提高JS中trig计算精度

在JavaScript中，三角函数（如sin、cos、tan等）的计算精度问题通常是由于JavaScript使用IEEE 754标准的64位浮点数表示法导致的。这种表示法在处理非常大或非常小的数字时可能会出现精度损失。

基础概念

JavaScript中的数字是基于IEEE 754标准的64位浮点数，这意味着它们有52位的有效数字精度。对于大多数应用来说，这已经足够了，但在处理三角函数时，特别是当角度值非常大或非常小时，可能会出现精度问题。

类型

JavaScript的三角函数主要有以下几种：

Math.sin(x)：计算x的正弦值。
Math.cos(x)：计算x的余弦值。
Math.tan(x)：计算x的正切值。

应用场景

三角函数广泛应用于图形学、动画、物理模拟等领域。

问题与解决方案

问题

当角度值非常大或非常小时，JavaScript的三角函数可能会出现精度问题。

原因

JavaScript的浮点数表示法在处理极端值时可能会导致精度损失。

解决方案

使用弧度制：JavaScript的三角函数默认使用弧度制，而不是角度制。确保输入值是弧度制可以减少误差。
使用高精度库：可以使用一些高精度计算库，如decimal.js或big.js，来提高计算精度。
角度归一化：将角度值归一化到[-π, π]范围内，可以减少计算误差。

示例代码

以下是一个使用decimal.js库提高三角函数计算精度的示例：

// 引入decimal.js库
const Decimal = require('decimal.js');

// 设置精度
Decimal.set({ precision: 50 });

// 将角度转换为弧度
function toRadians(degrees) {
  return new Decimal(degrees).mul(Math.PI / 180);
}

// 计算sin值
function sin(degrees) {
  const radians = toRadians(degrees);
  return new Decimal(Math.sin(radians.toNumber())).toDecimalPlaces(50);
}

// 示例
console.log(sin(90)); // 输出：1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000