论文标题
二元理性的循环函数的无曲计算
Tableless Calculation of Circular Functions on Dyadic Rationals
论文作者
论文摘要
我想讲一个故事。一个关于美丽的数学关系的故事，阐明了关于三角学经典主题的计算观点。所有故事都需要一种语言，对于这个特定的故事，算法应该做得很好。是什么使语言算法？从我们作为功能编程社区的角度来看，一种算法语言提供了表达功能计算的手段，而没有实施限制。我们开发了一种新算法，用于计算二元函数在二元理性上，以及在方案中用来表达它的语言。我们提供了一种机械衍生的算法，用于计算目标函数的倒置。我们解决了与硬件或软件中提出的算法实现有关的效率和准确性问题。
I would like to tell a story. A story about a beautiful mathematical relationship that elucidates the computational view on the classic subject of trigonometry. All stories need a language, and for this particular story an algorithmic language ought to do well. What makes a language algorithmic? From our perspective as the functional programming community, an algorithmic language provides means to express computation in terms of functions, with no implementation-imposed limitations. We develop a new algorithm for the computation of trigonometric functions on dyadic rationals, together with the language used to express it, in Scheme. We provide a mechanically-derived algorithm for the computation of the inverses of our target functions. We address efficiency and accuracy concerns that pertain to the implementation of the proposed algorithm either in hardware or software.
