1/6 = 1/2 * 1/3

#include <stdio.h>
#include <stdlib.h>

typedef unsigned int u32;

double canonical_div(u32 interations) {
    double rv = 0;
    for (u32 x=1; x<interations; x++) {
        rv += 1.0/x;
    }
    return rv;
}

#define M (2U * 1024*1024*1024)

double fast_div(u32 interations) {
    double rv = 0;

    double *prev = malloc(M);

    for (u32 x=1; x<interations; x++) {
        prev[x] = 1.0/x;
        rv += prev[x];
        x++;
        prev[x] = 0.5 * prev[x>>1];
        rv += prev[x];
    }

    return rv;
}

int main() {
    printf("%.12f\n", canonical_div(M/8));
    //~ printf("%.12f\n", fast_div(M/8));

    return 0;
}