#*name: Roger Hockney #*establishment: University of Southampton #*email: rwh@pac.soton.ac.uk #telephone: 0635 578679 #date sent: 01/11/94 #*date benchmarked: 07/SEP/1994 #*benchmark suite and revision: Parkbench (LOWLEV_1.0) #*message passing library and revision: N/A #*benchmark: POLY2 #*problem size (if applicable): N/A #*number of nodes: 1 #*file number if one of a group: 1 of 1 #*manufacturer: IBM #*model number: RS6000-590 Workstation #cpu: #cpu speed (MHz): #fpu: integrated #primary cache: #secondary cache: #other cache: #memory: #disk and connection: #interconnect type: #switching: #other hardware: #operating system and version: AIX 3.2.5 #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 === === === === POLY2 === === === === Program: Out-cache (r-hat f-half) === === Version: Standard Fortran 77 === === Author: Roger Hockney === === Update: November 1993; Release: 1.0 === === === ================================================= This run started Wed Sep 7 09:48:40 1994 Run on single IBM RS/6000 Model 590 at Old Dominion University, VA, USA (CCPO) Software levels are AIX 3.2.5 Contact: Roger Hockney, rwh@pac.soton.ac.uk POLYNOMIAL BENCHMARK FOR FHALF ------------------------------ (DOUBLE PRECISION) This benchmark determines the 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 -------------------------------------------------------------- ICASE= 1 NCASE= 1 NMAX=100000 NTIMES= 1 NPROCS= 1 COMPUTATIONAL INTENSITY = flop per mem ref 1.000000000 ------------------------------------------ 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 10000 6.520E-04 .000000 .000 0.000E+00 .00 30.673342 6.520E-04 1 20000 1.281E-03 31.822811 374.745 7.495E+02 .00 31.237505 2.355E-05 1 30000 1.904E-03 31.939901 425.183 8.504E+02 .57 31.506250 2.662E-05 1 40000 2.525E-03 32.034195 475.642 9.513E+02 .76 31.680859 2.970E-05 1 50000 3.208E-03 31.458885 107.916 2.158E+02 5.06 31.167717 6.861E-06 1 60000 3.843E-03 31.304380 -7.213 -1.443E+01 4.18 31.222940 -4.608E-07 1 70000 4.467E-03 31.328320 13.175 2.635E+01 3.34 31.339540 8.411E-07 1 80000 5.039E-03 31.613859 286.728 5.735E+02 4.63 31.753288 1.814E-05 1 90000 5.671E-03 31.749954 431.459 8.629E+02 4.31 31.739492 2.718E-05 1 100000 6.365E-03 31.645084 308.923 6.178E+02 3.96 31.423458 1.952E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 2.000000000 ------------------------------------------ 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 10000 7.058E-04 .000000 .000 0.000E+00 .00 56.673923 7.058E-04 1 20000 1.394E-03 58.085495 249.070 9.963E+02 .00 57.371029 1.715E-05 1 30000 2.078E-03 58.280491 294.666 1.179E+03 .52 57.734943 2.022E-05 1 40000 2.763E-03 58.352322 315.570 1.262E+03 .44 57.913273 2.163E-05 1 50000 3.453E-03 58.291363 294.349 1.177E+03 .43 57.926151 2.020E-05 1 60000 4.143E-03 58.219688 265.295 1.061E+03 .52 57.924004 1.823E-05 1 70000 4.829E-03 58.205280 258.630 1.035E+03 .42 57.980808 1.777E-05 1 80000 5.519E-03 58.178448 244.682 9.787E+02 .39 57.977737 1.682E-05 1 90000 6.415E-03 57.015144 -426.727 -1.707E+03 8.63 56.117561 -2.994E-05 1 100000 6.957E-03 57.144867 -344.271 -1.377E+03 7.63 57.499817 -2.410E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 3.000000000 ------------------------------------------ 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 10000 8.456E-04 .000000 .000 0.000E+00 .00 70.958214 8.456E-04 1 20000 1.726E-03 68.132263 -398.256 -2.390E+03 .00 69.516533 -3.507E-05 1 30000 2.507E-03 72.237633 381.159 2.287E+03 9.41 71.806068 3.166E-05 1 40000 3.336E-03 72.719521 494.882 2.969E+03 6.31 71.949348 4.083E-05 1 50000 4.208E-03 71.993553 290.280 1.742E+03 5.27 71.294945 2.419E-05 1 60000 5.055E-03 71.617996 167.046 1.002E+03 4.36 71.213348 1.399E-05 1 70000 5.890E-03 71.509521 126.402 7.584E+02 3.51 71.303619 1.061E-05 1 80000 6.664E-03 71.929634 303.392 1.820E+03 3.75 72.026733 2.531E-05 1 90000 7.552E-03 71.817062 250.753 1.505E+03 3.20 71.501816 2.095E-05 1 100000 8.394E-03 71.729347 205.661 1.234E+03 2.79 71.477577 1.720E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 4.000000000 ------------------------------------------ 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 10000 1.076E-03 .000000 .000 0.000E+00 .00 74.333969 1.076E-03 1 20000 2.144E-03 74.922081 79.118 6.329E+02 .00 74.626862 8.448E-06 1 30000 3.213E-03 74.886177 72.690 5.815E+02 .08 74.701195 7.765E-06 1 40000 4.277E-03 74.968819 91.163 7.293E+02 .26 74.818939 9.728E-06 1 50000 5.346E-03 74.961624 89.235 7.139E+02 .19 74.825211 9.523E-06 1 60000 6.464E-03 74.453888 -69.411 -5.553E+02 2.22 74.260361 -7.458E-06 1 70000 7.534E-03 74.303040 -123.300 -9.864E+02 1.92 74.326393 -1.328E-05 1 80000 8.587E-03 74.379883 -92.401 -7.392E+02 1.63 74.533417 -9.938E-06 1 90000 9.666E-03 74.399742 -83.526 -6.682E+02 1.37 74.489502 -8.981E-06 1 100000 1.073E-02 74.459450 -54.167 -4.333E+02 1.23 74.571655 -5.820E-06 1 COMPUTATIONAL INTENSITY = flop per mem ref 5.000000000 ------------------------------------------ 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 10000 1.523E-03 .000000 .000 0.000E+00 .00 65.640228 1.523E-03 1 20000 3.088E-03 63.921623 -261.822 -2.618E+03 .00 64.769524 -4.096E-05 1 30000 4.598E-03 65.060791 -28.870 -2.887E+02 2.81 65.252792 -4.437E-06 1 40000 6.104E-03 65.574120 102.401 1.024E+03 2.57 65.535614 1.562E-05 1 50000 7.568E-03 66.207626 296.609 2.966E+03 3.30 66.070999 4.480E-05 1 60000 9.123E-03 66.108383 261.190 2.612E+03 2.54 65.767319 3.951E-05 1 70000 1.069E-02 65.841354 152.421 1.524E+03 2.50 65.509705 2.315E-05 1 80000 1.252E-02 64.625877 -404.212 -4.042E+03 7.66 63.916386 -6.255E-05 1 90000 1.371E-02 65.058083 -183.992 -1.840E+03 7.23 65.647575 -2.828E-05 1 100000 1.522E-02 65.338257 -26.875 -2.687E+02 6.50 65.695427 -4.113E-06 1 COMPUTATIONAL INTENSITY = flop per mem ref 6.000000000 ------------------------------------------ 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 10000 1.820E-03 .000000 .000 0.000E+00 .00 65.928268 1.820E-03 1 20000 3.678E-03 64.574997 -205.264 -2.463E+03 .00 65.244621 -3.814E-05 1 30000 5.488E-03 65.431320 -31.174 -3.741E+02 2.09 65.596138 -5.717E-06 1 40000 7.244E-03 66.364166 205.994 2.472E+03 3.53 66.259094 3.725E-05 1 50000 9.096E-03 66.232887 166.024 1.992E+03 2.57 65.961670 3.008E-05 1 60000 1.091E-02 66.194534 152.417 1.829E+03 1.97 66.005630 2.763E-05 1 70000 1.276E-02 66.031418 86.331 1.036E+03 1.80 65.834351 1.569E-05 1 80000 1.458E-02 65.964386 55.787 6.694E+02 1.53 65.859955 1.015E-05 1 90000 1.638E-02 65.967857 57.545 6.905E+02 1.28 65.929298 1.047E-05 1 100000 1.818E-02 66.001915 76.505 9.181E+02 1.12 65.992317 1.391E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 7.000000000 ------------------------------------------ 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 10000 2.117E-03 .000000 .000 0.000E+00 .00 66.135567 2.117E-03 1 20000 4.227E-03 66.336121 30.324 4.245E+02 .00 66.235695 6.400E-06 1 30000 6.381E-03 65.667030 -104.467 -1.463E+03 1.59 65.822464 -2.227E-05 1 40000 8.488E-03 65.828278 -63.797 -8.932E+02 1.18 65.973999 -1.357E-05 1 50000 1.068E-02 65.484596 -167.880 -2.350E+03 1.70 65.567825 -3.589E-05 1 60000 1.270E-02 65.881302 -27.546 -3.856E+02 2.39 66.134239 -5.854E-06 1 70000 1.497E-02 65.550926 -161.132 -2.256E+03 2.63 65.467133 -3.441E-05 1 80000 1.692E-02 65.894890 -4.561 -6.386E+01 3.05 66.202621 -9.691E-07 1 90000 1.907E-02 65.998291 47.738 6.683E+02 2.64 66.070763 1.013E-05 1 100000 2.118E-02 66.066368 85.612 1.199E+03 2.31 66.091606 1.814E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 8.000000000 ------------------------------------------ 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 10000 2.464E-03 .000000 .000 0.000E+00 .00 64.928322 2.464E-03 1 20000 4.869E-03 66.524750 245.876 3.934E+03 .00 65.716843 5.914E-05 1 30000 7.271E-03 66.570808 255.277 4.084E+03 .11 66.014153 6.135E-05 1 40000 9.667E-03 66.636108 271.876 4.350E+03 .23 66.202370 6.528E-05 1 50000 1.228E-02 65.520493 -67.513 -1.080E+03 4.71 65.172050 -1.649E-05 1 60000 1.461E-02 65.618370 -32.757 -5.241E+02 3.65 65.708778 -7.987E-06 1 70000 1.693E-02 66.010582 126.438 2.023E+03 3.66 66.173576 3.065E-05 1 80000 1.933E-02 66.215225 219.834 3.517E+03 3.25 66.212891 5.312E-05 1 90000 2.179E-02 66.232887 228.782 3.661E+03 2.72 66.083176 5.527E-05 1 100000 2.429E-02 66.115517 163.401 2.614E+03 2.46 65.867821 3.954E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 9.000000000 ------------------------------------------ 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 10000 2.619E-03 .000000 .000 0.000E+00 .00 68.724953 2.619E-03 1 20000 5.181E-03 70.249275 221.800 3.992E+03 .00 69.478752 5.683E-05 1 30000 7.740E-03 70.301956 231.965 4.175E+03 .12 69.768311 5.939E-05 1 40000 1.034E-02 69.982880 155.268 2.795E+03 1.03 69.633568 3.994E-05 1 50000 1.290E-02 69.957123 147.850 2.661E+03 .75 69.740631 3.804E-05 1 60000 1.555E-02 69.689079 57.883 1.042E+03 1.38 69.474182 1.495E-05 1 70000 1.798E-02 70.036110 190.963 3.437E+03 2.14 70.094215 4.908E-05 1 80000 2.058E-02 70.114929 224.937 4.049E+03 1.81 69.987053 5.775E-05 1 90000 2.314E-02 70.163986 248.418 4.472E+03 1.55 70.021523 6.373E-05 1 100000 2.570E-02 70.190201 262.210 4.720E+03 1.33 70.037956 6.724E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 10.00000000 ------------------------------------------ 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 10000 3.018E-03 .000000 .000 0.000E+00 .00 66.258156 3.018E-03 1 20000 6.082E-03 65.283699 -147.070 -2.941E+03 .00 65.767319 -4.506E-05 1 30000 9.030E-03 66.540337 106.750 2.135E+03 3.02 66.446007 3.209E-05 1 40000 1.208E-02 66.345940 57.747 1.155E+03 2.06 66.202011 1.741E-05 1 50000 1.517E-02 65.989525 -50.003 -1.000E+03 2.11 65.913811 -1.515E-05 1 60000 1.814E-02 66.094643 -12.916 -2.583E+02 1.70 66.167435 -3.908E-06 1 70000 2.115E-02 66.163574 14.883 2.977E+02 1.40 66.198814 4.499E-06 1 80000 2.420E-02 66.142761 5.443 1.089E+02 1.15 66.120071 1.646E-06 1 90000 2.720E-02 66.166130 17.221 3.444E+02 .98 66.177719 5.205E-06 1 100000 3.021E-02 66.196815 34.231 6.846E+02 .86 66.210991 1.034E-05 1 CALCULATION OF FHALF -------------------- F RINF RHAT FHALF ERROR f/m Mflop/s Mflop/s flop/mref % 1.0 31.645084 .000000 .0000 .00 2.0 57.144867 294.265808 8.2989 .00 3.0 71.729347 195.629562 5.0703 1.93 4.0 74.459450 136.639618 3.0388 3.97 5.0 65.338257 92.106071 1.3966 7.00 6.0 66.001915 80.830528 .9400 6.30 7.0 66.066368 75.762276 .7138 5.40 8.0 66.115517 73.003647 .5786 4.62 9.0 70.190201 74.079453 .6362 4.15 10.0 66.196815 71.904449 .5099 3.58 LAST VALUES : RHAT = 71.904449 Mflop/s FHALF = .5099 flop/mref TOTAL EXECUTION TIME IS 1.6646595001E+00 SECONDS.