[mota7]

'half' is ambiguous here: They lose 1 bit of expressiveness for the mantissa, and 1 bit in the exponent, giving an efficiency loss of 2 bits from 32 == ~3%.

So there's very little loss in using single-precision floating point, and a lot of gains in smoothly handling larger numbers that arise from addition et al.

edit: I'm half wrong. The bit in mantissa isn't wasted, the only bit that's wasted in the sign bit in the exponent, so the efficiency loss is ~1.5%

[defaultcompany]

It agrees with my intuition that one bit lost would reduce the values by half. I probably don't understand what is meant by efficiency loss but my point is that a different (theoretical non floating point) encoding would be able to represent twice as many values within [-1,1] for the same 32 bits. For some applications that seems like it would be a win.