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Tidy up comments.

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jzmaddock
2015-04-30 18:32:48 +01:00
parent 5c022355ac
commit a0fb417bc0
3 changed files with 120 additions and 105 deletions
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47
example/root_finding_multiprecision_example.cpp
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@@ -87,15 +87,16 @@ struct cbrt_functor_2deriv
// using boost::math::tuple; // to return three values.
std::tuple<T, T, T> operator()(T const& x)
{ // Return both f(x) and f'(x) and f''(x).
T fx = x*x*x - a; // Difference (estimate x^3 - value).
// std::cout << "x = " << x << "\nfx = " << fx << std::endl;
T dx = 3 * x*x; // 1st derivative = 3x^2.
T d2x = 6 * x; // 2nd derivative = 6x.
return std::make_tuple(fx, dx, d2x); // 'return' fx, dx and d2x.
{
// Return both f(x) and f'(x) and f''(x).
T fx = x*x*x - a; // Difference (estimate x^3 - value).
// std::cout << "x = " << x << "\nfx = " << fx << std::endl;
T dx = 3 * x*x; // 1st derivative = 3x^2.
T d2x = 6 * x; // 2nd derivative = 6x.
return std::make_tuple(fx, dx, d2x); // 'return' fx, dx and d2x.
}
private:
T a; // to be 'cube_rooted'.
T a; // to be 'cube_rooted'.
}; // struct cbrt_functor_2deriv
template <int n, class T>
@@ -103,37 +104,37 @@ struct nth_functor_2deriv
{ // Functor returning both 1st and 2nd derivatives.
nth_functor_2deriv(T const& to_find_root_of) : value(to_find_root_of)
{ // Constructor stores value to find root of, for example:
}
{ /* Constructor stores value to find root of, for example: */ }
// using boost::math::tuple; // to return three values.
// using std::tuple; // to return three values.
std::tuple<T, T, T> operator()(T const& x)
{ // Return both f(x) and f'(x) and f''(x).
{
// Return both f(x) and f'(x) and f''(x).
using boost::math::pow;
T fx = pow<n>(x) -value; // Difference (estimate x^3 - value).
T dx = n * pow<n - 1>(x); // 1st derivative = 5x^4.
T d2x = n * (n - 1) * pow<n - 2 >(x); // 2nd derivative = 20 x^3
return std::make_tuple(fx, dx, d2x); // 'return' fx, dx and d2x.
T fx = pow<n>(x) - value; // Difference (estimate x^3 - value).
T dx = n * pow<n - 1>(x); // 1st derivative = 5x^4.
T d2x = n * (n - 1) * pow<n - 2 >(x); // 2nd derivative = 20 x^3
return std::make_tuple(fx, dx, d2x); // 'return' fx, dx and d2x.
}
private:
T value; // to be 'nth_rooted'.
T value; // to be 'nth_rooted'.
}; // struct nth_functor_2deriv
template <int n, class T>
T nth_2deriv(T x)
{ // return nth root of x using 1st and 2nd derivatives and Halley.
{
// return nth root of x using 1st and 2nd derivatives and Halley.
using namespace std; // Help ADL of std functions.
using namespace boost::math; // For halley_iterate.
int exponent;
frexp(x, &exponent); // Get exponent of z (ignore mantissa).
T guess = ldexp(static_cast<T>(1.), exponent / n); // Rough guess is to divide the exponent by three.
T min = ldexp(static_cast<T>(0.5), exponent / n); // Minimum possible value is half our guess.
T max = ldexp(static_cast<T>(2.), exponent / n); // Maximum possible value is twice our guess.
frexp(x, &exponent); // Get exponent of z (ignore mantissa).
T guess = ldexp(static_cast<T>(1.), exponent / n); // Rough guess is to divide the exponent by three.
T min = ldexp(static_cast<T>(0.5), exponent / n); // Minimum possible value is half our guess.
T max = ldexp(static_cast<T>(2.), exponent / n); // Maximum possible value is twice our guess.
int digits = std::numeric_limits<T>::digits / 2; // Half maximum possible binary digits accuracy for type T.
int digits = std::numeric_limits<T>::digits / 2; // Half maximum possible binary digits accuracy for type T.
const boost::uintmax_t maxit = 50;
boost::uintmax_t it = maxit;
T result = halley_iterate(nth_functor_2deriv<n, T>(x), guess, min, max, digits, it);