Power.cs

using System;
using System.Collections.Generic;
using System.Threading.Tasks;
using Waher.Script.Abstraction.Elements;
using Waher.Script.Exceptions;
using Waher.Script.Functions.Analytic;
using Waher.Script.Model;
using Waher.Script.Objects;
 
namespace Waher.Script.Operators.Arithmetics
{
    public class Power : BinaryOperator, IDifferentiable
    {
        public Power(ScriptNode Left, ScriptNode Right, int Start, int Length, Expression Expression)
            : base(Left, Right, Start, Length, Expression)
        {
        }
 
        public override IElement Evaluate(Variables Variables)
        {
            IElement Left = this.left.Evaluate(Variables);
            IElement Right = this.right.Evaluate(Variables);
 
            return EvaluatePower(Left, Right, this);
        }
 
        public override async Task<IElement> EvaluateAsync(Variables Variables)
        {
            if (!this.isAsync)
                return this.Evaluate(Variables);
 
            IElement Left = await this.left.EvaluateAsync(Variables);
            IElement Right = await this.right.EvaluateAsync(Variables);
 
            return EvaluatePower(Left, Right, this);
        }
 
        public static IElement EvaluatePower(IElement Left, IElement Right, ScriptNode Node)
        {
            if (Right.AssociatedObjectValue is double DR)
            {
                if (Left.AssociatedObjectValue is double DL)
                    return new DoubleNumber(Math.Pow(DL, DR));
 
                if (Left is IRingElement LE)
                {
                    if (DR >= long.MinValue && DR <= long.MaxValue && Math.Truncate(DR) == DR)
                    {
                        long n = (long)DR;
 
                        if (n < 0)
                        {
                            LE = LE.Invert();
                            if (LE is null)
                                throw new ScriptRuntimeException("Base element not invertible.", Node);
 
                            n = -n;
                        }
                        else if (n == 0)
                        {
                            if (!(LE is ICommutativeRingWithIdentityElement LE2))
                                throw new ScriptRuntimeException("Base element ring does not have unity.", Node);
 
                            return LE2.One;
                        }
 
                        IRingElement Result = null;
 
                        while (n > 0)
                        {
                            if ((n & 1) == 1)
                            {
                                if (Result is null)
                                    Result = LE;
                                else
                                    Result = (IRingElement)Multiply.EvaluateMultiplication(Result, LE, Node);
                            }
 
                            n >>= 1;
                            if (n > 0)
                                LE = (IRingElement)Multiply.EvaluateMultiplication(LE, LE, Node);
                        }
 
                        return Result;
                    }
                    else
                        throw new ScriptRuntimeException("Exponent too large.", Node);
                }
            }
 
            if (Left.IsScalar)
            {
                if (Right.IsScalar)
                    throw new ScriptRuntimeException("Power operation could not be computed.", Node);
                else
                {
                    LinkedList<IElement> Elements = new LinkedList<IElement>();
 
                    foreach (IElement RightChild in Right.ChildElements)
                        Elements.AddLast(EvaluatePower(Left, RightChild, Node));
 
                    return Right.Encapsulate(Elements, Node);
                }
            }
            else
            {
                if (Right.IsScalar)
                {
                    LinkedList<IElement> Elements = new LinkedList<IElement>();
 
                    foreach (IElement LeftChild in Left.ChildElements)
                        Elements.AddLast(EvaluatePower(LeftChild, Right, Node));
 
                    return Left.Encapsulate(Elements, Node);
                }
                else
                {
                    ICollection<IElement> LeftChildren = Left.ChildElements;
                    ICollection<IElement> RightChildren = Right.ChildElements;
 
                    if (LeftChildren.Count == RightChildren.Count)
                    {
                        LinkedList<IElement> Elements = new LinkedList<IElement>();
                        IEnumerator<IElement> eLeft = LeftChildren.GetEnumerator();
                        IEnumerator<IElement> eRight = RightChildren.GetEnumerator();
 
                        try
                        {
                            while (eLeft.MoveNext() && eRight.MoveNext())
                                Elements.AddLast(EvaluatePower(eLeft.Current, eRight.Current, Node));
                        }
                        finally
                        {
                            eLeft.Dispose();
                            eRight.Dispose();
                        }
 
                        return Left.Encapsulate(Elements, Node);
                    }
                    else
                    {
                        LinkedList<IElement> LeftResult = new LinkedList<IElement>();
 
                        foreach (IElement LeftChild in LeftChildren)
                        {
                            LinkedList<IElement> RightResult = new LinkedList<IElement>();
 
                            foreach (IElement RightChild in RightChildren)
                                RightResult.AddLast(EvaluatePower(LeftChild, RightChild, Node));
 
                            LeftResult.AddLast(Right.Encapsulate(RightResult, Node));
                        }
 
                        return Left.Encapsulate(LeftResult, Node);
                    }
                }
            }
        }
 
        public ScriptNode Differentiate(string VariableName, Variables Variables)
        {
            int Start = this.Start;
            int Len = this.Length;
            Expression Expression = this.Expression;
 
            if (this.left is ConstantElement ConstantBase)
            {
                return this.DifferentiationChainRule(VariableName, Variables, this.right,
                    new Multiply(
                        this,
                        new Ln(ConstantBase, Start, Len, Expression),
                        Start, Len, Expression));
            }
            else if (this.left is IDifferentiable Left)
            {
                if (this.right is ConstantElement ConstantExp)
                {
                    if (ConstantExp.Constant.Equals(DoubleNumber.OneElement))
                        return Left.Differentiate(VariableName, Variables);
                    else if (ConstantExp.Constant.Equals(DoubleNumber.TwoElement))
                    {
                        return this.DifferentiationChainRule(VariableName, Variables, this.left,
                            new Multiply(
                                ConstantExp,
                                this.left,
                                Start, Len, Expression));
                    }
                    else
                    {
                        return this.DifferentiationChainRule(VariableName, Variables, this.left,
                            new Multiply(
                                ConstantExp,
                                new Power(
                                    this.left,
                                    new ConstantElement(Subtract.EvaluateSubtraction(ConstantExp.Constant, DoubleNumber.OneElement, this), Start, Len, Expression),
                                    Start, Len, Expression),
                                Start, Len, Expression));
                    }
                }
                else if (this.right is IDifferentiable Right)
                {
                    return new Multiply(
                        this,
                        new Add(
                            new Multiply(
                                Left.Differentiate(VariableName, Variables),
                                new Divide(this.right, this.left, Start, Len, Expression),
                                Start, Len, Expression),
                            new Multiply(
                                Right.Differentiate(VariableName, Variables),
                                new Ln(this.left, Start, Len, Expression),
                                Start, Len, Expression),
                            Start, Len, Expression),
                        Start, Len, Expression);
                }
                else
                    throw new ScriptRuntimeException("Operands not differentiable.", this);
            }
            else
                throw new ScriptRuntimeException("Operands not differentiable.", this);
        }
 
    }
}