学步园

//超越方程求解
function f1(x)
{
	return 2 * x * x * Math.pow(Math.sin(x), 7) + 
	       3 * Math.sqrt(x) * Math.cos(x) - Math.exp(x)/5;
}

//多解情况
function f2(x)
{
	return Math.sin(2 * Math.PI * x);
}

//在两个x之间折半寻找精确解
function getAnswer(x0, x1, y0, y1, func, precision)
{
	var mid, val;
	while(true)
	{
		mid = (x0 + x1) / 2;
		val = func(mid);
		if (Math.abs(val) < precision) break;
		if (y0 * val < 0)
		{
			x1 = mid;
			y1 = val;
		}
		else
		{
			x0 = mid;
			y0 = val;
		}
	}
	return {x:mid, y:val};
}

//在指定范围内求解---计算[start, end]间的所有解
function solve(start, end, func)
{
	var rst = [];
	var lastx = start + 1e-5;
	var y0, y1, y2;
	y0 = func(lastx);
	y1 = y0;
		
	for(var x = start; x <= end + 0.001; x+= 0.001)
	{
		y2 = func(x);
		if (y2 * y1 < 0)
		{
			 	rst.push(getAnswer(lastx, x, y1, y2, func, 1e-8));
		}		
		y1 = y2;
		lastx = x;
	}
	
	return rst;
}

//测试两个方程的解
var rst = solve(2, 3, f1);
console.log(rst); 

var rst = solve(0, 5, f2);
console.log(rst.length);
console.log(rst);