Base Type Requirements for Standard Math Functions

base_std_math

@(@\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}} }@)@ This is cppad-20221105 documentation. Here is a link to its current documentation . 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 = acosh(x)`	inverse hyperbolic cosine
`y = asin(x)`	inverse sine
`y = asinh(x)`	inverse hyperbolic sin
`y = atan(x)`	inverse tangent
`y = atanh(x)`	inverse hyperbolic tangent
`y = cos(x)`	cosine
`y = cosh(x)`	hyperbolic cosine
`y = erf(x)`	error function
`y = erfc(x)`	complementary error function
`y = exp(x)`	exponential
`y = expm1(x)`	exponential of x minus one
`y = fabs(x)`	absolute value
`y = log(x)`	natural logarithm
`y = log1p(x)`	logarithm of one plus x
`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 @[@ y = \left\{ \begin{array}{ll} +1 & {\rm if} \; x > 0 \\ 0 & {\rm if} \; x = 0 \\ -1 & {\rm if} \; x < 0 \end{array} \right. @]@ where x and y have the same prototype as above. 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 @(@ z = x^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 .

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 .

Input File: include/cppad/core/base_std_math.hpp