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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 New Balance 7504 WW847 Grande Fibra Balance sintética Zapatos New para Caminar ed7d4e8 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
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  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
      New Balance Kl574u3g - Zapatilla Baja Unisex Niños - , Merrell WATERPRO MAIPO J85119 - Zapatillas de deporte para hombre, color beige, talla 45 - Nike 852431-001, Zapatillas de Baloncesto Para Hombre Negro (Black / Metallic Silver-dark Grey) , New Balance wbora B – BK3 Black/White, Negro negro , Milwaukee piel de hombre Classic botas de motocicleta (negro, tamaño 8) - , Nike 844677-005, Zapatillas de Baloncesto para Hombre - , KG by Kurt Geiger 0178884209, Botas Cortas Hombre - , ZAPATILLA MBT 700901-1035Y GT 17 M AZUL White Green Black , Dune Captains, Botas para Hombre - , Rockport Ledge Hill 2 del Hombres Chukka Boot, - , Vans M ATWOOD (CANVAS) NVY/WHT - Zapatillas de lona hombre Azul - Blau ((Canvas)nvy/Wht) , Timberland Chilmark 6 Inch, Botas Clasicas para Hombre Gris (Forged Iron Barefoot Buffed C64) , Botas de los EE.UU.-Botas western BO-9285-65-E (pie normal), diseño de hombre, color azul y marrón Botas altas para mujer Botas altas para tubo Botas grandes del lugar de trabajo Retro Martin botas Talla grande... - Mizuno Zapatillas de Running Wave Elevation Wos Morado/Plata EU 36.5 (US 6.5) - Mjus 687220-0301-6205 - Botas de Vaquero Mujer - , Botas Zapatos de Mujer Femeninas Otoño Invierno Gamuza Cabeza Redonda Áspero con Tubo bajo Cremallera Lateral... - , Cocorose Zapatos Plegables - Shoreditch Mocasines Mujer - Adidas Kanadia 7 TR GTX W - Botas de Montaña para Mujer, Color Negro/Azul/Blanco - FRAU - Mocasines de Piel para mujer VINACCIO 35 - Adidas Supernova Glide 8 GFX W, Zapatillas de Running para Mujer Negro / Gris (Negbas / Negbas / Gris) , mysChuck Taylor - Zapatillas altas Mujer Muck Boot Arctic Weekend Prints-Quilted Print - Botas de Lluvia Mujer Negro/Púrpura Hirschkogel 3611506, Botas para Mujer Azul (Jeans 274) , Melvin & Hamilton MH15-490 - Botas de Piel Lisa para Mujer Marrón Marrón 37 EU - , Sandales Baotou Medias Zapatillas De Cuero Femenino Señaló Dos Gruesas con Sandalias De Verano Joker Baotou Zapatos De Tacón Alto (Color : Negro, Tamaño : 35) Negro Ecco Soft 5, Sandalias con Punta Abierta para Mujer Negro (Black) WGP Zapatos de cuero primavera Mary Jane zapatos planos zapatos zapatos de abuela femenina plana con zapatos casuales,Negro,36 Negro , GAOLIM Lazy Bones Hembra Solo Zapatos Zapatos Zapatos Cómodos Para Dirigir Ese Otoño E Invierno Calcetines Calzado Plano ,39, Blanco Blanco LGK&FA Señora de la primavera botines botas de cabeza redonda, fondo plano con cremallera botas y cómodos zapatos botas de terciopelo azul,35 35 blue 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
   

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  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
      New Balance 7504 WW847 Grande Fibra Balance sintética Zapatos New para Caminar ed7d4e8 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
      Nordic Walking 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
      3653960
5808319
6170791
6264014
6821470
7831692
10012732
13428213
17587813
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