re = Math.atan(x / (y * Math.sqrt(0.5 * (apx / (r + xp1) + apx / (s + xm1)))));
                    }
                }

                if (a <= A_CROSSOVER) {
                    double am1;
                    if (x < 1) {
                        am1 = 0.5 * (yy / (r + xp1) + yy / (s - xm1));
                    } else {
                        am1 = 0.5 * (yy / (r + xp1) + (s + xm1));
                    }
                    im = Math.log1p(am1 + Math.sqrt(am1 * (a + 1)));
                } else {
                    im = Math.log(a + Math.sqrt(a * a - 1));
                }
            } else {
                // Hull et al: Exception handling code from figure 4
                if (y <= (EPSILON * Math.abs(xm1))) {
                    if (x < 1) {
                        re = Math.asin(x);