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Binary Search Volume

There are many things I have made that I am quite proud of, and many plans in my head that could be great but I will never have time for.
This is the most perfect of all of them. It is the only one I can see no fault with or improvement for, and believe should be everywhere.

Premise

Volume is annoying. Either my volume keys' step is large, and I have to use the cursor to fine-tune, or their step is small which can cost up to an entire second if I have to travel a large distance after switching audio sources and/or playing something at a different time of day than before. Sometimes a device is too loud on level 1 and I'm out of luck entirely and have to suffer. Sometimes 22 is a touch too quiet, but 23 a touch too loud.

I am a software engineer; obviously binary search is the first thing that came to mind when I got frustrated enough to decide to roll my own volume key solution. How does one do so without blowing out one's eardrums or requiring 'resetting' after a misclick or when a small adjustment is needed, though?

The Rules

My first attempt worked quite well, and has been my daily driver (that's a horrible term in regards to volume keys but I suppose it is accurate) for three years now with no changes. Its implementation is pretty simple:
  • Move in steps of 5%
  • If the opposite direction of the last one used is pressed, halve the step size before applying it
  • If the same direction is pressed thrice in a row, floor/ceil (in the direction of travel) to a multiple of 5 and set the step size back to 5%
  • If a while has passed since the last press, immediately floor/ceil in the direction of travel to a multiple of 5 and set the step size back to 5%

Effects

5% is around double what I would prefer if I had fixed steps (2%). This results in ~double the travel speed when moving very large distances. Once close, one seamlessly enters binary search to find the perfect volume.
  • Overshooting one's preferred volume is surprisingly noticeable (especially since one is approaching from an error on the other side)
    • I tweak my volume much less nowadays after selecting a good spot for the current ambient noise (all of my music is ReplayGain'd)
  • No additional thought is required - just press up if it's too quiet and down if it's too loud, repeat until one is satisfied
  • Doubling the step size is nearly free; a multiple of 2.5 can be reached by overshooting by one step and going back one
    • Reaching a 2.5 multiple is more efficient with binary search volume in all cases with a 10% movement or greater

Efficiency

Binary search is great and all, but it needs to still be usable. How is the performance in actual usage?
My gut instinct was that fine-tuning for small movements takes around 3-5 presses which, after graphing, appears to be correct. Here is a near worst-case example of reaching some volume with nicer numbers. It is bad because of the distance to travel and alignment of the starting value (causing the first press, which ceils, to be nearly ineffectual).
Start: 55
Target: 73
Base Step: 8 (eqv. to fixed step of 4)
55 up
56 up
64 up
72 up
80 down
76 down
74 down
73
Steps: 7
Steps with fixed step of 2: 9
Steps with fixed step of 3: 6
Steps with fixed step of 4: 4, to 71


Scale 73-55=18 by your preferred step divided by 4 for an idea of how large of a movement that is. For me it is 11.25%, a reasonable movement for the same audio source and device at a different time of day.
Binary search volume reaches a better approximation than the fixed step of 4 by chance in four steps, matches its error in six, and reaches the target exactly in seven.

Here is a graph (open to play with variables) of:
  • Green: the number of steps to reach the best approximation of a X% travel with fixed steps
  • Black: the number of steps to match/beat that approximation with binary search volume - after which point one could binary search for more precision if desired


As you can see, the tradeoff is not too bad at low distances and in binary search volume's favor at larger ones.

Try It

For Windows, here is an AutoHotkey V2 script that implements this.

Unfortunately my Linux implementation is melded with my horrible status bar code that uses undefined and explicitly illegal Bash behavior, and input hooking on Linux is not very portable anyway. Here is a Bash script so you can try it in a terminal with your arrow keys, though (only requires Bash 4 or later, ps, grep, and tr).

Mac people. . . can you even make macros?

Conclusion

Now if only my thermostat would stop doing whatever the hell it wants.