The Alogrithm Research And Design For Low Error Elementary Function Computation

Elementary function computation is essential in the fields of signal processing,image processing and scientific computing,and lies in the critical path.With the rapid development of integrated circuit technology,elementary function is implemented with hardware on the chip to improve the overall performance.The research in this paper,based on X-DSP project,aims to enhance algorithms and implementations for FPUs in its cores.1.Propose pipelined range reduction based truncated multiplier.Our pipelined range reduction is achieved by the bit-width optimization of truncated multiplier,especially 2 /? truncated multiplier,and it completes the range reduction for arbitrary input.According to performance analysis,our pipelined range reduction reduces the area and delay overhead significantly,and guarantees the accuracy within 1ulp.2.Propose TCORDIC algorithm to compute floating-point sine/cosine function.TCORDIC algorithm combines fixed-point CORDIC and Taylor expansion.Taylor expansion is used to compute sine/cosine function with the input close to 0 or ?/ 2and CORDIC algorithm completes the computation for other inputs.Besides,low latency CORDIC algorithm adopts sign prediction,compressive iteration and parallel iteration techniques.Finally,the calculation boundary N in TCORDIC algorithm is evaluated to achieve the balance between area and delay.As shown in performance analysis,compared with various methods to compute floating-point sine/cosine function,TCORDIC algorithm achieves low area and delay,and the accuracy within 1ulp.3.Propose unified TCORDIC algorithm to compute floating-point elementary function,including sine,cosine,arctan,sinh,cosh,arctanh,square root,exponential,logarithm functions.After analyzing the relative error of floating-point elementary function computation based CORDIC algorithm,the accuracy problem of computing floating-point elementary function based fixed CORDIC algorithm is found out.Unified TCORDIC algorithm combines fixed-point CORDIC algorithm and Taylor expansion.When the output of fixed-CORDIC algorithm is close to 0,the elementary function computation is completed by Taylor expansion.And,the other inputs are computed by fixed-CORDIC algorithm.As the synthesized results based on 45 nm standard cells shows,the area of the additional Taylor expansion path occupies 7.33% of TCORDIC algorithm,and a sheer volume of random inputs verified the accuracy goal of 1ulp.