\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

ad_in_c.cpp

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Example and Test Linking CppAD to Languages Other than C++

# include <cstdio>
# include <cppad/cppad.hpp>
# include <list>

namespace { // Begin empty namespace *****************************************

/*
void debug_print(const char *label, double d)
{  using std::printf;

   unsigned char *byte = reinterpret_cast<unsigned char *>(&d);
   size_t n_byte = sizeof(d);
   printf("%s", label);
   for(size_t i = 0; i < n_byte; i++)
      printf("%x", byte[i]);
   printf("\n");
}
*/

// type in C corresponding to an AD<double> object
typedef struct { void*  p_void; } cad;

// type in C corresponding to a an ADFun<double>
typedef struct { void* p_void; } cad_fun;

// type in C corresponding to a C AD binary operator
typedef enum { op_add, op_sub, op_mul, op_div } cad_binary_op;

// type in C corresponding to a C AD unary operator
typedef enum {
   op_abs, op_acos, op_asin, op_atan, op_cos, op_cosh,
   op_exp, op_log,  op_sin,  op_sinh, op_sqrt
} cad_unary_op;

// --------------------------------------------------------------------------
// helper code not intended for use by C code  ------------------------------
using CppAD::AD;
using CppAD::ADFun;
using CppAD::vector;
using CppAD::NearEqual;

void cad2vector(size_t n, cad* p_cad, vector< AD<double> >& v)
{  assert( n == v.size() );
   for(size_t j = 0; j < n; j++)
   {  AD<double>* p_ad =
         reinterpret_cast< AD<double>* > (p_cad[j].p_void);
      v[j] = *p_ad;
   }
}

void vector2cad(size_t n, vector< AD<double> >& v, cad* p_cad)
{  assert( n == v.size() );
   for(size_t j = 0; j < n; j++)
   {  AD<double>* p_ad =
         reinterpret_cast< AD<double>* > (p_cad[j].p_void);
      *p_ad = v[j];
   }
}

void double2vector(size_t n, double* p_dbl, vector<double>& v)
{  assert( n == v.size() );
   for(size_t j = 0; j < n; j++)
      v[j] = p_dbl[j];
}

void vector2double(size_t n, vector<double>& v, double *p_dbl)
{  assert( n == v.size() );
   for(size_t j = 0; j < n; j++)
      p_dbl[j] = v[j];
}

std::list<void*> allocated;
# ifdef NDEBUG
inline void push_allocated(void *p)
{ }
inline void pop_allocated(void *p)
{ }
# else
inline void push_allocated(void *p)
{  assert( p != 0 );
   allocated.push_front(p);
}
inline void pop_allocated(void *p)
{  std::list<void*>::iterator i;
   for(i = allocated.begin(); i != allocated.end(); ++i)
   {  if( *i == p )
      {  allocated.erase(i);
         return;
      }
   }
   assert( 0 );
}

# endif
// --------------------------------------------------------------------------
// Here is the code that links C to CppAD. You will have to add more
// functions and operators to make a complete language link.
//
extern "C"
bool cad_near_equal(double x, double y)
{  double eps = 10. * std::numeric_limits<double>::epsilon();
   return NearEqual(x, y, eps, 0.);
}

// create a C++ AD object
// value is the value that the C++ AD object will have
// p_cad->p_void: on input is 0, on output points to C++ AD object
extern "C"
void cad_new_ad(cad *p_cad, double value)
{  // make sure pointer is not currently allocated
   assert( p_cad->p_void == 0 );

   AD<double>* p_ad   = new AD<double>(value);
   p_cad->p_void      = reinterpret_cast<void*>(p_ad);

   // put in list of allocate pointers
   push_allocated( p_cad->p_void );
}

// delete a C++ AD object
// p_cad->value: not used
// p_cad->p_void: on input points to C++ AD object, on output is 0
extern "C"
void cad_del_ad(cad* p_cad)
{  // make sure that p_cad has been allocated
   pop_allocated( p_cad->p_void );

   AD<double>* p_ad   = reinterpret_cast< AD<double>* >( p_cad->p_void );
   delete p_ad;

   // special value for pointers that are not allocated
   p_cad->p_void = 0;
}

// extract the value from a C++ AD object
// extern "C"
double cad_value(cad* p_cad)
{  AD<double>* p_ad = reinterpret_cast< AD<double>* > (p_cad->p_void);
   return Value( Var2Par(*p_ad) );
}

// preform a C AD unary operation
extern "C"
void cad_unary(cad_unary_op op, cad* p_operand, cad* p_result)
{  AD<double> *operand, *result;
   result  = reinterpret_cast< AD<double>* > (p_result->p_void);
   operand = reinterpret_cast< AD<double>* > (p_operand->p_void);
   switch(op)
   {
      case op_abs:
      *result = fabs( *operand );
      break;

      case op_acos:
      *result = acos( *operand );
      break;

      case op_asin:
      *result = asin( *operand );
      break;

      case op_atan:
      *result = atan( *operand );
      break;

      case op_cos:
      *result = cos( *operand );
      break;

      case op_cosh:
      *result = cosh( *operand );
      break;

      case op_exp:
      *result = exp( *operand );
      break;

      case op_log:
      *result = log( *operand );
      break;

      case op_sin:
      *result = sin( *operand );
      break;

      case op_sinh:
      *result = sinh( *operand );
      break;

      case op_sqrt:
      *result = sqrt( *operand );
      break;

      default:
      // not a unary operator
      assert(0);
      break;

   }
   return;
}

// perform a C AD binary operation
extern "C"
void cad_binary(cad_binary_op op, cad* p_left, cad* p_right, cad* p_result)
{  AD<double> *result, *left, *right;
   result = reinterpret_cast< AD<double>* > (p_result->p_void);
   left   = reinterpret_cast< AD<double>* > (p_left->p_void);
   right  = reinterpret_cast< AD<double>* > (p_right->p_void);
   assert( result != 0 );
   assert( left != 0 );
   assert( right != 0 );

   switch(op)
   {  case op_add:
      *result         = *left + (*right);
      break;

      case op_sub:
      *result         = *left - (*right);
      break;

      case op_mul:
      *result         = *left * (*right);
      break;

      case op_div:
      *result         = *left / (*right);
      break;

      default:
      // not a binary operator
      assert(0);
   }
   return;
}

// declare the independent variables in C++
extern "C"
void cad_independent(size_t n, cad* px_cad)
{  vector< AD<double> > x(n);
   cad2vector(n, px_cad, x);
   CppAD::Independent(x);
   vector2cad(n, x, px_cad);
}

// create an ADFun object in C++
extern "C"
cad_fun cad_new_fun(size_t n, size_t m, cad* px_cad, cad* py_cad)
{  cad_fun fun;

   ADFun<double>* p_adfun = new ADFun<double>;
   vector< AD<double> > x(n);
   vector< AD<double> > y(m);
   cad2vector(n, px_cad, x);
   cad2vector(m, py_cad, y);
   p_adfun->Dependent(x, y);

   fun.p_void = reinterpret_cast<void*>( p_adfun );

   // put in list of allocate pointers
   push_allocated( fun.p_void );

   return fun;
}

// delete an AD function object in C
extern "C"
void cad_del_fun(cad_fun *fun)
{  // make sure this pointer has been allocated
   pop_allocated( fun->p_void );

   ADFun<double>* p_adfun
      = reinterpret_cast< ADFun<double>* > (fun->p_void);
   delete p_adfun;

   // special value for pointers that are not allocated
   fun->p_void = 0;
}

// evaluate the Jacobian corresponding to a function object
extern "C"
void cad_jacobian(cad_fun fun,
   size_t n, size_t m, double* px, double* pjac )
{  assert( fun.p_void != 0 );

   ADFun<double>* p_adfun =
      reinterpret_cast< ADFun<double>* >(fun.p_void);
   vector<double> x(n), jac(n * m);

   double2vector(n, px, x);
   jac = p_adfun->Jacobian(x);
   vector2double(n * m, jac, pjac);
}

// forward mode
extern "C"
void cad_forward(cad_fun fun,
   size_t order, size_t n, size_t m, double* px, double* py )
{  assert( fun.p_void != 0 );

   ADFun<double>* p_adfun =
      reinterpret_cast< ADFun<double>* >(fun.p_void);
   vector<double> x(n), y(m);

   double2vector(n, px, x);
   y = p_adfun->Forward(order, x);
   vector2double(m, y, py);
}

// check that allocated list has been completely freed
extern "C"
bool cad_allocated_empty(void)
{  return allocated.empty();
}

} // End empty namespace ****************************************************

# include <math.h> // used to check results in c code below

# define N 2       // number of independent variables in example
# define M 5       // number of dependent variables in example

// -------------------------------------------------------------------------
// Here is the C code that uses the CppAD link above
bool ad_in_c(void)
{  // This routine is intentionally coded as if it were written in C
   // as an example of how you can link C, and other languages to CppAD
   bool ok = true;

   // x vector of AD objects in C
   double value;
   size_t j, n = N;
   cad X[N];
   for(j = 0; j < n; j++)
   {  value       = (double) (j+1) / (double) n;
      X[j].p_void = 0;
      cad_new_ad(X + j, value);
   }

   // y vector of AD objects in C
   size_t i, m = M;
   cad Y[M];
   for(i = 0; i < m; i++)
   {  value       = 0.; // required, but not used
      Y[i].p_void = 0;
      cad_new_ad(Y + i, value);
   }

   // declare X as the independent variable vector
   cad_independent(n, X);

   // y[0] = x[0] + x[1]
   cad_binary(op_add, X+0, X+1, Y+0);
   ok &= cad_near_equal( cad_value(Y+0), cad_value(X+0)+cad_value(X+1) );

   // y[1] = x[0] - x[1]
   cad_binary(op_sub, X+0, X+1, Y+1);
   ok &= cad_near_equal( cad_value(Y+1), cad_value(X+0)-cad_value(X+1) );

   // y[2] = x[0] * x[1]
   cad_binary(op_mul, X+0, X+1, Y+2);
   ok &= cad_near_equal( cad_value(Y+2), cad_value(X+0)*cad_value(X+1) );

   // y[3] = x[0] * x[1]
   cad_binary(op_div, X+0, X+1, Y+3);
   ok &= cad_near_equal( cad_value(Y+3), cad_value(X+0)/cad_value(X+1) );

   // y[4] = sin(x[0]) + asin(sin(x[0]))
   cad sin_x0 = { 0 };       // initialize p_void as zero
   cad_new_ad( &sin_x0, 0.);
   cad_unary(op_sin, X+0, &sin_x0);
   ok &= cad_near_equal(cad_value(&sin_x0), sin(cad_value(X+0)) );

   cad asin_sin_x0 = { 0 };  // initialize p_void as zero
   cad_new_ad( &asin_sin_x0, 0.);
   cad_unary(op_asin, &sin_x0, &asin_sin_x0);
   ok &= cad_near_equal(
      cad_value(&asin_sin_x0),
      asin( cad_value(&sin_x0) )
   );

   cad_binary(op_add, &sin_x0, &asin_sin_x0, Y+4);
   ok &= cad_near_equal(
      cad_value(Y+4),
      cad_value(&sin_x0) + cad_value(&asin_sin_x0)
   );

   // declare y as the dependent variable vector and stop recording
   // and store function object in f
   cad_fun f = cad_new_fun(n, m, X, Y);

   // now use the function object
   double x[N], jac[N * M];
   x[0] = 1.;
   x[1] = .5;

   // compute the Jacobian
   cad_jacobian(f, n, m, x, jac);

   // check the Jacobian values
   size_t k = 0;
   // partial y[0] w.r.t. x[0]
   ok &= cad_near_equal(jac[k++], 1.);
   // partial y[0] w.r.t. x[1]
   ok &= cad_near_equal(jac[k++], 1.);
   // partial y[1] w.r.t. x[0]
   ok &= cad_near_equal(jac[k++], 1.);
   // partial y[1] w.r.t. x[1]
   ok &= cad_near_equal(jac[k++], -1.);
   // partial y[2] w.r.t. x[0]
   ok &= cad_near_equal(jac[k++], x[1]);
   // partial y[2] w.r.t. x[1]
   ok &= cad_near_equal(jac[k++], x[0]);
   // partial y[3] w.r.t. x[0]
   ok &= cad_near_equal(jac[k++], 1./x[1]);
   // partial y[3] w.r.t. x[1]
   ok &= cad_near_equal(jac[k++], -x[0]/(x[1]*x[1]));
   // partial y[4] w.r.t x[0]
   ok &= cad_near_equal(jac[k++],  cos(x[0]) + 1.);
   // partial y[4] w.r.t x[1]
   ok &= cad_near_equal(jac[k++],  0.);

   // evaluate the function f at a different x
   size_t order = 0;
   double y[M];
   x[0] = .5;
   x[1] = 1.;
   cad_forward(f, order, n, m, x, y);

   // check the function values
   ok &= cad_near_equal(y[0] , x[0] + x[1] );
   ok &= cad_near_equal(y[1] , x[0] - x[1] );
   ok &= cad_near_equal(y[2] , x[0] * x[1] );
   ok &= cad_near_equal(y[3] , x[0] / x[1] );
   ok &= cad_near_equal(y[4] , sin(x[0]) + asin(sin(x[0])) );

   // delete All C++ copies of the AD objects
   cad_del_fun( &f );
   cad_del_ad( &sin_x0 );
   cad_del_ad( &asin_sin_x0 );
   for(j = 0; j < n; j++)
      cad_del_ad(X + j);
   for(i = 0; i < m; i++)
      cad_del_ad(Y + i);

   ok     &= cad_allocated_empty();
   return ok;
}