//atan(x) = i/2*ln( (i+x)/ (i-x))
public static Complex atan(object x)
{
Complex num = GetComplexNum(x);
Complex i = Complex.ImaginaryOne;
return(i * 0.5 * (log(i + num) - log(i - num)));
}
//asin(x) = -i*ln( i*x + (1-x*x)^1/2)
public static Complex asin(object x)
{
Complex num = GetComplexNum(x);
double a = MathUtils.Hypot(num.Real + 1.0, num.Imaginary());
double b = MathUtils.Hypot(num.Real - 1.0, num.Imaginary());
double c = 0.5 * (a + b);
double real = Math.Asin(0.5 * (a - b));
double imag = Math.Log(c + Math.Sqrt(c + 1) * Math.Sqrt(c - 1));
return(new Complex(real, num.Imaginary() >= 0 ? imag : -imag));
}
private static double GetAngle(Complex num)
{
if (IsNaN(num))
{
return(double.NaN);
}
if (double.IsPositiveInfinity(num.Real))
{
if (double.IsPositiveInfinity(num.Imaginary()))
{
return(Math.PI * 0.25);
}
else if (double.IsNegativeInfinity(num.Imaginary()))
{
return(Math.PI * -0.25);
}
else
{
return(0.0);
}
}
if (double.IsNegativeInfinity(num.Real))
{
if (double.IsPositiveInfinity(num.Imaginary()))
{
return(Math.PI * 0.75);
}
else if (double.IsNegativeInfinity(num.Imaginary()))
{
return(Math.PI * -0.75);
}
else
{
return(DoubleOps.Sign(num.Imaginary()) * Math.PI);
}
}
if (num.Real == 0.0)
{
if (num.Imaginary() != 0.0)
{
return(Math.PI * 0.5 * Math.Sign(num.Imaginary()));
}
else
{
return((DoubleOps.IsPositiveZero(num.Real) ? 0.0 : Math.PI) * DoubleOps.Sign(num.Imaginary()));
}
}
return(Math.Atan2(num.Imaginary(), num.Real));
}
public static PythonTuple polar(object x)
{
Complex num = GetComplexNum(x);
double[] res = new double[] { num.Abs(), GetAngle(num) };
// check for overflow
if (double.IsInfinity(res[0]) && !IsInfinity(num))
{
throw PythonOps.OverflowError("math range error");
}
return(new PythonTuple(res));
}
//asin(x) = ln( x + (x*x +1)^1/2)
public static Complex asinh(object x)
{
Complex num = GetComplexNum(x);
if (num.IsZero())
{
// preserve -0.0 imag component
return(MathUtils.MakeImaginary(num.Imaginary()));
}
Complex recip = 1 / num;
return(log(num) + log(1 + sqrt(recip * recip + 1)));
}
//ln(re^iO) = ln(r) + iO
public static Complex log(object x)
{
Complex num = GetComplexNum(x);
if (num.IsZero())
{
throw PythonOps.ValueError("math domain error");
}
double r, theta;
r = num.Abs();
theta = GetAngle(num);
return(new Complex(Math.Log(r), theta));
}
public static Complex tanh(object x)
{
Complex num = GetComplexNum(x);
// limit as num.Real -> Infinity
if (double.IsPositiveInfinity(num.Real))
{
return(Complex.One);
}
// limit as num.Real -> -Infinity
if (double.IsNegativeInfinity(num.Real))
{
return(new Complex(-1.0, 0.0));
}
return(sinh(num) / cosh(num));
}
public static Complex tan(object x)
{
Complex num = GetComplexNum(x);
// limit as num.Imaginary() -> Infinity
if (double.IsPositiveInfinity(num.Imaginary()))
{
return(Complex.ImaginaryOne);
}
// limit as num.Imaginary() -> -Infinity
if (double.IsNegativeInfinity(num.Imaginary()))
{
return(new Complex(0.0, -1.0));
}
return(sin(num) / cos(num));
}
public static Complex sqrt(object x)
{
Complex num = GetComplexNum(x);
if (num.Imaginary() == 0.0)
{
if (num.Real >= 0.0)
{
return(MathUtils.MakeReal(Math.Sqrt(num.Real)));
}
else
{
return(MathUtils.MakeImaginary(Math.Sqrt(-num.Real)));
}
}
double c = num.Abs() + num.Real;
double real = Math.Sqrt(0.5 * c);
double imag = num.Imaginary() / Math.Sqrt(2 * c);
return(new Complex(real, imag));
}
//sin(a+ ib) = sina*coshb + i*cosa*sinhb
public static Complex sin(object x)
{
Complex num = GetComplexNum(x);
// magnitude is always NaN
if (double.IsNaN(num.Imaginary()))
{
return(new Complex(double.NaN, double.NaN));
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(num.Real))
{
throw PythonOps.ValueError("math domain error");
}
double real, imag;
real = Math.Sin(num.Real) * Math.Cosh(num.Imaginary());
imag = Math.Cos(num.Real) * Math.Sinh(num.Imaginary());
return(new Complex(real, imag));
}
private static bool IsNaN(Complex num)
{
return(double.IsNaN(num.Real) || double.IsNaN(num.Imaginary()));
}
public static bool isnan(object x)
{
Complex num = GetComplexNum(x);
return(IsNaN(num));
}
public static bool isinf(object x)
{
Complex num = GetComplexNum(x);
return(IsInfinity(num));
}
public static double phase(object x)
{
Complex num = GetComplexNum(x);
return(GetAngle(num));
}
private static double GetAngle(Complex num) {
if (IsNaN(num)) {
return double.NaN;
}
if (double.IsPositiveInfinity(num.Real)) {
if (double.IsPositiveInfinity(num.Imaginary())) {
return Math.PI * 0.25;
} else if (double.IsNegativeInfinity(num.Imaginary())) {
return Math.PI * -0.25;
} else {
return 0.0;
}
}
if (double.IsNegativeInfinity(num.Real)) {
if (double.IsPositiveInfinity(num.Imaginary())) {
return Math.PI * 0.75;
} else if (double.IsNegativeInfinity(num.Imaginary())) {
return Math.PI * -0.75;
} else {
return DoubleOps.Sign(num.Imaginary()) * Math.PI;
}
}
if (num.Real == 0.0) {
if (num.Imaginary() != 0.0) {
return Math.PI * 0.5 * Math.Sign(num.Imaginary());
} else {
return (DoubleOps.IsPositiveZero(num.Real) ? 0.0 : Math.PI) * DoubleOps.Sign(num.Imaginary());
}
}
return Math.Atan2(num.Imaginary(), num.Real);
}
//atanh(x) = (ln(1 +x) - ln(1-x))/2
public static Complex atanh(object x)
{
Complex num = GetComplexNum(x);
return((log(1 + num) - log(1 - num)) * 0.5);
}
//acosh(x) = ln( x + (x*x -1)^1/2)
public static Complex acosh(object x)
{
Complex num = GetComplexNum(x);
return(log(num + sqrt(num + 1) * sqrt(num - 1)));
}
public static Complex exp(object x)
{
Complex num = GetComplexNum(x);
// degenerate case: num is real
if (num.Imaginary() == 0.0)
{
if (double.IsPositiveInfinity(num.Real))
{
return(new Complex(double.PositiveInfinity, 0.0));
}
double expt = Math.Exp(num.Real);
if (double.IsInfinity(expt))
{
throw PythonOps.OverflowError("math range error");
}
return(new Complex(expt, 0.0));
}
// magnitude is always 0
if (double.IsNegativeInfinity(num.Real))
{
return(Complex.Zero);
}
// magnitude is always NaN
if (double.IsNaN(num.Real))
{
return(new Complex(double.NaN, double.NaN));
}
// angle is always NaN
if (double.IsNaN(num.Imaginary()))
{
return(new Complex(double.IsInfinity(num.Real) ? double.PositiveInfinity : double.NaN, double.NaN));
}
// can't take sin or cos of +/-infinity
if (double.IsInfinity(num.Imaginary()))
{
throw PythonOps.ValueError("math domain error");
}
// use c*(e^x) = (sign(c))*e^(x+log(abs(c))) for fewer overflows in corner cases
double real;
double cosImag = Math.Cos(num.Imaginary());
if (cosImag > 0.0)
{
real = Math.Exp(num.Real + Math.Log(cosImag));
}
else if (cosImag < 0.0)
{
real = -Math.Exp(num.Real + Math.Log(-cosImag));
}
else
{
real = 0.0;
}
// use c*(e^x) = (sign(c))*e^(x+log(abs(c))) for fewer overflows in corner cases
double imag;
double sinImag = Math.Sin(num.Imaginary());
if (sinImag > 0.0)
{
imag = Math.Exp(num.Real + Math.Log(sinImag));
}
else if (sinImag < 0.0)
{
imag = -Math.Exp(num.Real + Math.Log(-sinImag));
}
else
{
imag = 0.0;
}
// check for overflow
if ((double.IsInfinity(real) || double.IsInfinity(imag)) && !double.IsInfinity(num.Real))
{
throw PythonOps.OverflowError("math range error");
}
return(new Complex(real, imag));
}
private static bool IsNaN(Complex num) {
return double.IsNaN(num.Real) || double.IsNaN(num.Imaginary());
}
