The accessing time of traversal a array via a constant length

问题

I want to measure the speed of the cache (I asked a question about that), so I write this code:

#include<cstdio>
#include<ctime>
#include<windows.h>
const int mod = 100000007;
volatile int f[100000007];
volatile int *p;
int main()
{
    FILE *f1;
    f1=fopen("CacheTest.txt","w");
    for(int l=1;l<=100000;)
    {
        clock_t st,ed;
        st=clock();
        int now=0;
        for(int i=0;i<mod;i++)
        {
            now+=l;//note:mod is a prime and that will traversal the array
            if (now>=mod) now-=mod;
        }
        ed=clock();
        double extime=(double)(ed-st)/CLOCKS_PER_SEC;
        st=clock();
        now=0;
        for(int i=0;i<mod;i++)
        {
            p=&f[now];
            *p=1;
            now+=l;
            if (now>=mod) now-=mod;
        }
        ed=clock();
        double cost=(double)(ed-st)/CLOCKS_PER_SEC;
        fprintf(f1,"length %d costs %f seconds access time:%f\n",l,cost,cost-extime);
        printf("length %d costs %f seconds access time:%f\n",l,cost,cost-extime);
        if (l<50) l++;
        else if (l<100) l+=2;
        else if (l<1000) l+=20;
        else if (l<10000) l+=200;
        else if (l<100000) l+=2000;
        else l+=20000;
    }
}

The result is below:

length 1 costs 0.994000 seconds access time:0.153000
length 2 costs 0.651000 seconds access time:-0.048000
length 3 costs 1.034000 seconds access time:0.414000
length 4 costs 1.151000 seconds access time:0.018000
length 5 costs 1.221000 seconds access time:0.086000
length 6 costs 1.313000 seconds access time:0.179000
length 7 costs 1.475000 seconds access time:0.442000
length 8 costs 1.584000 seconds access time:0.437000
length 9 costs 1.700000 seconds access time:0.567000
length 10 costs 1.672000 seconds access time:0.665000
length 11 costs 1.578000 seconds access time:0.573000
length 12 costs 2.166000 seconds access time:1.280000
length 13 costs 2.070000 seconds access time:0.988000
length 14 costs 2.430000 seconds access time:1.402000
length 15 costs 2.564000 seconds access time:1.428000
length 16 costs 2.651000 seconds access time:1.519000
length 17 costs 2.721000 seconds access time:1.654000
length 18 costs 2.648000 seconds access time:1.518000
length 19 costs 2.775000 seconds access time:1.638000
length 20 costs 2.757000 seconds access time:1.636000
length 21 costs 2.816000 seconds access time:1.684000
length 22 costs 2.842000 seconds access time:1.706000
length 23 costs 2.856000 seconds access time:1.751000
length 24 costs 2.702000 seconds access time:1.568000
length 25 costs 2.624000 seconds access time:1.618000
length 26 costs 2.912000 seconds access time:1.777000
length 27 costs 2.617000 seconds access time:1.468000
length 28 costs 2.910000 seconds access time:1.778000
length 29 costs 2.779000 seconds access time:1.649000
length 30 costs 2.803000 seconds access time:1.727000
length 31 costs 2.596000 seconds access time:1.465000
length 32 costs 2.068000 seconds access time:1.188000
length 33 costs 2.012000 seconds access time:1.294000
length 34 costs 3.258000 seconds access time:2.381000
length 35 costs 3.538000 seconds access time:2.406000
length 36 costs 3.619000 seconds access time:2.556000
length 37 costs 3.847000 seconds access time:2.717000
length 38 costs 3.958000 seconds access time:2.827000
length 39 costs 3.910000 seconds access time:2.841000
length 40 costs 3.722000 seconds access time:2.592000
length 41 costs 4.095000 seconds access time:2.960000
length 42 costs 3.440000 seconds access time:2.420000
length 43 costs 4.217000 seconds access time:3.085000
length 44 costs 4.413000 seconds access time:3.457000
length 45 costs 4.637000 seconds access time:3.507000
length 46 costs 4.248000 seconds access time:3.115000
length 47 costs 4.924000 seconds access time:3.856000
length 48 costs 5.072000 seconds access time:3.942000
length 49 costs 4.619000 seconds access time:3.615000
length 50 costs 5.025000 seconds access time:4.136000
length 52 costs 5.196000 seconds access time:4.059000
length 54 costs 4.937000 seconds access time:3.806000
length 56 costs 5.264000 seconds access time:4.132000
length 58 costs 5.137000 seconds access time:4.004000
length 60 costs 5.113000 seconds access time:4.107000
length 62 costs 4.665000 seconds access time:3.537000
length 64 costs 5.030000 seconds access time:3.900000
length 66 costs 4.969000 seconds access time:4.016000
length 68 costs 5.201000 seconds access time:4.096000
length 70 costs 5.066000 seconds access time:3.931000
...
for the length 70~10000 , the access time is around 4s.

First few lines the access time is very low, I don't know why.

And then the program goes stable and the access time is around 0.4s, I think the reason is that most access hit the L1 level cache.

With the larger length, the time becomes around 1.5s. Maybe L1 cache not works but L2 cache do.

Then the time goes to 4s, maybe no cache hit at all?

The results above seem to meet my expectation generally.

BUT! Something unexpected happened and I am astonished.

When the length beyond 20000, the access time becomes:

length 20000 costs 1.828000 seconds access time:1.453000
length 22000 costs 1.867000 seconds access time:1.492000
length 24000 costs 1.959000 seconds access time:1.584000
length 26000 costs 1.977000 seconds access time:1.603000
length 28000 costs 1.987000 seconds access time:1.613000
length 30000 costs 2.045000 seconds access time:1.669000
length 32000 costs 1.951000 seconds access time:1.575000
length 34000 costs 1.980000 seconds access time:1.611000
length 36000 costs 1.988000 seconds access time:1.613000
length 38000 costs 1.993000 seconds access time:1.619000
length 40000 costs 1.850000 seconds access time:1.473000
length 42000 costs 2.010000 seconds access time:1.634000
length 44000 costs 1.991000 seconds access time:1.615000
length 46000 costs 1.977000 seconds access time:1.601000
length 48000 costs 1.977000 seconds access time:1.601000
length 50000 costs 1.927000 seconds access time:1.552000
length 52000 costs 1.907000 seconds access time:1.531000
length 54000 costs 2.013000 seconds access time:1.637000
length 56000 costs 2.014000 seconds access time:1.639000
length 58000 costs 2.011000 seconds access time:1.640000
length 60000 costs 1.978000 seconds access time:1.606000
length 62000 costs 2.046000 seconds access time:1.672000
length 64000 costs 2.076000 seconds access time:1.700000
length 66000 costs 2.068000 seconds access time:1.693000
length 68000 costs 2.014000 seconds access time:1.639000
length 70000 costs 2.123000 seconds access time:1.748000
length 72000 costs 2.032000 seconds access time:1.646000
length 74000 costs 2.015000 seconds access time:1.638000
length 76000 costs 2.023000 seconds access time:1.646000
length 78000 costs 1.873000 seconds access time:1.497000
length 80000 costs 1.655000 seconds access time:1.278000

Can anybody explain why these strange things happened? I'm stuck now and have no idea about that.

Thanks in advance.