Bad attempt at solution per tstanisl at https://stackoverflow.com/a/68959383/5660198

not_solution.c

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

int compare (const void * a, const void * b)
{
  if (*(double*)a > *(double*)b) return 1;
  else if (*(double*)a < *(double*)b) return -1;
  else return 0;
}

double grand_f_0_1(){
  static FILE * fp = NULL;
  uint64_t bits;

  if(fp == NULL) fp = fopen("/dev/urandom", "r");
  fread(&bits, sizeof(bits), 1, fp);
  return (double)bits * 5.421010862427522170037264004349e-020; // https://stackoverflow.com/a/26867455
}

int main()
{
  const int n = 10;
  double values[n];
  double diffs[n];
  double shift;
  int i, j;
  
  for(j=0; j<10000; j++) {
  
    values[0] = 0.; // https://stackoverflow.com/a/68959383/5660198
    for(i=1; i<n; i++) values[i] = grand_f_0_1();
    qsort(values, n, sizeof(double), compare);
    shift = grand_f_0_1();
    for(i=0; i<n; i++) {
      values[i] += shift;
      if(values[i] >= 1.) values[i] -= 1.;
    }
    qsort(values, n, sizeof(double), compare);
    
    for(i=0; i<(n-1); i++) diffs[i] = values[i+1] - values[i];
    diffs[n-1] = 1. + values[0] - values[n-1];

    for(i=0; i<n; i++) printf("%.5f%s", diffs[i], i<(n-1)?"\t":"\n");

  }
  
  return(0);
}