\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
base_double.hpp
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 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
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 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); }
}
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;
using std::asinh;
using std::acosh;
using std::atanh;
using std::erf;
using std::erfc;
using std::expm1;
using std::log1p;
}
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.