package org.matheclipse.core.reflection.system;

import static org.matheclipse.core.expression.F.C0;
import static org.matheclipse.core.expression.F.C1;
import static org.matheclipse.core.expression.F.C1D2;
import static org.matheclipse.core.expression.F.C1D4;
import static org.matheclipse.core.expression.F.C2;
import static org.matheclipse.core.expression.F.C3;
import static org.matheclipse.core.expression.F.C5;
import static org.matheclipse.core.expression.F.CComplexInfinity;
import static org.matheclipse.core.expression.F.CN1;
import static org.matheclipse.core.expression.F.Cot;
import static org.matheclipse.core.expression.F.List;
import static org.matheclipse.core.expression.F.Pi;
import static org.matheclipse.core.expression.F.Plus;
import static org.matheclipse.core.expression.F.Power;
import static org.matheclipse.core.expression.F.Set;
import static org.matheclipse.core.expression.F.Sqrt;
import static org.matheclipse.core.expression.F.Times;
import static org.matheclipse.core.expression.F.fraction;
import static org.matheclipse.core.expression.F.integer;

import org.matheclipse.core.eval.interfaces.AbstractFunctionEvaluator;
import org.matheclipse.core.eval.interfaces.AbstractTrigArg1;
import org.matheclipse.core.eval.interfaces.INumeric;
import org.matheclipse.core.expression.ComplexNum;
import org.matheclipse.core.expression.ComplexUtils;
import org.matheclipse.core.expression.F;
import org.matheclipse.core.expression.Num;
import org.matheclipse.core.interfaces.IAST;
import org.matheclipse.core.interfaces.IExpr;
import org.matheclipse.core.interfaces.ISymbol;
import org.matheclipse.parser.client.SyntaxError;

/**
 * Cotangent function
 * 
 * See Trigonometric
 * functions
 */
public class Cot extends AbstractTrigArg1 implements INumeric {

//{ 
//Cot[Pi/4]=1,
//Cot[Pi/5]=1/5*Sqrt[25+10*Sqrt[5]],
//Cot[Pi/6]=3^(1/2),
//Cot[Pi/8]=Sqrt[2]+1,
//Cot[Pi/10]=Sqrt[5+2*Sqrt[5]],
//Cot[Pi/12]=2+3^(1/2),
//Cot[0]=ComplexInfinity,
//Cot[5/12*Pi]=2-Sqrt[3],
//Cot[2/5*Pi]=1/5*Sqrt[25-10*Sqrt[5]],
//Cot[3/10*Pi]=Sqrt[5-2*Sqrt[5]]
//}
	final static IAST RULES = List(
			Set(Cot(Times(C1D4,Pi)),C1),
			Set(Cot(Times(fraction(1L,5L),Pi)),Times(fraction(1L,5L),Sqrt(Plus(integer(25L),Times(integer(10L),Sqrt(C5)))))),
			Set(Cot(Times(fraction(1L,6L),Pi)),Power(C3,C1D2)),
			Set(Cot(Times(fraction(1L,8L),Pi)),Plus(Sqrt(C2),C1)),
			Set(Cot(Times(fraction(1L,10L),Pi)),Sqrt(Plus(C5,Times(C2,Sqrt(C5))))),
			Set(Cot(Times(fraction(1L,12L),Pi)),Plus(C2,Power(C3,C1D2))),
			Set(Cot(C0),CComplexInfinity),
			Set(Cot(Times(fraction(5L,12L),Pi)),Plus(C2,Times(CN1,Sqrt(C3)))),
			Set(Cot(Times(fraction(2L,5L),Pi)),Times(fraction(1L,5L),Sqrt(Plus(integer(25L),Times(CN1,Times(integer(10L),Sqrt(C5))))))),
			Set(Cot(Times(fraction(3L,10L),Pi)),Sqrt(Plus(C5,Times(CN1,Times(C2,Sqrt(C5))))))
			);

	@Override
	public IAST getRuleAST() {
		return RULES;
	}

	public Cot() {
	}
	
	@Override
	public IExpr evaluateArg1(final IExpr arg1) {
		if (AbstractFunctionEvaluator.isNegativeExpression(arg1)) { 
			return Times(CN1, Cot(Times(CN1, arg1)));
		}
		IExpr imPart = AbstractFunctionEvaluator.getPureImaginaryPart(arg1);
		if (imPart != null) {
			return F.Times(F.CNI, F.Coth(imPart));
		}
		IExpr[] parts = AbstractFunctionEvaluator.getPeriodicParts(arg1);
		if (parts != null) {
			if (parts[1].isInteger()) {
				// period Pi
				return F.Cot(parts[0]);
			}
		}
		return null;
	}
	
	@Override
	public IExpr numericEvalD1(final Num arg1) {
		return F.num(1.0D / Math.tan(arg1.getRealPart()));
	}

	@Override
	public IExpr numericEvalDC1(final ComplexNum arg1) {
		return ComplexUtils.tan(arg1).inverse();
	}

	public double evalReal(final double[] stack, final int top, final int size) {
		if (size != 1) {
			throw new UnsupportedOperationException();
		}
		return 1.0D / Math.tan(stack[top]);
	}

	@Override
	public void setUp(final ISymbol symbol) throws SyntaxError {
		symbol.setAttributes(ISymbol.LISTABLE | ISymbol.NUMERICFUNCTION);
		super.setUp(symbol);
	}
}