Mathematics Utils

MathUtils.java

public class MathUtils {
    @SuppressWarnings("ManualMinMaxCalculation")
    public static int isqrt(int s) {
        int x0, x1 = 1;
        int d0, d1 = s;

        do {
            d0 = d1;
            x0 = x1;

            x1 = (x0 + s / x0) / 2;
            d1 = x1 > x0 ? x1 - x0 : x0 - x1;
        } while (d1 < d0);

        return x0 < x1 ? x0 : x1;
    }
}

MathUtilsTest.java

import org.junit.Test;

import static org.junit.Assert.assertTrue;

public class MathUtilsTest {
    @Test
    public void test_isqrt() {
        for (int i = 0; i < 100_000_000; ++i) {
            int r = MathUtils.isqrt(i);

            assertTrue(r * r <= i);
            assertTrue((r + 1L) * (r + 1L) > i);
        }
    }
}