Proof of Napier''s log and Analysis of Precision

1.Department of Autonomous Driving Technology, Baidu Inc.;2.Department of Technology Management, Baidu Inc.;3.School of Systems Science, Beijing Normal University;4.Shenzhen Institute of Advanced Technology CAS, Shenzhen


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    In the automatic driving systems, logarithm function has been widely used. For example, logarithm function is often used to design loss function in deep learning or convolutional neural network, which serves as the basis for the automatic driving perception system. Therefore, studying the history of invention of logarithm is of great significance to master the concept and application. This paper studies the definition of Napier''s logarithm and his three tables, analyzes two kinds of proof methods of predecessors, and puts forward new proof methods based on the exponential function. Meanwhile, this paper also analyzes Napier''s calculation method. Compared with other alternative methods, the optimization results of Napier''s interval approximation are given. The calculation by MPRF library shows that Napier''s method is more convergent to the true value.

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  • Received:August 17,2023
  • Revised:August 17,2023
  • Adopted:November 21,2023
  • Online: November 21,2023
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