What is the rationale for exponent and mantissa sizes in IEEE floating point standards?

Question

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? H

Answer 1

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.

Answer 2

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...