Rounding percentages

Let's say you're downloading a file and you see this:

How do you know the download actually started? Similarly, if you see this:

Is it actually done? Or did it download 999/1000 bytes and then hang?

I know this is a relatively minor thing, but I find myself frustrated by UIs like this so often that I'm proposing these rules for rounding percentages that are shown to users:

• 0% means exactly zero percent. If the user sees 0%, they can assume that absolutely nothing has happened yet except rendering the progress bar.

• 100% means finished. If the user sees 100%, the process is finished, done, over, complete. They shouldn't have to wait for anything else to happen to start using the thing. Don't show 100% and then call fsync() or something silly.

In between those values, interpolate as normal.

There are a few ways to implement this. With (truncating) integer division, you just have to fix up the 0% case:

>>> def percent(progress, total):
...     ret = 100 * progress // total
...     if ret == 0 and progress > 0:
...         return 1
...     else:
...         return ret
...
>>> percent(0, 1000)
0
>>> percent(1, 1000)
1
>>> percent(999, 1000)
99
>>> percent(1000, 1000)
100

There's also a neat trick with floating point: the default rounding mode is typically ties-to-even. So if we interpolate between $[0.5, 99.5]$ instead of $[0, 100]$, the endpoints will round correctly and everything else will stay within $[1, 99]$:

>>> def percent(progress, total):
...     return round(99 * progress / total + 0.5)
...
>>> percent(0, 1000)
0
>>> percent(1, 1000)
1
>>> percent(999, 1000)
99
>>> percent(1000, 1000)
100

(If your language has bad defaults, you may have to ask for the right rounding mode explicitly.)