High-Speed Numeric Function Generator, Using Piecewise Quadratic Approximations

The CORDIC algorithm is an accurate way to compute the value of a function like sin(x), for a given value of x. However, it is iterative and slow. In this thesis, we show that a wide class of arithmetic functions can be realized on the SRC-6, a reconfigurable computer, using polynomial approximations. The function is realized by partitioning its domain into segments and then approximating the function in each segment by a quadratic polynomial. This is not an iterative approach, and so it is faster than the CORDIC algorithm Two approximation methods are implemented. In one method, non-uniform segments are used. Here, larger segments can be used where the function is close to quadratic, while highly non-quadratic regions require smaller segments. This approach minimizes the number of segments. In the other method, uniform segments are used. Although more segments are needed than in the non-uniform method, the circuit is simpler. We show that accuracies of up to 33 bits are possible. A pipelined circuit was built on the SRC-6 in two’s complement and floating point. We also show an efficient algorithm for segmenting the function, which is faster than previous methods.