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Copy pathsqrt.ts
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59 lines (49 loc) · 1.45 KB
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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;
}