[GrantMoyer]

Without a mantissa, way too much precision is allocated to the near zero range and not enough to the "near infinity" range. Consider that without a mantissa, the second largest float is only half of the largest float. With a 23 bit mantissa, there are 2^23 floats from half the largest to the largest.

[deckar01]

You could change the scaling factor to target any bounds you want. On average the precision is equal. The mantissa just adds linear segments to a logarithmic curve.

[GrantMoyer]

> On average the precision is equal. The mantissa just adds linear segments to a logarithmic curve.

Yes, exactly; the linear regions are needed to more evenly distribute precision, while the average precision remains the same. Alternatively, you can omit the mantissa, but use an exponent base much closer to 1 (perhaps 1 + 2⁻²³).