A primer on posits
There is a finite way of storing numbers on a computer. As bits can only be in zero or one states, converting the decimal numerical system of zero to nine means needing more digits—more bits—to represent the same number. That is computationally taxing and highly energy-inefficient for non-integer real numbers like fractions and square roots.
As the dominant standard accepted by the Institute of Electrical and Electronics Engineers (IEEE), the floating-point format allocates bits to the significand and exponent components in a predetermined way.
In a trade-off between accuracy and range, approximations are inevitable as computers run out of bit-width and calculations become littered with unusable elements like negative infinity or not-a-number representations.
“It assumes that you want the same accuracy, no matter how big or small the number is. In reality, you don’t really want that—you want more accuracy for the commonly used numbers that are close to one,” Gustafson said.
This insight underlies the introduction of a regime bit in posit representation. Unlike floats, the number of bits per part is not fixed, with priority given to the regime term ahead of the exponent and fractional components.
“The regime bit allows the accuracy to taper automatically. This sliding scale works very elegantly to create the effect of putting more emphasis where you have the common numbers,” explained Gustafson.
In effect, this enables choosing the right balance between dynamic range and accuracy to suit the task at hand. Because the regime field only requires two bits for most computations, posits are well-optimized—assuring that the bits are allocated where they are needed most.
