matheval.hpp

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// Copyright (C) 2011-2013 Rhys Ulerich
// Copyright (C) ??? Martin Bauer
// Copyright (C) 2017 Henri Menke
//
// This code borrows heavily from code written by Rhys Ulerich and
// Martin Bauer.  They licensed it under the Mozilla Public License,
// v. 2.0 and the GNU General Public License (no version info),
// respectively.  I believe that I have made enough contributions and
// altered this code far enough from the originals that I can
// relicense it under the Boost Software License.
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
#pragma once
 
#include <algorithm>
#include <cmath>
#include <functional>
#include <iterator>
#include <limits>
#include <map>
#include <sstream>
#include <stdexcept>
#include <string>
 
#define BOOST_RESULT_OF_USE_DECLTYPE
#define BOOST_SPIRIT_USE_PHOENIX_V3
#include <boost/math/constants/constants.hpp>
#include <boost/spirit/include/phoenix.hpp>
#include <boost/spirit/include/qi.hpp>
#include <boost/variant.hpp>
 
 
namespace matheval {
 
    namespace detail {
 
        namespace qi = boost::spirit::qi;
        namespace ascii = boost::spirit::ascii;
 
        namespace math {
 
            template < typename T >
            T sgn(T x) { return (T{0} < x) - (x < T{0}); }
 
            template < typename T >
            T isnan(T x) { return std::isnan(x); }
 
            template < typename T >
            T isinf(T x) { return std::isinf(x); }
 
            template < typename T >
            T deg(T x) { return x*boost::math::constants::radian<T>(); }
 
            template < typename T >
            T rad(T x) { return x*boost::math::constants::degree<T>(); }
 
        }
 
        // AST
 
        template < typename real_t > struct unary_op;
        template < typename real_t > struct binary_op;
 
        struct nil {};
 
        template < typename real_t >
        struct expr_ast
        {
            using tree_t = boost::variant<
                nil // can't happen!
                , real_t
                , std::string
                , boost::recursive_wrapper<expr_ast<real_t>>
                , boost::recursive_wrapper<binary_op<real_t>>
                , boost::recursive_wrapper<unary_op<real_t>>
                >;
        public:
            tree_t tree;
 
            expr_ast() : tree(nil{}) {}
 
            template <typename Expr>
            expr_ast(Expr other) : tree(std::move(other)) {} // NOLINT
 
            expr_ast& operator+=(expr_ast const &rhs);
            expr_ast& operator-=(expr_ast const &rhs);
            expr_ast& operator*=(expr_ast const &rhs);
            expr_ast& operator/=(expr_ast const &rhs);
        };
 
        template < typename real_t >
        struct unary_op
        {
            using op_t = std::function<real_t(real_t)>;
 
            unary_op(op_t op, expr_ast<real_t> rhs)
                : op(std::move(op)), rhs(std::move(rhs))
            {}
 
            op_t op;
            expr_ast<real_t> rhs;
        };
 
        template < typename real_t >
        struct binary_op
        {
            using op_t = std::function<real_t(real_t,real_t)>;
 
            binary_op(op_t op, expr_ast<real_t> lhs, expr_ast<real_t> rhs)
                : op(std::move(op)), lhs(std::move(lhs)), rhs(std::move(rhs))
            {}
 
            op_t op;
            expr_ast<real_t> lhs;
            expr_ast<real_t> rhs;
        };
 
        template < typename real_t >
        expr_ast<real_t>& expr_ast<real_t>::operator+=(expr_ast<real_t> const &rhs)
        {
            tree = binary_op<real_t>(std::plus<real_t>{}, tree, rhs);
            return *this;
        }
        template < typename real_t >
        expr_ast<real_t>& expr_ast<real_t>::operator-=(expr_ast<real_t> const &rhs)
        {
            tree = binary_op<real_t>(std::minus<real_t>{}, tree, rhs);
            return *this;
        }
        template < typename real_t >
        expr_ast<real_t>& expr_ast<real_t>::operator*=(expr_ast<real_t> const &rhs)
        {
            tree = binary_op<real_t>(std::multiplies<real_t>{}, tree, rhs);
            return *this;
        }
        template < typename real_t >
        expr_ast<real_t>& expr_ast<real_t>::operator/=(expr_ast<real_t> const &rhs)
        {
            tree = binary_op<real_t>(std::divides<real_t>{}, tree, rhs);
            return *this;
        }
 
        template < typename real_t >
        class eval_ast
        {
        public:
            using result_type = real_t;
 
            using symbol_table_t = std::map<std::string, result_type>;
 
            explicit eval_ast(symbol_table_t sym) : st(std::move(sym)) {}
 
            result_type operator()(nil /*unused*/) const { return 0; }
 
            result_type operator()(result_type n)  const { return n; }
 
            result_type operator()(std::string const &c) const
            {
                auto it = st.find(c);
                if (it == st.end()) {
                    throw std::invalid_argument("Unknown variable " + c); // NOLINT
                }
                return it->second;
            }
 
            result_type operator()(expr_ast<real_t> const& ast) const
            {
                return boost::apply_visitor(*this, ast.tree);
            }
 
            result_type operator()(binary_op<real_t> const& tree) const
            {
                return tree.op(
                               boost::apply_visitor(*this, tree.lhs.tree),
                               boost::apply_visitor(*this, tree.rhs.tree)
                               );
            }
 
            result_type operator()(unary_op<real_t> const& tree) const
            {
                return tree.op(
                               boost::apply_visitor(*this, tree.rhs.tree)
                               );
            }
 
        private:
            symbol_table_t st;
        };
 
        template <typename T> struct holds_alternative_impl {
            using result_type = bool;
 
            template <typename U> bool operator()(U const & /*unused*/) const {
                return std::is_same<U, T>::value;
            }
        };
 
        template <typename T, typename... Ts>
        bool holds_alternative(boost::variant<Ts...> const &v) {
            return boost::apply_visitor(holds_alternative_impl<T>(), v);
        }
 
        template <typename real_t> struct ConstantFolder {
            using result_type = typename expr_ast<real_t>::tree_t;
 
            result_type operator()(nil /*unused*/) const { return 0; }
 
            result_type operator()(real_t n) const { return n; }
 
            result_type operator()(std::string const &c) const { return c; }
 
            result_type operator()(expr_ast<real_t> const &ast) const {
                return boost::apply_visitor(*this, ast.tree);
            }
 
            result_type operator()(binary_op<real_t> const &tree) const {
                auto lhs = boost::apply_visitor(*this, tree.lhs.tree);
                auto rhs = boost::apply_visitor(*this, tree.rhs.tree);
 
                /* If both operands are known, we can directly evaluate the function,
                 * else we just update the children with the new expressions. */
                if (holds_alternative<real_t>(lhs) && holds_alternative<real_t>(rhs)) {
                    return tree.op(boost::get<real_t>(lhs), boost::get<real_t>(rhs));
                }
                return binary_op<real_t>(tree.op, lhs, rhs);
            }
 
            result_type operator()(unary_op<real_t> const &tree) const {
                auto rhs = boost::apply_visitor(*this, tree.rhs.tree);
                /* If the operand is known, we can directly evaluate the function. */
                if (holds_alternative<real_t>(rhs)) {
                    return tree.op(boost::get<real_t>(rhs));
                }
                return unary_op<real_t>(tree.op, rhs);
            }
        };
 
        // Expressions
 
        template < typename real_t >
        struct unary_expr_ {
            template < typename T > struct result { using type = T; };
 
            expr_ast<real_t> operator()(typename unary_op<real_t>::op_t op,
                                        expr_ast<real_t> const &rhs) const {
                return expr_ast<real_t>(unary_op<real_t>(op, rhs));
            }
        };
 
        template < typename real_t >
        struct binary_expr_ {
            template < typename T > struct result { using type = T; };
 
            expr_ast<real_t> operator()(typename binary_op<real_t>::op_t op,
                                        expr_ast<real_t> const &lhs,
                                        expr_ast<real_t> const &rhs) const {
                return expr_ast<real_t>(binary_op<real_t>(op, lhs, rhs));
            }
        };
 
        struct expectation_handler {
            template < typename Iterator >
            void operator()(Iterator first, Iterator last,
                            boost::spirit::info const& info) const {
                std::stringstream msg;
                msg << "Expected "
                    << info
                    << " at \""
                    << std::string{first, last}
                << "\"";
 
                throw std::runtime_error(msg.str()); // NOLINT
            }
        };
 
 
        // Grammar
 
        template < typename real_t, typename Iterator >
        struct grammar
            : qi::grammar<
            Iterator, expr_ast<real_t>(), ascii::space_type
              >
        {
        private:
            expectation_handler err_handler;
            qi::rule<Iterator, expr_ast<real_t>(), ascii::space_type> expression;
            qi::rule<Iterator, expr_ast<real_t>(), ascii::space_type> term;
            qi::rule<Iterator, expr_ast<real_t>(), ascii::space_type> factor;
            qi::rule<Iterator, expr_ast<real_t>(), ascii::space_type> primary;
            qi::rule<Iterator, std::string()> variable;
        public:
            struct constant_
                : boost::spirit::qi::symbols<
            typename std::iterator_traits<Iterator>::value_type,
            real_t
            >
            {
                constant_()
                {
                    this->add
                        ("e"      , boost::math::constants::e<real_t>()   )
                        ("epsilon", std::numeric_limits<real_t>::epsilon())
                        ("phi"    , boost::math::constants::phi<real_t>() )
                        ("pi"     , boost::math::constants::pi<real_t>()  )
                        ;
                }
            } constant;
 
            struct ufunc_
                : boost::spirit::qi::symbols<
                typename std::iterator_traits<Iterator>::value_type,
                typename unary_op<real_t>::op_t
                >
            {
                ufunc_()
                {
                    this->add
                        ("abs"    , static_cast<real_t(*)(real_t)>(&std::abs   ))
                        ("acos"   , static_cast<real_t(*)(real_t)>(&std::acos  ))
                        ("acosh"  , static_cast<real_t(*)(real_t)>(&std::acosh ))
                        ("asin"   , static_cast<real_t(*)(real_t)>(&std::asin  ))
                        ("asinh"  , static_cast<real_t(*)(real_t)>(&std::asinh ))
                        ("atan"   , static_cast<real_t(*)(real_t)>(&std::atan  ))
                        ("atanh"  , static_cast<real_t(*)(real_t)>(&std::atanh ))
                        ("cbrt"   , static_cast<real_t(*)(real_t)>(&std::cbrt  ))
                        ("ceil"   , static_cast<real_t(*)(real_t)>(&std::ceil  ))
                        ("cos"    , static_cast<real_t(*)(real_t)>(&std::cos   ))
                        ("cosh"   , static_cast<real_t(*)(real_t)>(&std::cosh  ))
                        ("deg2rad", static_cast<real_t(*)(real_t)>(&math::deg  ))
                        ("erf"    , static_cast<real_t(*)(real_t)>(&std::erf   ))
                        ("erfc"   , static_cast<real_t(*)(real_t)>(&std::erfc  ))
                        ("exp"    , static_cast<real_t(*)(real_t)>(&std::exp   ))
                        ("exp2"   , static_cast<real_t(*)(real_t)>(&std::exp2  ))
                        ("floor"  , static_cast<real_t(*)(real_t)>(&std::floor ))
                        ("isinf"  , static_cast<real_t(*)(real_t)>(&math::isinf))
                        ("isnan"  , static_cast<real_t(*)(real_t)>(&math::isnan))
                        ("log"    , static_cast<real_t(*)(real_t)>(&std::log   ))
                        ("log2"   , static_cast<real_t(*)(real_t)>(&std::log2  ))
                        ("log10"  , static_cast<real_t(*)(real_t)>(&std::log10 ))
                        ("rad2deg", static_cast<real_t(*)(real_t)>(&math::rad  ))
                        ("round"  , static_cast<real_t(*)(real_t)>(&std::round ))
                        ("sgn"    , static_cast<real_t(*)(real_t)>(&math::sgn  ))
                        ("sin"    , static_cast<real_t(*)(real_t)>(&std::sin   ))
                        ("sinh"   , static_cast<real_t(*)(real_t)>(&std::sinh  ))
                        ("sqrt"   , static_cast<real_t(*)(real_t)>(&std::sqrt  ))
                        ("tan"    , static_cast<real_t(*)(real_t)>(&std::tan   ))
                        ("tanh"   , static_cast<real_t(*)(real_t)>(&std::tanh  ))
                        ("tgamma" , static_cast<real_t(*)(real_t)>(&std::tgamma))
                        ;
                }
            } ufunc;
 
            struct bfunc_
                : boost::spirit::qi::symbols<
                typename std::iterator_traits<Iterator>::value_type,
                typename binary_op<real_t>::op_t
                >
            {
                bfunc_()
                {
                    this->add
                        ("atan2", static_cast<real_t(*)(real_t,real_t)>(&std::atan2))
                        ("max"  , static_cast<real_t(*)(real_t,real_t)>(&std::fmax ))
                        ("min"  , static_cast<real_t(*)(real_t,real_t)>(&std::fmin ))
                        ("pow"  , static_cast<real_t(*)(real_t,real_t)>(&std::pow  ))
                        ;
                }
            } bfunc;
 
            grammar() : grammar::base_type(expression)
            {
                using boost::spirit::qi::real_parser;
                using boost::spirit::qi::real_policies;
                real_parser<real_t,real_policies<real_t>> real;
 
                using boost::spirit::lexeme;
                using boost::spirit::qi::_1;
                using boost::spirit::qi::_2;
                using boost::spirit::qi::_3;
                using boost::spirit::qi::_4;
                using boost::spirit::qi::_val;
                using boost::spirit::qi::alpha;
                using boost::spirit::qi::alnum;
                using boost::spirit::qi::raw;
 
                boost::phoenix::function<unary_expr_<real_t>> unary_expr;
                boost::phoenix::function<binary_expr_<real_t>> binary_expr;
 
                auto fmod = static_cast<real_t(*)(real_t,real_t)>(&std::fmod);
                auto pow = static_cast<real_t(*)(real_t,real_t)>(&std::pow);
 
                expression =
                    term                  [_val =  _1]
                    >> *(  ('+' > term    [_val += _1])
                           |  ('-' > term    [_val -= _1])
                           )
                    ;
 
                term =
                    factor                [_val =  _1]
                    >> *(  ('*' > factor  [_val *= _1])
                           |  ('/' > factor  [_val /= _1])
                           |  ('%' > factor  [_val = binary_expr(fmod, _val, _1)])
                           )
                    ;
 
                factor =
                    primary               [_val =  _1]
                    >> *(  ("**" > factor [_val = binary_expr(pow, _val, _1)])
                           )
                    ;
 
                variable =
                    raw[lexeme[alpha >> *(alnum | '_')]];
 
                primary =
                    real                   [_val =  _1]
                    |   ('(' > expression  [_val =  _1] > ')')
                    |   ('-' > primary     [_val = unary_expr(std::negate<real_t>{}, _1)])
                    |   ('+' > primary     [_val =  _1])
                    |   (bfunc > '(' > expression > ',' > expression > ')')
                    [_val = binary_expr(_1, _2, _3)]
                    |   (ufunc > '(' > expression > ')')
                    [_val = unary_expr(_1, _2)]
                    |   constant           [_val =  _1]
                    |   variable           [_val =  _1]
                    ;
 
                expression.name("expression");
                term.name("term");
                factor.name("factor");
                variable.name("variable");
                primary.name("primary");
 
                using boost::spirit::qi::fail;
                using boost::spirit::qi::on_error;
                using boost::phoenix::bind;
                using boost::phoenix::ref;
 
                on_error<fail>
                    (
                     expression,
                     bind(ref(err_handler), _3, _2, _4)
                     );
            }
        };
 
        template <typename real_t, typename Iterator>
        detail::expr_ast<real_t> parse(Iterator first, Iterator last) {
            static detail::grammar<real_t, Iterator> const g;
 
            auto ast = detail::expr_ast<real_t>{};
 
            bool r = qi::phrase_parse(first, last, g, ascii::space, ast);
 
            if (!r || first != last) {
                std::string rest(first, last);
                throw std::runtime_error("Parsing failed at " + rest); // NOLINT
            }
 
            return ast;
        }
 
    } // namespace detail
 
 
    template < typename real_t >
    class Parser
    {
        detail::expr_ast<real_t> ast;
    public:
        template < typename Iterator >
        void parse(Iterator first, Iterator last)
        {
            ast = detail::parse<real_t>(first, last);
        }
 
        void parse(std::string const &str)
        {
            parse(str.begin(), str.end());
        }
 
        void optimize() {
            ast.tree = boost::apply_visitor(detail::ConstantFolder<real_t>{}, ast.tree);
        }
 
        real_t evaluate(typename detail::eval_ast<real_t>::symbol_table_t const &st)
        {
            detail::eval_ast<real_t> solver(st);
            return solver(ast);
        }
    };
 
 
    template < typename real_t, typename Iterator >
    real_t parse(Iterator first, Iterator last,
                 typename detail::eval_ast<real_t>::symbol_table_t const &st)
    {
        Parser<real_t> parser;
        parser.parse(first, last);
        return parser.evaluate(st);
    }
 
    template < typename real_t >
    real_t parse(std::string const &str,
                 typename detail::eval_ast<real_t>::symbol_table_t const &st)
    {
        return parse<real_t>(str.begin(), str.end(), st);
    }
 
} // namespace matheval