Path: utzoo!attcan!uunet!know!zaphod.mps.ohio-state.edu!ncar!gatech!udel!nigel.ee.udel.edu!mccalpin From: mccalpin@perelandra.cms.udel.edu (John D. McCalpin) Newsgroups: comp.unix.aix Subject: (LONG!) 32-bit Livermore Fortran Kernels Benchmark Results Message-ID: Date: 11 Nov 90 12:45:22 GMT Sender: usenet@ee.udel.edu Organization: College of Marine Studies, U. Del. Lines: 1054 Nntp-Posting-Host: perelandra.cms.udel.edu 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@perelandra.cms.udel.edu Assistant Professor mccalpin@vax1.udel.edu College of Marine Studies, U. Del. J.MCCALPIN/OMNET