Fast Fourier Transform (radix2): Takes any function and converts it to an equivalent set of sine waves; applications such as audio, spectral analysis, and image compression (computed at radix 2).

Linear Algebra (linear_alg): Derived from Linpack; useful for understanding balancing forces in structural engineering, converting between reference frames in relativity, solving differential equations, and understanding rotation and fluid flow, for example.

Enhanced Livermore Loops (loops, inner-product): This one kernel contains two dozen real-world functions extracted from programs used at Lawrence Livermore Labs. They are used to test the computational capabilities of parallel hardware and cover areas such as 2D Particle-in-Cell, Tri-diagonal Elimnation and Planckian Distribution.

LU Decomposition (lu): Performs lower-upper matrix decomposition.

Neural Net (nnet): A small neural-net inference engine.

Ray-Tracer (ray): A technique for image generation by tracing light path through pixels in an image plane and simulating the effects of its encounters with virtual objects.

Fourier Coefficients (xp1px): Numerical analysis routine for calculating series or representing a periodic function by a discrete sum of complex exponentials, also known as (x+1)^x, defined on the interval [0+epsilon,2-epsilon].

Example Output

Out of the box, FPMark can be compiled using the GNU make utility, and for convenience, a PERL script computes all of the summary marks from the dozens of component runs. Here is example output running all of the kernels and computing all of the marks. In the example below, each of the kernels is run with three different dataset sizes (small, medium, large) and both single-precision (SP) and double-precision (DP). The final marks reflect different groupings of these kernel results' geometric means. The benchmark was run with XCMD='-c4' which runs the benchmark with four contexts. When compared to a single core run, the last column indicates the scaling factor between four contexts and one.

% make TARGET=macos certify-all XCMD='-c4'

WORKLOAD RESULTS TABLE

                                                   MultiCore   SingleCore           
Workload Name                                       (iter/s)     (iter/s)      Scaling
------------------------------------------------ ----------- ------------ ------------
atan-1M                                               144.93      47.8469       3.0290
atan-1M-sp                                            172.41      59.8802       2.8793
atan-1k                                            188679.25   53475.9358       3.5283
atan-1k-sp                                         217391.30   60975.6098       3.5652
atan-64k                                             3246.75     888.0995       3.6558
atan-64k-sp                                          3759.40     983.2842       3.8233
blacks-big-n5000v200                                   16.34       4.9652       3.2909
blacks-big-n5000v200-sp                                21.55       6.5703       3.2802
blacks-mid-n1000v40                                   400.00     123.4568       3.2400
blacks-mid-n1000v40-sp                                526.32     161.2903       3.2632
blacks-sml-n500v20                                   1666.67     500.0000       3.3333
blacks-sml-n500v20-sp                                2000.00     625.0000       3.2000
horner-big-100k                                       598.80     169.2047       3.5389
horner-big-100k-sp                                    606.06     169.2047       3.5818
horner-mid-10k                                       6097.56    1686.3406       3.6159
horner-mid-10k-sp                                    6097.56    1686.3406       3.6159
horner-sml-1k                                       58139.53   16129.0323       3.6047
horner-sml-1k-sp                                    58139.53   16181.2298       3.5930
inner-product-big-100k                                 79.68      42.3729       1.8805
inner-product-big-100k-sp                             138.89      58.9971       2.3542
inner-product-mid-10k                                1606.43     571.4286       2.8112
inner-product-mid-10k-sp                             2259.89     720.7207       3.1356
inner-product-sml-1k                                23255.81    7407.4074       3.1395
inner-product-sml-1k-sp                             31250.00    8333.3333       3.7500
linear_alg-big-1000x1000                                1.90       1.2509       1.5198
linear_alg-big-1000x1000-sp                             4.90       2.5694       1.9060
linear_alg-mid-100x100                                980.39     292.3977       3.3529
linear_alg-mid-100x100-sp                            1515.15     420.1681       3.6061
linear_alg-sml-50x50                                 6410.26    1811.5942       3.5385
linear_alg-sml-50x50-sp                              7812.50    2222.2222       3.5156
loops-all-big-100k                                      0.93       0.4135       2.2547
loops-all-big-100k-sp                                   1.12       0.4770       2.3535
loops-all-mid-10k                                      19.67       5.4951       3.5795
loops-all-mid-10k-sp                                   22.48       6.3540       3.5382
loops-all-tiny                                       9803.92    2793.2961       3.5098
loops-all-tiny-sp                                   10638.30    3048.7805       3.4894
lu-big-2000x2_50                                       20.16       6.4433       3.1290
lu-big-2000x2_50-sp                                    20.24       6.4893       3.1194
lu-mid-200x2_50                                      1760.56     476.8717       3.6919
lu-mid-200x2_50-sp                                   1754.39     479.6163       3.6579
lu-sml-20x2_50                                      20242.92    5488.4742       3.6883
lu-sml-20x2_50-sp                                   20366.60    5515.7198       3.6925
nnet-data1-sp                                       24390.24    6802.7211       3.5854
nnet_data1                                          18867.92    5347.5936       3.5283
nnet_test                                              33.22      10.6270       3.1262
nnet_test-sp                                           33.90      10.8696       3.1186
radix2-big-64k                                       1669.45     450.8566       3.7028
radix2-mid-8k                                       25773.20    6988.1202       3.6881
radix2-sml-2k                                      187969.92   51867.2199       3.6241
ray-1024x768at24s                                       0.11       0.0283       3.7279
ray-320x240at8s                                         2.71       0.8635       3.1384
ray-64x48at4s                                         150.60      41.9111       3.5934
xp1px-big-c10000n2000                                   2.01       0.6384       3.1537
xp1px-mid-c1000n200                                   188.68      62.5000       3.0189
xp1px-sml-c100n20                                   24390.24    6666.6667       3.6585

MARK RESULTS TABLE

Mark Name                                        MultiCore SingleCore    Scaling
----------------------------------------------- ---------- ---------- ----------
FPMark                                            66007.92   20419.76       3.23
FPv1.0. DP Small Dataset                          14723.08    4183.84       3.52
FPv1.1. DP Medium Dataset                           458.69     137.21       3.34
FPv1.2. DP Big Dataset                               16.43       5.84       2.81
FPv1.3. SP Small Dataset                          20614.55    5814.44       3.55
FPv1.4. SP Medium Dataset                           696.27     201.17       3.46
FPv1.5. SP Big Dataset                               32.06      11.77       2.72
FPv1.D. DP Mark                                     533.97     165.64       3.22
FPv1.S. SP Mark                                     886.56     273.21       3.25
MicroFPMark                                       20614.55    5814.44       3.55