A Perspective into Squarer Optimization
Katherine Parry · 2019
Artificial Intelligence applications do millions of square calculations, such as within Gradient Descent or Principle Component Analysis (PCA). Any time measured or observed data is analyzed; the error, residual, or a comparison against a norm, it is evaluated using a square operation. Squarers are special purpose multipliers that can be employed when the operands are identical. Most calculations use slower multipliers, even though squarers calculate faster, use less power, and occupy less area. Multiplication is composed of a series of partial products that are accumulated to result in the multiplied product. Multiplier and squarer propagation delay is assessed using the number of partial products, or more their addition. The calculation of partial products can occur in parallel, thus does not significantly tax the propagation delay, but carries from their addition create computational dependencies. A standard 8-bit multiplier requires 56 partial product additions and previous work has reduced a squarer to 22 partial products sums. This paper reviews the previous technology and illustrates further Boolean optimizations that minimize the number of additions to 15 partial products.