# Radix sort slower than Quick sort?

I would like to demonstrate that sometime radix-sort is better than quick-sort. In this example I am using the program below:

``#include <stdio.h> #include <stdlib.h> #include <assert.h> #include <string.h> #include <time.h> #include <math.h>  int cmpfunc (const void * a, const void * b) {    return ( *(int*)a - *(int*)b ); }  void bin_radix_sort(int *a, const long long size, int digits) {     assert(digits % 2 == 0);      long long count[2];     int *b = malloc(size * sizeof(int));     int exp = 0;      while(digits--) {         // Count elements         count[0] = count[1] = 0;         for (int i = 0; i < size; i++)             count[(a[i] >> exp) & 0x01]++;          // Cumulative sum         count[1] += count[0];          // Build output array         for (int i = size - 1; i >= 0; i--)             b[--count[(a[i] >> exp) & 0x01]] = a[i];          exp++;         int *p = a; a = b; b = p;     };      free(b); }  struct timespec start;  void tic() {     timespec_get(&start, TIME_UTC); }  double toc() {     struct timespec stop;     timespec_get(&stop, TIME_UTC);     return stop.tv_sec - start.tv_sec + (         stop.tv_nsec - start.tv_nsec     ) * 1e-9; }  int main(void) {     const long long n = 1024 * 1024 * 50;     printf("Init memory (%lld MB)...\n", n / 1024 / 1024 * sizeof(int));      int *data = calloc(n, sizeof(int));      printf("Sorting n = %lld data elements...\n", n);      long long O;     tic();     O = n * log(n);     qsort(data, n, sizeof(data[0]), cmpfunc);     printf("%lld %lf s\n", O, toc());      int d = 6;     tic();     O = d * (n + 2);     bin_radix_sort(data, n, d);     printf("%lld %lf s\n", O, toc()); } ``

It performs as follow:

``$$gcc bench.c -lm$$ ./a.out  Init memory (200 MB)... Sorting n = 52428800 data elements... 931920169 1.858300 s 314572812 1.541998 s ``

I know that Quick Sort will perform in O(n log n) while Radix Sort will be in O(d (n + r)) ~= O(6 * n). For `n = 52428800`, `log(n) = 17`. I am then expecting Radix Sort to be 3 times faster than Quick Sort…

This is not what I observe.

What am I missing?