#*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: 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 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 === === === === 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 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 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 1.254E-02 0.000000 0.000 0.000E+00 0.00 1.595156 1.254E-02 1 20000 2.490E-02 1.617331 139.009 2.780E+02 0.00 1.606167 1.719E-04 1 30000 3.803E-02 1.569299 -261.094 -5.222E+02 4.69 1.577824 -3.328E-04 1 40000 4.964E-02 1.607379 137.004 2.740E+02 6.37 1.611637 1.705E-04 1 50000 6.204E-02 1.616252 248.162 4.963E+02 4.81 1.611811 3.071E-04 1 60000 7.460E-02 1.615355 235.064 4.701E+02 3.66 1.608556 2.910E-04 1 70000 8.686E-02 1.616758 258.441 5.169E+02 2.93 1.611808 3.197E-04 1 80000 9.920E-02 1.617620 274.573 5.491E+02 2.41 1.612837 3.395E-04 1 90000 1.117E-01 1.617246 266.788 5.336E+02 2.02 1.612080 3.299E-04 1 100000 1.240E-01 1.616868 258.170 5.163E+02 1.73 1.612254 3.193E-04 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 1.608E-02 0.000000 0.000 0.000E+00 0.00 2.487430 1.608E-02 1 20000 3.220E-02 2.481213 -24.994 -9.997E+01 0.00 2.484317 -4.029E-05 1 30000 4.835E-02 2.479379 -34.827 -1.393E+02 0.12 2.482057 -5.619E-05 1 40000 6.425E-02 2.489892 35.692 1.428E+02 0.97 2.490310 5.734E-05 1 50000 8.038E-02 2.489862 35.455 1.418E+02 0.69 2.488086 5.696E-05 1 60000 9.652E-02 2.488201 19.858 7.943E+01 0.57 2.486456 3.192E-05 1 70000 1.128E-01 2.483749 -27.885 -1.115E+02 0.80 2.481566 -4.491E-05 1 80000 1.288E-01 2.484245 -21.904 -8.762E+01 0.66 2.485359 -3.527E-05 1 90000 1.458E-01 2.474859 -147.755 -5.910E+02 1.74 2.469239 -2.388E-04 1 100000 1.610E-01 2.478243 -97.831 -3.913E+02 1.63 2.484750 -1.579E-04 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 1.981E-02 0.000000 0.000 0.000E+00 0.00 3.028779 1.981E-02 1 20000 3.975E-02 3.008413 -67.243 -4.035E+02 0.00 3.018562 -1.341E-04 1 30000 5.920E-02 3.046452 100.497 6.030E+02 1.98 3.040538 1.979E-04 1 40000 7.889E-02 3.050547 123.037 7.382E+02 1.32 3.042212 2.420E-04 1 50000 9.848E-02 3.053960 145.551 8.733E+02 1.00 3.046455 2.860E-04 1 60000 1.185E-01 3.046689 89.648 5.379E+02 1.09 3.038131 1.765E-04 1 70000 1.380E-01 3.047553 97.233 5.834E+02 0.87 3.043941 1.914E-04 1 80000 1.578E-01 3.046752 89.329 5.360E+02 0.72 3.042655 1.759E-04 1 90000 1.774E-01 3.046803 89.883 5.393E+02 0.60 3.043815 1.770E-04 1 100000 1.973E-01 3.045434 73.366 4.402E+02 0.56 3.041562 1.445E-04 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 2.353E-02 0.000000 0.000 0.000E+00 0.00 3.400052 2.353E-02 1 20000 4.684E-02 3.431713 93.120 7.450E+02 0.00 3.415809 2.171E-04 1 30000 7.016E-02 3.431415 91.952 7.356E+02 0.01 3.420896 2.144E-04 1 40000 9.345E-02 3.432448 97.001 7.760E+02 0.07 3.424402 2.261E-04 1 50000 1.171E-01 3.421030 30.143 2.411E+02 0.94 3.414428 7.049E-05 1 60000 1.405E-01 3.418546 13.183 1.055E+02 0.75 3.416418 3.085E-05 1 70000 1.639E-01 3.417017 1.251 1.001E+01 0.62 3.415865 2.929E-06 1 80000 1.870E-01 3.420643 33.082 2.647E+02 0.67 3.422405 7.737E-05 1 90000 2.106E-01 3.420107 27.856 2.228E+02 0.56 3.418494 6.516E-05 1 100000 2.338E-01 3.421358 41.282 3.303E+02 0.51 3.421448 9.653E-05 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 2.831E-02 0.000000 0.000 0.000E+00 0.00 3.532685 2.831E-02 1 20000 5.407E-02 3.881854 988.393 9.884E+03 0.00 3.699048 2.546E-03 1 30000 8.105E-02 3.791847 656.321 6.563E+03 3.56 3.701335 1.731E-03 1 40000 1.083E-01 3.747450 453.498 4.535E+03 3.50 3.694746 1.210E-03 1 50000 1.352E-01 3.730347 360.152 3.602E+03 2.81 3.696969 9.655E-04 1 60000 1.628E-01 3.711368 239.602 2.396E+03 2.70 3.686228 6.456E-04 1 70000 1.890E-01 3.715555 269.960 2.700E+03 2.20 3.704255 7.266E-04 1 80000 2.160E-01 3.715677 270.950 2.709E+03 1.80 3.703240 7.292E-04 1 90000 2.436E-01 3.709246 212.794 2.128E+03 1.68 3.693883 5.737E-04 1 100000 2.703E-01 3.708190 202.293 2.023E+03 1.44 3.699442 5.455E-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 3.076E-02 0.000000 0.000 0.000E+00 0.00 3.901300 3.076E-02 1 20000 6.142E-02 3.913662 31.687 3.802E+02 0.00 3.907471 9.716E-05 1 30000 9.202E-02 3.917721 45.549 5.466E+02 0.16 3.912232 1.395E-04 1 40000 1.228E-01 3.913574 27.856 3.343E+02 0.26 3.909816 8.541E-05 1 50000 1.534E-01 3.914059 30.341 3.641E+02 0.19 3.911880 9.302E-05 1 60000 1.842E-01 3.911258 13.621 1.634E+02 0.28 3.908817 4.179E-05 1 70000 2.154E-01 3.902882 -43.513 -5.222E+02 0.82 3.899342 -1.338E-04 1 80000 2.454E-01 3.907173 -10.581 -1.270E+02 0.81 3.911453 -3.250E-05 1 90000 2.760E-01 3.910043 13.899 1.668E+02 0.75 3.912420 4.266E-05 1 100000 3.077E-01 3.904628 -36.901 -4.428E+02 0.91 3.899586 -1.134E-04 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 3.447E-02 0.000000 0.000 0.000E+00 0.00 4.061746 3.447E-02 1 20000 6.896E-02 4.058911 -6.980 -9.772E+01 0.00 4.060328 -2.408E-05 1 30000 1.029E-01 4.092489 103.265 1.446E+03 1.30 4.082190 3.533E-04 1 40000 1.380E-01 4.064623 -10.920 -1.529E+02 1.76 4.058823 -3.761E-05 1 50000 1.716E-01 4.078737 58.488 8.188E+02 1.60 4.079631 2.008E-04 1 60000 2.060E-01 4.080604 69.195 9.687E+02 1.23 4.076939 2.374E-04 1 70000 2.400E-01 4.085043 98.280 1.376E+03 1.06 4.082483 3.368E-04 1 80000 2.743E-01 4.087038 112.976 1.582E+03 0.89 4.083016 3.870E-04 1 90000 3.088E-01 4.086033 104.753 1.467E+03 0.75 4.080244 3.589E-04 1 100000 3.436E-01 4.081963 68.124 9.537E+02 0.79 4.074317 2.336E-04 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 3.817E-02 0.000000 0.000 0.000E+00 0.00 4.191763 3.817E-02 1 20000 7.622E-02 4.204566 30.543 4.887E+02 0.00 4.198154 1.162E-04 1 30000 1.141E-01 4.213191 57.958 9.273E+02 0.32 4.206024 2.201E-04 1 40000 1.528E-01 4.191275 -29.042 -4.647E+02 1.20 4.188868 -1.109E-04 1 50000 1.900E-01 4.208911 54.997 8.800E+02 1.47 4.211368 2.091E-04 1 60000 2.282E-01 4.210265 62.514 1.000E+03 1.12 4.206633 2.376E-04 1 70000 2.704E-01 4.161423 -247.557 -3.961E+03 4.35 4.141752 -9.518E-04 1 80000 3.039E-01 4.186022 -71.684 -1.147E+03 4.35 4.211579 -2.740E-04 1 90000 3.418E-01 4.200169 40.720 6.515E+02 3.94 4.213027 1.551E-04 1 100000 3.817E-01 4.196667 10.114 1.618E+02 3.37 4.192048 3.856E-05 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 4.169E-02 0.000000 0.000 0.000E+00 0.00 4.317780 4.169E-02 1 20000 8.327E-02 4.328387 24.566 4.422E+02 0.00 4.323078 1.022E-04 1 30000 1.247E-01 4.336567 49.810 8.966E+02 0.30 4.330287 2.067E-04 1 40000 1.669E-01 4.315009 -33.293 -5.993E+02 1.15 4.313239 -1.389E-04 1 50000 2.082E-01 4.320778 -6.599 -1.188E+02 0.91 4.323661 -2.749E-05 1 60000 2.497E-01 4.324211 11.932 2.148E+02 0.74 4.325259 4.967E-05 1 70000 2.912E-01 4.326920 28.648 5.157E+02 0.63 4.327085 1.192E-04 1 80000 3.328E-01 4.327972 35.954 6.472E+02 0.53 4.326949 1.495E-04 1 90000 3.751E-01 4.323862 4.259 7.666E+01 0.60 4.319403 1.773E-05 1 100000 4.162E-01 4.324628 10.757 1.936E+02 0.52 4.325082 4.477E-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 4.555E-02 0.000000 0.000 0.000E+00 0.00 4.391068 4.555E-02 1 20000 9.065E-02 4.433901 97.547 1.951E+03 0.00 4.412381 4.400E-04 1 30000 1.359E-01 4.427863 79.257 1.585E+03 0.21 4.415529 3.580E-04 1 40000 1.814E-01 4.417185 38.875 7.775E+02 0.57 4.410241 1.760E-04 1 50000 2.263E-01 4.422607 63.470 1.269E+03 0.53 4.419167 2.870E-04 1 60000 2.716E-01 4.422414 62.452 1.249E+03 0.41 4.417709 2.824E-04 1 70000 3.174E-01 4.416603 27.325 5.465E+02 0.58 4.410740 1.237E-04 1 80000 3.629E-01 4.412689 0.717 1.434E+01 0.60 4.409231 3.251E-06 1 90000 4.077E-01 4.413915 9.975 1.995E+02 0.51 4.414697 4.520E-05 1 100000 4.948E-01 4.203247 -1740.532 -3.481E+04 21.53 4.042095 -8.282E-03 1 CALCULATION OF FHALF -------------------- F RINF RHAT FHALF ERROR f/m Mflop/s Mflop/s flop/mref % 1.0 1.616868 0.000000 0.0000 0.00 2.0 2.478243 5.303806 2.2803 0.00 3.0 3.045434 5.455510 2.3837 0.25 4.0 3.421358 5.464487 2.3903 0.18 5.0 3.708190 5.488845 2.4099 0.17 6.0 3.904628 5.469719 2.3934 0.16 7.0 4.081963 5.477673 2.4007 0.14 8.0 4.196667 5.458918 2.3822 0.16 9.0 4.324628 5.466810 2.3905 0.14 10.0 4.203247 5.289189 2.1937 1.22 LAST VALUES : RHAT = 5.289189 Mflop/s FHALF = 2.1937 flop/mref TOTAL EXECUTION TIME IS 2.7710531235E+01 SECONDS.