/* ****************************************************************************
*
* Copyright (c) Microsoft Corporation.
*
* This source code is subject to terms and conditions of the Microsoft Public License. A
* copy of the license can be found in the License.html file at the root of this distribution. If
* you cannot locate the Microsoft Public License, please send an email to
* dlr@microsoft.com. By using this source code in any fashion, you are agreeing to be bound
* by the terms of the Microsoft Public License.
*
* You must not remove this notice, or any other, from this software.
*
*
* ***************************************************************************/
using System;
using Microsoft.Scripting.Utils;
#if !CLR2
using BigIntSystem.Numerics.BigInteger;
#endif
namespace Microsoft.Scripting.Math{
/// <summary>
/// Implementation of the complex number data type.
/// </summary>
[Serializable]
public struct Complex64 {
public static readonly Complex64 Zero = new Complex64(0.0, 0.0);
public static readonly Complex64 One = new Complex64(1.0, 0.0);
public static readonly Complex64 ImaginaryOne = new Complex64(0.0, 1.0);
private readonly double real, imag;
public static Complex64 MakeImaginary(double imag) {
return new Complex64(0.0, imag);
}
public static Complex64 MakeReal(double real) {
return new Complex64(real, 0.0);
}
public static Complex64 Make(double real, double imag) {
return new Complex64(real, imag);
}
public Complex64(double real)
: this(real, 0.0) {
}
public Complex64(double real, double imag) {
this.real = real;
this.imag = imag;
}
public bool IsZero {
get {
return real == 0.0 && imag == 0.0;
}
}
public double Real {
get {
return real;
}
}
public double Imag {
get {
return imag;
}
}
public Complex64 Conjugate() {
return new Complex64(real, -imag);
}
public override string ToString() {
if (real == 0.0) return imag.ToString(System.Globalization.CultureInfo.InvariantCulture.NumberFormat) + "j";
else if (imag < 0.0) return string.Format(System.Globalization.CultureInfo.InvariantCulture.NumberFormat, "({0}{1}j)", real, imag);
else return string.Format(System.Globalization.CultureInfo.InvariantCulture.NumberFormat, "({0}+{1}j)", real, imag);
}
public static implicit operator Complex64(bool b) {
return b ? One : Zero;
}
public static implicit operator Complex64(int i) {
return MakeReal(i);
}
[CLSCompliant(false)]
public static implicit operator Complex64(uint i) {
return MakeReal(i);
}
public static implicit operator Complex64(short i) {
return MakeReal(i);
}
[CLSCompliant(false)]
public static implicit operator Complex64(ushort i) {
return MakeReal(i);
}
public static implicit operator Complex64(long l) {
return MakeReal(l);
}
[CLSCompliant(false)]
public static implicit operator Complex64(ulong i) {
return MakeReal(i);
}
[CLSCompliant(false)]
public static implicit operator Complex64(sbyte i) {
return MakeReal(i);
}
public static implicit operator Complex64(byte i) {
return MakeReal(i);
}
public static implicit operator Complex64(float f) {
return MakeReal(f);
}
public static implicit operator Complex64(double d) {
return MakeReal(d);
}
[System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Design", "CA1065:DoNotRaiseExceptionsInUnexpectedLocations")] // TODO: fix
public static implicit operator Complex64(BigInteger i) {
ContractUtils.RequiresNotNull(i, "i");
// throws an overflow exception if we can't handle the value.
return MakeReal((double)i);
}
#if !CLR2
public static implicit operator Complex64(BigInt i) {
// throws an overflow exception if we can't handle the value.
return MakeReal((double)i);
}
#endif
public static bool operator ==(Complex64 x, Complex64 y) {
return x.real == y.real && x.imag == y.imag;
}
public static bool operator !=(Complex64 x, Complex64 y) {
return x.real != y.real || x.imag != y.imag;
}
public static Complex64 Add(Complex64 x, Complex64 y) {
return x + y;
}
public static Complex64 operator +(Complex64 x, Complex64 y) {
return new Complex64(x.real + y.real, x.imag + y.imag);
}
public static Complex64 Subtract(Complex64 x, Complex64 y) {
return x - y;
}
public static Complex64 operator -(Complex64 x, Complex64 y) {
return new Complex64(x.real - y.real, x.imag - y.imag);
}
public static Complex64 Multiply(Complex64 x, Complex64 y) {
return x * y;
}
public static Complex64 operator *(Complex64 x, Complex64 y) {
return new Complex64(x.real * y.real - x.imag * y.imag, x.real * y.imag + x.imag * y.real);
}
public static Complex64 Divide(Complex64 x, Complex64 y) {
return x / y;
}
public static Complex64 operator /(Complex64 a, Complex64 b) {
if (b.IsZero) {
throw new DivideByZeroException("complex division by zero");
}
double real, imag, den, r;
if (System.Math.Abs(b.real) >= System.Math.Abs(b.imag)) {
r = b.imag / b.real;
den = b.real + r * b.imag;
real = (a.real + a.imag * r) / den;
imag = (a.imag - a.real * r) / den;
} else {
r = b.real / b.imag;
den = b.imag + r * b.real;
real = (a.real * r + a.imag) / den;
imag = (a.imag * r - a.real) / den;
}
return new Complex64(real, imag);
}
public static Complex64 Negate(Complex64 x) {
return -x;
}
public static Complex64 operator -(Complex64 x) {
return new Complex64(-x.real, -x.imag);
}
public static Complex64 Plus(Complex64 x) {
return +x;
}
public static Complex64 operator +(Complex64 x) {
return x;
}
[Obsolete("Deprecated - consider using MS.Scripting.Utils.MathUtils.Hypot")]
public static double Hypot(double x, double y) {
return MathUtils.Hypot(x, y);
}
public double Abs() {
return MathUtils.Hypot(real, imag);
}
public Complex64 Power(Complex64 y) {
double c = y.real;
double d = y.imag;
int power = (int)c;
if (power == c && power >= 0 && d == .0) {
Complex64 result = One;
if (power == 0) return result;
Complex64 factor = this;
while (power != 0) {
if ((power & 1) != 0) {
result = result * factor;
}
factor = factor * factor;
power >>= 1;
}
return result;
} else if (IsZero) {
return y.IsZero ? One : Zero;
} else {
double a = real;
double b = imag;
double powers = a * a + b * b;
double arg = System.Math.Atan2(b, a);
double mul = System.Math.Pow(powers, c / 2) * System.Math.Exp(-d * arg);
double common = c * arg + .5 * d * System.Math.Log(powers);
return new Complex64(mul * System.Math.Cos(common), mul * System.Math.Sin(common));
}
}
public override int GetHashCode() {
// The Object.GetHashCode function needs to be consistent with the Object.Equals function.
// Languages that build on top of this may have a more flexible equality function and
// so may not be able to use this hash function directly.
// For example, Python allows that c=Complex64(1.5, 0), f = 1.5f, c==f.
// so then the hash(f) == hash(c). Since the python (and other languages) can define an arbitrary
// hash(float) function, the language may need to define a matching hash(complex) function for
// the cases where the float and complex numbers overlap.
return (int)real + (int)imag * 1000003;
}
public override bool Equals(object obj) {
if (!(obj is Complex64)) return false;
return this == ((Complex64)obj);
}
}
}
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