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@(@\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}} }@)@
Enable use of AD<Base> where Base is double

CondExpOp
The type double is a relatively simple type that supports <, <=, ==, >=, and > operators; see ordered type . Hence its CondExpOp function is defined by 
namespace CppAD {
     inline double CondExpOp(
          enum CompareOp     cop          ,
          const double&       left         ,
          const double&       right        ,
          const double&       exp_if_true  ,
          const double&       exp_if_false )
     {     return CondExpTemplate(cop, left, right, exp_if_true, exp_if_false);
     }
}

CondExpRel
The CPPAD_COND_EXP_REL macro invocation 

namespace CppAD {
     CPPAD_COND_EXP_REL(double)
}
uses CondExpOp above to define CondExpRel for double arguments and Rel equal to Lt, Le, Eq, Ge, and Gt.

EqualOpSeq
The type double is simple (in this respect) and so we define 
namespace CppAD {
     inline bool EqualOpSeq(const double& x, const double& y)
     {     return x == y; }
}

Identical
The type double is simple (in this respect) and so we define 
namespace CppAD {
     inline bool IdenticalPar(const double& x)
     {     return true; }
     inline bool IdenticalZero(const double& x)
     {     return (x == 0.); }
     inline bool IdenticalOne(const double& x)
     {     return (x == 1.); }
     inline bool IdenticalEqualPar(const double& x, const double& y)
     {     return (x == y); }
}

Integer 
namespace CppAD {
     inline int Integer(const double& x)
     {     return static_cast<int>(x); }
}

azmul 

namespace CppAD {
     CPPAD_AZMUL( double )
}

Ordered
The double type supports ordered comparisons 
namespace CppAD {
     inline bool GreaterThanZero(const double& x)
     {     return x > 0.; }
     inline bool GreaterThanOrZero(const double& x)
     {     return x >= 0.; }
     inline bool LessThanZero(const double& x)
     {     return x < 0.; }
     inline bool LessThanOrZero(const double& x)
     {     return x <= 0.; }
     inline bool abs_geq(const double& x, const double& y)
     {     return std::fabs(x) >= std::fabs(y); }
}

Unary Standard Math
The following macro invocations import the double versions of the unary standard math functions into the CppAD namespace. Importing avoids ambiguity errors when using both the CppAD and std namespaces. Note this also defines the float versions of these functions. 
namespace CppAD {
     using std::acos;
     using std::asin;
     using std::atan;
     using std::cos;
     using std::cosh;
     using std::exp;
     using std::fabs;
     using std::log;
     using std::log10;
     using std::sin;
     using std::sinh;
     using std::sqrt;
     using std::tan;
     using std::tanh;
# if CPPAD_USE_CPLUSPLUS_2011
     using std::erf;
     using std::asinh;
     using std::acosh;
     using std::atanh;
     using std::expm1;
     using std::log1p;
# endif
}
The absolute value function is special because its std name is fabs 
namespace CppAD {
     inline double abs(const double& x)
     {     return std::fabs(x); }
}

sign
The following defines the CppAD::sign function that is required to use AD<double>: 
namespace CppAD {
     inline double sign(const double& x)
     {     if( x > 0. )
               return 1.;
          if( x == 0. )
               return 0.;
          return -1.;
     }
}

pow
The following defines a CppAD::pow function that is required to use AD<double>. As with the unary standard math functions, this has the exact same signature as std::pow, so use it instead of defining another function. 

namespace CppAD {
     using std::pow;
}

numeric_limits
The following defines the CppAD numeric_limits for the type double: 

namespace CppAD {
     CPPAD_NUMERIC_LIMITS(double, double)
}

to_string
There is no need to define to_string for double because it is defined by including cppad/utility/to_string.hpp; see to_string . See base_complex.hpp for an example where it is necessary to define to_string for a Base type.
Input File: cppad/core/base_double.hpp