Abstract: The elementary function approximation using piecewise quadratic polynomial interpolation requires larger area of the look-up table(LUT) and circuit. To solve the problem, this paper presents an algorithm for elementary function approximation in single-precision floating-point format, which is based on Minimax piecewise cubic polynomial approximation. The algorithm can efficiently achieve the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithm, and trigonometric function in single-precision floating-point format. At the beginning of the algorithm, the range of parameters is narrowed to a specific interval, and this interval is evenly segmented. The Minimax piecewise cubic polynomial approximation is then used in each segment. The errors in corresponding segments are synthetically considered, and the optimal truncated bit width of coefficients is obtained by successive optimization using Remes algorithm, so as to reduce the area of LUT and circuit. Also, the output bit width of multiplier, squarer unit and cubic unit is truncated, in order to reduce the area of circuit. At last, the overall framework of hardware circuit is designed. The analysis and experimental results show that compared with piecewise quadratic polynomial approximation in the same precision, the circuit delay is reduced by 17.25%, the area of LUT is decreased by 53.60% and total area of circuits is reduced by 19.73%.