What is the rationale for exponent and mantissa si

问题:

I have a decent understanding of how floating point works, but I want to know how the specific exponent and mantissa sizes were decided upon. Are they optimal in some way? How can optimality be measured for floating point representations (I assume there are several ways)? I imagine these issues are addressed in the official standard, but I don't have access to it.

回答1:

According to this interview with Will Kahan, they were based on the VAX F and G formats of the era.

Of course that doesn't answer the question of how those formats were chosen...

回答2:

For 32-bit IEEE floats, the reasoning is that the precision should be at least as good as 24 bits fixed point.

Why exactly 24 bits, I don't know, but it seems like a reasonable tradeoff.

I suppose having a nice "round" number like that (mantissa + sign = 3 bytes, exponent = 1 byte) can also make implementations more efficient.