#*name: Roger Hockney #*establishment: University of Southampton #*email: rwh@pac.soton.ac.uk #telephone: 0635 578679 #date sent: 01/11/94 #*date benchmarked: 13/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: SUN #*model number: SPARC Station 20 #cpu: Sparc #cpu speed (MHz): 50MHz #fpu: integrated #primary cache: #secondary cache: none #other cache: none #memory: 112MB #disk and connection: #interconnect type: #switching: #other hardware: #operating system and version: Solaris 2.3 #compilers, libraries and versions: f77 version 3.0 #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 === === === ================================================= Run on single SUN SPARC Station 20 50MHz without second level cache +112MByte at Old Dominion University, VA, USA (CCPO) Software levels are Solaris 2.3 F77 version 3.0 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 -------------------------------------------------------------- POLYNOMIALS : A(I)=S0+B(I)*(S1+B(I)*(S2+B(I)*S3)) ICASE= 1 NCASE= 1 NMAX=100000 NTIMES= 1 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 10000 3.253E-03 0.000000 0.000 0.000E+00 0.00 6.147977 3.253E-03 1 20000 6.760E-03 5.703044 -723.707 -1.447E+03 0.00 5.917159 -2.538E-04 1 30000 9.830E-03 6.081896 113.949 2.279E+02 10.48 6.103765 3.747E-05 1 40000 1.308E-02 6.146558 292.358 5.847E+02 7.24 6.118104 9.513E-05 1 50000 1.629E-02 6.172905 379.340 7.587E+02 5.33 6.136868 1.229E-04 1 60000 1.959E-02 6.166287 353.916 7.078E+02 4.06 6.126500 1.148E-04 1 70000 2.283E-02 6.163659 342.401 6.848E+02 3.23 6.131800 1.111E-04 1 80000 2.611E-02 6.157299 311.088 6.222E+02 2.68 6.127936 1.010E-04 1 90000 2.937E-02 6.152840 286.728 5.735E+02 2.26 6.128713 9.320E-05 1 100000 3.266E-02 6.146289 247.382 4.948E+02 2.00 6.123318 8.050E-05 1 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 10000 4.211E-03 0.000000 0.000 0.000E+00 0.00 9.499047 4.211E-03 1 20000 8.390E-03 9.571666 76.449 3.058E+02 0.00 9.535218 3.195E-05 1 30000 1.258E-02 9.563618 65.174 2.607E+02 0.13 9.541997 2.726E-05 1 40000 1.687E-02 9.490315 -63.072 -2.523E+02 1.75 9.487095 -2.658E-05 1 50000 2.093E-02 9.542594 46.754 1.870E+02 2.01 9.554713 1.960E-05 1 60000 2.517E-02 9.543261 48.388 1.936E+02 1.52 9.535941 2.028E-05 1 70000 2.925E-02 9.569258 121.163 4.847E+02 1.58 9.571315 5.065E-05 1 80000 3.363E-02 9.543616 40.449 1.618E+02 1.68 9.516491 1.695E-05 1 90000 3.828E-02 9.462722 -242.436 -9.697E+02 3.94 9.405382 -1.025E-04 1 100000 4.177E-02 9.511153 -56.011 -2.240E+02 4.20 9.575326 -2.356E-05 1 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 10000 5.145E-03 0.000000 0.000 0.000E+00 0.00 11.661642 5.145E-03 1 20000 1.023E-02 11.788100 108.439 6.506E+02 0.00 11.724530 5.519E-05 1 30000 1.567E-02 11.403763 -329.814 -1.979E+03 5.16 11.488446 -1.735E-04 1 40000 2.049E-02 11.656376 32.076 1.925E+02 6.12 11.711844 1.651E-05 1 50000 2.556E-02 11.746037 186.163 1.117E+03 4.90 11.738448 9.509E-05 1 60000 3.074E-02 11.747254 188.600 1.132E+03 3.72 11.711117 9.633E-05 1 70000 3.581E-02 11.756964 210.798 1.265E+03 2.97 11.728569 1.076E-04 1 80000 4.111E-02 11.724124 126.411 7.585E+02 2.67 11.677132 6.469E-05 1 90000 4.599E-02 11.744086 183.382 1.100E+03 2.37 11.740894 9.369E-05 1 100000 5.123E-02 11.738484 165.805 9.948E+02 2.03 11.712361 8.475E-05 1 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 10000 6.164E-03 0.000000 0.000 0.000E+00 0.00 12.978681 6.164E-03 1 20000 1.229E-02 13.054675 58.553 4.684E+02 0.00 13.016567 3.588E-05 1 30000 1.845E-02 13.022882 25.939 2.075E+02 0.38 13.008115 1.593E-05 1 40000 2.463E-02 12.995620 -9.005 -7.204E+01 0.54 12.991746 -5.543E-06 1 50000 3.067E-02 13.038873 57.531 4.602E+02 1.02 13.041230 3.530E-05 1 60000 3.679E-02 13.056627 89.380 7.150E+02 0.89 13.047061 5.476E-05 1 70000 4.300E-02 13.043158 61.778 4.942E+02 0.80 13.022070 3.789E-05 1 80000 4.907E-02 13.050196 78.001 6.240E+02 0.69 13.043638 4.782E-05 1 90000 5.550E-02 13.010069 -24.734 -1.979E+02 1.46 12.972269 -1.521E-05 1 100000 6.143E-02 13.015794 -8.611 -6.889E+01 1.27 13.023792 -5.293E-06 1 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 10000 7.303E-03 0.000000 0.000 0.000E+00 0.00 13.693003 7.303E-03 1 20000 1.564E-02 11.999153 -1237.019 -1.237E+04 0.00 12.790242 -1.031E-03 1 30000 2.198E-02 13.628601 405.623 4.056E+03 21.37 13.650001 2.976E-04 1 40000 2.948E-02 13.724975 526.349 5.263E+03 13.89 13.570396 3.835E-04 1 50000 3.664E-02 13.789115 622.274 6.223E+03 10.08 13.644806 4.513E-04 1 60000 4.480E-02 13.564631 232.281 2.323E+03 9.19 13.391668 1.712E-04 1 70000 5.127E-02 13.664748 430.815 4.308E+03 7.92 13.652698 3.153E-04 1 80000 5.865E-02 13.697997 504.860 5.049E+03 6.55 13.640955 3.686E-04 1 90000 6.600E-02 13.707081 527.300 5.273E+03 5.50 13.636564 3.847E-04 1 100000 7.336E-02 13.704588 520.534 5.205E+03 4.69 13.630660 3.798E-04 1 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 10000 8.549E-03 0.000000 0.000 0.000E+00 0.00 14.036771 8.549E-03 1 20000 1.708E-02 14.067962 22.221 2.666E+02 0.00 14.052349 1.895E-05 1 30000 2.561E-02 14.069632 23.806 2.857E+02 0.02 14.058661 2.030E-05 1 40000 3.410E-02 14.088615 46.325 5.559E+02 0.31 14.077060 3.946E-05 1 50000 4.283E-02 14.022458 -47.808 -5.737E+02 1.34 14.009539 -4.091E-05 1 60000 5.115E-02 14.058436 11.937 1.432E+02 1.33 14.075699 1.019E-05 1 70000 5.968E-02 14.072900 39.385 4.726E+02 1.12 14.075324 3.358E-05 1 80000 6.839E-02 14.053234 -2.593 -3.112E+01 1.08 14.036525 -2.214E-06 1 90000 7.672E-02 14.066906 29.834 3.580E+02 1.00 14.076442 2.545E-05 1 100000 8.541E-02 14.059899 11.554 1.387E+02 0.88 14.049877 9.862E-06 1 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 10000 9.818E-03 0.000000 0.000 0.000E+00 0.00 14.259585 9.818E-03 1 20000 1.955E-02 14.388516 90.417 1.266E+03 0.00 14.323760 8.798E-05 1 30000 2.931E-02 14.361947 65.630 9.188E+02 0.29 14.327663 6.398E-05 1 40000 3.907E-02 14.354452 56.898 7.966E+02 0.22 14.332195 5.549E-05 1 50000 4.886E-02 14.341480 38.772 5.428E+02 0.30 14.325193 3.785E-05 1 60000 5.860E-02 14.343198 41.573 5.820E+02 0.23 14.334221 4.058E-05 1 70000 6.863E-02 14.301067 -36.880 -5.163E+02 1.10 14.278631 -3.610E-05 1 80000 7.817E-02 14.313835 -10.128 -1.418E+02 0.97 14.326841 -9.906E-06 1 90000 8.797E-02 14.318787 1.400 1.960E+01 0.83 14.323703 1.369E-06 1 100000 9.781E-02 14.315838 -6.151 -8.611E+01 0.71 14.313182 -6.015E-06 1 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 10000 1.097E-02 0.000000 0.000 0.000E+00 0.00 14.589042 1.097E-02 1 20000 2.198E-02 14.531232 -39.625 -6.340E+02 0.00 14.560080 -4.363E-05 1 30000 3.281E-02 14.651391 70.300 1.125E+03 1.30 14.630549 7.677E-05 1 40000 7.562E-02 7.813400 -7741.056 -1.239E+05 115.38 8.463830 -1.585E-02 1 50000 5.480E-02 11.323295 -2234.157 -3.575E+04 217.05 14.598817 -3.157E-03 1 60000 6.590E-02 13.463155 1753.135 2.805E+04 177.94 14.566875 2.083E-03 1 70000 7.669E-02 14.591942 4135.929 6.617E+04 144.90 14.603669 4.535E-03 1 80000 8.790E-02 15.091647 5304.923 8.488E+04 119.02 14.562351 5.624E-03 1 90000 9.859E-02 15.328200 5910.554 9.457E+04 100.26 14.606383 6.170E-03 1 100000 1.096E-01 15.401234 6113.421 9.781E+04 85.55 14.592563 6.351E-03 1 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 10000 1.217E-02 0.000000 0.000 0.000E+00 0.00 14.788058 1.217E-02 1 20000 2.427E-02 14.882069 63.572 1.144E+03 0.00 14.834914 7.689E-05 1 30000 3.648E-02 14.807417 -3.629 -6.533E+01 0.79 14.800958 -4.412E-06 1 40000 4.854E-02 14.835919 28.444 5.120E+02 0.68 14.832509 3.451E-05 1 50000 6.068E-02 14.839345 33.070 5.953E+02 0.49 14.830906 4.011E-05 1 60000 7.279E-02 14.845037 42.033 7.566E+02 0.39 14.837805 5.097E-05 1 70000 8.512E-02 14.820015 -2.986 -5.375E+01 0.69 14.802825 -3.627E-06 1 80000 9.702E-02 14.834602 26.538 4.777E+02 0.70 14.842461 3.220E-05 1 90000 1.097E-01 14.798931 -53.678 -9.662E+02 1.20 14.770907 -6.529E-05 1 100000 1.214E-01 14.812084 -21.136 -3.805E+02 1.11 14.831037 -2.569E-05 1 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 10000 1.377E-02 0.000000 0.000 0.000E+00 0.00 14.526482 1.377E-02 1 20000 2.720E-02 14.894282 253.193 5.064E+03 0.00 14.708083 3.400E-04 1 30000 4.077E-02 14.813666 179.655 3.593E+03 0.84 14.716685 2.426E-04 1 40000 5.436E-02 14.777795 138.862 2.777E+03 0.78 14.717792 1.879E-04 1 50000 6.816E-02 14.712352 49.677 9.935E+02 1.37 14.671785 6.753E-05 1 60000 8.159E-02 14.719394 60.870 1.217E+03 1.05 14.708384 8.271E-05 1 70000 9.527E-02 14.710506 44.731 8.946E+02 0.86 14.694777 6.081E-05 1 80000 1.087E-01 14.722564 69.357 1.387E+03 0.78 14.720359 9.422E-05 1 90000 1.228E-01 14.693900 4.325 8.651E+01 1.07 14.663589 5.887E-06 1 100000 1.361E-01 14.697371 12.988 2.598E+02 0.93 14.699629 1.767E-05 1 CALCULATION OF FHALF -------------------- F RINF RHAT FHALF ERROR f/m Mflop/s Mflop/s flop/mref % 1.0 6.146289 0.000000 0.0000 0.00 2.0 9.511153 21.017391 2.4195 0.00 3.0 11.738484 21.535524 2.5120 0.21 4.0 13.015794 20.870396 2.3830 0.47 5.0 13.704588 19.947239 2.1891 0.93 6.0 14.059899 19.066671 1.9895 1.29 7.0 14.315838 18.408804 1.8288 1.44 8.0 15.401234 18.827024 1.9385 1.47 9.0 14.812084 18.218517 1.7681 1.65 10.0 14.697371 17.615456 1.5882 1.91 LAST VALUES : RHAT = 17.615456 Mflop/s FHALF = 1.5882 flop/mref TOTAL EXECUTION TIME IS 7.6623101234E+00 SECONDS.