### Question:
SpecialMath { public static double[] calculateJacobianEllipticFunctionsValues(double u, double m) { double ai, b, phi, t, twon; double sn, cn, ph, dn; double[] a = new double[9]; double[] c = new double[9]; int i; if (m < 0.0 || m > 1.0 || Double.isNaN(m)) throw new IllegalArgumentException("m should be in <0,1>"); if (m < 1.0e-9) { t = Math.sin(u); b = Math.cos(u); ai = 0.25 * m * (u - t * b); sn = t - ai * b; cn = b + ai * t; ph = u - ai; dn = 1.0 - 0.5 * m * t * t; return new double[] {sn, cn, dn, ph}; } if (m >= 0.9999999999) { ai = 0.25 * (1.0 - m); b = Math.cosh(u); t = Math.tanh(u); phi = 1.0 / b; twon = b * Math.sinh(u); sn = t + ai * (twon - u) / (b * b); ph = 2.0 * Math.atan(Math.exp(u)) - Math.PI / 2 + ai * (twon - u) / b; ai *= t * phi; cn = phi - ai * (twon - u); dn = phi + ai * (twon + u); return new double[] {sn, cn, dn, ph}; } a[0] = 1.0; b = Math.sqrt(1.0 - m); c[0] = Math.sqrt(m); twon = 1.0; i = 0; while (Math.abs(c[i] / a[i]) > getMachineEpsilon()) { if (i > 7) throw new IllegalArgumentException("Jacobian elliptic functions cannot be calculated due to overflow range error"); ai = a[i]; i++; c[i] = (ai - b)/ 2.0; t = Math.sqrt(ai * b); a[i] = (ai + b)/ 2.0; b = t; twon *= 2.0; } phi = twon * a[i] * u; do { t = c[i] * Math.sin(phi) / a[i]; b = phi; phi = (Math.asin(t) + phi) / 2.0; i--; } while (i > 0); sn = Math.sin(phi); t = Math.cos(phi); cn = t; dn = t / Math.cos(phi - b); ph = phi; return new double[] {sn, cn, dn, ph}; }  static double getMachineEpsilon(); static double evaluatePolynomial(double x, double[] coefficients); static double calculateCompleteEllipticIntegralOfTheFirstKind(double m); static double[] calculateJacobianEllipticFunctionsValues(double u, double m); static int factorial(int n); static int combinations(int n, int k); static double complement(double angle); static double[] unwrap(double[] angles); static boolean isOdd(int x); static boolean isEven(int x); static double acosh(final double a); static double asinh(double a);  }### Answer:
@Test public void testCalculateJacobianEllipticFunctions() { double result[] = calculateJacobianEllipticFunctionsValues(0.5, 0.7); assertEquals(4, result.length); assertEquals(0.46729200535903359, result[0], 1e-16); assertEquals(0.8841030379585475, result[1], 1e-16); assertEquals(0.92040574053472368, result[2], 1e-16); assertEquals(0.48622530445618917, result[3], 1e-16); }