build(CppAD): brought in CppAD for autodiff

we need an autodiff library at some point (or we need to roll our own but I do not think that makes sense). CppAD is well tested and header only and easy to include. It is also Liscene compatible with GPL v3.0. Here we bring it in as a dependency

build-config/cppad/include/cppad/utility/pow_int.hpp

@@ -0,0 +1,140 @@
+# ifndef CPPAD_UTILITY_POW_INT_HPP
+# define CPPAD_UTILITY_POW_INT_HPP
+/* --------------------------------------------------------------------------
+CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-20 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 pow_int$$
+$spell
+    cppad.hpp
+    CppAD
+    namespace
+    const
+$$
+
+
+$section The Integer Power Function$$
+
+$head Syntax$$
+$codei%# include <cppad/utility/pow_int.hpp>
+%$$
+$icode%z% = pow(%x%, %y%)%$$
+
+$head See Also$$
+$cref pow$$
+
+$head Purpose$$
+Determines the value of the power function
+$latex \[
+    {\rm pow} (x, y) = x^y
+\] $$
+for integer exponents $icode n$$
+using multiplication and possibly division to compute the value.
+The other CppAD $cref pow$$ function may use logarithms and exponentiation
+to compute derivatives of the same value
+(which will not work if $icode x$$ is less than or equal zero).
+
+$head Include$$
+The file $code cppad/utility/pow_int.hpp$$
+is included by $code cppad/cppad.hpp$$
+but it can also be included separately with out the rest of
+the $code CppAD$$ routines.
+Including this file defines
+this version of the $code pow$$ within the $code CppAD$$ namespace.
+
+$head x$$
+The argument $icode x$$ has prototype
+$codei%
+    const %Type%& %x%
+%$$
+
+$head y$$
+The argument $icode y$$ has prototype
+$codei%
+    const int& %y%
+%$$
+
+$head z$$
+The result $icode z$$ has prototype
+$codei%
+    %Type% %z%
+%$$
+
+$head Type$$
+The type $icode Type$$ must support the following operations
+where $icode a$$ and $icode b$$ are $icode Type$$ objects
+and $icode i$$ is an $code int$$:
+$table
+$bold Operation$$  $pre  $$
+    $cnext $bold Description$$
+    $cnext $bold Result Type$$
+$rnext
+$icode%Type% %a%(%i%)%$$
+    $cnext construction of a $icode Type$$ object from an $code int$$
+    $cnext $icode Type$$
+$rnext
+$icode%a% * %b%$$
+    $cnext binary multiplication of $icode Type$$ objects
+    $cnext $icode Type$$
+$rnext
+$icode%a% / %b%$$
+    $cnext binary division of $icode Type$$ objects
+    $cnext $icode Type$$
+$tend
+
+$head Operation Sequence$$
+The $icode Type$$ operation sequence used to calculate $icode z$$ is
+$cref/independent/glossary/Operation/Independent/$$
+of $icode x$$.
+
+$head Example$$
+$children%
+    example/utility/pow_int.cpp
+%$$
+The file $cref pow_int.cpp$$
+is an example and test of this function.
+
+
+$end
+-------------------------------------------------------------------------------
+*/
+
+namespace CppAD {
+
+    template <class Type>
+    inline Type pow (const Type& x, const int& n)
+    {
+        Type p(1);
+        int n2 = n / 2;
+
+        if( n == 0 )
+            return p;
+        if( n < 0 )
+            return p / pow(x, -n);
+        if( n == 1 )
+            return x;
+
+        // p = (x^2)^(n/2)
+        p = pow( x * x , n2 );
+
+        // n is even case
+        if( n % 2 == 0 )
+            return p;
+
+        // n is odd case
+        return p * x;
+    }
+
+}
+
+# endif