Floating-Point Accumulation and Sum of Products

Summing many independent terms or products is a very common operation. Scalar product, matrix-vector and matrix-matrix products, tensor products, and linear digital filters are based upon sums of products. Other applications, such as numerical integration or Monte Carlo simulations, also involve sums of many independent terms. For all these applications, this chapter describes a family of floating-point accumulators that accept one floating-point summand at each cycle and compute the sum with arbitrary accuracy.