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Controlling Taylor Coefficient Memory Allocation: Example and Test
`

    # include <cppad/cppad.hpp>

    namespace {
         bool test(void)
         {     bool ok = true;
              using CppAD::AD;
              using CppAD::NearEqual;
              using CppAD::thread_alloc;

              // domain space vector
              size_t n(1), m(1);
              CPPAD_TESTVECTOR(AD<double>) ax(n), ay(n);

              // declare independent variables and start tape recording
              ax[0]  = 1.0;
              CppAD::Independent(ax);

              // Set y = x^3, use enough variables so more that the minimal amount
              // of memory is allocated for Taylor coefficients
              ay[0] = 0.;
              for( size_t i = 0; i < 10; i++)
                   ay[0] += ax[0] * ax[0] * ax[0];
              ay[0] = ay[0] / 10.;

              // create f: x -> y and stop tape recording
              // (without running zero order forward mode).
              CppAD::ADFun<double> f;
              f.Dependent(ax, ay);

              // check that this is master thread
              size_t thread = thread_alloc::thread_num();
              ok           &= thread == 0; // this should be master thread

              // The highest order forward mode calculation below is first order.
              // This corresponds to two Taylor coefficient per variable,direction
              // (orders zero and one). Preallocate memory for speed.
              size_t inuse  = thread_alloc::inuse(thread);
              f.capacity_order(2);
              ok &= thread_alloc::inuse(thread) > inuse;

              // zero order forward mode
              CPPAD_TESTVECTOR(double) x(n), y(m);
              x[0] = 0.5;
              y    = f.Forward(0, x);
              double eps = 10. * CppAD::numeric_limits<double>::epsilon();
              ok  &= NearEqual(y[0], x[0] * x[0] * x[0], eps, eps);

              // forward computation of partials w.r.t. x
              CPPAD_TESTVECTOR(double) dx(n), dy(m);
              dx[0] = 1.;
              dy    = f.Forward(1, dx);
              ok   &= NearEqual(dy[0], 3. * x[0] * x[0], eps, eps);

              // Suppose we no longer need the first order Taylor coefficients.
              inuse = thread_alloc::inuse(thread);
              f.capacity_order(1); // just keep zero order coefficients
              ok   &= thread_alloc::inuse(thread) < inuse;

              // Suppose we no longer need the zero order Taylor coefficients
              // (could have done this first and not used f.capacity_order(1)).
              inuse = thread_alloc::inuse(thread);
              f.capacity_order(0);
              ok   &= thread_alloc::inuse(thread) < inuse;

              // turn off memory holding
              thread_alloc::hold_memory(false);

              return ok;
         }
    }
    bool capacity_order(void)
    {     bool ok = true;
         using CppAD::thread_alloc;

         // original amount of memory inuse
         size_t thread = thread_alloc::thread_num();
         ok           &= thread == 0; // this should be master thread
         size_t inuse  = thread_alloc::inuse(thread);

         // do test in separate routine so all objects are destroyed
         ok &= test();

         // check that the amount of memroy inuse has not changed
         ok &= thread_alloc::inuse(thread) == inuse;

         // Test above uses hold_memory, so return available memory
         thread_alloc::free_available(thread);

         return ok;
    }

`

Input File: example/general/capacity_order.cpp