Research And Design Of Elementary Functions Calculator

With the rapid development of the integrated circuit, the performance requirement for the processor is also growing. In terms of numerical calculation, we hope the hardware can run fast and compute accurately with a small size and low power consumption. The floating-point data computation has become the most basic requirement to the processor. In addition to complete simple calculation like floating-point addition, subtraction and multiplication, we also need the processor to complete the computation of the elementary functions, such as the reciprocal, square root, inverse square root, exponential, logarithmic and so on.This study focus on the low-cost design for computing the elementary functions in single-precision floating point field, which is suit for the mobile devices. According to the study of hardware implementation of the elementary functions, piecewise polynomial approximation based on look-up table is currently the best method for elementary functions with single-precision data. It can not only balance the area and speed well, but also can implement most elementary functions’computation.Then, by using of the theory of constrained parameters in adjacent interval, the number of parameters need to be stored in the look-up table can be reduced with only a small extra error and the performance of error can still be better with the solution of MILP(Mixed integer linear programming). The traditional calculation of quadratic polynomial need one squarer, two multiplications and three additions. But this design only need two MAC(multiply-and-accumulate) operations by the deformation of quadratic polynomial, and can complete the calculation by reusing the MAC architecture. The design also truncates the Wallace tree for the reduction of hardware logic. In the result, the area can be reduced by40%for the function computation including look-up table and polynomial calculation. The design also adds the pre-processing and post-processing part for floating point data calculation. The entire design is synthesized with SMIC0.18technology.300MHz clock frequency and 0.22mm2area are the results.