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.
> 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).
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).