*can't just manipulate the exponent if you have to deal with infinities / NaNs / subnormals, to be clear

I forgot that you can use ldexp with a mantissa that isn't in [1, 2) :P

I suspect the "why" is because of a combination of supporting large exponents (can't use `x * (1<<n)` if n=100) and edge cases (can't just manipulate the exponent). So it's slow in software, but shouldn't be too bad in silicon.

But why *shouldn't* I be able to write `1.5 << x`, and have it translate to a single instruction which just alters the exponent (+ handles any special cases)? Why do we instead have to write `1.5 * (1 << x)`, and have that translate to three instructions, including a generic floating-point multiply?

That's only a weak proxy for financial cost, but it still suggests that electricity costs >> initial purchase price if you're planning to run these devices 24/7. So power efficiency improvements pay off *very* quickly.

Corroborating this: I read up on the environmental TCO of computers a while ago, and the consensus seems to be that *for servers*, lifetime electricity usage has a much higher environmental cost than the initial manufacturing (and the opposite for consumer devices, due to different usage patterns)

The vaccine is pretty astonishing. Just look at that green line.