//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));
}
public static string __str__(CodeContext /*!*/ context, Complex x)
{
if (x.Real != 0)
{
if (x.Imaginary() < 0 || DoubleOps.IsNegativeZero(x.Imaginary()))
{
return("(" + FormatComplexValue(context, x.Real) + FormatComplexValue(context, x.Imaginary()) + "j)");
}
else /* x.Imaginary() is NaN or >= +0.0 */
{
return("(" + FormatComplexValue(context, x.Real) + "+" + FormatComplexValue(context, x.Imaginary()) + "j)");
}
}
return(FormatComplexValue(context, x.Imaginary()) + "j");
}
public static int __hash__(Complex x)
{
if (x.Imaginary() == 0)
{
return(DoubleOps.__hash__(x.Real));
}
return(x.GetHashCode());
}
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 string __str__(CodeContext /*!*/ context, Complex x)
{
string j = (double.IsInfinity(x.Imaginary()) || double.IsNaN(x.Imaginary())) ? "*j" : "j";
if (x.Real != 0)
{
if (x.Imaginary() < 0 || DoubleOps.IsNegativeZero(x.Imaginary()))
{
return("(" + FormatComplexValue(context, x.Real) + FormatComplexValue(context, x.Imaginary()) + j + ")");
}
else /* x.Imaginary() is NaN or >= +0.0 */
{
return("(" + FormatComplexValue(context, x.Real) + "+" + FormatComplexValue(context, x.Imaginary()) + j + ")");
}
}
return(FormatComplexValue(context, x.Imaginary()) + j);
}
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 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));
}
//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)));
}
//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));
}
public static Complex op_Power(Complex x, Complex y)
{
if (x.IsZero())
{
if (y.Real < 0.0 || y.Imaginary() != 0.0)
{
throw PythonOps.ZeroDivisionError("0.0 to a negative or complex power");
}
return(y.IsZero() ? Complex.One : Complex.Zero);
}
#if FEATURE_NUMERICS
// Special case for higher precision with real integer powers
// TODO: A similar check may get added to CLR 4 upon resolution of Dev10 bug 863171,
// in which case this code should go away.
if (y.Imaginary == 0.0)
{
int power = (int)y.Real;
if (power >= 0 && y.Real == power)
{
Complex res = Complex.One;
if (power == 0)
{
return(res);
}
Complex factor = x;
while (power != 0)
{
if ((power & 1) != 0)
{
res = res * factor;
}
factor = factor * factor;
power >>= 1;
}
return(res);
}
}
#endif
return(x.Pow(y));
}
public static object __new__(
CodeContext context,
PythonType cls,
[DefaultParameterValue(null)] object real,
[DefaultParameterValue(null)] object imag
)
{
Complex real2, imag2;
real2 = imag2 = new Complex();
if (real == null && imag == null && cls == TypeCache.Complex)
{
throw PythonOps.TypeError("argument must be a string or a number");
}
if (imag != null)
{
if (real is string)
{
throw PythonOps.TypeError("complex() can't take second arg if first is a string");
}
if (imag is string)
{
throw PythonOps.TypeError("complex() second arg can't be a string");
}
imag2 = Converter.ConvertToComplex(imag);
}
if (real != null)
{
if (real is string)
{
real2 = LiteralParser.ParseComplex((string)real);
}
else if (real is Extensible <string> )
{
real2 = LiteralParser.ParseComplex(((Extensible <string>)real).Value);
}
else if (real is Complex)
{
if (imag == null && cls == TypeCache.Complex)
{
return(real);
}
else
{
real2 = (Complex)real;
}
}
else
{
real2 = Converter.ConvertToComplex(real);
}
}
double real3 = real2.Real - imag2.Imaginary();
double imag3 = real2.Imaginary() + imag2.Real;
if (cls == TypeCache.Complex)
{
return(new Complex(real3, imag3));
}
else
{
return(cls.CreateInstance(context, real3, imag3));
}
}
public static double Abs(Complex x)
{
double res = x.Abs();
if (double.IsInfinity(res) && !double.IsInfinity(x.Real) && !double.IsInfinity(x.Imaginary()))
{
throw PythonOps.OverflowError("absolute value too large");
}
return(res);
}
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));
}
public static double Getimag(Complex self)
{
return(self.Imaginary());
}
private void WriteComplex(Complex val)
{
_bytes.Add((byte)'x');
WriteDoubleString(val.Real);
WriteDoubleString(val.Imaginary());
}
private void WriteComplex (Complex val) {
_bytes.Add ((byte)'x');
WriteDoubleString (val.Real);
WriteDoubleString (val.Imaginary ());
}
public static double Abs(Complex x)
{
#if CLR2
double res = x.Abs();
#else
// TODO: remove after CodePlex 26224 and MS internal 861649 are resolved
double res = MathUtils.Hypot(x.Real, x.Imaginary);
#endif
if (double.IsInfinity(res) && !double.IsInfinity(x.Real) && !double.IsInfinity(x.Imaginary()))
{
throw PythonOps.OverflowError("absolute value too large");
}
return(res);
}
private static bool IsNaN(Complex num)
{
return(double.IsNaN(num.Real) || double.IsNaN(num.Imaginary()));
}