I don't know the answer to your question... but instead I converted your example to the interpolation algorithm I tend to use. It seems to me that my way looks smoother, but that might be my brain lying to me. I didn't feel like setting up a double blind experiment to test 
.
Also... it looks a lot smoother if you use vsync, at least on my computer. If you're on Linux, uncomment the al_wait_for_vsync line. If you're on Windows, uncomment al_set_new_display_option(ALLEGRO_VSYNC...) line. The fact that's its different is probably an Allegro bug.
Here's your code (with added functions to make it run. I also slowed down the ball a bit.):
1#include <allegro5/allegro.h>
2#include <allegro5/allegro_primitives.h>
3#include <allegro5/allegro_font.h>
4
5int main()
6{
7 al_init();
8 al_init_primitives_addon();
9 al_init_font_addon();
10 auto font = al_create_builtin_font();
11
12 //al_set_new_display_option(ALLEGRO_VSYNC, ALLEGRO_REQUIRE, 1); // For Windows
13 auto d = al_create_display(800, 600);
14
15 // alpha is used for interpolation
16 // counter_old_time is to do with displaying the fps
17 double alpha = 0, counter_old_time = 0;
18 double accumulator = 0, delta_time = 0, current_time = 0, previous_time = 0;
19 unsigned frame_counter = 0, current_fps = 0; // also used for displaying the fps
20 const unsigned physics_rate = 40, max_step_count = 5;
21
22 // information about the magic ball (position and velocity)
23 int old_pos_x = 100, new_pos_x = 100, render_pos_x = 100, velocity_x = 10;
24
25 const double
26 step_duration = 1.0 / 40.0,
27 accumulator_max = step_duration * 5;
28
29 previous_time = al_get_time();
30
31 while(true) {
32 current_time = al_get_time();
33 delta_time = current_time - previous_time;
34 previous_time = current_time;
35 accumulator += delta_time;
36
37 if(accumulator > accumulator_max) {
38 accumulator = accumulator_max;
39 }
40
41 while(accumulator >= step_duration) {
42 if(new_pos_x > al_get_display_width(d) - 70) velocity_x = -10;
43 else if(new_pos_x < 70) velocity_x = 10;
44
45 old_pos_x = new_pos_x;
46 new_pos_x += velocity_x;
47 accumulator -= step_duration;
48 }
49
50 alpha = accumulator / static_cast<double>(step_duration);
51 render_pos_x = old_pos_x + (new_pos_x - old_pos_x) * alpha;
52
53 al_clear_to_color(al_map_rgb(20, 20, 40)); // clears the screen
54 al_draw_textf(font, al_map_rgb(255, 255, 255), 20, 20, 0, "current_fps: %i", current_fps); // print fps
55 al_draw_filled_circle(render_pos_x, 400, 15, al_map_rgb(255, 255, 255)); // draw circle
56 // I've added this to test how the program will behave when rendering takes
57 // considerably longer than updating the game.
58 //al_wait_for_vsync(); // For Linux
59 al_rest(0.008);
60 al_flip_display(); // swaps the buffers
61
62 frame_counter++;
63
64 if(al_get_time() - counter_old_time >= 1) {
65 current_fps = frame_counter;
66 frame_counter = 0;
67 counter_old_time = al_get_time();
68 }
69 }
70}
And here's mine:
1#include <allegro5/allegro.h>
2#include <allegro5/allegro_primitives.h>
3#include <allegro5/allegro_font.h>
4
5int main()
6{
7 al_init();
8 al_init_primitives_addon();
9 al_init_font_addon();
10 auto font = al_create_builtin_font();
11
12 //al_set_new_display_option(ALLEGRO_VSYNC, ALLEGRO_REQUIRE, 1); // For Windows
13 auto d = al_create_display(800, 600);
14
15 double counter_old_time = 0;
16 unsigned frame_counter = 0, current_fps = 0; // also used for displaying the fps
17 const unsigned physics_rate = 40, max_step_count = 5;
18 auto dt = 1.0 / physics_rate;
19
20 auto q = al_create_event_queue();
21 auto t = al_create_timer(dt);
22 al_register_event_source(q, al_get_timer_event_source(t));
23 al_start_timer(t);
24
25 // information about the magic ball (position and velocity)
26 int old_pos_x = 100, new_pos_x = 100, render_pos_x = 100, velocity_x = 10;
27
28 float game_time = 0;
29 float offset = al_get_time();
30
31 while(true) {
32 int steps = 0;
33 ALLEGRO_EVENT e;
34
35 while(al_get_next_event(q, &e)) {
36 if(e.type == ALLEGRO_EVENT_TIMER) {
37 game_time = e.timer.count * dt;
38
39 if(new_pos_x > al_get_display_width(d) - 70) velocity_x = -10;
40 else if(new_pos_x < 70) velocity_x = 10;
41
42 old_pos_x = new_pos_x;
43 new_pos_x += velocity_x;
44
45 steps++;
46
47 if(steps >= max_step_count)
48 break;
49 }
50 }
51
52 float alpha = (al_get_time() - offset - game_time) / dt;
53 render_pos_x = old_pos_x + (new_pos_x - old_pos_x) * alpha;
54
55 al_clear_to_color(al_map_rgb(20, 20, 40)); // clears the screen
56 al_draw_textf(font, al_map_rgb(255, 255, 255), 20, 20, 0, "current_fps: %i", current_fps); // print fps
57 al_draw_filled_circle(render_pos_x, 400, 15, al_map_rgb(255, 255, 255)); // draw circle
58 // I've added this to test how the program will behave when rendering takes
59 // considerably longer than updating the game.
60 //al_wait_for_vsync(); // For Linux
61 al_rest(0.008);
62 al_flip_display(); // swaps the buffers
63
64 frame_counter++;
65
66 if(al_get_time() - counter_old_time >= 1) {
67 current_fps = frame_counter;
68 frame_counter = 0;
69 counter_old_time = al_get_time();
70 }
71 }
72}
]]>
