Digital signal processing circuits, systems, and methods implementing approximations for a reciprocal

A method of determining an approximate reciprocal of a value of x, comprising:

• identifying a bounded region within which x falls, wherein the bounded region is one of a plurality of bounded regions and wherein each bounded region has a corresponding slope value and corresponds to a different value of an integer n and is bounded on a lower side by a first endpoint bn and on a higher side by a second endpoint bn+1;
• determining the approximate reciprocal by determining an offset from a reciprocal value at one of the first and second endpoints by a measure equal to a distance of the value of x from the one of the first and second endpoints times the slope value corresponding to the bounded region within which x is identified as falling;
• wherein the value of x has a base b;
• wherein each bounded region has a corresponding slope value equal to 0.5/22n;
• wherein the value of x is represented in a binary representation having a most significant digit and one or more lesser significant bits;
• and
• wherein the step of identifying the bounded region identifies the bounded region in response to the most significant digit of the binary representation of the value of x.