Nvidia R&D chief on how AI is improving chip design(hpcwire.com)

  #include <iostream>
  #include <iomanip>
  #include <cmath>
  #include <tuple>

  // solve ax^2+bx+c=0
  template<typename T> auto
  solve_quadratic(T const& a, T const& b, T const& c) -> std::tuple<T, T> {
    auto t = std::sqrt(b*b - T(4)*a*c);
    return {(-b + t) / (T(2)*a), (-b - t) / (T(2)*a)};
  }

  int main() {
    std::cout << "Expected x1=0.000000075 x2=-200.000000075\n"
    std::cout << "Single precision:\n";
    {
      float a=1.0f, b=200.0f, c=-0.000015f;
      auto [x1, x2] = solve_quadratic<float>(a, b, c);
      std::cout << "x1=" << x1 << ", x2=" << x2 << "\n";
      std::cout << "ax1^2+bx1+c=" << (a*x1*x1 + b*x1 + c) << "\n";
      std::cout << "ax2^2+bx2+c=" << (a*x2*x2 + b*x2 + c) << "\n";
    }
    std::cout << "\nExpected x1=1.000000028975958 x2=1.000000000000000\n";
    std::cout << "Double precision:\n";
    {
      double a=94906265.625, b=-189812534, c=94906268.375;
      auto [x1, x2] = solve_quadratic<double>(a, b, c);
      std::cout << std::setprecision(16);
      std::cout << "x1=" << x1 << ", x2=" << x2 << "\n";
      std::cout << "ax1^2+bx1+c=" << (a*x1*x1 + b*x1 + c) << "\n";
      std::cout << "ax2^2+bx2+c=" << (a*x2*x2 + b*x2 + c) << "\n";
    }
  }

  template<typename T> auto
  solve_quadratic(T const& a, T const& b, T const& c) -> std::tuple<T, T> {
    auto sign_b = b < 0.0 ? -1.0 : 1.0;
    auto t = -b - sign_b*std::sqrt(b*b - T(4)*a*c);
    return {(T(2)*c) / t, t / (T(2)*a)};
  }