(LONG!) 32-bit Livermore Fortran Kernels Benchmark Results

John D. McCalpin mccalpin at perelandra.cms.udel.edu
Sun Nov 11 23:45:22 AEST 1990


This message contains the complete output for the Livermore Fortran
Kernels benchmark test running on an IBM RS/6000 Model 320 in default
REAL precision (32-bit).

The following note contains the same results for double-precision
arithmetic (64-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 32-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   .0000E+00     100.00%    100.00%    100.00%
            8   .0000E+00     100.00%    100.00%    100.00%
           16   .0000E+00     100.00%    100.00%    100.00%
           32   .1000E-01        .00%    264.57%     54.22%
           64   .1000E-01        .00%    264.57%     22.89%
          128   .1000E-01        .00%    129.10%     15.66%
          256   .1000E-01        .00%     77.46%      3.61%
          512   .2000E-01        .00%     35.21%      6.02%
         1024   .3000E-01        .00%     18.44%      1.20%
         2048   .6000E-01        .00%      6.45%      1.20%
         4096   .1100E+00        .00%      4.67%       .00%
         6800              current run:   multi=   50.000
        -----     -------     -------    -------   --------

         approximate serial job time=    .6E+02 sec.    ( nruns= 7 runs)

 trial=      1      chksum=  403      pass=      0      fail=      0
 trial=      2      chksum=  403      pass=      1      fail=      0
 trial=      3      chksum=  403      pass=      2      fail=      0
 trial=      4      chksum=  403      pass=      3      fail=      0
 trial=      5      chksum=  403      pass=      4      fail=      0
 trial=      6      chksum=  403      pass=      5      fail=      0
 trial=      7      chksum=  403      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    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 tick   7    .000000E+00    .000000E+00    .000000E+00    .000000E+00
 data   7    .999774E-01    .923435E-05    .999856E-01    .999877E-01
 data   7    .100025E+00    .394902E-04    .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  .1400E+00  .1429E+00  .1500E+00  3.16%   .00%     0
  2  .1200E+00  .1200E+00  .1200E+00   .00%   .00%     0
  3  .1100E+00  .1157E+00  .1200E+00  4.28%   .00%     0
  4  .1000E+00  .1086E+00  .1100E+00  3.22%   .00%     0
  5  .1800E+00  .1800E+00  .1800E+00   .00%   .00%     0
  6  .7001E-01  .7857E-01  .8000E-01  4.45%   .00%     0
  7  .1600E+00  .1600E+00  .1600E+00   .00%   .00%     0
  8  .1900E+00  .1900E+00  .1900E+00   .00%   .00%     0
  9  .1900E+00  .1957E+00  .2100E+00  3.72%   .00%     0
 10  .4800E+00  .4914E+00  .5000E+00  1.30%   .00%     0
 11  .1400E+00  .1429E+00  .1600E+00  4.90%   .00%     0
 12  .1200E+00  .1243E+00  .1300E+00  3.98%   .00%     0
 13  .7200E+00  .7314E+00  .7500E+00  1.14%   .00%     0
 14  .5800E+00  .5800E+00  .5800E+00   .00%   .00%     0
 15  .2800E+00  .2886E+00  .2900E+00  1.21%   .00%     0
 16  .1800E+00  .1871E+00  .1900E+00  2.41%   .00%     0
 17  .3100E+00  .3114E+00  .3200E+00  1.12%   .00%     0
 18  .2300E+00  .2300E+00  .2300E+00   .00%   .00%     0
 19  .2000E+00  .2014E+00  .2100E+00  1.74%   .00%     0
 20  .2900E+00  .2900E+00  .2900E+00   .00%   .00%     0
 21  .6400E+00  .6486E+00  .6600E+00   .98%   .00%     0
 22  .2900E+00  .2900E+00  .2900E+00   .00%   .00%     0
 23  .1900E+00  .1900E+00  .1900E+00   .00%   .00%     0
 24  .1600E+00  .1671E+00  .1700E+00  2.70%   .00%     0
 --  ---------  ---------  --------- -----  -----   ---


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

                 average        standev        minimum        maximum
     terr          1.68%          1.67%           .00%          4.90%












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

              computer : IBM RS/6000 Model 320        
              system   : 20 MHz, 32 kB cache  
              compiler : xlf -O , AIX 3.1                
              date     : 11/09/90                
         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  .1429E+06     12.2623 1001   1.00   .3580256875000000E+06  8
  2  .1300E+07  .1200E+06     10.8317  101   1.00   .3605241699218750E+04  8
  3  .9009E+06  .1157E+06      7.7855 1001   1.00   .7005165100097656E+02  5
  4  .8400E+06  .1086E+06      7.7369 1001   1.00   .4199475288391114E+01  8
  5  .1000E+07  .1800E+06      5.5556 1001   1.00   .3184210156250000E+05  8
  6  .5952E+06  .7857E+05      7.5752   64   1.00   .2288732270579523E+26  0
  7  .3184E+07  .1600E+06     19.9000  995   1.00   .4272975937500000E+06  7
  8  .3564E+07  .1900E+06     18.7581  100   1.00   .1050887625000000E+07  8
  9  .3091E+07  .1957E+06     15.7914  101   1.00   .8326105000000000E+06  8
 10  .1545E+07  .4914E+06      3.1445  101   1.00   .5117258750000000E+06  8
 11  .5500E+06  .1429E+06      3.8500 1001   1.00   .2340050240000000E+09  5
 12  .6000E+06  .1243E+06      4.8276 1000   1.00   .2126321196556091E-03  1
 13  .8064E+06  .7314E+06      1.1025   64   1.00   .1552298147840000E+12  0
 14  .1101E+07  .5800E+06      1.8985 1001   1.00   .2087503052800000E+11  4
 15  .8250E+06  .2886E+06      2.8589  101   1.00   .2760671562500000E+06  8
 16  .6625E+06  .1871E+06      3.5400   75   1.00   .9892820000000000E+06  0
 17  .1591E+07  .3114E+06      5.1079  101   1.00   .7802493164062500E+04  7
 18  .2178E+07  .2300E+06      9.4696  100   1.00   .4342689375000000E+06  1
 19  .1182E+07  .2014E+06      5.8666  101   1.00   .3795271972656250E+04  8
 20  .1300E+07  .2900E+06      4.4827 1000   1.00   .2128452480000000E+09  6
 21  .6312E+07  .6486E+06      9.7330  101   1.00   .2812027200000000E+09  0
 22  .9444E+06  .2900E+06      3.2564  101   1.00   .2057022949218750E+04  8
 23  .2178E+07  .1900E+06     11.4632  100   1.00   .2484929687500000E+06  5
 24  .2500E+06  .1671E+06      1.4957 1001   1.00   .3500000000000000E+04  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 24  .3825E+08  .6166E+07      6.2040  471                               113

         mflops    range:             report all range statistics:
         maximum   rate =     19.9000 mega-flops/sec.
         quartile  q3   =     10.2824 mega-flops/sec.
         average   rate =      7.4289 mega-flops/sec.
         geometric mean =      5.7489 mega-flops/sec.
         median    q2   =      5.7111 mega-flops/sec.
         harmonic  mean =      4.2690 mega-flops/sec.
         quartile  q1   =      3.3982 mega-flops/sec.
         minimum   rate =      1.1025 mega-flops/sec.


         standard  dev. =      5.1313 mega-flops/sec.
         geom.mean dev. =      5.3993 mega-flops/sec.
         mean precision =      4.71   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    1.95   2.71   4.45   5.67   7.81  10.03  14.02

   .95  .05    2.02   2.81   4.44   5.49   7.40   8.84  12.17

   .90  .10    2.10   2.93   4.43   5.32   7.03   7.90  10.75

   .80  .20    2.28   3.17   4.40   5.01   6.39   6.51   8.71

   .70  .30    2.49   3.47   4.38   4.74   5.86   5.54   7.33

   .60  .40    2.75   3.83   4.35   4.49   5.41   4.82   6.32

   .50  .50    3.06   4.27   4.33   4.27   5.03   4.27   5.56
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






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

    2.71   3.23   4.00   5.25   6.23    7.64    9.89   11.60   14.02

     .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    .999774E-01    .923435E-05    .999856E-01    .999877E-01
 data   7    .100025E+00    .394902E-04    .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  .1600E+00  .1643E+00  .1700E+00  3.01%   .00%     0
  2  .1400E+00  .1400E+00  .1400E+00   .00%   .00%     0
  3  .1300E+00  .1386E+00  .1400E+00  2.52%   .00%     0
  4  .1300E+00  .1371E+00  .1400E+00  3.30%   .00%     0
  5  .1900E+00  .1914E+00  .2000E+00  1.83%   .00%     0
  6  .9000E-01  .9000E-01  .9000E-01   .00%   .00%     0
  7  .1800E+00  .1800E+00  .1800E+00   .00%   .00%     0
  8  .2200E+00  .2243E+00  .2300E+00  2.21%   .00%     0
  9  .2200E+00  .2286E+00  .2300E+00  1.53%   .00%     0
 10  .5300E+00  .5557E+00  .6100E+00  4.18%   .00%     0
 11  .1600E+00  .1629E+00  .1700E+00  2.78%   .00%     0
 12  .1300E+00  .1400E+00  .1500E+00  3.82%   .00%     0
 13  .8200E+00  .8257E+00  .8300E+00   .60%   .00%     0
 14  .5400E+00  .5471E+00  .5500E+00   .83%   .00%     0
 15  .5500E+00  .5700E+00  .5800E+00  1.62%   .00%     0
 16  .2000E+00  .2057E+00  .2100E+00  2.40%   .00%     0
 17  .3400E+00  .3514E+00  .3600E+00  1.82%   .00%     0
 18  .2200E+00  .2286E+00  .2300E+00  1.53%   .00%     0
 19  .2200E+00  .2329E+00  .2400E+00  3.01%   .00%     0
 20  .4400E+00  .4514E+00  .4600E+00  1.42%   .00%     0
 21  .6300E+00  .6457E+00  .6600E+00  1.63%   .00%     0
 22  .3700E+00  .3700E+00  .3700E+00   .00%   .00%     0
 23  .2300E+00  .2386E+00  .2400E+00  1.47%   .00%     0
 24  .2000E+00  .2043E+00  .2100E+00  2.42%   .00%     0
 --  ---------  ---------  --------- -----  -----   ---


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

                 average        standev        minimum        maximum
     terr          1.83%          1.17%           .00%          4.18%












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

              computer : IBM RS/6000 Model 320        
              system   : 20 MHz, 32 kB cache  
              compiler : xlf -O , AIX 3.1                
              date     : 11/09/90                
         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  .1643E+06     12.2957  101   2.00   .3677341308593750E+04  8
  2  .1552E+07  .1400E+06     11.0858  101   2.00   .3605241699218750E+04  8
  3  .1071E+07  .1386E+06      7.7259  101   2.00   .7068186759948730E+01  6
  4  .8400E+06  .1371E+06      6.1251  101   2.00   .4199475288391114E+01  8
  5  .1100E+07  .1914E+06      5.7463  101   2.00   .3212322387695312E+03  8
  6  .6720E+06  .9000E+05      7.4667   32   2.00   .1960837633747154E+30  0
  7  .3555E+07  .1800E+06     19.7511  101   2.00   .4441910644531250E+04  8
  8  .4277E+07  .2243E+06     19.0684  100   2.00   .1050887625000000E+07  8
  9  .3606E+07  .2286E+06     15.7749  101   2.00   .8326105000000000E+06  8
 10  .1727E+07  .5557E+06      3.1079  101   2.00   .5117258750000000E+06  8
 11  .6400E+06  .1629E+06      3.9298  101   2.00   .2403492187500000E+06  7
 12  .6800E+06  .1400E+06      4.8572  100   2.00   .4923343658447266E-04  2
 13  .9184E+06  .8257E+06      1.1122   32   2.00   .1001316843520000E+12  0
 14  .1111E+07  .5471E+06      2.0305  101   2.00   .2139451200000000E+09  2
 15  .1650E+07  .5700E+06      2.8947  101   2.00   .2760671562500000E+06  8
 16  .7560E+06  .2057E+06      3.6750   40   2.00   .1134287000000000E+07  0
 17  .1818E+07  .3514E+06      5.1732  101   2.00   .7802493164062500E+04  7
 18  .2178E+07  .2286E+06      9.5288  100   2.00   .4342689375000000E+06  1
 19  .1394E+07  .2329E+06      5.9856  101   2.00   .3795271972656250E+04  8
 20  .2080E+07  .4514E+06      4.6076  100   2.00   .2188343750000000E+06  7
 21  .6250E+07  .6457E+06      9.6792   50   2.00   .1373433440000000E+09  0
 22  .1202E+07  .3700E+06      3.2484  101   2.00   .2057022949218750E+04  8
 23  .2722E+07  .2386E+06     11.4116  100   2.00   .2484929687500000E+06  6
 24  .3100E+06  .2043E+06      1.5175  101   2.00   .3500000000000000E+03  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 24  .4413E+08  .7224E+07      6.1084   90                               118

         mflops    range:             report all range statistics:
         maximum   rate =     19.7511 mega-flops/sec.
         quartile  q3   =     10.3825 mega-flops/sec.
         average   rate =      7.4083 mega-flops/sec.
         geometric mean =      5.7540 mega-flops/sec.
         median    q2   =      5.8659 mega-flops/sec.
         harmonic  mean =      4.3088 mega-flops/sec.
         quartile  q1   =      3.4617 mega-flops/sec.
         minimum   rate =      1.1122 mega-flops/sec.


         standard  dev. =      5.1346 mega-flops/sec.
         geom.mean dev. =      5.3946 mega-flops/sec.
         mean precision =      4.92   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    1.98   2.76   4.56   5.66   7.48   9.78  14.10

   .95  .05    2.06   2.87   4.54   5.49   7.13   8.67  12.24

   .90  .10    2.14   2.98   4.52   5.33   6.81   7.80  10.82

   .80  .20    2.32   3.23   4.49   5.03   6.25   6.48   8.78

   .70  .30    2.53   3.52   4.45   4.76   5.78   5.55   7.39

   .60  .40    2.78   3.88   4.42   4.53   5.37   4.85   6.37

   .50  .50    3.10   4.31   4.39   4.31   5.02   4.31   5.61
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






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

    2.76   3.29   4.07   5.34   6.32    7.74   10.00   11.70   14.10

     .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    .999774E-01    .923435E-05    .999856E-01    .999877E-01
 data   7    .100025E+00    .394902E-04    .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  .1100E+00  .1157E+00  .1200E+00  4.28%   .00%     0
  3  .1000E+00  .1043E+00  .1100E+00  4.75%   .00%     0
  4  .1200E+00  .1271E+00  .1300E+00  3.55%   .00%     0
  5  .1400E+00  .1471E+00  .1500E+00  3.07%   .00%     0
  6  .7000E-01  .8000E-01  .9000E-01  6.68%   .00%     0
  7  .1300E+00  .1386E+00  .1400E+00  2.53%   .00%     0
  8  .1800E+00  .1857E+00  .1900E+00  2.66%   .00%     0
  9  .1600E+00  .1686E+00  .1700E+00  2.08%   .00%     0
 10  .4200E+00  .4300E+00  .4400E+00  1.24%   .00%     0
 11  .1300E+00  .1300E+00  .1300E+00   .00%   .00%     0
 12  .9999E-01  .1029E+00  .1100E+00  4.39%   .00%     0
 13  .6200E+00  .6257E+00  .6300E+00   .79%   .00%     0
 14  .4600E+00  .4643E+00  .4700E+00  1.07%   .00%     0
 15  .3100E+00  .3157E+00  .3200E+00  1.57%   .00%     0
 16  .1600E+00  .1657E+00  .1700E+00  2.99%   .00%     0
 17  .2600E+00  .2600E+00  .2600E+00   .00%   .00%     0
 18  .2400E+00  .2414E+00  .2500E+00  1.45%   .00%     0
 19  .1700E+00  .1771E+00  .1800E+00  2.55%   .00%     0
 20  .4100E+00  .4143E+00  .4200E+00  1.19%   .00%     0
 21  .1070E+01  .1071E+01  .1080E+01   .33%   .00%     0
 22  .2500E+00  .2500E+00  .2500E+00   .00%   .00%     0
 23  .1700E+00  .1771E+00  .1800E+00  2.55%   .00%     0
 24  .1600E+00  .1629E+00  .1700E+00  2.77%   .00%     0
 --  ---------  ---------  --------- -----  -----   ---


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

                 average        standev        minimum        maximum
     terr          2.35%          1.67%           .00%          6.68%












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

              computer : IBM RS/6000 Model 320        
              system   : 20 MHz, 32 kB cache  
              compiler : xlf -O , AIX 3.1                
              date     : 11/09/90                
         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  .1243E+06     12.1655   27   1.00   .2698573303222656E+03  8
  2  .8096E+06  .1157E+06      6.9965   15   1.00   .8398933410644531E+02  8
  3  .7992E+06  .1043E+06      7.6635   27   1.00   .1889516472816467E+01  7
  4  .4560E+06  .1271E+06      3.5865   27   1.00   .4199475288391114E+01  8
  5  .8320E+06  .1471E+06      5.6544   27   1.00   .2227830696105957E+02  8
  6  .4032E+06  .8000E+05      5.0401    8   1.00   .3503744641159660E+18  0
  7  .2688E+07  .1386E+06     19.3979   21   1.00   .1992004089355469E+03  8
  8  .3370E+07  .1857E+06     18.1442   14   1.00   .2072380664062500E+05  8
  9  .2652E+07  .1686E+06     15.7321   15   1.00   .1836777929687500E+05  8
 10  .1350E+07  .4300E+06      3.1395   15   1.00   .1155903906250000E+05  8
 11  .4784E+06  .1300E+06      3.6800   27   1.00   .4585812500000000E+04  7
 12  .4992E+06  .1029E+06      4.8533   26   1.00   .1356005668640137E-04  2
 13  .6944E+06  .6257E+06      1.1098    8   1.00   .2729297715200000E+11  0
 14  .9504E+06  .4643E+06      2.0470   27   1.00   .1851535400000000E+08  1
 15  .9240E+06  .3157E+06      2.9267   15   1.00   .7762981445312500E+04  7
 16  .6160E+06  .1657E+06      3.7173   15   1.00   .9017120000000000E+06  0
 17  .1404E+07  .2600E+06      5.4000   15   1.00   .2063157958984375E+03  8
 18  .2288E+07  .2414E+06      9.4769   14   1.00   .6790452636718750E+04  7
 19  .1008E+07  .1771E+06      5.6903   15   1.00   .8877615356445312E+02  7
 20  .1893E+07  .4143E+06      4.5688   26   1.00   .4191399414062500E+04  8
 21  .1000E+08  .1071E+07      9.3334   20   1.00   .8773447200000000E+08  0
 22  .8160E+06  .2500E+06      3.2640   15   1.00   .4276977920532226E+02  8
 23  .2002E+07  .1771E+06     11.3016   14   1.00   .3395238281250000E+04  7
 24  .2392E+06  .1629E+06      1.4688   27   1.00   .9100000000000000E+02  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 24  .3868E+08  .6180E+07      6.2595   19                               125

         mflops    range:             report all range statistics:
         maximum   rate =     19.3979 mega-flops/sec.
         quartile  q3   =      9.4051 mega-flops/sec.
         average   rate =      6.9316 mega-flops/sec.
         geometric mean =      5.3790 mega-flops/sec.
         median    q2   =      5.2200 mega-flops/sec.
         harmonic  mean =      4.1063 mega-flops/sec.
         quartile  q1   =      3.4252 mega-flops/sec.
         minimum   rate =      1.1098 mega-flops/sec.


         standard  dev. =      5.0017 mega-flops/sec.
         geom.mean dev. =      5.2372 mega-flops/sec.
         mean precision =      5.21   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    1.98   2.68   4.16   5.08   6.53   8.79  13.44

   .95  .05    2.05   2.78   4.15   4.96   6.29   7.89  11.67

   .90  .10    2.12   2.88   4.15   4.85   6.06   7.16  10.31

   .80  .20    2.29   3.11   4.14   4.64   5.64   6.04   8.37

   .70  .30    2.49   3.38   4.14   4.45   5.28   5.22   7.04

   .60  .40    2.73   3.71   4.13   4.27   4.97   4.60   6.08

   .50  .50    3.02   4.11   4.12   4.11   4.69   4.11   5.34
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






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

    2.68   3.19   3.94   5.16   6.09    7.45    9.59   11.19   13.44

     .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   : 20 MHz, 32 kB cache  
              compiler : xlf -O , AIX 3.1                
              date     : 11/09/90                
         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  .1243E+06     12.1655   27   1.00   .2698573303222656E+03  8
  2  .8096E+06  .1157E+06      6.9965   15   1.00   .8398933410644531E+02  8
  3  .7992E+06  .1043E+06      7.6635   27   1.00   .1889516472816467E+01  7
  4  .4560E+06  .1271E+06      3.5865   27   1.00   .4199475288391114E+01  8
  5  .8320E+06  .1471E+06      5.6544   27   1.00   .2227830696105957E+02  8
  6  .4032E+06  .8000E+05      5.0401    8   1.00   .3503744641159660E+18  0
  7  .2688E+07  .1386E+06     19.3979   21   1.00   .1992004089355469E+03  8
  8  .3370E+07  .1857E+06     18.1442   14   1.00   .2072380664062500E+05  8
  9  .2652E+07  .1686E+06     15.7321   15   1.00   .1836777929687500E+05  8
 10  .1350E+07  .4300E+06      3.1395   15   1.00   .1155903906250000E+05  8
 11  .4784E+06  .1300E+06      3.6800   27   1.00   .4585812500000000E+04  7
 12  .4992E+06  .1029E+06      4.8533   26   1.00   .1356005668640137E-04  2
 13  .6944E+06  .6257E+06      1.1098    8   1.00   .2729297715200000E+11  0
 14  .9504E+06  .4643E+06      2.0470   27   1.00   .1851535400000000E+08  1
 15  .9240E+06  .3157E+06      2.9267   15   1.00   .7762981445312500E+04  7
 16  .6160E+06  .1657E+06      3.7173   15   1.00   .9017120000000000E+06  0
 17  .1404E+07  .2600E+06      5.4000   15   1.00   .2063157958984375E+03  8
 18  .2288E+07  .2414E+06      9.4769   14   1.00   .6790452636718750E+04  7
 19  .1008E+07  .1771E+06      5.6903   15   1.00   .8877615356445312E+02  7
 20  .1893E+07  .4143E+06      4.5688   26   1.00   .4191399414062500E+04  8
 21  .1000E+08  .1071E+07      9.3334   20   1.00   .8773447200000000E+08  0
 22  .8160E+06  .2500E+06      3.2640   15   1.00   .4276977920532226E+02  8
 23  .2002E+07  .1771E+06     11.3016   14   1.00   .3395238281250000E+04  7
 24  .2392E+06  .1629E+06      1.4688   27   1.00   .9100000000000000E+02  8
  1  .2020E+07  .1643E+06     12.2957  101   2.00   .3677341308593750E+04  8
  2  .1552E+07  .1400E+06     11.0858  101   2.00   .3605241699218750E+04  8
  3  .1071E+07  .1386E+06      7.7259  101   2.00   .7068186759948730E+01  6
  4  .8400E+06  .1371E+06      6.1251  101   2.00   .4199475288391114E+01  8
  5  .1100E+07  .1914E+06      5.7463  101   2.00   .3212322387695312E+03  8
  6  .6720E+06  .9000E+05      7.4667   32   2.00   .1960837633747154E+30  0
  7  .3555E+07  .1800E+06     19.7511  101   2.00   .4441910644531250E+04  8
  8  .4277E+07  .2243E+06     19.0684  100   2.00   .1050887625000000E+07  8
  9  .3606E+07  .2286E+06     15.7749  101   2.00   .8326105000000000E+06  8
 10  .1727E+07  .5557E+06      3.1079  101   2.00   .5117258750000000E+06  8
 11  .6400E+06  .1629E+06      3.9298  101   2.00   .2403492187500000E+06  7
 12  .6800E+06  .1400E+06      4.8572  100   2.00   .4923343658447266E-04  2
 13  .9184E+06  .8257E+06      1.1122   32   2.00   .1001316843520000E+12  0
 14  .1111E+07  .5471E+06      2.0305  101   2.00   .2139451200000000E+09  2
 15  .1650E+07  .5700E+06      2.8947  101   2.00   .2760671562500000E+06  8
 16  .7560E+06  .2057E+06      3.6750   40   2.00   .1134287000000000E+07  0
 17  .1818E+07  .3514E+06      5.1732  101   2.00   .7802493164062500E+04  7
 18  .2178E+07  .2286E+06      9.5288  100   2.00   .4342689375000000E+06  1
 19  .1394E+07  .2329E+06      5.9856  101   2.00   .3795271972656250E+04  8
 20  .2080E+07  .4514E+06      4.6076  100   2.00   .2188343750000000E+06  7
 21  .6250E+07  .6457E+06      9.6792   50   2.00   .1373433440000000E+09  0
 22  .1202E+07  .3700E+06      3.2484  101   2.00   .2057022949218750E+04  8
 23  .2722E+07  .2386E+06     11.4116  100   2.00   .2484929687500000E+06  6
 24  .3100E+06  .2043E+06      1.5175  101   2.00   .3500000000000000E+03  8
  1  .1752E+07  .1429E+06     12.2623 1001   1.00   .3580256875000000E+06  8
  2  .1300E+07  .1200E+06     10.8317  101   1.00   .3605241699218750E+04  8
  3  .9009E+06  .1157E+06      7.7855 1001   1.00   .7005165100097656E+02  5
  4  .8400E+06  .1086E+06      7.7369 1001   1.00   .4199475288391114E+01  8
  5  .1000E+07  .1800E+06      5.5556 1001   1.00   .3184210156250000E+05  8
  6  .5952E+06  .7857E+05      7.5752   64   1.00   .2288732270579523E+26  0
  7  .3184E+07  .1600E+06     19.9000  995   1.00   .4272975937500000E+06  7
  8  .3564E+07  .1900E+06     18.7581  100   1.00   .1050887625000000E+07  8
  9  .3091E+07  .1957E+06     15.7914  101   1.00   .8326105000000000E+06  8
 10  .1545E+07  .4914E+06      3.1445  101   1.00   .5117258750000000E+06  8
 11  .5500E+06  .1429E+06      3.8500 1001   1.00   .2340050240000000E+09  5
 12  .6000E+06  .1243E+06      4.8276 1000   1.00   .2126321196556091E-03  1
 13  .8064E+06  .7314E+06      1.1025   64   1.00   .1552298147840000E+12  0
 14  .1101E+07  .5800E+06      1.8985 1001   1.00   .2087503052800000E+11  4
 15  .8250E+06  .2886E+06      2.8589  101   1.00   .2760671562500000E+06  8
 16  .6625E+06  .1871E+06      3.5400   75   1.00   .9892820000000000E+06  0
 17  .1591E+07  .3114E+06      5.1079  101   1.00   .7802493164062500E+04  7
 18  .2178E+07  .2300E+06      9.4696  100   1.00   .4342689375000000E+06  1
 19  .1182E+07  .2014E+06      5.8666  101   1.00   .3795271972656250E+04  8
 20  .1300E+07  .2900E+06      4.4827 1000   1.00   .2128452480000000E+09  6
 21  .6312E+07  .6486E+06      9.7330  101   1.00   .2812027200000000E+09  0
 22  .9444E+06  .2900E+06      3.2564  101   1.00   .2057022949218750E+04  8
 23  .2178E+07  .1900E+06     11.4632  100   1.00   .2484929687500000E+06  5
 24  .2500E+06  .1671E+06      1.4957 1001   1.00   .3500000000000000E+04  8
 ------  -----   --------   --------- ---- ------  ---------------------- --
 72  .1211E+09  .1957E+08      6.1862  167                               356

         mflops    range:             report all range statistics:
         maximum   rate =     19.9000 mega-flops/sec.
         quartile  q3   =      9.6792 mega-flops/sec.
         average   rate =      7.2943 mega-flops/sec.
         geometric mean =      5.6566 mega-flops/sec.
         median    q2   =      5.6544 mega-flops/sec.
         harmonic  mean =      4.2465 mega-flops/sec.
         quartile  q1   =      3.2640 mega-flops/sec.
         minimum   rate =      1.1025 mega-flops/sec.


         standard  dev. =      5.1052 mega-flops/sec.
         geom.mean dev. =      5.3614 mega-flops/sec.
         mean precision =      4.94   decimal digits
1


 top quartile: best architecture/application match



 kernel  flops   microsec   mflop/sec span weight 
 ------  -----   --------   --------- ---- ------ 
  7  .3184E+07  .1600E+06     19.9000  995   1.00
  7  .3555E+07  .1800E+06     19.7511  101   2.00
  7  .2688E+07  .1386E+06     19.3979   21   1.00
  8  .4277E+07  .2243E+06     19.0684  100   2.00
  8  .3564E+07  .1900E+06     18.7581  100   1.00
  8  .3370E+07  .1857E+06     18.1442   14   1.00
  9  .3091E+07  .1957E+06     15.7914  101   1.00
  9  .3606E+07  .2286E+06     15.7749  101   2.00
  9  .2652E+07  .1686E+06     15.7321   15   1.00
  1  .2020E+07  .1643E+06     12.2957  101   2.00
  1  .1752E+07  .1429E+06     12.2623 1001   1.00
  1  .1512E+07  .1243E+06     12.1655   27   1.00
 23  .2178E+07  .1900E+06     11.4632  100   1.00
 23  .2722E+07  .2386E+06     11.4116  100   2.00
 23  .2002E+07  .1771E+06     11.3016   14   1.00
  2  .1552E+07  .1400E+06     11.0858  101   2.00
  2  .1300E+07  .1200E+06     10.8317  101   1.00
 21  .6312E+07  .6486E+06      9.7330  101   1.00
 ------  -----   --------   --------- ---- ------ 

         frac.  weights =       .2500
         average   rate =     14.7607 mega-flops/sec.
         harmonic  mean =     13.9299 mega-flops/sec.
         standard  dev. =      3.5617 mega-flops/sec.



 kernel  flops   microsec   mflop/sec span weight 
 ------  -----   --------   --------- ---- ------ 
 21  .6250E+07  .6457E+06      9.6792   50   2.00
 18  .2178E+07  .2286E+06      9.5288  100   2.00
 18  .2288E+07  .2414E+06      9.4769   14   1.00
 18  .2178E+07  .2300E+06      9.4696  100   1.00
 21  .1000E+08  .1071E+07      9.3334   20   1.00
  3  .9009E+06  .1157E+06      7.7855 1001   1.00
  4  .8400E+06  .1086E+06      7.7369 1001   1.00
  3  .1071E+07  .1386E+06      7.7259  101   2.00
  3  .7992E+06  .1043E+06      7.6635   27   1.00
  6  .5952E+06  .7857E+05      7.5752   64   1.00
  6  .6720E+06  .9000E+05      7.4667   32   2.00
  2  .8096E+06  .1157E+06      6.9965   15   1.00
  4  .8400E+06  .1371E+06      6.1251  101   2.00
 19  .1394E+07  .2329E+06      5.9856  101   2.00
 19  .1182E+07  .2014E+06      5.8666  101   1.00
  5  .1100E+07  .1914E+06      5.7463  101   2.00
 19  .1008E+07  .1771E+06      5.6903   15   1.00
  5  .8320E+06  .1471E+06      5.6544   27   1.00
  5  .1000E+07  .1800E+06      5.5556 1001   1.00
 17  .1404E+07  .2600E+06      5.4000   15   1.00
 17  .1818E+07  .3514E+06      5.1732  101   2.00
 17  .1591E+07  .3114E+06      5.1079  101   1.00
  6  .4032E+06  .8000E+05      5.0401    8   1.00
 12  .6800E+06  .1400E+06      4.8572  100   2.00
 12  .4992E+06  .1029E+06      4.8533   26   1.00
 12  .6000E+06  .1243E+06      4.8276 1000   1.00
 20  .2080E+07  .4514E+06      4.6076  100   2.00
 20  .1893E+07  .4143E+06      4.5688   26   1.00
 20  .1300E+07  .2900E+06      4.4827 1000   1.00
 11  .6400E+06  .1629E+06      3.9298  101   2.00
 11  .5500E+06  .1429E+06      3.8500 1001   1.00
 16  .6160E+06  .1657E+06      3.7173   15   1.00
 11  .4784E+06  .1300E+06      3.6800   27   1.00
 16  .7560E+06  .2057E+06      3.6750   40   2.00
  4  .4560E+06  .1271E+06      3.5865   27   1.00
 16  .6625E+06  .1871E+06      3.5400   75   1.00
 ------  -----   --------   --------- ---- ------ 

         frac.  weights =       .5000
         average   rate =      6.0512 mega-flops/sec.
         harmonic  mean =      5.5057 mega-flops/sec.
         standard  dev. =      1.9031 mega-flops/sec.



 kernel  flops   microsec   mflop/sec span weight 
 ------  -----   --------   --------- ---- ------ 
 22  .8160E+06  .2500E+06      3.2640   15   1.00
 22  .9444E+06  .2900E+06      3.2564  101   1.00
 22  .1202E+07  .3700E+06      3.2484  101   2.00
 10  .1545E+07  .4914E+06      3.1445  101   1.00
 10  .1350E+07  .4300E+06      3.1395   15   1.00
 10  .1727E+07  .5557E+06      3.1079  101   2.00
 15  .9240E+06  .3157E+06      2.9267   15   1.00
 15  .1650E+07  .5700E+06      2.8947  101   2.00
 15  .8250E+06  .2886E+06      2.8589  101   1.00
 14  .9504E+06  .4643E+06      2.0470   27   1.00
 14  .1111E+07  .5471E+06      2.0305  101   2.00
 14  .1101E+07  .5800E+06      1.8985 1001   1.00
 24  .3100E+06  .2043E+06      1.5175  101   2.00
 24  .2500E+06  .1671E+06      1.4957 1001   1.00
 24  .2392E+06  .1629E+06      1.4688   27   1.00
 13  .9184E+06  .8257E+06      1.1122   32   2.00
 13  .6944E+06  .6257E+06      1.1098    8   1.00
 13  .8064E+06  .7314E+06      1.1025   64   1.00
 ------  -----   --------   --------- ---- ------ 

         frac.  weights =       .2500
         average   rate =      2.3139 mega-flops/sec.
         harmonic  mean =      1.9728 mega-flops/sec.
         standard  dev. =       .8261 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    1.97   2.72   4.37   5.45   7.26   9.53  13.88

   .95  .05    2.04   2.82   4.36   5.30   6.93   8.47  12.04

   .90  .10    2.12   2.92   4.35   5.16   6.62   7.62  10.64

   .80  .20    2.30   3.17   4.33   4.89   6.09   6.34   8.62

   .70  .30    2.50   3.46   4.31   4.64   5.64   5.44   7.25

   .60  .40    2.75   3.80   4.29   4.43   5.25   4.76   6.26

   .50  .50    3.06   4.23   4.27   4.23   4.91   4.23   5.50
  ---- ----
             ------ ------ ------ ------ ------ ------ ------






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

    2.73   3.25   4.02   5.27   6.24    7.65    9.87   11.56   13.93

     .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   .5114652734375000E+05   .5253344726562500E+03   .3855104827880860E+02
  2   .5150345458984375E+03   .5150345458984375E+03   .1199847602844238E+02
  3   .1000737857818604E+02   .1009740948677063E+01   .2699309289455414E+00
  4   .5999250411987305E+00   .5999250411987305E+00   .5999250411987305E+00
  5   .4548871582031250E+04   .4589031982421875E+02   .3182615280151367E+01
  6   .3269617364696246E+25   .2801196585907602E+29   .5005349303300915E+17
  7   .6104251171875000E+05   .6345586547851562E+03   .2845720100402832E+02
  8   .1501267968750000E+06   .1501267968750000E+06   .2960543701171875E+04
  9   .1189443593750000E+06   .1189443593750000E+06   .2623968505859375E+04
 10   .7310369531250000E+05   .7310369531250000E+05   .1651291259765625E+04
 11   .3342929000000000E+08   .3433560156250000E+05   .6551160888671875E+03
 12   .3037601709365844E-04   .7033348083496094E-05   .1937150955200195E-05
 13   .2217568665600000E+11   .1430452633600000E+11   .3898996736000000E+10
 14   .2982147072000000E+10   .3056358800000000E+08   .2645050500000000E+07
 15   .3943816406250000E+05   .3943816406250000E+05   .1108997314453125E+04
 16   .1413260000000000E+06   .1620410000000000E+06   .1288160000000000E+06
 17   .1114641845703125E+04   .1114641845703125E+04   .2947368621826172E+02
 18   .6203842187500000E+05   .6203842187500000E+05   .9700646362304688E+03
 19   .5421817016601562E+03   .5421817016601562E+03   .1268230724334717E+02
 20   .3040646400000000E+08   .3126205273437500E+05   .5987713623046875E+03
 21   .4017181600000000E+08   .1962047800000000E+08   .1253349600000000E+08
 22   .2938604125976562E+03   .2938604125976562E+03   .6109968662261963E+01
 23   .3549899609375000E+05   .3549899609375000E+05   .4850340576171875E+03
 24   .5000000000000000E+03   .5000000000000000E+02   .1300000000000000E+02


  cumulative checksums:  run=    7

  k    vl=  471                      90                      19
  1   .3580256875000000E+06   .3677341308593750E+04   .2698573303222656E+03
  2   .3605241699218750E+04   .3605241699218750E+04   .8398933410644531E+02
  3   .7005165100097656E+02   .7068186759948730E+01   .1889516472816467E+01
  4   .4199475288391114E+01   .4199475288391114E+01   .4199475288391114E+01
  5   .3184210156250000E+05   .3212322387695312E+03   .2227830696105957E+02
  6   .2288732270579523E+26   .1960837633747154E+30   .3503744641159660E+18
  7   .4272975937500000E+06   .4441910644531250E+04   .1992004089355469E+03
  8   .1050887625000000E+07   .1050887625000000E+07   .2072380664062500E+05
  9   .8326105000000000E+06   .8326105000000000E+06   .1836777929687500E+05
 10   .5117258750000000E+06   .5117258750000000E+06   .1155903906250000E+05
 11   .2340050240000000E+09   .2403492187500000E+06   .4585812500000000E+04
 12   .2126321196556091E-03   .4923343658447266E-04   .1356005668640137E-04
 13   .1552298147840000E+12   .1001316843520000E+12   .2729297715200000E+11
 14   .2087503052800000E+11   .2139451200000000E+09   .1851535400000000E+08
 15   .2760671562500000E+06   .2760671562500000E+06   .7762981445312500E+04
 16   .9892820000000000E+06   .1134287000000000E+07   .9017120000000000E+06
 17   .7802493164062500E+04   .7802493164062500E+04   .2063157958984375E+03
 18   .4342689375000000E+06   .4342689375000000E+06   .6790452636718750E+04
 19   .3795271972656250E+04   .3795271972656250E+04   .8877615356445312E+02
 20   .2128452480000000E+09   .2188343750000000E+06   .4191399414062500E+04
 21   .2812027200000000E+09   .1373433440000000E+09   .8773447200000000E+08
 22   .2057022949218750E+04   .2057022949218750E+04   .4276977920532226E+02
 23   .2484929687500000E+06   .2484929687500000E+06   .3395238281250000E+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 rs/6000  c180-875 m/2000   vax-785 
 --------  ----  ------   -------- -------- -------- -------- -------- --------


 cray      am=   78.230 :    1.000    4.455   10.725   19.364   19.412  285.511
 ymp1      gm=   36.630 :    1.000    2.995    6.476   10.008   10.175  140.885
 cft771.2  hm=   17.660 :    1.000    1.958    4.159    5.401    5.697   71.789
           sd=   86.750


 ibm       am=   17.560 :     .224    1.000    2.407    4.347    4.357   64.088
 3090s180  gm=   12.230 :     .334    1.000    2.162    3.342    3.397   47.038
 vsf2.2.0  hm=    9.020 :     .511    1.000    2.124    2.758    2.910   36.667
           sd=   16.320


 ibm 6000  am=    7.294 :     .093     .415    1.000    1.806    1.810   26.621
 mod 320   gm=    5.657 :     .154     .463    1.000    1.546    1.571   21.756
 AIX 3.1   hm=    4.247 :     .240     .471    1.000    1.299    1.370   17.262
           sd=    5.105


 cdc       am=    4.040 :     .052     .230     .554    1.000    1.002   14.745
 c180-875  gm=    3.660 :     .100     .299     .647    1.000    1.017   14.077
 ftn 1.6   hm=    3.270 :     .185     .363     .770    1.000    1.055   13.293
           sd=    1.720


 mips      am=    4.030 :     .052     .229     .552     .998    1.000   14.708
 m/2000    gm=    3.600 :     .098     .294     .636     .984    1.000   13.846
 f77 1.31  hm=    3.100 :     .176     .344     .730     .948    1.000   12.602
           sd=    1.680


 dec       am=     .274 :     .004     .016     .038     .068     .068    1.000
 vax-785   gm=     .260 :     .007     .021     .046     .071     .072    1.000
 f77 4.2   hm=     .246 :     .014     .027     .058     .075     .079    1.000
           sd=     .080
1

 version: 22/dec/86  mf392 
 check for clock calibration only: 
 total job    cpu time =      .15400E+03 sec.
 total 24 kernels time =      .13699E+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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