>Real numbers can’t be perfectly represented in hardware simply because there are infinitely many of them. To fit into a designated number of bits, many real numbers have to be rounded. The advantage of posits comes from the way the numbers they represent exactly are distributed along the number line. In the middle of the number line, around 1 and -1, there are more posit representations than floating point. And at the wings, going out to large negative and positive numbers, posit accuracy falls off more gracefully than floating point.
>“It’s a better match for the natural distribution of numbers in a calculation,” says Gustafson. “It’s the right dynamic range, and it’s the right accuracy where you need more accuracy. There’s an awful lot of bit patterns in floating-point arithmetic no one ever uses. And that’s waste.”