Title: Fast Trigonometric Functions using the RLIBM Approach Show Chinese title

Title: 使用RLIBM方法的快速三角函数

Abstract: This paper describes our experience developing polynomial approximations for trigonometric functions that produce correctly rounded results for multiple representations and rounding modes using the RLIBM approach. A key challenge with trigonometric functions concerns range reduction with "pi", which reduces a given input in the domain of a 32-bit float to a small domain. Any rounding error in the value of "pi" is amplified during range reduction, which can result in wrong results. We describe our experience implementing fast range reduction techniques that maintain a large number of bits of "pi" both with floating-point and integer computations. The resulting implementations for trigonometric functions are fast and produce correctly rounded results for all inputs for multiple representations up to 32-bits with a single implementation. Show Chinese abstract

Abstract: 本文描述了我们使用RLIBM方法开发三角函数的多项式近似的经验，这些近似对于多种表示和舍入模式都能产生正确舍入的结果。 与三角函数相关的一个关键挑战是使用"pi"进行范围缩减，这会将32位浮点数域中的给定输入缩减到一个小域。 "pi"值中的任何舍入误差都会在范围缩减过程中被放大，这可能导致错误的结果。 我们描述了我们在实现快速范围缩减技术方面的经验，这些技术在浮点数和整数计算中都能保持"pi"的大量位数。 对于三角函数的最终实现，在单个实现中能够对多达32位的多种表示的所有输入快速产生正确舍入的结果。