/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

  CppAD is distributed under the terms of the
               Eclipse Public License Version 2.0.

  This Source Code may also be made available under the following
  Secondary License when the conditions for such availability set forth
  in the Eclipse Public License, Version 2.0 are satisfied:
        GNU General Public License, Version 2.0 or later.
-------------------------------------------------------------------------- */

/*
$begin NumericType$$
$spell
    const
    std
    valarray
$$


$section Definition of a Numeric Type$$

$head Type Requirements$$
A $icode NumericType$$ is any type
that satisfies the requirements below.
The following is a list of some numeric types:
$code int$$, $code float$$, $code double$$,
$code AD<double>$$, $code AD< AD<double> >$$.
The routine $cref CheckNumericType$$ can be used to check
that a type satisfies these conditions.

$head Default Constructor$$
The syntax
$codei%
    %NumericType% %x%;
%$$
creates a $icode NumericType$$ object
with an unspecified value.

$head Constructor From Integer$$
If $icode i$$ is an $code int$$,
the syntax
$codei%
    %NumericType% %x%(%i%);
%$$
creates a $icode NumericType$$ object with a value
equal to $icode i$$ where $icode i$$ can be $code const$$.

$head Copy Constructor$$
If $icode x$$ is a $icode NumericType$$ object
the syntax
$codei%
    %NumericType% %y%(%x%);
%$$
creates a $icode NumericType$$ object $icode y$$
with the same value as $icode x$$
where $icode x$$ can be $code const$$.

$head Assignment$$
If $icode x$$ and $icode y$$ are $icode NumericType$$ objects,
the syntax
$codei%
    %x% = %y%
%$$
sets the value of $icode x$$ equal to the value of $icode y$$
where $icode y$$ can be $code const$$.
The expression corresponding to this operation is unspecified; i.e.,
it could be $code void$$ and hence
$codei%
    %x% = %y% = %z%
%$$
may not be legal.

$head Operators$$
Suppose $icode x$$, $icode y$$ and $icode z$$
$icode NumericType$$ objects where
$icode x$$ and $icode y$$ may be $code const$$.
In the result type column,
$icode NumericType$$ can be replaced by any type that can
be used just like a $icode NumericType$$ object.
$table
$bold Operation$$     $cnext $bold Description$$               $cnext
    $bold Result Type$$  $rnext
$codei%+%x%$$        $cnext unary plus                        $cnext
    $icode NumericType$$    $rnext
$codei%-%x%$$        $cnext unary minus                       $cnext
    $icode NumericType$$    $rnext
$icode%x% +  %y%$$  $cnext binary addition                   $cnext
    $icode NumericType$$    $rnext
$icode%x% -  %y%$$  $cnext binary subtraction                $cnext
    $icode NumericType$$    $rnext
$icode%x% *  %y%$$  $cnext binary multiplication             $cnext
    $icode NumericType$$    $rnext
$icode%x% /  %y%$$  $cnext binary division                   $cnext
    $icode NumericType$$    $rnext
$icode%z% += %y%$$  $cnext compound assignment addition       $cnext
    unspecified          $rnext
$icode%z% -= %y%$$  $cnext compound assignment subtraction    $cnext
    unspecified          $rnext
$icode%z% *= %y%$$  $cnext compound assignment multiplication $cnext
    unspecified          $rnext
$icode%z% /= %y%$$  $cnext compound assignment division       $cnext
    unspecified
$tend

$head Example$$
$children%
    example/general/numeric_type.cpp
%$$
The file
$cref numeric_type.cpp$$
contains an example and test of using numeric types.
(It is easy to modify to test additional numeric types.)

$head Exercise$$

$list number$$
List three operators that are not supported by every
numeric type but that are supported by the numeric types
$code int$$,
$code float$$,
$code double$$.

$lnext
Which of the following are numeric types:
$code std::complex<double>$$,
$code std::valarray<double>$$,
$code std::vector<double>$$ ?

$lend

$end