text: /**
   *
   * "A Collection of Useful C++ Classes for Digital Signal Processing"
   * By Vinnie Falco and Bernd Porr
   *
   * Official project location:
   * https://github.com/berndporr/iir1
   *
   * See Documentation.cpp for contact information, notes, and bibliography.
   *
   * -----------------------------------------------------------------
   *
   * License: MIT License (http://www.opensource.org/licenses/mit-license.php)
   * Copyright (c) 2009 by Vinnie Falco
   * Copyright (c) 2011 by Bernd Porr
   *
   * Permission is hereby granted, free of charge, to any person obtaining a copy
   * of this software and associated documentation files (the "Software"), to deal
   * in the Software without restriction, including without limitation the rights
   * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   * copies of the Software, and to permit persons to whom the Software is
   * furnished to do so, subject to the following conditions:
   *
   * The above copyright notice and this permission notice shall be included in
   * all copies or substantial portions of the Software.
   *
   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
   * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
   * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
   * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
   * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
   * THE SOFTWARE.
   **/
  
  #ifndef IIR1_MATHSUPPLEMENT_H
  #define IIR1_MATHSUPPLEMENT_H
  
  #include "Common.h"
  
  #include <complex>
  
  #ifdef _MSC_VER
  // Under Unix these have already default instantiations but not under Vis Studio
  template class DllExport std::complex<double>;
  template class DllExport std::complex<float>;
  #endif
  
  namespace Iir {
  
    const double doublePi   = 3.1415926535897932384626433832795028841971;
    const double doublePi_2 = 1.5707963267948966192313216916397514420986;
    const double doubleLn2  = 0.69314718055994530941723212145818;
    const double doubleLn10 = 2.3025850929940456840179914546844;
  
    typedef std::complex<double>            complex_t;
    typedef std::pair<complex_t, complex_t> complex_pair_t;
  
    template<typename Real>
    inline std::complex<Real> solve_quadratic_1(Real a, Real b, Real c) {
      return (-b + sqrt(std::complex<Real>(b * b - 4 * a * c, 0))) / (2. * a);
    }
  
    template<typename Real>
    inline std::complex<Real> solve_quadratic_2(Real a, Real b, Real c) {
      return (-b - sqrt(std::complex<Real>(b * b - 4 * a * c, 0))) / (2. * a);
    }
  
    inline const complex_t infinity() {
      return complex_t(std::numeric_limits<double>::infinity());
    }
  
    inline const complex_t adjust_imag(const complex_t& c) {
      if (fabs(c.imag()) < 1e-30)
        return complex_t(c.real(), 0);
      else
        return c;
    }
  
    template<typename Ty, typename To>
    inline std::complex<Ty> addmul(const std::complex<Ty>& c, Ty v, const std::complex<To>& c1) {
      return std::complex<Ty>(c.real() + v * c1.real(), c.imag() + v * c1.imag());
    }
  
    template<typename Ty>
    inline std::complex<Ty> recip(const std::complex<Ty>& c) {
      Ty n = 1.0 / std::norm(c);
  
      return std::complex<Ty>(n * c.real(), n * c.imag());
    }
  
    template<typename Ty>
    inline Ty asinh(Ty x) {
      return log(x + std::sqrt(x * x + 1));
    }
  
    template<typename Ty>
    inline Ty acosh(Ty x) {
      return log(x + std::sqrt(x * x - 1));
    }
  
    template<typename Ty>
    inline bool is_nan(Ty v) {
      return !(v == v);
    }
  
    template<>
    inline bool is_nan<complex_t>(complex_t v) {
      return Iir::is_nan(v.real()) || Iir::is_nan(v.imag());
    }
  
  }  // namespace Iir
  
  #endif
  