import { divide } from "./divide";

import add from "./add";

import multiply from "./multiply";

/**

* Function to compute square root using Newton's method

* @param num - number as string

* @param precision - precision for the result (default 20)

* @returns square root of the number

*/

export default function sqrt(num: string, precision: number = 20): string {

if (typeof num !== "string") {

throw new Error("Input must be a string");

}

// Remove leading/trailing whitespace

num = num.trim();

// Check for negative numbers

if (num.startsWith("-")) {

throw new Error("Cannot compute square root of negative number");

}

// Handle zero

if (num === "0" || num === "0.0" || num === "+0") {

return "0";

}

// Handle one

if (num === "1" || num === "1.0" || num === "+1") {

return "1";

}

// Newton's method: x_{n+1} = (x_n + num/x_n) / 2

let x = num; // Initial guess

let prevX = "0";

// Iterate until convergence

for (let i = 0; i < precision * 2; i++) {

prevX = x;

// x = (x + num/x) / 2

const quotient = divide(num, x, precision + 10);

const sum = add(x, quotient);

x = divide(sum, "2", precision + 10);

// Check for convergence (simplified)

if (x === prevX) {

break;

}

}

// Round to desired precision

const dotIndex = x.indexOf(".");

if (dotIndex !== -1 && x.length > dotIndex + precision + 1) {

x = x.substring(0, dotIndex + precision + 1);

}

return x;

}