Complexity measure needs to be able to present smaller values

While benchmarking the CUDA FFT library, I noticed that the minimum speed given by theBigO complexity measure is 0.01NlgN. This is a problem because when I try to benchmark the speed of the CUDA FFT library when including the fft_plan in the timing, it is an order of magnitude faster than not including the plan creation in the timing, and I cannot cleanly present that one is faster than the other.

Results:

-------------------------------------------------------------------
Benchmark                            Time           CPU Iterations
-------------------------------------------------------------------
BM_R2CcuFFTWPlan/131072         454637 ns     454399 ns       1538
BM_R2CcuFFTWPlan/262144         688168 ns     687630 ns        946
BM_R2CcuFFTWPlan/524288         748108 ns     747737 ns        888
BM_R2CcuFFTWPlan/1048576        873088 ns     872584 ns        768
BM_R2CcuFFTWPlan/2097152       1106280 ns    1094416 ns        627
BM_R2CcuFFTWPlan/4194304       1532492 ns    1531535 ns        452
BM_R2CcuFFTWPlan/8388608       2412579 ns    2410158 ns        290
BM_R2CcuFFTWPlan/16777216      4169790 ns    4169792 ns        168
BM_R2CcuFFTWPlan/33554432      7691030 ns    7687242 ns         85
BM_R2CcuFFTWPlan/67108864     14719201 ns   14705280 ns         47
BM_R2CcuFFTWPlan/134217728    34119589 ns   34104306 ns         20
BM_R2CcuFFTWPlan/268435456    67600672 ns   67550141 ns          9
BM_R2CcuFFTWPlan/536870912   135257566 ns  135193994 ns          5
BM_R2CcuFFTWPlan_BigO             0.01 NlgN       0.01 NlgN 
BM_R2CcuFFTWPlan_RMS                 5 %          5 % 
BM_R2CcuFFTNoPlan/131072         28320 ns      28320 ns      24627
BM_R2CcuFFTNoPlan/262144         46122 ns      46122 ns      13658
BM_R2CcuFFTNoPlan/524288        110148 ns     110053 ns       6193
BM_R2CcuFFTNoPlan/1048576       230731 ns     230638 ns       3013
BM_R2CcuFFTNoPlan/2097152       446010 ns     445790 ns       1384
BM_R2CcuFFTNoPlan/4194304       875786 ns     875366 ns        751
BM_R2CcuFFTNoPlan/8388608      1719761 ns    1719761 ns        399
BM_R2CcuFFTNoPlan/16777216     3403089 ns    3403088 ns        206
BM_R2CcuFFTNoPlan/33554432     6780352 ns    6777032 ns         95
BM_R2CcuFFTNoPlan/67108864    13519571 ns   13513831 ns         51
BM_R2CcuFFTNoPlan/134217728   32368661 ns   32344896 ns         22
BM_R2CcuFFTNoPlan/268435456   64653697 ns   64625494 ns         10
BM_R2CcuFFTNoPlan/536870912  130039288 ns  129979247 ns          5
BM_R2CcuFFTNoPlan_BigO            0.01 NlgN       0.01 NlgN 
BM_R2CcuFFTNoPlan_RMS                4 %          4 % 

Code:

#include <benchmark/benchmark.h>
#include <cufft.h>


static void BM_R2CcuFFTWPlan(benchmark::State& state)
{
    int NX = state.range(0);
    int BATCH = 1;

    for (auto _ : state)
    {
        cufftHandle plan;
        cufftComplex *data;
        cudaMalloc((void**)&data, sizeof(cufftComplex)*(NX/2+1)*BATCH);
        if (cudaGetLastError() != cudaSuccess){
            fprintf(stderr, "Cuda error: Failed to allocate\n");
            return;
        }

        if (cufftPlan1d(&plan, NX, CUFFT_R2C, BATCH) != CUFFT_SUCCESS){
            fprintf(stderr, "CUFFT error: Plan creation failed");
            return;
        }

        if (cufftExecR2C(plan, (cufftReal*)data, data) != CUFFT_SUCCESS){
            fprintf(stderr, "CUFFT error: ExecC2C Forward failed");
            return;
        }

        if (cudaDeviceSynchronize() != cudaSuccess){
            fprintf(stderr, "Cuda error: Failed to synchronize\n");
            return;
        }

        cufftDestroy(plan);
        cudaFree(data);
    }
    state.SetComplexityN(state.range(0));
}

static void BM_R2CcuFFTNoPlan(benchmark::State& state)
{
    int NX = state.range(0);
    int BATCH = 1;
    cufftHandle plan;
    cufftComplex *data;
    cudaMalloc((void**)&data, sizeof(cufftComplex)*(NX/2+1)*BATCH);
    if (cudaGetLastError() != cudaSuccess){
        fprintf(stderr, "Cuda error: Failed to allocate\n");
        return;
    }

    if (cufftPlan1d(&plan, NX, CUFFT_R2C, BATCH) != CUFFT_SUCCESS){
        fprintf(stderr, "CUFFT error: Plan creation failed");
        return;
    }


    for (auto _ : state)
    {
        if (cufftExecR2C(plan, (cufftReal*)data, data) != CUFFT_SUCCESS){
            fprintf(stderr, "CUFFT error: ExecC2C Forward failed");
            return;
        }

        benchmark::DoNotOptimize(cudaDeviceSynchronize());

    }
    cufftDestroy(plan);
    cudaFree(data);
    state.SetComplexityN(state.range(0));
}

BENCHMARK(BM_R2CcuFFTWPlan)->RangeMultiplier(2)->Range(131072, 1<<29)->Complexity(benchmark::oNLogN);
BENCHMARK(BM_R2CcuFFTNoPlan)->RangeMultiplier(2)->Range(131072, 1<<29)->Complexity(benchmark::oNLogN);


BENCHMARK_MAIN();