Boost C++ Libraries of the most highly regarded and expertly designed C++ library projects in the world. Herb Sutter and Andrei Alexandrescu, C++ Coding Standards


Using C++11 Lambda's

Since all the root finding functions accept a function-object, they can be made to work (often in a lot less code) with C++11 lambda's. Here's the much reduced code for our "toy" cube root function:

template <class T>
T cbrt_2deriv_lambda(T x)
   // return cube root of x using 1st and 2nd derivatives and Halley.
   //using namespace std;  // Help ADL of std functions.
   using namespace boost::math::tools;
   int exponent;
   frexp(x, &exponent);                                // Get exponent of z (ignore mantissa).
   T guess = ldexp(1., exponent / 3);                    // Rough guess is to divide the exponent by three.
   T min = ldexp(0.5, exponent / 3);                     // Minimum possible value is half our guess.
   T max = ldexp(2., exponent / 3);                      // Maximum possible value is twice our guess.
   const int digits = std::numeric_limits<T>::digits;  // Maximum possible binary digits accuracy for type T.
   // digits used to control how accurate to try to make the result.
   int get_digits = static_cast<int>(digits * 0.4);    // Accuracy triples with each step, so stop when just
   // over one third of the digits are correct.
   boost::uintmax_t maxit = 20;
   T result = halley_iterate(
      // lambda function:
      [x](const T& g){ return std::make_tuple(g * g * g - x, 3 * g * g, 6 * g); },
      guess, min, max, get_digits, maxit);
   return result;

Full code of this example is at root_finding_example.cpp,