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/* ****************************************************************************
*
* Copyright (c) Microsoft Corporation.
*
* This source code is subject to terms and conditions of the Apache License, Version 2.0. A
* copy of the license can be found in the License.html file at the root of this distribution. If
* you cannot locate the Apache License, Version 2.0, please send an email to
* [email protected]. By using this source code in any fashion, you are agreeing to be bound
* by the terms of the Apache License, Version 2.0.
*
* You must not remove this notice, or any other, from this software.
*
*
* ***************************************************************************/
using System;
using System.Numerics;
using IronPython.Runtime;
using IronPython.Runtime.Operations;
using Microsoft.Scripting.Utils;
[assembly: PythonModule("cmath", typeof(IronPython.Modules.ComplexMath))]
namespace IronPython.Modules {
public class ComplexMath {
public const double pi = Math.PI;
public const double e = Math.E;
public const string __doc__ = "Provides access to functions for operating on complex numbers";
//cos(a+ ib) = cosa*coshb - i*sina*sinhb
public static Complex cos(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.Cos(num.Real) * Math.Cosh(num.Imaginary());
imag = -(Math.Sin(num.Real) * Math.Sinh(num.Imaginary()));
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);
}
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);
}
//cosh(a+ ib) = cosha*cosb + i*sinha*sinb
public static Complex cosh(object x) {
Complex num = GetComplexNum(x);
// magnitude is always NaN
if (double.IsNaN(num.Real)) {
return new Complex(double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(num.Imaginary())) {
throw PythonOps.ValueError("math domain error");
}
double real, imag;
real = Math.Cosh(num.Real) * Math.Cos(num.Imaginary());
imag = Math.Sinh(num.Real) * Math.Sin(num.Imaginary());
return new Complex(real, imag);
}
//sin(a+ ib) = sinha*cosb + i*cosha*sinb
public static Complex sinh(object x) {
Complex num = GetComplexNum(x);
// magnitude is always NaN
if (double.IsNaN(num.Real)) {
return new Complex(double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(num.Imaginary())) {
throw PythonOps.ValueError("math domain error");
}
double real, imag;
real = Math.Sinh(num.Real) * Math.Cos(num.Imaginary());
imag = Math.Cosh(num.Real) * Math.Sin(num.Imaginary());
return new Complex(real, imag);
}
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);
}
//acos(x) = -i*ln( x + i*(1-x*x)^1/2)
public static Complex acos(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.Acos(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);
}
//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);
}
//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));
}
//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));
}
//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));
}
//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;
}
//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);
}
//log b to base a = ln b / ln a
public static Complex log(object x, object logBase) {
return log(x) / log(logBase);
}
public static Complex log10(object x) {
return log(x, 10);
}
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 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);
}
public static double phase(object x) {
Complex num = GetComplexNum(x);
return GetAngle(num);
}
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);
}
public static Complex rect(double r, double theta) {
// magnitude is always 0
if (r == 0.0) {
return Complex.Zero;
}
// angle is always 0
if (theta == 0.0) {
return new Complex(r, 0.0);
}
// magnitude is always NaN
if (double.IsNaN(r)) {
return new Complex(double.NaN, double.NaN);
}
// angle is always NaN
if (double.IsNaN(theta)) {
return new Complex(double.IsInfinity(r) ? double.PositiveInfinity : double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(theta)) {
throw PythonOps.ValueError("math domain error");
}
return new Complex(r * Math.Cos(theta), r * Math.Sin(theta));
}
public static bool isinf(object x) {
Complex num = GetComplexNum(x);
return IsInfinity(num);
}
public static bool isnan(object x) {
Complex num = GetComplexNum(x);
return IsNaN(num);
}
#region Helpers
private static bool IsInfinity(Complex num) {
return double.IsInfinity(num.Real) || double.IsInfinity(num.Imaginary());
}
private static bool IsNaN(Complex num) {
return double.IsNaN(num.Real) || double.IsNaN(num.Imaginary());
}
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);
}
private static Complex GetComplexNum(object num) {
Complex complexNum;
if (num != null) {
complexNum = Converter.ConvertToComplex(num);
} else {
throw new NullReferenceException("The input was null");
}
return complexNum;
}
#endregion
}
}