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Defines a User Atomic Operation that Computes Square Root

Syntax
atomic_user a_square_root
 a_square_root(au, ay)

Purpose
This user atomic operation computes a square root using Newton's method. It is meant to be very inefficient in order to demonstrate timing results.

au
This argument has prototype
     const ADvector& au
 where ADvector is a simple vector class with elements of type AD<double>. The size of au is three.

num_itr
We use the notation
     num_itr = size_t( Integer( au[0] ) )
 for the number of Newton iterations in the computation of the square root function. The component au[0] must be a parameter .

y_initial
We use the notation
     y_initial = au[1]
 for the initial value of the Newton iterate.

y_squared
We use the notation
     y_squared = au[2]
 for the value we are taking the square root of.

ay
This argument has prototype
     ADvector& ay
 The size of ay is one and ay[0] is the square root of y_squared .

Limitations
Only zero order forward mode is implements for the atomic_user class.

Source 

// includes used by all source code in multi_atomic.cpp file
# include <cppad/cppad.hpp>
# include "multi_atomic.hpp"
# include "team_thread.hpp"
//
namespace {
using CppAD::thread_alloc; // fast multi-threading memory allocator
using CppAD::vector;       // uses thread_alloc

class atomic_user : public CppAD::atomic_base<double> {
public:
     // ctor
     atomic_user(void)
     : CppAD::atomic_base<double>("atomic_square_root")
     { }
private:
     // forward mode routine called by CppAD
     virtual bool forward(
          size_t                   p   ,
          size_t                   q   ,
          const vector<bool>&      vu  ,
          vector<bool>&            vy  ,
          const vector<double>&    tu  ,
          vector<double>&          ty  )
     {
# ifndef NDEBUG
          size_t n = tu.size() / (q + 1);
          size_t m = ty.size() / (q + 1);
          assert( n == 3 );
          assert( m == 1 );
# endif
          // only implementing zero order forward for this example
          if( q != 0 )
               return false;

          // extract components of argument vector
          size_t num_itr    = size_t( tu[0] );
          double y_initial  = tu[1];
          double y_squared  = tu[2];

          // check for setting variable information
          if( vu.size() > 0 )
          {     if( vu[0] )
                    return false;
               vy[0] = vu[1] || vu[2];
          }

          // Use Newton's method to solve f(y) = y^2 = y_squared
          double y_itr = y_initial;
          for(size_t itr = 0; itr < num_itr; itr++)
          {     // solve (y - y_itr) * f'(y_itr) = y_squared - y_itr^2
               double fp_itr = 2.0 * y_itr;
               y_itr         = y_itr + (y_squared - y_itr * y_itr) / fp_itr;
          }

          // return the Newton approximation for f(y) = y_squared
          ty[0] = y_itr;
          return true;
     }
};
}
Input File: example/multi_thread/multi_atomic.cpp