Will it float? The glory and shame of floating-point audio

In which we discuss the embarrassing topic of floating-point audio,
and the benefits and criticisms that will come your way if you dare to try it.
16-bit PCM is one of the most common formats in digital audio.
But it's getting old; do you remember CDs? Time to consider something else beyond integer and fixed-point.
Let your fellow programmers mock. You will rock.