> However a point can be made that if you even need to consider such behavior, you should probably be using something more precise than your current number representation.
I would agree with this. If you're in a place where you actually need to care about how accurately you're representing numbers with IEEE 754, you almost certainly should look at a precise numeric data type instead and should set aside IEEE 754 entirely. It's less common that we think that we need both the range of values that a float or double represent and need those values represented precisely enough to endure aggregation.
It would be nice to be able to give fewer digits to the exponent in a double, though. How often have I really needed 1e308 or 1e-324? How often have I even needed 1e38 or 1e-45? Then again, I don't remember how much precision we'd get back with more digits in the mantissa.
Precision is a really funny thing, too. Remember, pi to ~37 decimal places is precise enough to calculate the circumference of a circle of atoms (~10^-10 m) the size of the observable universe (~10^26 m), as at that point the primary source of imprecision is the fact that you used atoms to construct your circle.
> It would be nice to be able to give fewer digits to the exponent in a double, though. How often have I really needed 1e308 or 1e-324? How often have I even needed 1e38 or 1e-45? Then again, I don't remember how much precision we'd get back with more digits in the mantissa.
I'm not sure that helps. Going from 10^308 to 10^38, approximately, takes 3 bits from the 11-bit exponent and adds 3 bits to the 52-bit mantissa. This gives you _almost_ one extra decimal digit in your precision. It's not worth it, and if it is you certainly need a more special-purpose number type.
I would agree with this. If you're in a place where you actually need to care about how accurately you're representing numbers with IEEE 754, you almost certainly should look at a precise numeric data type instead and should set aside IEEE 754 entirely. It's less common that we think that we need both the range of values that a float or double represent and need those values represented precisely enough to endure aggregation.
It would be nice to be able to give fewer digits to the exponent in a double, though. How often have I really needed 1e308 or 1e-324? How often have I even needed 1e38 or 1e-45? Then again, I don't remember how much precision we'd get back with more digits in the mantissa.
Precision is a really funny thing, too. Remember, pi to ~37 decimal places is precise enough to calculate the circumference of a circle of atoms (~10^-10 m) the size of the observable universe (~10^26 m), as at that point the primary source of imprecision is the fact that you used atoms to construct your circle.