#include "../libraries/lepton/include/Lepton.h"

#include <iostream>
#include <limits>
#include <map>

using namespace Lepton;
using namespace std;

#define ASSERT_EQUAL_TOL(expected, found, tol) {double _scale_ = std::fabs(expected) > 1.0 ? std::fabs(expected) : 1.0; if (!(std::fabs((expected)-(found))/_scale_ <= (tol))) throw exception();};

/**
 * This is a custom function equal to f(x,y) = 2*x*y.
 */

class ExampleFunction : public CustomFunction {
    int getNumArguments() const {
        return 2;
    }
    double evaluate(const double* arguments) const {
        return 2.0*arguments[0]*arguments[1];
    }
    double evaluateDerivative(const double* arguments, const int* derivOrder) const {
        if (derivOrder[0] == 1) {
            if (derivOrder[1] == 0)
                return 2.0*arguments[1];
            else if (derivOrder[1] == 1)
                return 2.0;
            else
                return 0.0;
        }
        if (derivOrder[1] == 1) {
            if (derivOrder[0] == 0)
                return 2.0*arguments[0];
            else
                return 0.0;
        }
        return 0.0;
    }
    CustomFunction* clone() const {
        return new ExampleFunction();
    }
};

/**
 * Verify that an expression gives the correct value.
 */

void verifyEvaluation(const string& expression, double expectedValue) {
    map<string, CustomFunction*> customFunctions;
    ParsedExpression parsed = Parser::parse(expression, customFunctions);
    double value = parsed.evaluate();
    ASSERT_EQUAL_TOL(expectedValue, value, 1e-10);

    // Try optimizing it and make sure the result is still correct.

    value = parsed.optimize().evaluate();
    ASSERT_EQUAL_TOL(expectedValue, value, 1e-10);

    // Create an ExpressionProgram and see if that also gives the same result.

    ExpressionProgram program = parsed.createProgram();
    value = program.evaluate();
    ASSERT_EQUAL_TOL(expectedValue, value, 1e-10);
}

/**
 * Verify that an expression with variables gives the correct value.
 */

void verifyEvaluation(const string& expression, double x, double y, double expectedValue) {
    map<string, double> variables;
    variables["x"] = x;
    variables["y"] = y;
    ParsedExpression parsed = Parser::parse(expression);
    double value = parsed.evaluate(variables);
    ASSERT_EQUAL_TOL(expectedValue, value, 1e-10);

    // Try optimizing it and make sure the result is still correct.

    value = parsed.optimize().evaluate(variables);
    ASSERT_EQUAL_TOL(expectedValue, value, 1e-10);

    // Try optimizing with predefined values for the variables.

    value = parsed.optimize(variables).evaluate();
    ASSERT_EQUAL_TOL(expectedValue, value, 1e-10);

    // Create an ExpressionProgram and see if that also gives the same result.

    ExpressionProgram program = parsed.createProgram();
    value = program.evaluate(variables);
    ASSERT_EQUAL_TOL(expectedValue, value, 1e-10);
}

/**
 * Confirm that a parse error gets thrown.
 */

void verifyInvalidExpression(const string& expression) {
    try {
        Parser::parse(expression);
    }
    catch (const exception& ex) {
        return;
    }
    throw exception();
}

/**
 * Verify that two expressions give the same value.
 */

void verifySameValue(const ParsedExpression& exp1, const ParsedExpression& exp2, double x, double y) {
    map<string, double> variables;
    variables["x"] = x;
    variables["y"] = y;
    double val1 = exp1.evaluate(variables);
    double val2 = exp2.evaluate(variables);
    const double inf = numeric_limits<double>::infinity();
    if (val1 == val1 || val2 == val2) // If both are NaN, that's fine.
        if (val1 != inf || val2 != inf) // Both infinity is also fine.
            if (val1 != -inf || val2 != -inf) // Same for -infinity.
                ASSERT_EQUAL_TOL(val1, val2, 1e-10);
}

/**
 * Verify that the derivative of an expression is calculated correctly.
 */

void verifyDerivative(const string& expression, const string& expectedDeriv) {
    ParsedExpression computed = Parser::parse(expression).differentiate("x").optimize();
    ParsedExpression expected = Parser::parse(expectedDeriv);
    verifySameValue(computed, expected, 1.0, 2.0);
    verifySameValue(computed, expected, 2.0, 3.0);
    verifySameValue(computed, expected, -2.0, 3.0);
    verifySameValue(computed, expected, 2.0, -3.0);
}

/**
 * Test the use of a custom function.
 */

void testCustomFunction(const string& expression, const string& equivalent) {
    map<string, CustomFunction*> functions;
    functions["custom"] = new ExampleFunction();
    ParsedExpression exp1 = Parser::parse(expression, functions);
    ParsedExpression exp2 = Parser::parse(equivalent);
    verifySameValue(exp1, exp2, 1.0, 2.0);
    verifySameValue(exp1, exp2, 2.0, 3.0);
    verifySameValue(exp1, exp2, -2.0, 3.0);
    verifySameValue(exp1, exp2, 2.0, -3.0);
    ParsedExpression deriv1 = exp1.differentiate("x");
    ParsedExpression deriv2 = exp2.differentiate("x");
    verifySameValue(deriv1, deriv2, 1.0, 2.0);
    verifySameValue(deriv1, deriv2, 2.0, 3.0);
    verifySameValue(deriv1, deriv2, -2.0, 3.0);
    verifySameValue(deriv1, deriv2, 2.0, -3.0);
    ParsedExpression deriv3 = deriv1.differentiate("y");
    ParsedExpression deriv4 = deriv2.differentiate("y");
    verifySameValue(deriv3, deriv4, 1.0, 2.0);
    verifySameValue(deriv3, deriv4, 2.0, 3.0);
    verifySameValue(deriv3, deriv4, -2.0, 3.0);
    verifySameValue(deriv3, deriv4, 2.0, -3.0);
    delete functions["custom"];
}

int main() {
    try {
        verifyEvaluation("5", 5.0);
        verifyEvaluation("5*2", 10.0);
        verifyEvaluation("2*3+4*5", 26.0);
        verifyEvaluation("2^-3", 0.125);
        verifyEvaluation("-x", 2.0, 3.0, -2.0);
        verifyEvaluation("y^-x", 3.0, 2.0, 0.125);
        verifyEvaluation("1/-x", 3.0, 2.0, -1.0/3.0);
        verifyEvaluation("2.1e-4*x*(y+1)", 3.0, 1.0, 1.26e-3);
        verifyEvaluation("sin(2.5)", std::sin(2.5));
        verifyEvaluation("cot(x)", 3.0, 1.0, 1.0/std::tan(3.0));
        verifyEvaluation("x^2+y^3+x^-1+y^(1/2)", 1.0, 1.0, 4.0);
        verifyEvaluation("(2*x)*3", 4.0, 4.0, 24.0);
        verifyEvaluation("(x*2)*3", 4.0, 4.0, 24.0);
        verifyEvaluation("2*(x*3)", 4.0, 4.0, 24.0);
        verifyEvaluation("2*(3*x)", 4.0, 4.0, 24.0);
        verifyEvaluation("2*x/3", 1.0, 4.0, 2.0/3.0);
        verifyEvaluation("x*2/3", 1.0, 4.0, 2.0/3.0);
        verifyInvalidExpression("1..2");
        verifyInvalidExpression("1*(2+3");
        verifyInvalidExpression("5++4");
        verifyInvalidExpression("1+2)");
        verifyInvalidExpression("cos(2,3)");
        verifyDerivative("x", "1");
        verifyDerivative("x^2+x", "2*x+1");
        verifyDerivative("y^x-x", "log(y)*(y^x)-1");
        verifyDerivative("sin(x)", "cos(x)");
        verifyDerivative("cos(x)", "-sin(x)");
        verifyDerivative("tan(x)", "square(sec(x))");
        verifyDerivative("cot(x)", "-square(csc(x))");
        verifyDerivative("sec(x)", "sec(x)*tan(x)");
        verifyDerivative("csc(x)", "-csc(x)*cot(x)");
        verifyDerivative("exp(2*x)", "2*exp(2*x)");
        verifyDerivative("log(x)", "1/x");
        verifyDerivative("sqrt(x)", "0.5/sqrt(x)");
        verifyDerivative("asin(x)", "1/sqrt(1-x^2)");
        verifyDerivative("acos(x)", "-1/sqrt(1-x^2)");
        verifyDerivative("atan(x)", "1/(1+x^2)");
        verifyDerivative("sinh(x)", "cosh(x)");
        verifyDerivative("cosh(x)", "sinh(x)");
        verifyDerivative("tanh(x)", "1/(cosh(x)^2)");
        verifyDerivative("recip(x)", "-1/x^2");
        verifyDerivative("square(x)", "2*x");
        verifyDerivative("cube(x)", "3*x^2");
        testCustomFunction("custom(x, y)/2", "x*y");
        testCustomFunction("custom(x^2, 1)+custom(2, y-1)", "2*x^2+4*(y-1)");
        cout << Parser::parse("2*3*x").optimize() << endl;
        cout << Parser::parse("1/(1+x)").optimize() << endl;
        cout << Parser::parse("x^(1/2)").optimize() << endl;
        cout << Parser::parse("log(3*cos(x))^(sqrt(4)-2)").optimize() << endl;
    }
    catch(const exception& e) {
        cout << "exception: " << e.what() << endl;
        return 1;
    }
    cout << "Done" << endl;
    return 0;
}