/// <summary>
        /// Splits the range on the given <paramref name="splitPoint"/>.
        /// </summary>
        /// <param name="splitPoint">The point on the range to split it.</param>
        /// <param name="includeSplitPointToUpperRange">Which range gets the <paramref name="splitPoint"/>?</param>
        /// <param name="whatToDoWithResults">What to do with the result?</param>
        /// <returns>Result <see cref="IRangeMathableSingleSize{Int32, BigInteger}"/>s.</returns>
        public IRangeMathableSingleSize <Int32, BigInteger>[] Split(Int32 splitPoint, bool includeSplitPointToUpperRange, RangeMathematicResultUseage whatToDoWithResults)
        {
            IRangeMathableSingleSize <Int32, BigInteger>[] result;
            if (TheRange.EmptyRange)
            {
                result = new IRangeMathableSingleSize <Int32, BigInteger>[2] {
                    default(Int32RangeMathable), default(Int32RangeMathable)
                };
            }
            else
            {
                result = new IRangeMathableSingleSize <Int32, BigInteger> [2];
                switch (TheRange.CompareTo(splitPoint))
                {
                case -1:
                    result[0] = new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound);
                    result[1] = default(Int32RangeMathable);
                    break;

                case 0:
                    if (includeSplitPointToUpperRange)
                    {
                        if (TheRange.StartBound == TheRange.EndBound || TheRange.StartBound == splitPoint)
                        {
                            result[0] = default(Int32RangeMathable);
                            result[1] = new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound);
                        }
                        else
                        {
                            result[0] = new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, (splitPoint - 1));
                            result[1] = new Int32RangeMathable(TheRange.EmptyRange, splitPoint, TheRange.EndBound);
                        }
                    }
                    else
                    {
                        if (TheRange.StartBound == TheRange.EndBound || TheRange.EndBound == splitPoint)
                        {
                            result[0] = new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound);
                            result[1] = default(Int32RangeMathable);
                        }
                        else
                        {
                            result[0] = new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, splitPoint);
                            result[1] = new Int32RangeMathable(TheRange.EmptyRange, (splitPoint + 1), TheRange.EndBound);
                        }
                    }
                    break;

                case 1:
                    result[0] = default(Int32RangeMathable);
                    result[1] = new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound);
                    break;
                }
            }
            // working with the result to do the wanted actions
            if ((whatToDoWithResults & RangeMathematicResultUseage.UseLowestResultRangeOnOwnRange) > 0)
            {
                if (result[0].StartBound > TheRange.EndBound)
                {
                    TheRange.EndBound   = result[0].EndBound;
                    TheRange.StartBound = result[0].StartBound;
                }
                else
                {
                    TheRange.StartBound = result[0].StartBound;
                    TheRange.EndBound   = result[0].EndBound;
                }
                TheRange.EmptyRange = result[0].EmptyRange;
            }
            else if ((whatToDoWithResults & RangeMathematicResultUseage.UseHighestResultRangeOnOwnRange) > 0)
            {
                if (result[1].StartBound > TheRange.EndBound)
                {
                    TheRange.EndBound   = result[1].EndBound;
                    TheRange.StartBound = result[1].StartBound;
                }
                else
                {
                    TheRange.StartBound = result[1].StartBound;
                    TheRange.EndBound   = result[1].EndBound;
                }
                TheRange.EmptyRange = result[1].EmptyRange;
            }
            return(result);
        }
        /// <summary>
        /// Splits the range in nearly equal sized ranges.
        /// </summary>
        /// <param name="includeOddToUpperRange">If the range range is odd where to add the element on the split to?</param>
        /// <param name="whatToDoWithResults">What to do with the result?</param>
        /// <returns>Result <see cref="IRangeMathable{Int32, BigInteger}"/>s.</returns>
        public IRangeMathableSingleSize <Int32, BigInteger>[] Split(bool includeOddToUpperRange, RangeMathematicResultUseage whatToDoWithResults)
        {
            IRangeMathableSingleSize <Int32, BigInteger>[] result = new IRangeMathableSingleSize <Int32, BigInteger> [2];
            Int64 tempSize = BigInteger.ToInt64(RangeSize());

            switch (tempSize.CompareTo(1))
            {
            case -1:
                result[0] = default(Int32RangeMathable);
                result[1] = default(Int32RangeMathable);
                break;

            case 0:
                if (includeOddToUpperRange)
                {
                    result[0] = default(Int32RangeMathable);
                    result[1] = new Int32RangeMathable(true, TheRange.StartBound, TheRange.EndBound);
                }
                else
                {
                    result[0] = new Int32RangeMathable(true, TheRange.StartBound, TheRange.EndBound);
                    result[1] = default(Int32RangeMathable);
                }
                break;

            case 1:
                bool  storedOddBit = (tempSize & 1) == 1;
                Int64 halfSize     = tempSize >> 1;
                if (storedOddBit)
                {
                    if (halfSize > 0)
                    {
                        if (includeOddToUpperRange)
                        {
                            result[0] = new Int32RangeMathable(false, TheRange.StartBound, (TheRange.StartBound + (Int32)halfSize - 1));
                            result[1] = new Int32RangeMathable(false, (TheRange.EndBound - (Int32)halfSize), TheRange.EndBound);
                        }
                        else
                        {
                            result[0] = new Int32RangeMathable(false, TheRange.StartBound, (TheRange.StartBound + (Int32)halfSize));
                            result[1] = new Int32RangeMathable(false, (TheRange.EndBound - (Int32)halfSize + 1), TheRange.EndBound);
                        }
                    }
                    else
                    {
                        if (includeOddToUpperRange)
                        {
                            result[0] = default(Int32RangeMathable);
                            result[1] = new Int32RangeMathable(false, TheRange.EndBound, TheRange.EndBound);
                        }
                        else
                        {
                            result[0] = new Int32RangeMathable(false, TheRange.StartBound, TheRange.StartBound);
                            result[1] = default(Int32RangeMathable);
                        }
                    }
                }
                else
                {
                    if (halfSize > 0)
                    {
                        result[0] = new Int32RangeMathable(false, TheRange.StartBound, (TheRange.StartBound + (Int32)halfSize - 1));
                        result[1] = new Int32RangeMathable(false, (TheRange.EndBound - (Int32)halfSize + 1), TheRange.EndBound);
                    }
                    else
                    {
                        result[0] = default(Int32RangeMathable);
                        result[1] = default(Int32RangeMathable);
                    }
                }
                break;
            }
            // working with the result to do the wanted actions
            if ((whatToDoWithResults & RangeMathematicResultUseage.UseLowestResultRangeOnOwnRange) > 0)
            {
                if (result[0].StartBound > TheRange.EndBound)
                {
                    TheRange.EndBound   = result[0].EndBound;
                    TheRange.StartBound = result[0].StartBound;
                }
                else
                {
                    TheRange.StartBound = result[0].StartBound;
                    TheRange.EndBound   = result[0].EndBound;
                }
                TheRange.EmptyRange = result[0].EmptyRange;
            }
            else if ((whatToDoWithResults & RangeMathematicResultUseage.UseHighestResultRangeOnOwnRange) > 0)
            {
                if (result[1].StartBound > TheRange.EndBound)
                {
                    TheRange.EndBound   = result[1].EndBound;
                    TheRange.StartBound = result[1].StartBound;
                }
                else
                {
                    TheRange.StartBound = result[1].StartBound;
                    TheRange.EndBound   = result[1].EndBound;
                }
                TheRange.EmptyRange = result[1].EmptyRange;
            }
            return(result);
        }
        /// <summary>
        /// Combines this range with the given range <paramref name="toCombine"/> based on the given <see cref="RangeCombination"/>.
        /// </summary>
        /// <param name="toCombine">The other range to combine with.</param>
        /// <param name="combinationType">How to combine the 2 ranges.</param>
        /// <param name="whatToDoWithResults">What to do with the result?</param>
        /// <returns>Result <see cref="IRangeMathable{Int32, Int32}"/>s.</returns>
        /// <exception cref="ArgumentOutOfRangeException">The <paramref name="combinationType"/> is not a valid <see cref="RangeCombination"/> value!</exception>
        public                IRangeMathableSingleSize <Int32, BigInteger>[] Combine(IRangeMathableSingleSize <Int32, BigInteger> toCombine, RangeCombination combinationType, RangeMathematicResultUseage whatToDoWithResults)
        {
            IRangeMathableSingleSize <Int32, BigInteger>[] result;
            if (toCombine == null)
            {
                result = new IRangeMathableSingleSize <Int32, BigInteger> [1];
                switch (combinationType)
                {
                case RangeCombination.Difference:
                case RangeCombination.Union:
                    result[0] = new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound);
                    break;

                case RangeCombination.Intersect:
                    result[0] = default(Int32RangeMathable);
                    break;

                default:
                    throw new ArgumentOutOfRangeException("The combinationType is not a valid RangeCombinations value!");
                }
            }
            else
            {
                int comparationResult = CompareTo(toCombine);
                switch (combinationType)
                {
                case RangeCombination.Difference:
                    if (TheRange.EmptyRange)
                    {
                        result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                            new Int32RangeMathable(toCombine.EmptyRange, toCombine.StartBound, toCombine.EndBound)
                        };
                    }
                    else if (toCombine.EmptyRange)
                    {
                        result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                            new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound)
                        };
                    }
                    else
                    {
                        if (comparationResult == 0)
                        {
                            result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                new Int32RangeMathable(true, 0, 0)
                            };
                        }
                        else
                        {
                            if (TheRange.EndBound < toCombine.EndBound)
                            {
                                result = new IRangeMathableSingleSize <Int32, BigInteger> [2];
                                Int64 tempNewBound = (Int64)toCombine.StartBound - 1;
                                if (tempNewBound <= TheRange.StartBound)
                                {
                                    result[0] = new Int32RangeMathable(true, TheRange.StartBound, TheRange.StartBound);
                                }
                                else
                                {
                                    result[0] = new Int32RangeMathable(false, TheRange.StartBound, (Int32)tempNewBound);
                                }
                                tempNewBound = (Int64)TheRange.EndBound + 1;
                                if (tempNewBound >= toCombine.EndBound)
                                {
                                    result[1] = new Int32RangeMathable(true, toCombine.EndBound, toCombine.EndBound);
                                }
                                else
                                {
                                    result[1] = new Int32RangeMathable(false, (Int32)tempNewBound, toCombine.EndBound);
                                }
                            }
                            else
                            {
                                Int64 newEndBound = (Int64)toCombine.StartBound - 1;
                                if (newEndBound <= TheRange.StartBound)
                                {
                                    result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                        new Int32RangeMathable(true, TheRange.StartBound, TheRange.StartBound)
                                    };
                                }
                                else
                                {
                                    result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                        new Int32RangeMathable(false, TheRange.StartBound, (Int32)newEndBound)
                                    };
                                }
                            }
                        }
                    }
                    break;

                case RangeCombination.Intersect:
                    result = new IRangeMathableSingleSize <Int32, BigInteger> [1];
                    if (TheRange.EmptyRange || toCombine.EmptyRange)
                    {
                        result[0] = default(Int32RangeMathable);
                    }
                    else
                    {
                        switch (comparationResult)
                        {
                        case -1:
                            if (toCombine.StartBound > Int32.MinValue && TheRange.EndBound < (toCombine.StartBound - 1))
                            {
                                result[0] = default(Int32RangeMathable);
                            }
                            else
                            {
                                if (TheRange.EndBound > toCombine.EndBound)
                                {
                                    result[0] = new Int32RangeMathable(false, toCombine.StartBound, toCombine.EndBound);
                                }
                                else
                                {
                                    result[0] = new Int32RangeMathable(false, toCombine.StartBound, TheRange.EndBound);
                                }
                            }
                            break;

                        case 0:
                            result[0] = new Int32RangeMathable(false, TheRange.StartBound, TheRange.EndBound);
                            break;

                        case 1:
                            if (TheRange.StartBound < Int32.MinValue && toCombine.EndBound < (TheRange.StartBound - 1))
                            {
                                result[0] = default(Int32RangeMathable);
                            }
                            else
                            {
                                if (toCombine.EndBound > TheRange.EndBound)
                                {
                                    result[0] = new Int32RangeMathable(false, toCombine.StartBound, toCombine.EndBound);
                                }
                                else
                                {
                                    result[0] = new Int32RangeMathable(false, toCombine.StartBound, TheRange.EndBound);
                                }
                            }
                            break;
                        }
                    }
                    break;

                case RangeCombination.Union:
                    if (TheRange.EmptyRange && toCombine.EmptyRange)
                    {
                        result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                            default(Int32RangeMathable)
                        };
                    }
                    else
                    {
                        switch (comparationResult)
                        {
                        case -1:
                            if (TheRange.EmptyRange)
                            {
                                result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                    new Int32RangeMathable(toCombine.EmptyRange, toCombine.StartBound, toCombine.EndBound)
                                };
                            }
                            else if (toCombine.EmptyRange)
                            {
                                result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                    new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound)
                                };
                            }
                            else
                            {
                                if (TheRange.EndBound < Int32.MaxValue && (TheRange.EndBound + 1) < toCombine.StartBound)
                                {
                                    result    = new IRangeMathableSingleSize <Int32, BigInteger> [2];
                                    result[0] = new Int32RangeMathable(false, TheRange.StartBound, TheRange.EndBound);
                                    result[1] = new Int32RangeMathable(false, toCombine.StartBound, toCombine.EndBound);
                                }
                                else
                                {
                                    result = new IRangeMathableSingleSize <Int32, BigInteger> [1];
                                    if (TheRange.EndBound <= toCombine.EndBound)
                                    {
                                        result[0] = new Int32RangeMathable(false, TheRange.StartBound, toCombine.EndBound);
                                    }
                                    else
                                    {
                                        result[0] = new Int32RangeMathable(false, TheRange.StartBound, TheRange.EndBound);
                                    }
                                }
                            }
                            break;

                        case 0:
                            result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                new Int32RangeMathable(false, TheRange.StartBound, TheRange.EndBound)
                            };
                            break;

                        case 1:
                            if (TheRange.EmptyRange)
                            {
                                result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                    new Int32RangeMathable(toCombine.EmptyRange, toCombine.StartBound, toCombine.EndBound)
                                };
                            }
                            else if (toCombine.EmptyRange)
                            {
                                result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                                    new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound)
                                };
                            }
                            else
                            {
                                if (toCombine.EndBound < Int32.MaxValue && TheRange.StartBound < (toCombine.EndBound + 1))
                                {
                                    result    = new IRangeMathableSingleSize <Int32, BigInteger> [2];
                                    result[1] = new Int32RangeMathable(false, toCombine.StartBound, toCombine.EndBound);
                                    result[0] = new Int32RangeMathable(false, TheRange.StartBound, TheRange.EndBound);
                                }
                                else
                                {
                                    result = new IRangeMathableSingleSize <Int32, BigInteger> [1];
                                    if (TheRange.EndBound >= toCombine.EndBound)
                                    {
                                        result[0] = new Int32RangeMathable(false, toCombine.StartBound, TheRange.EndBound);
                                    }
                                    else
                                    {
                                        result[0] = new Int32RangeMathable(false, toCombine.StartBound, toCombine.EndBound);
                                    }
                                }
                            }
                            break;
                        }
                    }
                    result = new IRangeMathableSingleSize <Int32, BigInteger>[1] {
                        new Int32RangeMathable(TheRange.EmptyRange, TheRange.StartBound, TheRange.EndBound)
                    };
                    break;

                default:
                    throw new ArgumentOutOfRangeException("The combinationType is not a valid RangeCombinations value!");
                }
            }
            // working with the result to do the wanted actions
            if ((whatToDoWithResults & RangeMathematicResultUseage.UseLowestResultRangeOnOwnRange) > 0)
            {
                if (result[0].StartBound > TheRange.EndBound)
                {
                    TheRange.EndBound   = result[0].EndBound;
                    TheRange.StartBound = result[0].StartBound;
                }
                else
                {
                    TheRange.StartBound = result[0].StartBound;
                    TheRange.EndBound   = result[0].EndBound;
                }
                TheRange.EmptyRange = result[0].EmptyRange;
            }
            else if ((whatToDoWithResults & RangeMathematicResultUseage.UseHighestResultRangeOnOwnRange) > 0)
            {
                int targetPosition = result.Length - 1;
                if (result[targetPosition].StartBound > TheRange.EndBound)
                {
                    TheRange.EndBound   = result[targetPosition].EndBound;
                    TheRange.StartBound = result[targetPosition].StartBound;
                }
                else
                {
                    TheRange.StartBound = result[targetPosition].StartBound;
                    TheRange.EndBound   = result[targetPosition].EndBound;
                }
                TheRange.EmptyRange = result[targetPosition].EmptyRange;
            }
            return(result);
        }