#*name: Roger Hockney #*establishment: University of Southampton #*email: rwh@pac.soton.ac.uk #telephone: 0635 578679 #date sent: 01/11/94 #*date benchmarked: 09/SEP/1994 #*benchmark suite and revision: Parkbench (LOWLEV_1.0) #*message passing library and revision: N/A #*benchmark: POLY1 #*problem size (if applicable): N/A #*number of nodes: 1 #*file number if one of a group: 1 of 1 #*manufacturer: SUN #*model number: SPARC Station ELC #cpu: Sparc #cpu speed (MHz): #fpu: integrated #primary cache: #secondary cache: #other cache: #memory: #disk and connection: #interconnect type: #switching: #other hardware: #operating system and version: #compilers, libraries and versions: f77 #compiler switches: -O2 #additional tuning parameters: none #other software: #additional comments: Benchmarks performed on a workstation # at Old Dominion University, Norfolk, Virginia, USA # in the Center for Coastal Physical Oceanography (CCPO). # There were no other users during the measurements. ================================================= === === === PARKBENCH Parallel Benchmarks === === === === POLY1 === === === === Program: In-cache (r-hat f-half) === === Version: Standard Fortran 77 === === Author: Roger Hockney === === Update: November 1993; Release: 1.0 === === === ================================================= Run on single SUN SPARC Station ELC at Old Dominion University, VA, USA (CCPO) Software levels are Contact: Roger Hockney, rwh@pac.soton.ac.uk POLYNOMIAL BENCHMARK FOR FHALF ------------------------------ (DOUBLE PRECISION) This benchmark tests severity of memory bottlenecks by varying the amount of arithmetic per memory reference which is called the computational intensity of the loop. The performance for long loop (vector) lengths, RINF, is represented as : RINF = RHAT/(1 + FHALF/F) where RHAT = peak Mflop/s rate of arithmetic pipeline approached as F goes to infinity and F = computational intensity = ratio floating operations/memory references FHALF = F required to obtain RINF=RHAT/2 The loop executed is polynomial evaluation by Horners rule, F varies as the order increases from 1 to 10 Roger Hockney, August 1989 ------------------------------------------------------------ POLYNOMIALS : A(I)=S0+B(I)*(S1+B(I)*(S2+B(I)*S3)) ICASE= 1 NCASE= 1 NMAX= 10000 NTIMES= 1000000 NPROCS= 1 COMPUTATIONAL INTENSITY = flop per mem ref 1.00000 ------------------------------------------ Floating operations per iteration = 2 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 1.575E-06 0.000000 0.000 0.000E+00 0.00 1.270103 1.575E-06 500000 5 6.651E-06 1.575950 0.241 4.816E-01 0.00 1.503538 3.056E-07 100000 10 1.181E-05 1.765056 0.561 1.122E+00 20.97 1.693265 6.358E-07 50000 20 2.205E-05 1.877514 0.878 1.756E+00 14.67 1.813925 9.351E-07 25000 50 5.279E-05 1.931780 1.128 2.255E+00 6.71 1.894448 1.168E-06 10000 100 1.041E-04 1.941898 1.204 2.408E+00 3.24 1.920650 1.240E-06 5000 200 2.066E-04 1.947696 1.279 2.558E+00 1.61 1.936555 1.313E-06 2500 300 3.094E-04 1.947356 1.272 2.545E+00 1.01 1.938986 1.307E-06 1666 400 4.131E-04 1.944328 1.189 2.378E+00 0.88 1.936555 1.223E-06 1250 600 6.219E-04 1.936843 0.873 1.747E+00 1.26 1.929592 9.019E-07 833 800 8.465E-04 1.908890 -0.707 -1.413E+00 4.82 1.890105 -7.404E-07 625 1000 1.053E-03 1.902457 -1.173 -2.345E+00 3.92 1.898556 -1.233E-06 500 COMPUTATIONAL INTENSITY = flop per mem ref 2.00000 ------------------------------------------ Floating operations per iteration = 4 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 2.415E-06 0.000000 0.000 0.000E+00 0.00 1.656531 2.415E-06 250000 5 8.965E-06 2.442451 0.474 1.898E+00 0.00 2.230778 7.770E-07 50000 10 1.570E-05 2.719729 0.804 3.216E+00 19.38 2.547933 1.182E-06 25000 20 3.176E-05 2.607672 0.589 2.357E+00 10.92 2.519070 9.038E-07 12500 50 7.122E-05 2.859854 1.397 5.590E+00 13.66 2.808129 1.955E-06 5000 100 1.409E-04 2.878140 1.492 5.970E+00 6.41 2.839158 2.074E-06 2500 200 2.794E-04 2.883916 1.543 6.173E+00 3.01 2.863057 2.141E-06 1250 300 4.181E-04 2.884800 1.555 6.220E+00 1.89 2.870302 2.156E-06 833 400 5.591E-04 2.876901 1.408 5.631E+00 1.62 2.861582 1.957E-06 625 600 8.363E-04 2.876699 1.402 5.608E+00 1.03 2.869873 1.949E-06 416 800 1.154E-03 2.815250 -0.948 -3.792E+00 7.02 2.774104 -1.347E-06 312 1000 1.434E-03 2.799164 -1.737 -6.946E+00 5.82 2.788748 -2.482E-06 250 COMPUTATIONAL INTENSITY = flop per mem ref 3.00000 ------------------------------------------ Floating operations per iteration = 6 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 3.146E-06 0.000000 0.000 0.000E+00 0.00 1.907301 3.146E-06 166666 5 1.093E-05 3.082100 0.616 3.696E+00 0.00 2.744061 1.199E-06 33333 10 1.970E-05 3.267718 0.799 4.796E+00 10.23 3.045269 1.468E-06 16666 20 3.718E-05 3.369044 0.961 5.765E+00 7.08 3.227853 1.711E-06 8333 50 8.959E-05 3.416505 1.084 6.503E+00 3.23 3.348571 1.903E-06 3333 100 1.776E-04 3.415423 1.079 6.475E+00 1.49 3.378761 1.896E-06 1666 200 3.521E-04 3.425708 1.154 6.925E+00 0.89 3.408243 2.022E-06 833 300 5.271E-04 3.427624 1.175 7.052E+00 0.57 3.415070 2.057E-06 555 400 7.045E-04 3.420380 1.062 6.374E+00 0.82 3.406509 1.864E-06 416 600 1.054E-03 3.422200 1.106 6.636E+00 0.54 3.416989 1.939E-06 277 800 1.464E-03 3.335048 -1.688 -1.013E+01 8.31 3.279346 -3.037E-06 208 1000 1.817E-03 3.313333 -2.582 -1.549E+01 6.87 3.301272 -4.675E-06 166 COMPUTATIONAL INTENSITY = flop per mem ref 4.00000 ------------------------------------------ Floating operations per iteration = 8 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 3.908E-06 0.000000 0.000 0.000E+00 0.00 2.047280 3.908E-06 125000 5 1.312E-05 3.472564 0.696 5.569E+00 0.00 3.048150 1.604E-06 25000 10 2.371E-05 3.641727 0.848 6.787E+00 8.22 3.374240 1.864E-06 12500 20 4.480E-05 3.733923 0.982 7.852E+00 5.73 3.571199 2.103E-06 6250 50 1.081E-04 3.776550 1.081 8.651E+00 2.62 3.700675 2.291E-06 2500 100 2.138E-04 3.782448 1.104 8.833E+00 1.24 3.742221 2.335E-06 1250 200 4.247E-04 3.787857 1.140 9.118E+00 0.63 3.767543 2.407E-06 625 300 6.646E-04 3.661638 -0.119 -9.488E-01 8.75 3.611071 -2.591E-07 416 400 8.494E-04 3.728805 0.838 6.703E+00 9.00 3.767205 1.797E-06 312 600 1.272E-03 3.762436 1.574 1.259E+01 6.30 3.772887 3.347E-06 208 800 1.766E-03 3.679847 -0.845 -6.756E+00 8.37 3.624022 -1.836E-06 156 1000 2.195E-03 3.658674 -1.639 -1.311E+01 6.81 3.644567 -3.584E-06 125 COMPUTATIONAL INTENSITY = flop per mem ref 5.00000 ------------------------------------------ Floating operations per iteration = 10 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 4.695E-06 0.000000 0.000 0.000E+00 0.00 2.130066 4.695E-06 100000 5 1.540E-05 3.735017 0.753 7.535E+00 0.00 3.245879 2.017E-06 20000 10 2.775E-05 3.910164 0.903 9.027E+00 7.88 3.604137 2.309E-06 10000 20 5.256E-05 3.985932 1.006 1.006E+01 4.88 3.804842 2.523E-06 5000 50 1.302E-04 3.912682 0.844 8.444E+00 3.03 3.840864 2.158E-06 2000 100 2.503E-04 4.024326 1.253 1.253E+01 5.33 3.995574 3.113E-06 1000 200 4.977E-04 4.042428 1.366 1.366E+01 2.61 4.018872 3.378E-06 500 300 7.466E-04 4.037747 1.322 1.322E+01 1.66 4.018037 3.273E-06 333 400 9.944E-04 4.036382 1.303 1.303E+01 1.18 4.022364 3.229E-06 250 600 1.490E-03 4.035942 1.294 1.294E+01 0.75 4.026992 3.207E-06 166 800 2.077E-03 3.923834 -1.758 -1.758E+01 9.06 3.852066 -4.481E-06 125 1000 2.582E-03 3.892072 -2.869 -2.869E+01 7.62 3.873161 -7.371E-06 100 COMPUTATIONAL INTENSITY = flop per mem ref 6.00000 ------------------------------------------ Floating operations per iteration = 12 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 5.575E-06 0.000000 0.000 0.000E+00 0.00 2.152385 5.575E-06 83333 5 1.765E-05 3.975538 0.847 1.016E+01 0.00 3.399617 2.557E-06 16666 10 3.183E-05 4.117432 0.964 1.157E+01 5.95 3.769451 2.809E-06 8333 20 6.023E-05 4.185688 1.053 1.264E+01 3.92 3.985030 3.019E-06 4166 50 1.455E-04 4.212439 1.109 1.331E+01 1.68 4.123542 3.160E-06 1666 100 2.868E-04 4.229427 1.168 1.402E+01 1.06 4.183706 3.314E-06 833 200 5.707E-04 4.229692 1.170 1.404E+01 0.49 4.205154 3.319E-06 416 300 8.539E-04 4.231654 1.187 1.425E+01 0.33 4.215814 3.367E-06 277 400 1.140E-03 4.226782 1.126 1.351E+01 0.45 4.211681 3.196E-06 208 600 1.711E-03 4.219086 0.977 1.172E+01 0.61 4.207656 2.778E-06 138 800 2.378E-03 4.107596 -1.919 -2.303E+01 8.63 4.037283 -5.607E-06 104 1000 2.950E-03 4.081480 -2.791 -3.349E+01 7.08 4.068063 -8.204E-06 83 COMPUTATIONAL INTENSITY = flop per mem ref 7.00000 ------------------------------------------ Floating operations per iteration = 14 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 6.341E-06 0.000000 0.000 0.000E+00 0.00 2.208019 6.341E-06 71428 5 1.995E-05 4.115792 0.864 1.210E+01 0.00 3.509360 2.939E-06 14285 10 3.600E-05 4.252852 0.974 1.363E+01 5.55 3.888995 3.205E-06 7142 20 6.795E-05 4.331279 1.073 1.502E+01 4.03 4.120750 3.468E-06 3571 50 1.638E-04 4.367650 1.147 1.606E+01 1.87 4.273145 3.677E-06 1428 100 3.235E-04 4.376354 1.176 1.647E+01 0.93 4.327066 3.763E-06 714 200 6.480E-04 4.348560 1.017 1.424E+01 1.24 4.320687 3.276E-06 357 300 9.631E-04 4.369233 1.196 1.675E+01 1.48 4.360800 3.833E-06 238 400 1.285E-03 4.370652 1.214 1.699E+01 1.05 4.358375 3.888E-06 178 600 1.926E-03 4.369959 1.201 1.681E+01 0.67 4.360819 3.847E-06 119 800 2.567E-03 4.370164 1.206 1.688E+01 0.48 4.363740 3.863E-06 89 1000 3.326E-03 4.282992 -1.590 -2.226E+01 7.48 4.209280 -5.196E-06 71 COMPUTATIONAL INTENSITY = flop per mem ref 8.00000 ------------------------------------------ Floating operations per iteration = 16 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 8.127E-06 0.000000 0.000 0.000E+00 0.00 1.968768 8.127E-06 62500 5 2.286E-05 4.342690 1.206 1.929E+01 0.00 3.498901 4.443E-06 12500 10 4.004E-05 4.517615 1.352 2.163E+01 6.49 3.995715 4.789E-06 6250 20 7.570E-05 4.512073 1.345 2.152E+01 2.98 4.227059 4.770E-06 3125 50 2.026E-04 4.018081 0.347 5.558E+00 14.70 3.948061 1.383E-06 1250 100 3.770E-04 4.247189 1.135 1.816E+01 12.59 4.244231 4.275E-06 625 200 7.210E-04 4.444888 2.297 3.676E+01 10.48 4.438281 8.270E-06 312 300 1.072E-03 4.495838 2.744 4.390E+01 7.26 4.477069 9.764E-06 208 400 1.431E-03 4.499643 2.790 4.464E+01 5.13 4.470992 9.921E-06 156 600 2.153E-03 4.486571 2.547 4.076E+01 3.35 4.459889 9.084E-06 104 800 2.860E-03 4.488588 2.597 4.156E+01 2.41 4.475567 9.258E-06 78 1000 3.703E-03 4.401218 -0.158 -2.526E+00 7.50 4.321351 -5.739E-07 62 COMPUTATIONAL INTENSITY = flop per mem ref 9.00000 ------------------------------------------ Floating operations per iteration = 18 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 8.015E-06 0.000000 0.000 0.000E+00 0.00 2.245856 8.015E-06 55555 5 2.450E-05 4.367838 0.945 1.701E+01 0.00 3.673636 3.894E-06 11111 10 4.405E-05 4.499445 1.046 1.884E+01 4.99 4.085928 4.186E-06 5555 20 8.357E-05 4.538267 1.094 1.968E+01 2.70 4.307874 4.337E-06 2777 50 2.008E-04 4.582665 1.180 2.124E+01 1.65 4.481206 4.636E-06 1111 100 3.970E-04 4.587854 1.197 2.154E+01 0.79 4.534543 4.696E-06 555 200 7.889E-04 4.590597 1.212 2.181E+01 0.38 4.563532 4.752E-06 277 300 1.181E-03 4.590497 1.211 2.180E+01 0.24 4.572000 4.748E-06 185 400 1.581E-03 4.576369 1.046 1.884E+01 1.05 4.555062 4.116E-06 138 600 2.587E-03 4.298486 -3.923 -7.062E+01 17.45 4.174212 -1.643E-05 92 800 3.154E-03 4.446067 -0.329 -5.925E+00 17.98 4.565484 -1.333E-06 69 1000 4.081E-03 4.425592 -0.967 -1.741E+01 13.41 4.410410 -3.935E-06 55 COMPUTATIONAL INTENSITY = flop per mem ref 10.00000 ------------------------------------------ Floating operations per iteration = 20 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 1 9.309E-06 0.000000 0.000 0.000E+00 0.00 2.148477 9.309E-06 50000 5 2.679E-05 4.576589 1.130 2.260E+01 0.00 3.732849 4.939E-06 10000 10 4.839E-05 4.607284 1.154 2.308E+01 1.10 4.133443 5.010E-06 5000 20 9.118E-05 4.644914 1.199 2.399E+01 1.47 4.386792 5.165E-06 2500 50 2.195E-04 4.665798 1.240 2.480E+01 0.81 4.554875 5.314E-06 1000 100 4.335E-04 4.670372 1.254 2.508E+01 0.41 4.613356 5.371E-06 500 200 8.702E-04 4.628943 1.032 2.063E+01 1.63 4.596477 4.457E-06 250 300 1.290E-03 4.658356 1.271 2.542E+01 1.98 4.651423 5.456E-06 166 400 1.722E-03 4.660162 1.292 2.583E+01 1.40 4.646366 5.543E-06 125 600 2.581E-03 4.659814 1.285 2.571E+01 0.89 4.649645 5.517E-06 83 800 3.438E-03 4.660358 1.298 2.597E+01 0.64 4.653213 5.572E-06 62 1000 4.445E-03 4.573635 -1.311 -2.623E+01 6.99 4.499358 -5.735E-06 50 CALCULATION OF FHALF -------------------- F RINF RHAT FHALF ERROR f/m Mflop/s Mflop/s flop/mref % 1.0 1.902457 0.000000 0.0000 0.00 2.0 2.799164 5.294844 1.7832 0.00 3.0 3.313333 5.265975 1.7662 0.05 4.0 3.658674 5.280104 1.7754 0.06 5.0 3.892072 5.271907 1.7695 0.05 6.0 4.081480 5.286653 1.7810 0.08 7.0 4.282992 5.367534 1.8490 0.46 8.0 4.401218 5.409270 1.8867 0.46 9.0 4.425592 5.368580 1.8475 0.47 10.0 4.573635 5.400800 1.8806 0.48 LAST VALUES : RHAT = 5.400800 Mflop/s FHALF = 1.8806 flop/mref TOTAL EXECUTION TIME IS 4.5220485687E+01 SECONDS.