High Speed Transcendental Elementary Function Architecture in Support of the Vector Wave Equation (VWE)

摘要

In support of a Very High Speed Integrated Circuit (VHSIC) class processor for computation of a set of equations known as the Vector Wave Equations (VWE), certain elementary functions including sine, cosine, and division are required. These elementary functions are the bottlenecks in the VWE processor. Floating point multipliers and adders comprise the remainder of the pipeline stages in the VWE processor. To speed up the computation of the elementary functions, pipelining within the functions is considered. To compute sine, cosine, and division, the CORDIC algorithm is presented. Another method for computation of sine and cosine is the expansion of the Chebyshev polynomials. The equations for the CORDIC processor are recursive and the resulting hardware is very simple, consisting of three adders, three shifters, and lookup table for some of the coefficients. The shifters replace the multiplies, because in binary, i right shifts is the same as multiplying by 2 to the 8th power. The expansion of the Chebyshev polynomials can be used to compute other trigonometric functions as well as the exponential and logarithmic functions. The expansion of the Chebyshev polynomials can be used as a mathematic coprocessor. From these equations, a pipelined architecture can be realized that results in very fast computation times. The transformation of these equations as a function of x instead of the Chebyshev polynomials produces an architecture which requires less hardware, resulting in even faster computation times.