Stencil 3D r2 star constant heterogeneous float SkylakeSP_Gold-6148

Stencil Properties

dimension	3D
radius	2
weighting	heterogeneous
kind	star
coefficients	constant
datatype	float
machine	SkylakeSP_Gold-6148
FLOP per LUP	25

Julian Hammer says:

On Skylake, L2 and L3 caches can not be measured and modeled correctly due to missing documentation. This may explain the overprediction with ECM.

Julian Hammer says:

The correct way to measure and predict L2-Memory and L3-Memory traffic is unknown.

Benchmark raw data shown on this page can be found in the according folder of the git repository.

If you have feedback, issues or found errors on this page, please submit an issue on the github page.

Kernel Source Code

float a[M][N][P];
float b[M][N][P];
float c0;
float c1;
float c2;
float c3;
float c4;
float c5;
float c6;
float c7;
float c8;
float c9;
float c10;
float c11;
float c12;

for (long k = 2; k < M - 2; ++k) {
  for (long j = 2; j < N - 2; ++j) {
    for (long i = 2; i < P - 2; ++i) {
      b[k][j][i] = c0 * a[k][j][i] + c1 * a[k][j][i - 1] +
                   c2 * a[k][j][i + 1] + c3 * a[k - 1][j][i] +
                   c4 * a[k + 1][j][i] + c5 * a[k][j - 1][i] +
                   c6 * a[k][j + 1][i] + c7 * a[k][j][i - 2] +
                   c8 * a[k][j][i + 2] + c9 * a[k - 2][j][i] +
                   c10 * a[k + 2][j][i] + c11 * a[k][j - 2][i] +
                   c12 * a[k][j + 2][i];
    }
  }
}

Layer Conditions

1D Layer Condition:

L1: unconditionally fulfilled
L2: unconditionally fulfilled
L3: unconditionally fulfilled

2D Layer Condition:

L1: P <= 4096/5, that is P <= 810
L2: P <= 131072/5, that is P <= 26210
L3: P <= 3670016/5, that is P <= 734000

3D Layer Condition:

L1: 16*N*P + 8*P*(N - 2) + 16*P <= 32768, that is N*P <= 20²
L2: 16*N*P + 8*P*(N - 2) + 16*P <= 1048576, that is N*P <= 170²
L3: 16*N*P + 8*P*(N - 2) + 16*P <= 29360128, that is N*P <= 1020²

Have a look at the kernel source code for dimension naming.

How to test this stencil

Generate this stencil with:

stempel gen -D 3 -r 2 -t "float" -C constant -k star -e --store stencil.c

and generate the compilable benchmark code with:

stempel bench stencil.c -m SkylakeSP_Gold-6148.yml --store

Compiler flags

icc -O3 -fno-alias -xCORE-AVX512 -qopenmp -qopenmp -DLIKWID_PERFMON -Ilikwid-4.3.3/include -Llikwid-4.3.3/lib -Iheaders/dummy.c stencil_compilable.c -o stencil -llikwid

Single Core Grid Scaling

ECM Prediction vs. Performance

Comparison of the measured stencil performance (in cycles per cache line), roofline prediction and the (stacked) contributions of the ECM Performance Model predicted by kerncraft using Layer Conditions to model the cache behavior. The calculated layer conditions shown above correspond to the jumps in the ECM prediction in this plot.

Data Transfers between Caches

Data transfers between the different cache levels and main memory. The shown data for each level contains evicted and loaded data. The measured data is represented by points and the predicted transfer rates by kerncraft by lines.

Multi Core Thread Scaling

Single Core Spatial Blocking

How to replicate this data

Single Core Measurements

Using the generated stencil and kerncraft, all single core performance data shown on this page can be reproduced by:

Layer Condition Data

kerncraft -p ECM -p RooflineIACA -p Benchmark -p LC -P LC -m SkylakeSP_Gold-6148.yml stencil.c -D N $GRID_SIZE -D M $GRID_SIZE -D P $GRID_SIZE -vvv --cores 1 --compiler icc

Cache Simulator Data

kerncraft -p ECM -p RooflineIACA -p Benchmark -p LC -P CS -m SkylakeSP_Gold-6148.yml stencil.c -D N $GRID_SIZE -D M $GRID_SIZE -D P $GRID_SIZE -vvv --cores 1 --compiler icc

Thread Scaling Measurements

The generated benchmark code can be used to reproduce the thread scaling data shown on this page by:

kerncraft -p ECM -p RooflineIACA -p Benchmark -P LC -m SkylakeSP_Gold-6148.yml stencil.c -D N $GRID_SIZE -D M $GRID_SIZE -D P $GRID_SIZE -vvv --cores $CORES --compiler icc

The roofline prediction can be obtained with kerncraft and the generated stencil:

kerncraft -p RooflineIACA -P LC -m SkylakeSP_Gold-6148.yml stencil.c -D N $GRID_SIZE -D M $GRID_SIZE -D P $GRID_SIZE -vvv --cores ${threads} --compiler icc

Spatial Blocking Measurements

Generate benchmark code from the stencil with blocking and compile it as shown before:

stempel bench stencil.c -m SkylakeSP_Gold-6148.yml -b 2 --store

OMP_NUM_THREADS=1 likwid-pin -C S0:0 ./stencil $GRID_SIZE $GRID_SIZE $GRID_SIZE $BLOCKING_M $BLOCKING_N $BLOCKING_P