Evaluating a Num Linearly Spaced Intervals

We are frequently confronted with evaluating a mathematical expression at Num 
linearly spaced equidistant intervals.

Consider the following example;

     float start_time, end_time, y;
     int n, num=100;

     ...  /* start_time and end_time set to values by user  */

     for(n=0; n<=num; n++)
        t = start_time + (end_time - start_time) *n / num;  /* ****** */
        y = calculation(t); /* evaluate some kind of expression */
        printf("%f\t%f\n", y, t);   

Note how a simple index is used to painlessly determine num+1 equally spaced 
points.  In this case, 100 intervals; 101 points.

It is important that you understand the line marked thus /******/.

Also, note that the order is important.  In the above, (end_time - 
start_time) is a float.  Thus, (end_time - start_time) * n is a float (as a 
float times an int is a float).  Thus, (end_time - start_time) * n / num is a 
float and all is well.

The following might look the same, but it isn't and will not work as desired.

     t = start_time + n/num* (end_time - start_time); 

In this case n/num (an integer divided by an integer) is zero for n=0..99.  
Thus, t will always be start_time + 0.0, which isn't too useful.

However, the following will work.

     t = start_time + ((float) n)/num* (end_time - start_time); 
Note that n is type cast as a float.  A float divided by an int is a float.  
Again, all is well.