The Design And Implementation Of Elementary Functions' Mathematic Calculation Engine In X-DSP

X-DSP is a 64-bit data width multi-core universal digital signal processor researched and developed by China.It has been widely used in high-performance computing,image and video processing,etc.But the development of floating-point elementary function processing in it is still relatively slow.So there is still a large space to improve it.This paper relying on X-DSP project aims at improving the floating-point operation unit in its kernel operation unit.The research final results show that the performance and accuracy of the FPUs have been improved significantly.The main work of the paper includes:1.The design of single precision elementary function approximation by using piecewise polynomial based on Chebyshev interpolation algorithm has been done.Based on Chebyshev interpolation algorithm and analysis of parameter including polynomial terms and search bit width,etc,the cubic polynomial interpolator is chosen to calculate floating-point elementary function by analyzing parameter of polynomial piecewise algorithm.The top module includes three part:pre-processing module,piecewise polynomial module,post-processing module.Based on implementation of booth4 multiplication,leading zero and shift module,/2p multiplication and 4-2 adder,the top hardware implementation is completed.2.The design of half precision elementary function approximation by SIMD structure has been done.Based on Single precision elementary function approximation,we finally use quadratic polynomial interpolator to calculate floating-point elementary function.By designing the leading zero and shift module and the 4-2 adder properly,we complete the implementation of the SIMD structure of half precision elementary function approximation.In this design,the SIMD structure of half precision elementary function approximation area get over the area of as single precision elementary function approximation at most extent.It reduces the total hardware area.3.The thesis of multilevel approximation combined with Taylor expantion has been put forward.In this paper,the algorithm of Multilevel approximation combined with Taylor expantion is bring forward to solve the low accuracy of logarithm function and achieve the accuracy within 1 ulp.When the Xm of input data is all of 0,we choose the Multilevel approximation combined with Taylor expantion to calculate elementary function and other situation is still in traditional approximation.4.Verification and validation and logic synthesis of floating-point elementary function calculator has been done.By means of verification,the accuracy of the final single-precision and half-precision are both within 1ulp.The synthesis results showed that:compared with design in other paper,the latency of critical path is optimized.