High-speed numeric function generator using quadratic approximations
Butler, Jon T.
Loomis, Herschel H.
Frenzen, Christopher L.
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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.
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Knudstrup, Timothy A. (Monterey, California. Naval Postgraduate School, 2007-12);Numeric Function Generators (NFGs) have allowed computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise linear (or quadratic) approximations ...
Frenzen, Christopher L.; Macaria, Njuguna; Sasao, Tsutomu; Butler, Jon T. (2011-05);We give an efficient algorithm for partitioning the domain of a numeric function f into segments. The function f is realized as a polynomial in each segment, and a look-up table stores the coefficients of the polynomial...
Nagayama, Shinobu; Sasao, Tsutomu; Butler, Jon T. (2007-12);Numerical function generators (NPGs) realize arithmetic functions, such as ex, sin p(piex), and the square root of x, in hardware. They are used in applications where high-speed is essential, such as digital signal or ...