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LAIPE2 Exhibits a Consistent Performance On Intel and AMD Processors

[Posted by Jenn-Ching Luo on July 23, 2016 ]


        A consistent performance of LAIPE2 on Intel Xeon and AMD Opteron could be predictable. Generally, any software, not in any special instructions, could have a consistent performance on different processor architectures. LAIPE 2 is one of them, without any special instructions. A consistent performance could be expected. This post uses timing results to show it.

TESTING EXAMPLE

Compute [C]=[A][B], where matrices [A], [B] and [C] are 4-byte real matrix. Matrix [A] is of order (15,000-by-11,000), and matrix [B] is of order (11,000-by-12,000), and matrix [C] is of order (15,000-by-12,000).

The LAIPE2 subroutine laipe$matmul_4 is called to perform the computation. gfortran is the compiler for the executable. The compilation option included -O3, and the executable was linked against neuloop4. neuloop4 is a library for homogeneous soft core computing.

COMPUTER 1

Computer: a Dell PowerEdge R815 with quad Opteron 6168, a total of 48 cores.
Operating System: Core of Windows Server 2008 R2

COMPUTER 2

Computer: a Dell PoweEdge R810 with quad Intel Xeon L7555, a total of 32 physical cores. Because L7555 can run at a higher frequency when using 2 or less cores, processor's turbo boost was disabled for the purpose to measure speedup. Further, logical core (e.g., hyper-threading) was also disabled for the same purpose.
Operating System: Core of Windows Server 2008 R2

SPEEDUP AND PARALLEL EFFICIENCY ON AMD OPTERON

        First, let us see performance on AMD Opteron. The computer has 48 cores. Speedup and parallel efficiency are listed in the table below.

        From the table, we can see one to twenty cores can yield an almost perfect speedup; 35 cores yields an efficiency 90%; 48 cores can speed up the computation to 39x. Matrix multiplication is a good example of parallel computing. The detailed timing results are appended in this post for reference.

Number
of Cores Elapsed
Time (sec) Speedup Efficiency
(%) 1 3493.63 1.0000 100.00 2 1730.18 2.0192 100.96 3 1151.58 3.0338 101.13 4 865.85 4.0349 100.87 5 691.38 5.0531 101.06 6 580.70 6.0162 100.27 7 497.99 7.0155 100.22 8 434.81 8.0348 100.43 9 387.62 9.0130 100.14 10 350.72 9.9613 99.61 11 323.08 10.8135 98.30 12 295.59 11.8192 98.46 13 271.01 12.8912 99.16 14 254.64 13.7199 98.00 15 238.63 14.6404 97.60 16 225.39 15.5004 96.88 17 214.50 16.2873 95.81 18 201.57 17.3321 96.29 19 192.85 18.1158 95.35 20 183.69 19.0192 95.10 21 175.14 19.9476 94.99 22 169.01 20.6711 93.96 23 161.34 21.6538 94.15 24 156.10 22.3807 93.25 25 148.01 23.6040 94.42 BOTIN B073LY63CS TIMBERLAND - TIMBERLAND A1KC1 - 2db2dcc 26 144.46 24.1841 93.02 27 138.31 25.2594 93.55 28 135.66 25.7528 91.97 29 129.12 27.0572 93.30 30 127.03 27.5024 91.67 31 123.46 28.2977 91.28 32 119.61 29.2085 91.28 33 116.50 29.9882 90.87 34 114.44 30.5280 89.79 35 110.90 31.5025 90.01 36 108.17 32.2976 89.72 37 105.57 33.0930 89.44 38 103.37 33.7973 88.94 39 102.02 34.2446 87.81 40 100.34 34.8179 87.04 41 96.71 36.1248 88.11 42 96.21 36.3125 86.46 43 94.50 36.9696 85.98 44 92.76 37.6631 85.60 45 92.32 37.8426 84.09 46 90.62 38.5525 83.81 47 90.62 38.5525 82.03 48 88.58 39.4404 82.17

SPEEDUP AND PARALLEL EFFICIENCY ON INTEL XEON

        Next, let us see performance on Inten Xeon. The computer has 32 physical cores. Speedup and parallel efficiency are listed in the table below. It also shows a performance of high efficiency, consistent to results on AMD Opteron.

        On 28 cores, the computation was speeded up to 27x, 97% parallel performance, which is almost perfect; 32 cores improved the computing up to 28x, and yielded a parallel efficiency 87%. The performance was consistent to the one on AMD Opteron.

        The detailed timing results are appended in this post for reference.

Number
of Cores Elapsed
Time (sec) Speedup Efficiency
(%) 1 5678.17 1.0000 100.00 2 2839.25 1.9999 99.99 3 1896.50 2.9940 99.80 4 1420.37 3.9977 99.94 5 1136.58 4.9958 99.92 6 955.10 5.9451 99.09 7 820.92 3.9168 98.81 8 745.72 7.6143 95.18 9 63.60 8.8225 98.03 10 574.71 9.8801 98.80 11 548.58 10.3507 94.10 12 489.73 11.5945 96.62 13 457.27 12.4175 95.52 14 418.39 13.5715 96.94 15 406.26 13.9767 93.18 16 383.34 14.8124 92.58 17 357.17 15.8977 93.52 18 323.36 17.5599 97.56 19 325.95 17.4204 91.69 20 291.63 19.4705 97.35 21 277.24 20.4811 97.53 22 263.85 21.5204 97.82 23 255.29 22.2420 96.70 24 256.92 22.1009 92.09 25 240.10 23.6492 94.60 26 250.77 22.6429 87.09 27 243.02 23.3650 86.54 28 208.07 27.2897 97.46 29 224.42 25.3015 87.25 30 219.13 25.9123 86.37 31 213.16 26.6381 85.93 32 204.39 27.7811 86.82

TIMING RESULTS ON AMD OPTERON

        The following has detailed timing results implemented on AMD Opteron.

  number of cores: 1
      Elapsed Time (Seconds): 3493.63
      CPU Time in User Mode (Seconds): 3491.97
      CPU Time in Kernel Mode (Seconds): 1.31
      Total CPU Time (Seconds): 3493.28

  number of cores: 2
      Elapsed Time (Seconds): 1730.18
      CPU Time in User Mode (Seconds): 3452.29
      CPU Time in Kernel Mode (Seconds): 0.16
      Total CPU Time (Seconds): 3452.44

  number of cores: 3
      Elapsed Time (Seconds): 1151.58
      CPU Time in User Mode (Seconds): 3452.69
      CPU Time in Kernel Mode (Seconds): 0.36
      Total CPU Time (Seconds): 3453.05

  number of cores: 4
      Elapsed Time (Seconds): 865.85
      CPU Time in User Mode (Seconds): 3453.10
      CPU Time in Kernel Mode (Seconds): 0.41
      Total CPU Time (Seconds): 3453.50

  number of cores: 5
      Elapsed Time (Seconds): 691.38
      CPU Time in User Mode (Seconds): 3454.36
      CPU Time in Kernel Mode (Seconds): 0.44
      Total CPU Time (Seconds): 3454.80

  number of cores: 6
      Elapsed Time (Seconds): 580.70
      CPU Time in User Mode (Seconds): 3456.53
      CPU Time in Kernel Mode (Seconds): 0.44
      Total CPU Time (Seconds): 3456.97
BOTIN B073LY63CS TIMBERLAND - TIMBERLAND A1KC1 - 2db2dcc
  number of cores: 7
      Elapsed Time (Seconds): 497.99
      CPU Time in User Mode (Seconds): 3460.30
      CPU Time in Kernel Mode (Seconds): 0.31
      Total CPU Time (Seconds): 3460.62

  number of cores: 8
      Elapsed Time (Seconds): 434.81
      CPU Time in User Mode (Seconds): 3463.38
      CPU Time in Kernel Mode (Seconds): 0.70
      Total CPU Time (Seconds): 3464.08

  number of cores: 9
      Elapsed Time (Seconds): 387.62
      CPU Time in User Mode (Seconds): 3468.37
      CPU Time in Kernel Mode (Seconds): 0.30
      Total CPU Time (Seconds): 3468.67

  number of cores: 10
      Elapsed Time (Seconds): 350.72
      CPU Time in User Mode (Seconds): 3472.94
      CPU Time in Kernel Mode (Seconds): 0.53
      Total CPU Time (Seconds): 3473.47

  number of cores: 11
      Elapsed Time (Seconds): 323.08
      CPU Time in User Mode (Seconds): 3479.23
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      CPU Time in Kernel Mode (Seconds): 0.45
      Total CPU Time (Seconds): 3479.68

  number of cores: 12
      Elapsed Time (Seconds): 295.59
      CPU Time in User Mode (Seconds): 3488.31
      CPU Time in Kernel Mode (Seconds): 0.50
      Total CPU Time (Seconds): 3488.81

  number of cores: 13
      Elapsed Time (Seconds): 271.01
      CPU Time in User Mode (Seconds): 3483.75
      CPU Time in Kernel Mode (Seconds): 0.51
      Total CPU Time (Seconds): 3484.27

  number of cores: 14
      Elapsed Time (Seconds): 254.64
      CPU Time in User Mode (Seconds): 3505.55
      CPU Time in Kernel Mode (Seconds): 0.39
      Total CPU Time (Seconds): 3505.94

  number of cores: 15
      Elapsed Time (Seconds): 238.63
      CPU Time in User Mode (Seconds): 3529.73
      CPU Time in Kernel Mode (Seconds): 0.62
      Total CPU Time (Seconds): 3530.35

  number of cores: 16
      Elapsed Time (Seconds): 225.39
      CPU Time in User Mode (Seconds): 3536.64
      CPU Time in Kernel Mode (Seconds): 0.78
      Total CPU Time (Seconds): 3537.42

  number of cores: 17
      Elapsed Time (Seconds): 214.50
      CPU Time in User Mode (Seconds): 3565.95
      Converse All Star Customized - Zapatos Personalizados (Producto Artesano) Space Saturno - TG39 - , Dr. Martens 1f66 23592102, Botas Unisex Adulto - , Air MAX Uptempo 95 Triple White - 922935-100 - - , Yellow Cab Lease M, Zapatillas de Estar por Casa para Hombre - Nike Men s Jordan Super.Fly 2017 Low Basket, Zapatos de Baloncesto para Hombre Blanco (White/Black/Emerald Rise 117) Djinns Hombres Calzado/Zapatillas de Deporte Chunk Jersey Aloha Negro , Dr.Martens Mens Lea Grizzly Leather Boots - Retro of LondonRETRO BEAT BLACK PAT LEA PARENT - Botas Chelsea unisex - , Merrell Moab 2 Gore-Tex, Zapatillas de Senderismo para Hombre Gris (Beluga Beluga) , CLARKS Escalade Paso Resbalón-en Mocasín - , Saucony Jazz Original, Zapatillas Silver (Light Tan) , GUNAINDMX Casual/Sports/Running/Higher/Shoes,39,388 - Black 388-black , Vans Old Skool, Zapatillas Unisex Adulto Verde (Duck Green/Gum Q9v) Sandalia MBT 700958-118N Rocco M Marron Marron Converse All Star Customized Unisex - Zapatos Personalizados (Producto Artesano) Hippie Paisley - Converse All Star Customized Unisex - Zapatos Personalizados (Producto Artesano) Autumn Texture - Crocs Crocbandclogk, Zuecos Unisex Niños Azul (Ice Blue/White) Jenny 22-50137-07 Atlanta - Mocasines de Piel para mujer - , XIAOGANG H HFour Seasons Women (negro.) Rojo. Beige. Gris. (amarillo) pendiente de goma y resistencia de desgaste... - Birkenstock Arizona, Zapatos con Hebilla Unisex Adulto Azul (Bleu-v.1) New Balance 220, Zapatillas para Hombre Bleu marine , Zapatilla Saucony Original Jazz Fucsia NEGRO Kennel und Schmenger Pia XXL, Bailarinas con Plataforma para Mujer Blanco (Bianco/Blue Sohle Wei? 627) Sam Edelman Telsa, Zapatos de Tacón para Mujer Negro (Black Suede) , Melvin & Hamilton MH15-315 - Botas de Piel Lisa para Mujer Gris Gris 39 EU , JIANXIN Sandalias Planas Mujeres Verano Moda Cinta Perla Planas Sandalias (Tamaño : EU 37/US 6.5/UK 4) - , YUBIN Sandalias De Boca De Pescado De Cuero De Los Jóvenes Nueva Plataforma A Prueba De Agua Tacones Altos Coreanos De Espesor con Sandalias Salvajes Sandalias De Verano Femenino - , Zapatos de Cuero Hebilla de Las Mujeres Cabeza Cuadrada Zapatos Casuales de Tacón Grueso Set Mocasines de pie Mary Jane Zapatos Winered New Balance Mujeres ww496 V3 Walking Shoe-W Cush + Walking Zapatos Rosado (Komen Pink) HUAIHAIZ Tacones de mujer La chica novias zapatos de boda botas bodas crystal zapatos de tacones altos o zapatos de noche,35, 10 cm color champagne Champagne color 10CM CPU Time in Kernel Mode (Seconds): 0.73
      Total CPU Time (Seconds): 3566.68

  number of cores: 18
      Elapsed Time (Seconds): 201.57
      CPU Time in User Mode (Seconds): 3550.77
      CPU Time in Kernel Mode (Seconds): 0.44
      Total CPU Time (Seconds): 3551.21

  number of cores: 19
      Elapsed Time (Seconds): 192.85
      CPU Time in User Mode (Seconds): 3573.61
      CPU Time in Kernel Mode (Seconds): 0.81
      Total CPU Time (Seconds): 3574.42

  number of cores: 20
      Elapsed Time (Seconds): 183.69
      CPU Time in User Mode (Seconds): 3577.45
      CPU Time in Kernel Mode (Seconds): 0.64
      Total CPU Time (Seconds): 3578.09

  number of cores: 21
      Elapsed Time (Seconds): 175.14
      CPU Time in User Mode (Seconds): 3585.39
      CPU Time in Kernel Mode (Seconds): 0.78
      Total CPU Time (Seconds): 3586.17

  number of cores: 22
      Elapsed Time (Seconds): 169.01
      CPU Time in User Mode (Seconds): 3603.50
      CPU Time in Kernel Mode (Seconds): 1.01
      Total CPU Time (Seconds): 3604.51

  number of cores: 23
      Elapsed Time (Seconds): 161.34
      CPU Time in User Mode (Seconds): 3605.79
      CPU Time in Kernel Mode (Seconds): 0.86
      Total CPU Time (Seconds): 3606.65

  number of cores: 24
      Elapsed Time (Seconds): 156.10
      CPU Time in User Mode (Seconds): 3608.88
      CPU Time in Kernel Mode (Seconds): 0.86
      Total CPU Time (Seconds): 3609.74

  number of cores: 25
      Elapsed Time (Seconds): 148.01
      CPU Time in User Mode (Seconds): 3621.45
      CPU Time in Kernel Mode (Seconds): 0.86
      Total CPU Time (Seconds): 3622.31

  number of cores: 26
      Elapsed Time (Seconds): 144.46
      CPU Time in User Mode (Seconds): 3626.06
      CPU Time in Kernel Mode (Seconds): 0.81
      Total CPU Time (Seconds): 3626.87

  number of cores: 27
      Elapsed Time (Seconds): 138.31
      CPU Time in User Mode (Seconds): 3626.41
      CPU Time in Kernel Mode (Seconds): 0.97
      Total CPU Time (Seconds): 3627.38

  number of cores: 28
      Elapsed Time (Seconds): 135.66
      CPU Time in User Mode (Seconds): 3641.73
      CPU Time in Kernel Mode (Seconds): 1.08
      Total CPU Time (Seconds): 3642.81

  number of cores: 29
      Elapsed Time (Seconds): 129.12
      CPU Time in User Mode (Seconds): 3646.65
      CPU Time in Kernel Mode (Seconds): 0.83
      Total CPU Time (Seconds): 3647.48

  number of cores: 30
      Elapsed Time (Seconds): 127.03
      CPU Time in User Mode (Seconds): 3655.20
      CPU Time in Kernel Mode (Seconds): 0.89
      Total CPU Time (Seconds): 3656.09

  number of cores: 31
      Elapsed Time (Seconds): 123.46
      CPU Time in User Mode (Seconds): 3669.52
      CPU Time in Kernel Mode (Seconds): 1.03
      Total CPU Time (Seconds): 3670.55

  number of cores: 32
      Elapsed Time (Seconds): 119.61
      CPU Time in User Mode (Seconds): 3673.14
      CPU Time in Kernel Mode (Seconds): 1.03
      Total CPU Time (Seconds): 3674.17

  number of cores: 33
      Elapsed Time (Seconds): 116.50
      CPU Time in User Mode (Seconds): 3688.46
      CPU Time in Kernel Mode (Seconds): 0.98
      Total CPU Time (Seconds): 3689.44

  number of cores: 34
      Elapsed Time (Seconds): 114.44
      CPU Time in User Mode (Seconds): 3695.40
      CPU Time in Kernel Mode (Seconds): 0.76
      Total CPU Time (Seconds): 3696.16

  number of cores: 35
      Elapsed Time (Seconds): 110.90
      CPU Time in User Mode (Seconds): 3707.72
      CPU Time in Kernel Mode (Seconds): 0.80
      Total CPU Time (Seconds): 3708.52

  number of cores: 36
   

BOTIN B073LY63CS TIMBERLAND - TIMBERLAND A1KC1 - 2db2dcc - marketmiddle.space

  Elapsed Time (Seconds): 108.17
      CPU Time in User Mode (Seconds): 3725.34
      CPU Time in Kernel Mode (Seconds): 0.90
      Total CPU Time (Seconds): 3726.24

  number of cores: 37
      Elapsed Time (Seconds): 105.57
      CPU Time in User Mode (Seconds): 3745.55
      CPU Time in Kernel Mode (Seconds): 1.00
      Total CPU Time (Seconds): 3746.55

  number of cores: 38
      Elapsed Time (Seconds): 103.37
      CPU Time in User Mode (Seconds): 3757.44
      CPU Time in Kernel Mode (Seconds): 1.05
      Total CPU Time (Seconds): 3758.49

  number of cores: 39
      Elapsed Time (Seconds): 102.02
      CPU Time in User Mode (Seconds): 3773.71
      CPU Time in Kernel Mode (Seconds): 1.33
      Total CPU Time (Seconds): 3775.04

  number of cores: 40
      Elapsed Time (Seconds): 100.34
      CPU Time in User Mode (Seconds): 3801.43
      CPU Time in Kernel Mode (Seconds): 0.98
      Total CPU Time (Seconds): 3802.42

  number of cores: 41
      Elapsed Time (Seconds): 96.71
      CPU Time in User Mode (Seconds): 3818.86
      CPU Time in Kernel Mode (Seconds): 0.92
      Total CPU Time (Seconds): 3819.78

  number of cores: 42
      Elapsed Time (Seconds): 96.21
      CPU Time in User Mode (Seconds): 3843.96
      CPU Time in Kernel Mode (Seconds): 1.15
      Total CPU Time (Seconds): 3845.11

  number of cores: 43
      Elapsed Time (Seconds): 94.50
      CPU Time in User Mode (Seconds): 3854.24
      CPU Time in Kernel Mode (Seconds): 1.22
      Total CPU Time (Seconds): 3855.46

  number of cores: 44
      Elapsed Time (Seconds): 92.76
      CPU Time in User Mode (Seconds): 3879.04
      CPU Time in Kernel Mode (Seconds): 1.29
      Total CPU Time (Seconds): 3880.34

  number of cores: 45
      Elapsed Time (Seconds): 92.32
      CPU Time in User Mode (Seconds): 3910.18
      CPU Time in Kernel Mode (Seconds): 1.26
      Total CPU Time (Seconds): 3911.44

  number of cores: 46
      Elapsed Time (Seconds): 90.62
      CPU Time in User Mode (Seconds): 3942.27
      CPU Time in Kernel Mode (Seconds): 1.31
      Total CPU Time (Seconds): 3943.58

  number of cores: 47
      Elapsed Time (Seconds): 90.62
      CPU Time in User Mode (Seconds): 3984.56
      CPU Time in Kernel Mode (Seconds): 1.11
      Total CPU Time (Seconds): 3985.67

  number of cores: 48
      Elapsed Time (Seconds): 88.58
      CPU Time in User Mode (Seconds): 4025.09
      CPU Time in Kernel Mode (Seconds): 1.12
      Total CPU Time (Seconds): 4026.21

TIMING RESULTS ON INTEL XEON

        The following has detailed timing results implemented on Intel Xeon.

  number of cores: 1
      Elapsed Time (Seconds): 5678.17
      CPU Time in User Mode (Seconds): 5677.11
      CPU Time in Kernel Mode (Seconds): 0.72
      Total CPU Time (Seconds): 5677.83

  number of cores: 2
      Elapsed Time (Seconds): 2839.25
      CPU Time in User Mode (Seconds): 5677.53
      CPU Time in Kernel Mode (Seconds): 0.30
      Total CPU Time (Seconds): 5677.83

  number of cores: 3
      Elapsed Time (Seconds): 1896.50
      CPU Time in User Mode (Seconds): 5678.12
      CPU Time in Kernel Mode (Seconds): 0.27
      Total CPU Time (Seconds): 5678.39

  number of cores: 4
      Elapsed Time (Seconds): 1420.37
      BOTIN B073LY63CS TIMBERLAND - TIMBERLAND A1KC1 - 2db2dcc CPU Time in User Mode (Seconds): 5679.28
      CPU Time in Kernel Mode (Seconds): 0.41
      Total CPU Time (Seconds): 5679.68

  number of cores: 5
      Elapsed Time (Seconds): 1136.58
      CPU Time in User Mode (Seconds): 5680.54
      CPU Time in Kernel Mode (Seconds): 0.41
      Total CPU Time (Seconds): 5680.95

  number of cores: 6
      Elapsed Time (Seconds): 955.10
      CPU Time in User Mode (Seconds): 5682.24
      CPU Time in Kernel Mode (Seconds): 0.59
      Total CPU Time (Seconds): 5682.84

  number of cores: 7
      Elapsed Time (Seconds): 820.92
      CPU Time in User Mode (Seconds): 5694.96
      CPU Time in Kernel Mode (Seconds): 0.64
      Total CPU Time (Seconds): 5695.60

  number of cores: 8
      Elapsed Time (Seconds): 745.72
      CPU Time in User Mode (Seconds): 5911.72
      CPU Time in Kernel Mode (Seconds): 0.95
      Total CPU Time (Seconds): 5912.67

  number of cores: 9
      Elapsed Time (Seconds): 643.60
      CPU Time in User Mode (Seconds): 5737.51
      CPU Time in Kernel Mode (Seconds): 0.56
      Total CPU Time (Seconds): 5738.08

  number of cores: 10
      Elapsed Time (Seconds): 574.71
      CPU Time in User Mode (Seconds): 5726.95
      CPU Time in Kernel Mode (Seconds): 0.59
      Total CPU Time (Seconds): 5727.55

  number of cores: 11
      Elapsed Time (Seconds): 548.58
      CPU Time in User Mode (Seconds): 5964.87
      CPU Time in Kernel Mode (Seconds): 0.55
      Total CPU Time (Seconds): 5965.42

  number of cores: 12
      Elapsed Time (Seconds): 489.73
      CPU Time in User Mode (Seconds): 5822.60
      CPU Time in Kernel Mode (Seconds): 0.45
      Total CPU Time (Seconds): 5823.05

  number of cores: 13
      Elapsed Time (Seconds): 457.27
      CPU Time in User Mode (Seconds): 5874.45
      CPU Time in Kernel Mode (Seconds): 0.62
      Total CPU Time (Seconds): 5875.08

  number of cores: 14
      Elapsed Time (Seconds): 418.39
      CPU Time in User Mode (Seconds): 5794.88
      CPU Time in Kernel Mode (Seconds): 0.58
      Total CPU Time (Seconds): 5795.45

  number of cores: 15
      Elapsed Time (Seconds): 406.26
      CPU Time in User Mode (Seconds): 5994.48
      CPU Time in Kernel Mode (Seconds): 0.51
      Total CPU Time (Seconds): 5994.99

  number of cores: 16
      Elapsed Time (Seconds): 383.34
      CPU Time in User Mode (Seconds): 6040.25
      CPU Time in Kernel Mode (Seconds): 0.45
      Total CPU Time (Seconds): 6040.70

  number of cores: 17
      Elapsed Time (Seconds): 357.17
      CPU Time in User Mode (Seconds): 5978.49
      CPU Time in Kernel Mode (Seconds): 0.51
      Total CPU Time (Seconds): 5979.00

  number of cores: 18
      Elapsed Time (Seconds): 323.36
      CPU Time in User Mode (Seconds): 5758.32
      CPU Time in Kernel Mode (Seconds): 0.53
      - Total CPU Time (Seconds): 5758.85

  number of cores: 19
      Elapsed Time (Seconds): 325.95
      CPU Time in User Mode (Seconds): 6084.05
      CPU Time in Kernel Mode (Seconds): 0.53
      Total CPU Time (Seconds): 6084.58

  number of cores: 20
      Elapsed Time (Seconds): 291.63
      CPU Time in User Mode (Seconds): 5802.43
      CPU Time in Kernel Mode (Seconds): 0.73
      Total CPU Time (Seconds): 5803.16

  number of cores: 21
      Elapsed Time (Seconds): 277.24
      CPU Time in User Mode (Seconds): 5759.42
      CPU Time in Kernel Mode (Seconds): 0.76
      Total CPU Time (Seconds): 5760.18

  number of cores: 22
      Elapsed Time (Seconds): 263.85
      CPU Time in User Mode (Seconds): 5726.13
      CPU Time in Kernel Mode (Seconds): 0.55
      Total CPU Time (Seconds): 5726.67

  number of cores: 23
      Elapsed Time (Seconds): 255.29
      CPU Time in User Mode (Seconds): 5791.99
      CPU Time in Kernel Mode (Seconds): 0.67
      Total CPU Time (Seconds): 5792.66

  number of cores: 24
      Elapsed Time (Seconds): 256.92
      CPU Time in User Mode (Seconds): 6060.16
      CPU Time in Kernel Mode (Seconds): 0.70
      Total CPU Time (Seconds): 6060.86

  number of cores: 25
      Elapsed Time (Seconds): 240.10
      CPU Time in User Mode (Seconds): 5938.63
      CPU Time in Kernel Mode (Seconds): 0.66
      Total CPU Time (Seconds): 5939.29

  number of cores: 26
      Elapsed Time (Seconds): 250.77
      CPU Time in User Mode (Seconds): 6365.71
      CPU Time in Kernel Mode (Seconds): 0.81
      Total CPU Time (Seconds): 6366.53

  number of cores: 27
      Elapsed Time (Seconds): 243.02
      CPU Time in User Mode (Seconds): 6399.21
      CPU Time in Kernel Mode (Seconds): 0.90
      Total CPU Time (Seconds): 6400.11

  number of cores: 28
      Elapsed Time (Seconds): 208.07
      CPU Time in User Mode (Seconds): 5764.52
      CPU Time in Kernel Mode (Seconds): 0.78
      Total CPU Time (Seconds): 5765.30

  number of cores: 29
      Elapsed Time (Seconds): 224.42
      CPU Time in User Mode (Seconds): 6353.00
      CPU Time in Kernel Mode (Seconds): 0.61
      Total CPU Time (Seconds): 6353.61

  number of cores: 30
      Elapsed Time (Seconds): 219.13
      CPU Time in User Mode (Seconds): 6402.33
      1971711
2312673
4655167
9886706
13177272
13566028
16332414
16744576
18443253
CPU Time in Kernel Mode (Seconds): 0.59
      Total CPU Time (Seconds): 6402.92

  number of cores: 31
      Elapsed Time (Seconds): 213.16
      CPU Time in User Mode (Seconds): 6407.62
      CPU Time in Kernel Mode (Seconds): 0.67
      Total CPU Time (Seconds): 6408.29

  number of cores: 32
      Elapsed Time (Seconds): 204.39
      CPU Time in User Mode (Seconds): 6345.79
      CPU Time in Kernel Mode (Seconds): 0.69
      Total CPU Time (Seconds): 6346.48