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Up-> CppAD AD base_require base_std_math

CppAD-> Install Introduction AD ADFun multi_thread library cppad_ipopt_nlp Example preprocessor Appendix

AD-> ad_ctor ad_assign Convert ADValued BoolValued VecAD base_require

base_require-> base_member base_cond_exp base_identical base_ordered base_std_math base_example

base_std_math

Headings-> Purpose Unary Standard Math CPPAD_STANDARD_MATH_UNARY sign pow epsilon isnan

Base Type Requirements for Standard Math Functions
Purpose
These definitions are required for the user's code to use the type AD<Base> :

Unary Standard Math
The type Base must support the following functions unary standard math functions (in the CppAD namespace):

Syntax	Result
y = abs(x)	absolute value
y = acos(x)	inverse cosine
y = asin(x)	inverse sine
y = atan(x)	inverse tangent
y = cos(x)	cosine
y = cosh(x)	hyperbolic cosine
y = exp(x)	exponential
y = log(x)	natural logarithm
y = sin(x)	sine
y = sinh(x)	hyperbolic sine
y = sqrt(x)	square root
y = tan(x)	tangent

where the arguments and return value have the prototypes
     const Base& x
     Base        y
For example, base_alloc ,

CPPAD_STANDARD_MATH_UNARY
The macro invocation, within the CppAD namespace,
     CPPAD_STANDARD_MATH_UNARY(Base, Fun)
defines the syntax
     y = CppAD::Fun(x)
This macro uses the functions std::Fun which must be defined and have the same prototype as CppAD::Fun . For example, float .

sign
The type Base must support the syntax
     y = CppAD::sign(x)
which computes $$\mathit{z}=\{\begin{array}{cc}+1\hfill & \mathrm{if}\mathit{x}>0\hfill \\ 0\hfill & \mathrm{if}\mathit{x}=0\hfill \\ -1\hfill & \mathrm{if}\mathit{x}<0\hfill \end{array}$$ The arguments x has prototype
     const Base& x
and the return value z has prototype
     Base z
For example, see base_alloc . Note that, if ordered comparisons are not defined for the type Base , the code sign function should generate an assert if it is used; see complex invalid unary math .

pow
The type Base must support the syntax
     z = CppAD::pow(x, y)
which computes $\mathit{z}={\mathit{x}}^{\mathit{y}}$ . The arguments x and y have prototypes
     const Base& x
     const Base& y
and the return value z has prototype
     Base z
For example, see base_alloc .

epsilon
The template specialization
     Base CppAD::epsilon<Base>()
must return machine epsilon for the type Base . For example, see base_alloc .

isnan
If Base defines the isnan function, you may also have to provide a definition in the CppAD namespace (to avoid a function ambiguity). For example, see base_complex .

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Input File: cppad/local/base_std_math.hpp