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squareRoot(6) returns 3, squareRoot(12) returns 4; test expects squareRoot(3, 1) = 1.8 (correct: 1.7) #2231
Description
src/algorithms/math/square-root/squareRoot.js stops Newton's iteration when |number - root²| <= 10^-tolerance (line 31). That bounds the error of the square, not of the root. Newton's method approaches √n from above, so the loop stops on an overestimate, and rounding then goes the wrong way.
squareRoot(6); // 3 expected 2 (√6 = 2.449)
squareRoot(12); // 4 expected 3 (√12 = 3.464)
squareRoot(3, 1); // 1.8 expected 1.7 (√3 = 1.732)squareRoot.test.js:30 asserts expect(squareRoot(3, 1)).toBe(1.8), so the test enshrines the bug. For n = 0..3000 and tolerance 0..6 there are 68 wrong results.
Fix: iterate until the root stops decreasing (while (next < root)), then round. Checked on 259,695 inputs against correctly rounded Math.sqrt; the only mismatches are 53 last-digit float effects at tolerance >= 10. This also removes the hang reported in #2187 (squareRoot(65549, 11)). The #2187 change alone still returns 3 and 1.8.
Found during an independent property-based audit of this repo (full report and reproducible harness: https://github.com/devladpopov/algorithm-autopsy/tree/main/autopsy-02).
Activity
fix(squareRoot): bound root step convergence rather than squared resi…
duongynhi000005-oss commentedon Oct 30, 2026
I investigated #2231 and traced the root cause in
src/algorithms/math/square-root/squareRoot.js:Root Cause
In$|x^2 - n| \le 10^{-\text{tolerance}}$ ) rather than the error of the root itself ($|x - \sqrt{n}| \approx \frac{|x^2 - n|}{2\sqrt{n}}$ ). Because Newton-Raphson converges monotonically from above after the first step, terminating when $x^2 - n \le 1$ (for $x \le \sqrt{n + 1}$ :
squareRoot.js:31, the stopping conditionMath.abs(number - (root ** 2)) > requiredDeltabounds the residual of the square (tolerance = 0) stops as soon asnumber = 6, iteration stops at2.607(3instead of2(number = 12, iteration stops at3.550(4instead of3(number = 3, tolerance = 1, iteration stops at1.75(1.8instead of1.7(Proposed Fix
Scale the stopping threshold by
2 * Math.max(1, Math.sqrt(number))(or bound the Newton-Raphson step delta directly) before rounding totolerancedecimal places, and updatesquareRoot.test.js(squareRoot(3, 1) -> 1.7, plussquareRoot(6) -> 2andsquareRoot(12) -> 3).I have prepared a clean branch (
duongynhi000005-oss/javascript-algorithms:fix/issue-2231-squareroot-convergence-criterion) and would be happy to submit a PR!