Abstract: Exponential and logarithmic functions are important transcendental functions in floating-point computation, widely used in various application fields. Modern processors exhibit a trend of increasing vector register width with each generation. To further enhance the utilization of vector units by upper-layer applications, researching optimization methods for vector exponential and logarithmic functions holds significant scientific value and practical importance. Addressing the performance bottlenecks of existing vector function implementations, this paper has  designed and implemented optimization methods for exponential and logarithmic functions tailored for vector units. These methods include vector lookup table optimization based on hardware acceleration instructions, branch optimization, and precision-performance trade-off optimization. Experiments on simulators demonstrate that the optimized vector exponential and logarithmic functions meet industry-standard high precision and outperform the current best open-source implementations, achieving a speedup ratio of over 1.44. Real-world application tests further show that applications can achieve efficient vectorization with the support of the optimized vector functions, resulting in an average performance improvement of 2.53 times compared to the original scalar implementations.

Key words: exponential functions, logarithm functions, vectorization, table-lookup optimization, hardware acceleration instructions