run at optimal fortran rates














1
 ********************************************
 the livermore  fortran kernels:  * summary *
 ********************************************

              computer : IBM RS/6000 Model 320   
              system   : AIX 3.1, 64-bit, 20 MHz 
              compiler : xlf -O (v1.1) 32kB cache
              date     : 11/02/90                
         mean do span  =   167

         when the computer performance range is very large   
         the net mflops rate of many fortran programs and    
         workloads will be in the sub-range between the equi-
         weighted harmonic and arithmetic means depending    
         on the degree of code parallelism and optimization. 
         the least biased central measure is the geometric 
         mean of 72 rates,  quoted +- a standard deviation.

 kernel  flops   microsec   mflop/sec span weight  check-sums             ok
 ------  -----   --------   --------- ---- ------  ---------------------- --
  1  .1512E+07  .9429E+05     16.0364   27   1.00   .2698573244316686E+03  7
  2  .8096E+06  .1171E+06      6.9112   15   1.00   .8398933282494545E+02  8
  3  .7992E+06  .4857E+05     16.4541   27   1.00   .1889516363539674E+01  8
  4  .4560E+06  .1071E+06      4.2560   27   1.00   .4199475392699242E+01  8
  5  .8320E+06  .8286E+05     10.0414   27   1.00   .2227830674507612E+02  8
  6  .4032E+06  .7429E+05      5.4277    8   1.00   .3503988743573140E+18  0
  7  .2688E+07  .1229E+06     21.8791   21   1.00   .1992004156003820E+03  8
  8  .3370E+07  .1414E+06     23.8255   14   1.00   .2072380565635115E+05  8
  9  .2652E+07  .1514E+06     17.5132   15   1.00   .1836777921157486E+05  8
 10  .1350E+07  .2257E+06      5.9810   15   1.00   .1155903858502209E+05  8
 11  .4784E+06  .8143E+05      5.8751   27   1.00   .4585812909752131E+04  8
 12  .4992E+06  .8286E+05      6.0248   26   1.00   .1356005668640137E-04  2
 13  .6944E+06  .6271E+06      1.1072    8   1.00   .2729559141139016E+11  0
 14  .9504E+06  .3914E+06      2.4280   27   1.00   .1851535164869094E+08  1
 15  .9240E+06  .2986E+06      3.0947   15   1.00   .7762980993917696E+04  8
 16  .6160E+06  .1657E+06      3.7172   15   1.00   .9017120000000000E+06  0
 17  .1404E+07  .2014E+06      6.9702   15   1.00   .2063158045128956E+03  8
 18  .2288E+07  .2171E+06     10.5368   14   1.00   .6790452381066978E+04  8
 19  .1008E+07  .1100E+06      9.1636   15   1.00   .8877614968312321E+02  8
 20  .1893E+07  .3857E+06      4.9073   26   1.00   .4191399189884072E+04  8
 21  .1000E+08  .8757E+06     11.4192   20   1.00   .8773979719923909E+08  0
 22  .8160E+06  .2371E+06      3.4410   15   1.00   .4276978164173358E+02  8
 23  .2002E+07  .1614E+06     12.4018   14   1.00   .3395238412030041E+04  8
 24  .2392E+06  .1600E+06      1.4950   27   1.00   .9100000000000000E+02  8
  1  .2020E+07  .1243E+06     16.2529  101   2.00   .3677341471833584E+04  7
  2  .1552E+07  .1414E+06     10.9737  101   2.00   .3605241763137281E+04  8
  3  .1071E+07  .6000E+05     17.8433  101   2.00   .7068190058985076E+01  8
  4  .8400E+06  .8143E+05     10.3158  101   2.00   .4199475392699242E+01  8
  5  .1100E+07  .1143E+06      9.6250  101   2.00   .3212322355798968E+03  8
  6  .6720E+06  .6571E+05     10.2261   32   2.00   .1960856598681209E+30  0
  7  .3555E+07  .1600E+06     22.2200  101   2.00   .4441910425224146E+04  8
  8  .4277E+07  .1786E+06     23.9501  100   2.00   .1050887604075329E+07  8
  9  .3606E+07  .2071E+06     17.4068  101   2.00   .8326105274034671E+06  8
 10  .1727E+07  .4271E+06      4.0434  101   2.00   .5117258847672790E+06  8
 11  .6400E+06  .1000E+06      6.4000  101   2.00   .2403492284702882E+06  8
 12  .6800E+06  .1057E+06      6.4324  100   2.00   .4923343658447266E-04  2
 13  .9184E+06  .8257E+06      1.1122   32   2.00   .1001353007004402E+12  0
 14  .1111E+07  .5157E+06      2.1543  101   2.00   .2139450190318256E+09  2
 15  .1650E+07  .5571E+06      2.9615  101   2.00   .2760671680302306E+06  8
 16  .7560E+06  .2157E+06      3.5046   40   2.00   .1134287000000000E+07  0
 17  .1818E+07  .2714E+06      6.6979  101   2.00   .7802492407439027E+04  8
 18  .2178E+07  .2200E+06      9.9000  100   2.00   .4342684487413166E+06  1
 19  .1394E+07  .1414E+06      9.8552  101   2.00   .3795271869848748E+04  8
 20  .2080E+07  .4386E+06      4.7427  100   2.00   .2188343542345499E+06  7
 21  .6250E+07  .5086E+06     12.2893   50   2.00   .1373396176759844E+09  0
 22  .1202E+07  .3471E+06      3.4623  101   2.00   .2057023067602647E+04  8
 23  .2722E+07  .2243E+06     12.1385  100   2.00   .2484930351216168E+06  6
 24  .3100E+06  .2057E+06      1.5069  101   2.00   .3500000000000000E+03  8
  1  .1752E+07  .1057E+06     16.5706 1001   1.00   .3580257008721524E+06  7
  2  .1300E+07  .1157E+06     11.2328  101   1.00   .3605241763137281E+04  8
  3  .9009E+06  .4286E+05     21.0210 1001   1.00   .7005200179428446E+02  8
  4  .8400E+06  .4714E+05     17.8182 1001   1.00   .4199475392699242E+01  8
  5  .1000E+07  .1000E+06     10.0000 1001   1.00   .3184210149404855E+05  8
  6  .5952E+06  .5000E+05     11.9040   64   1.00   .2288741318728983E+26  0
  7  .3184E+07  .1400E+06     22.7429  995   1.00   .4272975754667242E+06  8
  8  .3564E+07  .1471E+06     24.2214  100   1.00   .1050887604075329E+07  8
  9  .3091E+07  .1771E+06     17.4469  101   1.00   .8326105274034671E+06  8
 10  .1545E+07  .3786E+06      4.0819  101   1.00   .5117258847672790E+06  8
 11  .5500E+06  .8286E+05      6.6379 1001   1.00   .2340037680671110E+09  8
 12  .6000E+06  .9000E+05      6.6667 1000   1.00   .2126321196556091E-03  1
 13  .8064E+06  .7229E+06      1.1156   64   1.00   .1552259922630282E+12  0
 14  .1101E+07  .5900E+06      1.8663 1001   1.00   .2087503090558357E+11  4
 15  .8250E+06  .2786E+06      2.9615  101   1.00   .2760671680302306E+06  8
 16  .6625E+06  .1800E+06      3.6806   75   1.00   .9892820000000000E+06  0
 17  .1591E+07  .2386E+06      6.6678  101   1.00   .7802492407439027E+04  8
 18  .2178E+07  .2186E+06      9.9647  100   1.00   .4342684487413166E+06  1
 19  .1182E+07  .1200E+06      9.8475  101   1.00   .3795271869848748E+04  8
 20  .1300E+07  .2786E+06      4.6667 1000   1.00   .2128450971917007E+09  8
 21  .6312E+07  .1689E+07      3.7384  101   1.00   .2812029997465708E+09  0
 22  .9444E+06  .2714E+06      3.4792  101   1.00   .2057023067602647E+04  8
 23  .2178E+07  .1771E+06     12.2952  100   1.00   .2484930351216168E+06  5
 24  .2500E+06  .1657E+06      1.5086 1001   1.00   .3500000000000000E+04  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 72  .1211E+09  .1781E+08      6.7992  167                               373

         mflops    range:             report all range statistics:
         maximum   rate =     24.2214 mega-flops/sec.
         quartile  q3   =     12.2139 mega-flops/sec.
         average   rate =      9.3237 mega-flops/sec.
         geometric mean =      6.9979 mega-flops/sec.
         median    q2   =      6.9702 mega-flops/sec.
         harmonic  mean =      4.8474 mega-flops/sec.
         quartile  q1   =      3.7172 mega-flops/sec.
         minimum   rate =      1.1072 mega-flops/sec.


         standard  dev. =      6.4344 mega-flops/sec.
         geom.mean dev. =      6.8418 mega-flops/sec.
         mean precision =      5.18   decimal digits
1


 top quartile: best architecture/application match



 kernel  flops   microsec   mflop/sec span weight 
 ------  -----   --------   --------- ---- ------ 
  8  .3564E+07  .1471E+06     24.2214  100   1.00
  8  .4277E+07  .1786E+06     23.9501  100   2.00
  8  .3370E+07  .1414E+06     23.8255   14   1.00
  7  .3184E+07  .1400E+06     22.7429  995   1.00
  7  .3555E+07  .1600E+06     22.2200  101   2.00
  7  .2688E+07  .1229E+06     21.8791   21   1.00
  3  .9009E+06  .4286E+05     21.0210 1001   1.00
  3  .1071E+07  .6000E+05     17.8433  101   2.00
  4  .8400E+06  .4714E+05     17.8182 1001   1.00
  9  .2652E+07  .1514E+06     17.5132   15   1.00
  9  .3091E+07  .1771E+06     17.4469  101   1.00
  9  .3606E+07  .2071E+06     17.4068  101   2.00
  1  .1752E+07  .1057E+06     16.5706 1001   1.00
  3  .7992E+06  .4857E+05     16.4541   27   1.00
  1  .2020E+07  .1243E+06     16.2529  101   2.00
  1  .1512E+07  .9429E+05     16.0364   27   1.00
 23  .2002E+07  .1614E+06     12.4018   14   1.00
 23  .2178E+07  .1771E+06     12.2952  100   1.00
 ------  -----   --------   --------- ---- ------ 

         frac.  weights =       .2396
         average   rate =     18.9379 mega-flops/sec.
         harmonic  mean =     18.2533 mega-flops/sec.
         standard  dev. =      3.5208 mega-flops/sec.



 kernel  flops   microsec   mflop/sec span weight 
 ------  -----   --------   --------- ---- ------ 
 21  .6250E+07  .5086E+06     12.2893   50   2.00
 23  .2722E+07  .2243E+06     12.1385  100   2.00
  6  .5952E+06  .5000E+05     11.9040   64   1.00
 21  .1000E+08  .8757E+06     11.4192   20   1.00
  2  .1300E+07  .1157E+06     11.2328  101   1.00
  2  .1552E+07  .1414E+06     10.9737  101   2.00
 18  .2288E+07  .2171E+06     10.5368   14   1.00
  4  .8400E+06  .8143E+05     10.3158  101   2.00
  6  .6720E+06  .6571E+05     10.2261   32   2.00
  5  .8320E+06  .8286E+05     10.0414   27   1.00
  5  .1000E+07  .1000E+06     10.0000 1001   1.00
 18  .2178E+07  .2186E+06      9.9647  100   1.00
 18  .2178E+07  .2200E+06      9.9000  100   2.00
 19  .1394E+07  .1414E+06      9.8552  101   2.00
 19  .1182E+07  .1200E+06      9.8475  101   1.00
  5  .1100E+07  .1143E+06      9.6250  101   2.00
 19  .1008E+07  .1100E+06      9.1636   15   1.00
 17  .1404E+07  .2014E+06      6.9702   15   1.00
  2  .8096E+06  .1171E+06      6.9112   15   1.00
 17  .1818E+07  .2714E+06      6.6979  101   2.00
 17  .1591E+07  .2386E+06      6.6678  101   1.00
 12  .6000E+06  .9000E+05      6.6667 1000   1.00
 11  .5500E+06  .8286E+05      6.6379 1001   1.00
 12  .6800E+06  .1057E+06      6.4324  100   2.00
 11  .6400E+06  .1000E+06      6.4000  101   2.00
 12  .4992E+06  .8286E+05      6.0248   26   1.00
 10  .1350E+07  .2257E+06      5.9810   15   1.00
 11  .4784E+06  .8143E+05      5.8751   27   1.00
  6  .4032E+06  .7429E+05      5.4277    8   1.00
 20  .1893E+07  .3857E+06      4.9073   26   1.00
 20  .2080E+07  .4386E+06      4.7427  100   2.00
 20  .1300E+07  .2786E+06      4.6667 1000   1.00
  4  .4560E+06  .1071E+06      4.2560   27   1.00
 10  .1545E+07  .3786E+06      4.0819  101   1.00
 10  .1727E+07  .4271E+06      4.0434  101   2.00
 21  .6312E+07  .1689E+07      3.7384  101   1.00
 ------  -----   --------   --------- ---- ------ 

         frac.  weights =       .5104
         average   rate =      8.1674 mega-flops/sec.
         harmonic  mean =      7.1970 mega-flops/sec.
         standard  dev. =      2.6685 mega-flops/sec.



 kernel  flops   microsec   mflop/sec span weight 
 ------  -----   --------   --------- ---- ------ 
 16  .6160E+06  .1657E+06      3.7172   15   1.00
 16  .6625E+06  .1800E+06      3.6806   75   1.00
 16  .7560E+06  .2157E+06      3.5046   40   2.00
 22  .9444E+06  .2714E+06      3.4792  101   1.00
 22  .1202E+07  .3471E+06      3.4623  101   2.00
 22  .8160E+06  .2371E+06      3.4410   15   1.00
 15  .9240E+06  .2986E+06      3.0947   15   1.00
 15  .8250E+06  .2786E+06      2.9615  101   1.00
 15  .1650E+07  .5571E+06      2.9615  101   2.00
 14  .9504E+06  .3914E+06      2.4280   27   1.00
 14  .1111E+07  .5157E+06      2.1543  101   2.00
 14  .1101E+07  .5900E+06      1.8663 1001   1.00
 24  .2500E+06  .1657E+06      1.5086 1001   1.00
 24  .3100E+06  .2057E+06      1.5069  101   2.00
 24  .2392E+06  .1600E+06      1.4950   27   1.00
 13  .8064E+06  .7229E+06      1.1156   64   1.00
 13  .9184E+06  .8257E+06      1.1122   32   2.00
 13  .6944E+06  .6271E+06      1.1072    8   1.00
 ------  -----   --------   --------- ---- ------ 

         frac.  weights =       .2500
         average   rate =      2.4708 mega-flops/sec.
         harmonic  mean =      2.0450 mega-flops/sec.
         standard  dev. =       .9548 mega-flops/sec.
1






                    sensitivity analysis


         the sensitivity of the harmonic mean rate (mflops)  
         to various weightings is shown in the table below.  
         seven work distributions are generated by assigning 
         two distinct weights to ranked kernels by quartiles.
         forty nine possible cpu workloads are then evaluated
         using seven sets of values for the total weights:   


             ------ ------ ------ ------ ------ ------ ------
   1st qt:       o      o      o      o      o      x      x
   2nd qt:       o      o      o      x      x      x      o
   3rd qt:       o      x      x      x      o      o      o
   4th qt:       x      x      o      o      o      o      o
             ------ ------ ------ ------ ------ ------ ------
   total
   weights                    net mflops:
    x    o
  ---- ----

  1.00  .00    2.05   2.96   5.35   7.01  10.19  13.03  18.03

   .95  .05    2.13   3.08   5.31   6.71   9.49  11.13  15.25

   .90  .10    2.22   3.21   5.27   6.43   8.88   9.72  13.21

   .80  .20    2.42   3.50   5.20   5.94   7.86   7.75  10.42

   .70  .30    2.66   3.85   5.12   5.51   7.05   6.45   8.60

   .60  .40    2.95   4.28   5.05   5.14   6.40   5.52   7.33

   .50  .50    3.32   4.82   4.99   4.82   5.85   4.82   6.38
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






 sensitivity of net mflops rate to use of optimal fortran code(sisd/simd model)

    2.97   3.57   4.46   5.97   7.17    8.99   12.05   14.52   18.25

     .00    .20    .40    .60    .70     .80     .90     .95    1.00
    fraction of operations run at optimal fortran rates


1


  cumulative checksums:  run=    1

  k    vl=  471                      90                      19
  1   .5114652869602179E+05   .5253344959762263E+03   .3855104634738123E+02
  2   .5150345375910401E+03   .5150345375910401E+03   .1199847611784935E+02
  3   .1000742882775492E+02   .1009741436997868E+01   .2699309090770962E+00
  4   .5999250560998917E+00   .5999250560998917E+00   .5999250560998917E+00
  5   .4548871642006936E+04   .4589031936855670E+02   .3182615249296590E+01
  6   .3269630455327118E+25   .2801223712401726E+29   .5005698205104486E+17
  7   .6104251078096059E+05   .6345586321748780E+03   .2845720222862600E+02
  8   .1501268005821899E+06   .1501268005821899E+06   .2960543665193022E+04
  9   .1189443610576381E+06   .1189443610576381E+06   .2623968458796409E+04
 10   .7310369782389700E+05   .7310369782389700E+05   .1651291226431728E+04
 11   .3342910972387299E+08   .3433560406718403E+05   .6551161299645901E+03
 12   .3037601709365844E-04   .7033348083496094E-05   .1937150955200195E-05
 13   .2217514175186118E+11   .1430504295720575E+11   .3899370201627166E+10
 14   .2982147272226224E+10   .3056357414740366E+08   .2645050235527276E+07
 15   .3943816686146150E+05   .3943816686146150E+05   .1108997284845385E+04
 16   .1413260000000000E+06   .1620410000000000E+06   .1288160000000000E+06
 17   .1114641772491289E+04   .1114641772491289E+04   .2947368635898508E+02
 18   .6203834982018809E+05   .6203834982018809E+05   .9700646258667111E+03
 19   .5421816956926782E+03   .5421816956926782E+03   .1268230709758903E+02
 20   .3040644245595724E+08   .3126205060493570E+05   .5987713128405817E+03
 21   .4017185710665298E+08   .1961994538228350E+08   .1253425674274844E+08
 22   .2938604382289496E+03   .2938604382289496E+03   .6109968805961940E+01
 23   .3549900501737382E+05   .3549900501737382E+05   .4850340588614345E+03
 24   .5000000000000000E+03   .5000000000000000E+02   .1300000000000000E+02


  cumulative checksums:  run=    7

  k    vl=  471                      90                      19
  1   .3580257008721524E+06   .3677341471833584E+04   .2698573244316686E+03
  2   .3605241763137281E+04   .3605241763137281E+04   .8398933282494545E+02
  3   .7005200179428446E+02   .7068190058985076E+01   .1889516363539674E+01
  4   .4199475392699242E+01   .4199475392699242E+01   .4199475392699242E+01
  5   .3184210149404855E+05   .3212322355798968E+03   .2227830674507612E+02
  6   .2288741318728983E+26   .1960856598681209E+30   .3503988743573140E+18
  7   .4272975754667242E+06   .4441910425224146E+04   .1992004156003820E+03
  8   .1050887604075329E+07   .1050887604075329E+07   .2072380565635115E+05
  9   .8326105274034671E+06   .8326105274034671E+06   .1836777921157486E+05
 10   .5117258847672790E+06   .5117258847672790E+06   .1155903858502209E+05
 11   .2340037680671110E+09   .2403492284702882E+06   .4585812909752131E+04
 12   .2126321196556091E-03   .4923343658447266E-04   .1356005668640137E-04
 13   .1552259922630282E+12   .1001353007004402E+12   .2729559141139016E+11
 14   .2087503090558357E+11   .2139450190318256E+09   .1851535164869094E+08
 15   .2760671680302306E+06   .2760671680302306E+06   .7762980993917696E+04
 16   .9892820000000000E+06   .1134287000000000E+07   .9017120000000000E+06
 17   .7802492407439027E+04   .7802492407439027E+04   .2063158045128956E+03
 18   .4342684487413166E+06   .4342684487413166E+06   .6790452381066978E+04
 19   .3795271869848748E+04   .3795271869848748E+04   .8877614968312321E+02
 20   .2128450971917007E+09   .2188343542345499E+06   .4191399189884072E+04
 21   .2812029997465708E+09   .1373396176759844E+09   .8773979719923909E+08
 22   .2057023067602647E+04   .2057023067602647E+04   .4276978164173358E+02
 23   .2484930351216168E+06   .2484930351216168E+06   .3395238412030041E+04
 24   .3500000000000000E+04   .3500000000000000E+03   .9100000000000000E+02
1


                          table of speed-up ratios of mean rates (72 samples)

                          arithmetic, geometric, harmonic means (am,gm,hm)
                          the geometric mean is the least biased statistic.

 --------  ----  ------   -------- -------- -------- -------- -------- --------
 system    mean  mflops   ymp1     3090s180 IBM RS/6 c180-875 m/2000   vax-785 
 --------  ----  ------   -------- -------- -------- -------- -------- --------


 cray      am=   78.230 :    1.000    4.455    8.390   19.364   19.412  285.511
 ymp1      gm=   36.630 :    1.000    2.995    5.234   10.008   10.175  140.885
 cft771.2  hm=   17.660 :    1.000    1.958    3.643    5.401    5.697   71.789
           sd=   86.750


 ibm       am=   17.560 :     .224    1.000    1.883    4.347    4.357   64.088
 3090s180  gm=   12.230 :     .334    1.000    1.748    3.342    3.397   47.038
 vsf2.2.0  hm=    9.020 :     .511    1.000    1.861    2.758    2.910   36.667
           sd=   16.320


 IBM RS/6  am=    9.324 :     .119     .531    1.000    2.308    2.314   34.028
 IBM RS/6  gm=    6.998 :     .191     .572    1.000    1.912    1.944   26.915
 xlf -O (  hm=    4.847 :     .274     .537    1.000    1.482    1.564   19.705
           sd=    6.434


 cdc       am=    4.040 :     .052     .230     .433    1.000    1.002   14.745
 c180-875  gm=    3.660 :     .100     .299     .523    1.000    1.017   14.077
 ftn 1.6   hm=    3.270 :     .185     .363     .675    1.000    1.055   13.293
           sd=    1.720


 mips      am=    4.030 :     .052     .229     .432     .998    1.000   14.708
 m/2000    gm=    3.600 :     .098     .294     .514     .984    1.000   13.846
 f77 1.31  hm=    3.100 :     .176     .344     .640     .948    1.000   12.602
           sd=    1.680


 dec       am=     .274 :     .004     .016     .029     .068     .068    1.000
 vax-785   gm=     .260 :     .007     .021     .037     .071     .072    1.000
 f77 4.2   hm=     .246 :     .014     .027     .051     .075     .079    1.000
           sd=     .080
1

 version: 22/dec/86  mf392 
 check for clock calibration only: 
 total job    cpu time =      .14365E+03 sec.
 total 24 kernels time =      .12464E+03 sec.
 total 24 kernels flops=      .84745E+09 flops

--
John D. McCalpin			mccalpin at perelandra.cms.udel.edu
Assistant Professor			mccalpin at vax1.udel.edu
College of Marine Studies, U. Del.	J.MCCALPIN/OMNET



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