Emily Boudreaux
856ab51b4c
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
141 lines
3.3 KiB
C++
141 lines
3.3 KiB
C++
# ifndef CPPAD_UTILITY_POW_INT_HPP
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# define CPPAD_UTILITY_POW_INT_HPP
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/* --------------------------------------------------------------------------
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CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-20 Bradley M. Bell
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CppAD is distributed under the terms of the
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Eclipse Public License Version 2.0.
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This Source Code may also be made available under the following
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Secondary License when the conditions for such availability set forth
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in the Eclipse Public License, Version 2.0 are satisfied:
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GNU General Public License, Version 2.0 or later.
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---------------------------------------------------------------------------- */
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/*
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-------------------------------------------------------------------------------
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$begin pow_int$$
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$spell
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cppad.hpp
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CppAD
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namespace
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const
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$$
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$section The Integer Power Function$$
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$head Syntax$$
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$codei%# include <cppad/utility/pow_int.hpp>
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%$$
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$icode%z% = pow(%x%, %y%)%$$
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$head See Also$$
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$cref pow$$
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$head Purpose$$
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Determines the value of the power function
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$latex \[
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{\rm pow} (x, y) = x^y
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\] $$
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for integer exponents $icode n$$
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using multiplication and possibly division to compute the value.
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The other CppAD $cref pow$$ function may use logarithms and exponentiation
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to compute derivatives of the same value
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(which will not work if $icode x$$ is less than or equal zero).
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$head Include$$
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The file $code cppad/utility/pow_int.hpp$$
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is included by $code cppad/cppad.hpp$$
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but it can also be included separately with out the rest of
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the $code CppAD$$ routines.
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Including this file defines
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this version of the $code pow$$ within the $code CppAD$$ namespace.
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$head x$$
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The argument $icode x$$ has prototype
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$codei%
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const %Type%& %x%
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%$$
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$head y$$
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The argument $icode y$$ has prototype
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$codei%
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const int& %y%
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%$$
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$head z$$
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The result $icode z$$ has prototype
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$codei%
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%Type% %z%
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%$$
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$head Type$$
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The type $icode Type$$ must support the following operations
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where $icode a$$ and $icode b$$ are $icode Type$$ objects
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and $icode i$$ is an $code int$$:
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$table
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$bold Operation$$ $pre $$
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$cnext $bold Description$$
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$cnext $bold Result Type$$
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$rnext
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$icode%Type% %a%(%i%)%$$
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$cnext construction of a $icode Type$$ object from an $code int$$
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$cnext $icode Type$$
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$rnext
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$icode%a% * %b%$$
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$cnext binary multiplication of $icode Type$$ objects
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$cnext $icode Type$$
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$rnext
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$icode%a% / %b%$$
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$cnext binary division of $icode Type$$ objects
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$cnext $icode Type$$
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$tend
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$head Operation Sequence$$
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The $icode Type$$ operation sequence used to calculate $icode z$$ is
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$cref/independent/glossary/Operation/Independent/$$
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of $icode x$$.
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$head Example$$
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$children%
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example/utility/pow_int.cpp
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%$$
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The file $cref pow_int.cpp$$
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is an example and test of this function.
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$end
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-------------------------------------------------------------------------------
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*/
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namespace CppAD {
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template <class Type>
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inline Type pow (const Type& x, const int& n)
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{
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Type p(1);
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int n2 = n / 2;
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if( n == 0 )
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return p;
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if( n < 0 )
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return p / pow(x, -n);
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if( n == 1 )
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return x;
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// p = (x^2)^(n/2)
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p = pow( x * x , n2 );
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// n is even case
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if( n % 2 == 0 )
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return p;
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// n is odd case
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return p * x;
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}
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}
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# endif
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