al_Complex.hpp

#ifndef INCLUDE_AL_COMPLEX_HPP
#define INCLUDE_AL_COMPLEX_HPP
 
/*  Allocore --
  Multimedia / virtual environment application class library
 
  Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.
  Copyright (C) 2012. The Regents of the University of California.
  All rights reserved.
 
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
 
    Redistributions of source code must retain the above copyright notice,
    this list of conditions and the following disclaimer.
 
    Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
 
    Neither the name of the University of California nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
 
 
  File description:
  Complex number class
 
  File author(s):
  Lance Putnam, 2006, putnam.lance@gmail.com
*/
 
#include <cmath>
#include "al/math/al_Constants.hpp"
 
namespace al {
 
template <class T>
class Complex;
template <class T>
class Polar;
 
typedef Polar<float> Polarf;
typedef Polar<double> Polard;
typedef Complex<float> Complexf;
typedef Complex<double> Complexd;
 
template <class T>
class Polar {
 public:
  union {
    struct {
      T m;  
      T p;  
    };
    T elems[2];
  };
 
  Polar(const T& phs = T(0)) : m(T(1)), p(phs) {}
 
  Polar(const T& mag, const T& phs) : m(mag), p(phs) {}
 
  Polar(const Complex<T>& v) { *this = v; }
 
  Polar& operator=(const Complex<T>& v) {
    m = v.norm();
    p = v.arg();
    return *this;
  }
};
 
template <class T>
class Complex {
 public:
  typedef Complex<T> C;
 
  union {
    struct {
      T r;  
      T i;  
    };
    T elems[2];
  };
 
  Complex(const Complex& v) : r(v.r), i(v.i) {}
  Complex(const Polar<T>& v) { *this = v; }
  Complex(const T& r = T(0), const T& i = T(0)) : r(r), i(i) {}
  Complex(const T& m, const T& p, int fromPolar) { (*this) = Polar<T>(m, p); }
 
  C& arg(T v) {
    return fromPolar(norm(), v);
  }  
  C& norm(T v) {
    return fromPolar(v, arg());
  }  
 
  C& fromPolar(T phase) {
    r = ::cos(phase);
    i = ::sin(phase);
    return *this;
  }  
  C& fromPolar(T m, T p) {
    return set(Polar<T>(m, p));
  }  
 
  C& set(T vr, T vi) {
    r = vr;
    i = vi;
    return *this;
  }
  C& set(const Polar<T>& p) { return *this = p; }
 
  T& operator[](int i) { return elems[i]; }
  const T& operator[](int i) const { return elems[i]; }
 
  // Accessors compatible with std::complex
  T& real() { return r; }
  const T& real() const { return r; }
  T& imag() { return i; }
  const T& imag() const { return i; }
 
  bool operator==(const C& v) const {
    return (r == v.r) && (i == v.i);
  }  
  bool operator==(const T& v) const {
    return (r == v) && (i == T(0));
  }  
  bool operator!=(const C& v) const {
    return (r != v.r) || (i != v.i);
  }  
  bool operator>(const C& v) const {
    return normSqr() > v.normSqr();
  }  
  bool operator<(const C& c) const {
    return normSqr() < c.normSqr();
  }  
 
  C& operator=(const Polar<T>& v) {
    r = v.m * ::cos(v.p);
    i = v.m * ::sin(v.p);
    return *this;
  }
  C& operator=(const C& v) {
    r = v.r;
    i = v.i;
    return *this;
  }
  C& operator=(T v) {
    r = v;
    i = T(0);
    return *this;
  }
  C& operator-=(const C& v) {
    r -= v.r;
    i -= v.i;
    return *this;
  }
  C& operator-=(T v) {
    r -= v;
    return *this;
  }
  C& operator+=(const C& v) {
    r += v.r;
    i += v.i;
    return *this;
  }
  C& operator+=(T v) {
    r += v;
    return *this;
  }
  C& operator*=(const C& v) {
    return set(r * v.r - i * v.i, i * v.r + r * v.i);
  }
  C& operator*=(T v) {
    r *= v;
    i *= v;
    return *this;
  }
  C& operator/=(const C& v) { return (*this) *= v.recip(); }
  C& operator/=(T v) {
    r /= v;
    i /= v;
    return *this;
  }
 
  C operator-() const { return C(-r, -i); }
  C operator-(const C& v) const { return C(*this) -= v; }
  C operator-(T v) const { return C(*this) -= v; }
  C operator+(const C& v) const { return C(*this) += v; }
  C operator+(T v) const { return C(*this) += v; }
  C operator*(const C& v) const { return C(*this) *= v; }
  C operator*(T v) const { return C(*this) *= v; }
  C operator/(const C& v) const { return C(*this) /= v; }
  C operator/(T v) const { return C(*this) /= v; }
 
  T arg() const { return atan2(i, r); }  
  T argUnit() const {
    T r = arg() / (2 * M_PI);
    return r > 0 ? r : r + 1;
  }  
  C conj() const { return C(r, -i); }  
  T dot(const C& v) const {
    return r * v.r + i * v.i;
  }  
  C exp() const { return Polar<T>(::exp(r), i); }  
  C log() const {
    return Complex<T>(T(0.5) * ::log(normSqr()), arg());
  }                                             
  T norm() const { return ::sqrt(normSqr()); }  
  T normSqr() const { return dot(*this); }  
  C& normalize(T m = T(1)) {
    return *this *= (m / norm());
  }  
  C pow(const C& v) const {
    return ((*this).log() * v).exp();
  }                                                       
  C pow(T v) const { return ((*this).log() * v).exp(); }  
  C recip() const {
    return conj() / normSqr();
  }  
  C sgn(T m = T(1)) const {
    return C(*this).normalize(m);
  }  
  C sqr() const { return C(r * r - i * i, T(2) * r * i); }  
 
  C sqrt() const {
    static const T c = T(1) / ::sqrt(T(2));
    T n = norm();
    T a = ::sqrt(n + r) * c;
    T b = ::sqrt(n - r) * (i < T(0) ? -c : c);
    return C(a, b);
  }
 
  C cos() const {
    return C(::cos(r) * ::cosh(i), -::sin(r) * ::sinh(i));
  }  
  C sin() const {
    return C(::sin(r) * ::cosh(i), ::cos(r) * ::sinh(i));
  }  
  C cosh() const {
    return C(::cos(i) * ::sinh(r), ::sin(i) * ::cosh(r));
  }  
  C sinh() const {
    return C(::cos(i) * ::cosh(r), ::sin(i) * ::sinh(r));
  }  
 
  T abs() const { return norm(); }        
  T mag() const { return norm(); }        
  T magSqr() const { return normSqr(); }  
  T phase() const { return arg(); }       
};
 
#define TEM          \
  template <class T> \
  inline
TEM T abs(const Complex<T>& c) { return c.mag(); }
TEM Complex<T> exp(const Complex<T>& c) { return c.exp(); }
TEM Complex<T> log(const Complex<T>& c) { return c.log(); }
TEM Complex<T> pow(const Complex<T>& b, const Complex<T>& e) {
  return b.pow(e);
}
TEM Complex<T> pow(const Complex<T>& b, const T& e) { return b.pow(e); }
// TEM Complex<T> sqrt(const Complex<T>& v){ return v.sqrt(); } // TODO: these
// ambiguate other functions TEM Complex<T> cos(const Complex<T>& v){ return
// v.cos(); } TEM Complex<T> sin(const Complex<T>& v){ return v.sin(); }
#undef TEM
 
template <class T>
inline Complex<T> operator+(T r, const Complex<T>& c) {
  return c + r;
}
 
template <class T>
inline Complex<T> operator-(T r, const Complex<T>& c) {
  return -c + r;
}
 
template <class T>
inline Complex<T> operator*(T r, const Complex<T>& c) {
  return c * r;
}
 
template <class T>
inline Complex<T> operator/(T r, const Complex<T>& c) {
  return c.conj() * (r / c.normSqr());
}
 
template <class VecN, class T>
VecN rotate(const VecN& v, const VecN& p, const Complex<T>& a) {
  return v * a.r + p * a.i;
}
 
template <class VecN, class T>
void rotatePlane(VecN& v1, VecN& v2, const Complex<T>& a) {
  VecN t = al::rotate(v1, v2, a);
  v2 = al::rotate(v2, VecN(-v1), a);
  v1 = t;
}
 
template <class Vec3, class T>
Vec3 sterProj(const al::Complex<T>& c) {
  T magSqr = c.magSqr();
  T mul = T(2) / (magSqr + T(1));
  return Vec3(c.r * mul, c.i * mul, (magSqr - T(1)) * mul * T(0.5));
}
 
}  // namespace al
 
#endif