@numio/bigmath/src/sqrt/utils.js

@numio/bigmath is an arbitrary-precision arithmetic library. It can be used for basic operations with decimal numbers (integers and float)

import { isLeftGreaterInner } from "../compare/utils.js";
import { PipeInner } from "../pipe/utils.js";
export const sqrtInner = (value, prec = [1n, 13], max = 100) => {
    if (value[0] < 0n) {
        throw new Error("Invalid input: Cannot take the square root of a negative value.");
    }
    let guess = value;
    for (let i = 0; i < max; i++) {
        const { bi: nextGuess } = new PipeInner()
            .div([value, guess])
            .add([guess])
            .mul([[5n, 1]]);
        const { bi } = new PipeInner().sub([nextGuess, guess]).abs();
        if (isLeftGreaterInner({ left: prec, right: bi })) {
            return [nextGuess, prec[1]];
        }
        guess = nextGuess;
    }
    return [guess, prec[1]];
};