package org.matheclipse.core.reflection.system;

import static org.matheclipse.core.expression.F.*;
import static org.matheclipse.core.expression.F.$p;
import static org.matheclipse.core.expression.F.$s;
import static org.matheclipse.core.expression.F.C0;
import static org.matheclipse.core.expression.F.CComplexInfinity;
import static org.matheclipse.core.expression.F.CN1;
import static org.matheclipse.core.expression.F.Condition;
import static org.matheclipse.core.expression.F.Less;
import static org.matheclipse.core.expression.F.List;
import static org.matheclipse.core.expression.F.Sec;
import static org.matheclipse.core.expression.F.Set;
import static org.matheclipse.core.expression.F.SetDelayed;
import static org.matheclipse.core.expression.F.SignCmp;
import static org.matheclipse.core.expression.F.Times;

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.IInteger;
import org.matheclipse.core.interfaces.ISymbol;
import org.matheclipse.parser.client.SyntaxError;

/**
 * Secant function
 * 
 * See Trigonometric functions
 */
public class Sec extends AbstractTrigArg1 implements INumeric {

	// {
	// Sec[0]=1,
	// Sec[Pi/2]=ComplexInfinity,
	// Sec[Pi/3]=2,
	// Sec[Pi/4]=Sqrt[2],
	// Sec[Pi/5]=Sqrt[5]-1,
	// Sec[Pi/6]=2/3*Sqrt[3],
	// Sec[Pi/8]=Sqrt[4-2*Sqrt[2]],
	// Sec[Pi/10]=1/5*Sqrt[50-10*Sqrt[5]],
	// Sec[Pi/12]=Sqrt[6]-Sqrt[2],
	// Sec[3/8*Pi]=Sqrt[4+2*Sqrt[2]],
	// Sec[3/10*Pi]=1/5*Sqrt[50+10*Sqrt[5]],
	// Sec[2/5*Pi]=1+Sqrt[5],
	// Sec[5/12*Pi]=Sqrt[6]+Sqrt[2]
	// }

	final static IAST RULES = List(
			Set(Sec(C0), C1),
			Set(Sec(Times(C1D2, Pi)), CComplexInfinity),
			Set(Sec(Times(C1D3, Pi)), C2),
			Set(Sec(Times(C1D4, Pi)), Sqrt(C2)),
			Set(Sec(Times(fraction(1L, 5L), Pi)), Plus(Sqrt(C5), Times(CN1, C1))),
			Set(Sec(Times(fraction(1L, 6L), Pi)), Times(fraction(2L, 3L), Sqrt(C3))),
			Set(Sec(Times(fraction(1L, 8L), Pi)), Sqrt(Plus(C4, Times(CN1, Times(C2, Sqrt(C2)))))),
			Set(Sec(Times(fraction(1L, 10L), Pi)),
					Times(fraction(1L, 5L), Sqrt(Plus(integer(50L), Times(CN1, Times(integer(10L), Sqrt(C5))))))),
			Set(Sec(Times(fraction(1L, 12L), Pi)), Plus(Sqrt(integer(6L)), Times(CN1, Sqrt(C2)))),
			Set(Sec(Times(fraction(3L, 8L), Pi)), Sqrt(Plus(C4, Times(C2, Sqrt(C2))))),
			Set(Sec(Times(fraction(3L, 10L), Pi)), Times(fraction(1L, 5L), Sqrt(Plus(integer(50L), Times(integer(10L), Sqrt(C5)))))),
			Set(Sec(Times(fraction(2L, 5L), Pi)), Plus(C1, Sqrt(C5))),
			Set(Sec(Times(fraction(5L, 12L), Pi)), Plus(Sqrt(integer(6L)), Sqrt(C2))));

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

	public Sec() {
	}

	@Override
	public IExpr evaluateArg1(final IExpr arg1) {
		if (AbstractFunctionEvaluator.isNegativeExpression(arg1)) {
			return Sec(Times(CN1, arg1));
		}
		IExpr imPart = AbstractFunctionEvaluator.getPureImaginaryPart(arg1);
		if (imPart != null) {
			return F.Sech(imPart);
		}
		IExpr[] parts = AbstractFunctionEvaluator.getPeriodicParts(arg1);
		if (parts != null) {
			if (parts[1].isInteger()) {
				// period 2*Pi
				IInteger i = (IInteger) parts[1];
				if (i.isEven()) {
					return F.Sec(parts[0]);
				} else {
					return F.Times(F.CN1, F.Sec(parts[0]));
				}
			}
		}
		return null;
	}

	@Override
	public IExpr numericEvalD1(final Num arg1) {
		return F.num(1.0D / Math.cos(arg1.getRealPart()));
	}

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

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

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