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A new method to implement faster than quadratic convergence for Goldschmidt division using simple logic circuits is presented. While the approximate quotient converges quadratically in conventional Goldschmidt division, the new method achieves nearly cubic convergence. Although division with cubic convergence has been regarded as impractical due to its complexity, the proposed method reduces the logic complexity and the delay by using an approximate squarer with a simple logic implementation and a redundant binary Booth recoder. It is especially effective in a system that already has a radix-8 multiplier. As a result, the effective area for the reciprocal table can be reduced by 25.4%. The proposed method has been verified by SystemC and Verilog models. The final results are confirmed by simulation with both random double precision numbers and an exhaustive suite of 17-bit test vectors.