lines 11-226 of file: include/cppad/core/base_double.hpp

{xrst_begin base_double.hpp}
{xrst_spell
   invocations
   namespaces
}

Enable use of AD<Base> where Base is double
###########################################

CondExpOp
*********
The type ``double`` is a relatively simple type that supports
``<`` , ``<=`` , ``==`` , ``>=`` , and ``>`` operators; see
:ref:`base_cond_exp@CondExpTemplate@Ordered Type` .
Hence its ``CondExpOp`` function is defined by
{xrst_spell_off}
{xrst_code cpp} */
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);
   }
}
/* {xrst_code}
{xrst_spell_on}

CondExpRel
**********
The :ref:`CPPAD_COND_EXP_REL<base_cond_exp@CondExpRel>` macro invocation
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   CPPAD_COND_EXP_REL(double)
}
/* {xrst_code}
{xrst_spell_on}
uses ``CondExpOp`` above to
define ``CondExp`` *Rel* 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
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   inline bool EqualOpSeq(const double& x, const double& y)
   {  return x == y; }
}
/* {xrst_code}
{xrst_spell_on}

Identical
*********
The type ``double`` is simple (in this respect) and so we define
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   inline bool IdenticalCon(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 IdenticalEqualCon(const double& x, const double& y)
   {  return (x == y); }
}
/* {xrst_code}
{xrst_spell_on}

Integer
*******
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   inline int Integer(const double& x)
   {  return static_cast<int>(x); }
}
/* {xrst_code}
{xrst_spell_on}

azmul
*****
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   CPPAD_AZMUL( double )
}
/* {xrst_code}
{xrst_spell_on}

Ordered
*******
The ``double`` type supports ordered comparisons
{xrst_spell_off}
{xrst_code cpp} */
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); }
}
/* {xrst_code}
{xrst_spell_on}

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 :ref:`float<base_float.hpp@Unary Standard Math>`
versions of these functions.
{xrst_spell_off}
{xrst_code cpp} */
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;
   using std::asinh;
   using std::acosh;
   using std::atanh;
   using std::erf;
   using std::erfc;
   using std::expm1;
   using std::log1p;
}
/* {xrst_code}
{xrst_spell_on}
The absolute value function is special because its ``std`` name is
``fabs``
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   inline double abs(const double& x)
   {  return std::fabs(x); }
}
/* {xrst_code}
{xrst_spell_on}

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

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.
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   using std::pow;
}
/* {xrst_code}
{xrst_spell_on}

numeric_limits
**************
The following defines the CppAD :ref:`numeric_limits-name`
for the type ``double`` :
{xrst_spell_off}
{xrst_code cpp} */
namespace CppAD {
   CPPAD_NUMERIC_LIMITS(double, double)
}
/* {xrst_code}
{xrst_spell_on}

to_string
*********
There is no need to define ``to_string`` for ``double``
because it is defined by including ``cppad/utility/to_string.hpp`` ;
see :ref:`to_string-name` .
See :ref:`base_complex.hpp<base_complex.hpp@to_string>` for an example where
it is necessary to define ``to_string`` for a *Base* type.

{xrst_end base_double.hpp}