Rational operator*(Rational num1, Rational num2)
{
    int c = num1.getB() * num2.getB();
    int d = num1.getA() * num2.getA();
    return Rational(d, c);
}

Rational Rational::Inverse() {
	if(num == 0)
		return Rational(num, den);
	else
		return Rational(den, num);
}

 Rational opposite() const
 {
     return Rational(-numerator, denominator);
 }

bool Rational::operator>(int right) const {
	return *this > Rational(right, 1);
}

bool QuadraticField::FindSqrt(std::vector<Rational> root_) {
	if(root_.size() != degree)
		return false;
	else if(degree==2) {
		// We look for a square root of the form a+b*R^(1/2) where a,b rational.
		// For the notes, we are finding the square root of X+Y*R^(1/2)
		// so that X = root_[0] and Y = root_[1].
		Rational newroot(1,1), newrootB(1,1); // Extra variables that will be necessary later
		if(root_[1].IsZero()) {
			// The case of finding square root of X
			// Solve a^2 + R b^2 = X and 2ab = 0

			// The case that a=0
			// Look at b = (X/R)^(1/2)
			newroot = root_[0]*Root[0].Inverse();
			if(newroot.FindSqrt()) { 
				Result[0] = Rational(0,1);
				Result[1] = newroot.GetSqrt();
				return true;
			}
			
			// The case that b=0
			// Look at a = X^(1/2)
			newroot = root_[0];
			if(newroot.FindSqrt()) {
				Result[0] = newroot.GetSqrt();
				Result[1] = Rational(0,1);
				return true;
			}

			// Neither Case Works, so there is no square root
			return false;
		}
		else { 
			// Looking at the hardest case of Y non-zero
			// Solve a^2 + R b^2 = X and 2ab = Y
			// Now know that a and b both are non-zero,
			// So it is safe to substitute b = Y/2a into the 
			// first equation.
			// So we must solve a^2 + (R/4) Y^2/a^2 = X
			// equivalent to a^4 - X a^2 + (R/4) Y^2 = 0.

			// Need to find a in Q satisfying quartic polynomial.
			// Quadratic Formula tells us a^2 is in Q iff
			// (X^2 - R Y^2)^(1/2) is in Q. First check this.

			newroot = root_[0]*root_[0] - Root[0]*root_[1]*root_[1];
			if(newroot.FindSqrt()) {

				// Know that a^2 is in the Q. Need to check square root
				// of either positive or negative root to see if any a
				// is in the field

				newroot = newroot.GetSqrt();

				// Check the plus root
				newrootB = (root_[0]+newroot)*Rational(1,2);
				if(newrootB.FindSqrt()) {
					Result[0] = newrootB.GetSqrt();
					Result[1] = root_[1]*Rational(1,2)*Result[0].Inverse();
					return true;
				}

				//Check the minus root
				newrootB = (root_[0]-newroot)*Rational(1,2);
				if(newrootB.FindSqrt()) {
					Result[0] = newrootB.GetSqrt();
					Result[1] = root_[1]*Rational(1,2)*Result[0].Inverse();
					return true;
				}

				// Neither plus/minus root has a root in Q. So there is no rational root
				return false;

			}
			else
				return false;
		}
	}
	else {
		return false;
	}

}

Rational Rational::operator-() const
{
  return Rational(-numerator, denominator, no_normalise_tag());
}

void WaveAudioEssenceReader::setEditRate(const Rational& rate)
{
    _editRate = rate;

    //WaveAudioEssenceDescriptor* waed =
    //    dynamic_cast<WaveAudioEssenceDescriptor*>(_descriptor);
    //if (waed == 0)
    //{
    //    /// \todo report error
    //    return;
    //}

    //waed->setSampleRate(rate);

    // A call to set the edit rate will also set the container duration.

    // Calculate frame and buffer sizes
    _baseSampleCount = 0; // reset so we can detect error
    if (rate == Rational(30000, 1001))
    {
        if (_fmtChunk->nSamplesPerSec == 48000)
        {
            _baseSampleCount = 1600;
            _additionalSampleCounts = 5;
            _additionalSampleCount[0] = 2;
            _additionalSampleCount[1] = 1;
            _additionalSampleCount[2] = 2;
            _additionalSampleCount[3] = 1;
            _additionalSampleCount[4] = 2;
        }
        /// \todo warn if audio data isn't 48kHz
    }
    else
    {
        _baseSampleCount = (UInt32)(
            _fmtChunk->nSamplesPerSec *
            (UInt64) rate.getDenominator() /
            (UInt64) rate.getNumerator());
        _additionalSampleCounts = 0;
    }

    _combinedDataLength = 0;
    if (_additionalSampleCounts > 0)
    {
        // Calculate the average buffer size
        for (UInt32 i = 0; i < _additionalSampleCounts; ++i)
        {
            _combinedDataLength +=
                (_baseSampleCount + _additionalSampleCount[i]) *
                (_fmtChunk->wBitsPerSample / 8) *
                _fmtChunk->nChannels;
        }
    }
    else
    {
        _combinedDataLength =
            _baseSampleCount *
            (_fmtChunk->wBitsPerSample / 8) *
            _fmtChunk->nChannels;
    }

    if (_baseSampleCount == 0 || _combinedDataLength == 0)
    {
        // We've failed to determine the size of an edit unit
        error(ESS_ERROR_FailedToDetermineFrameSize);
        return;
    }

    // Update the duration for the essence descriptor
    if (_additionalSampleCounts > 0)
    {
        Length duration = ((_dataLength * _additionalSampleCounts) / _combinedDataLength);

        // we have to do the rounding manually as ceil() takes a double
        // and VC6 can't handle unsigned int64 to double...
        Length rem = (_dataLength * _additionalSampleCounts) % _combinedDataLength;
        if (rem != 0)
            duration++; // round up
        
        //waed->setContainerDuration(duration);
		_containerDuration = duration;
    }
    else
    {
        Length duration = _dataLength / _combinedDataLength;

        // we have to do the rounding manually as ceil() takes a double
        // and VC6 can't handle unsigned int64 to double...
        Length rem = _dataLength % _combinedDataLength;
        if (rem != 0)
            duration++; // round up 

        //waed->setContainerDuration(duration);
		_containerDuration = duration;
    }
}

Expr Expr::operator-() const
{
  return Sum::rational_multiple(*this, Rational(-1)).simplify();
}

 Rational Xmpdatum::toRational(long n) const
 {
     return p_->value_.get() == 0 ? Rational(-1, 1) : p_->value_->toRational(n);
 }

VideoFormat::VideoFormat(AVCodecContext * ctx) {
    _width=ctx->width;
    _height=ctx->height;
    _framerate=Rational(ctx->time_base.num,ctx->time_base.den);
    _type=FORMAT_VIDEO;
}

	Point(const Rational& x = Rational(), const Rational& y = Rational()) : x_(x), y_(y) {
	}

Rational operator^(Rational num1, int power)
{
    int c = pow(num1.getB(), power);
    int d = pow(num1.getA(), power);
    return Rational(d, c);
}

 Rational & operator /=( int i ) {
     (*this) /= Rational(i);
     return * this ;
 }

void Broder86::computeNeighbours(const BipartiteMatching& s,
                                 boost::unordered_map<BipartiteMatching, Rational>& neighbors) const {

    // Variables
    const int n = g.getNumberOfNodes();
    const int k = s.k;
    int u, v;
    BipartiteMatching s2;
    edgelist edges;

    neighbors.clear();

    // Implementierung der Transitionen nach Vorlage JS89

    // Gehe über jede Kante
    g.getEdges(edges);

    //std::cout << "compute neighbors for s=" << s << std::endl;

    // Für jede Wahl einer Kante e=(u,v) wird Transition konstruiert
    for (typename edgelist::iterator it = edges.begin(); it != edges.end();
            ++it) {

        u = it->first;
        v = it->second;

        // create new state as copy of old one
        s2 = BipartiteMatching(s);

        // Transition 1
        if (2 * k == n && s.mates[u] == v) {
            // remove edge (u,v)
            s2.mates[u] = n;
            s2.mates[v] = n;
            s2.k = k - 1;
            s2.unmatched[0] = u;
            s2.unmatched[1] = v;
        } else if (2 * k + 2 == n) {

            // Transition 2
            if (s.mates[u] == n && s.mates[v] == n) {
                // add edge (u,v)
                s2.mates[u] = v;
                s2.mates[v] = u;
                s2.k = k + 1;
                s2.unmatched[0] = n;
                s2.unmatched[1] = n;
            }
            // Transition 3a
            else if (s.mates[u] != n && s.mates[v] == n) {
                // remove edge (u, mate[u])
                // add edge (u,v)
                int w = s.mates[u];
                s2.mates[w] = n;
                s2.mates[u] = v;
                s2.mates[v] = u;
                // w=mate[u] (>= n/2) becomes unmatched node in bipartition group 1
                s2.unmatched[1] = w;
            }
            // Transition 3b
            else if (s.mates[u] == n && s.mates[v] != n) {
                // remove edge (v, mate[v])
                // add edge (u,v)
                int w = s.mates[v];
                s2.mates[w] = n;
                s2.mates[u] = v;
                s2.mates[v] = u;
                // w=mate[v] (< n/2) becomes unmatched node in bipartition group 0
                s2.unmatched[0] = w;
            } else {
                // stay in s
            }
        }
        // sonst
        else {
            // Verbleibe im aktuellen Zustand
        }

        neighbors[s2] += Rational(1, edges.size());

        //std::cout << std::endl;
    }
}

//.........这里部分代码省略.........
						debug(LOG_ERROR, "Failed startMission(%d, %s)!", LDS_MKEEP_LIMBO, psNewLevel->apDataFiles[i]);
						return false;
					}
					break;
				default:
					ASSERT(psNewLevel->type >= LDS_MULTI_TYPE_START, "Unexpected mission type");
					debug(LOG_WZ, "default (MULTIPLAYER)");
					if (!startMission(LDS_CAMSTART, psNewLevel->apDataFiles[i]))
					{
						debug(LOG_ERROR, "Failed startMission(%d, %s) (default)!", LDS_CAMSTART, psNewLevel->apDataFiles[i]);
						return false;
					}
					break;
				}
			}
		}
		else if (psNewLevel->apDataFiles[i])
		{
			// load the data
			debug(LOG_WZ, "Loading %s", psNewLevel->apDataFiles[i]);
			if (!resLoad(psNewLevel->apDataFiles[i], i + CURRENT_DATAID))
			{
				debug(LOG_ERROR, "Failed resLoad(%s, %d) (default)!", psNewLevel->apDataFiles[i], i + CURRENT_DATAID);
				return false;
			}
		}
	}

	if (bMultiPlayer)
	{
		// This calls resLoadFile("SMSG", "multiplay.txt"). Must be before loadMissionExtras, which calls loadSaveMessage, which calls getViewData.
		loadMultiScripts();
	}

	if (pSaveName != nullptr)
	{
		//load MidMission Extras
		if (!loadMissionExtras(pSaveName, psNewLevel->type))
		{
			debug(LOG_ERROR, "Failed loadMissionExtras(%s, %d)!", pSaveName, psNewLevel->type);
			return false;
		}
	}

	if (pSaveName != nullptr && saveType == GTYPE_SAVE_MIDMISSION)
	{
		//load script stuff
		// load the event system state here for a save game
		debug(LOG_SAVE, "Loading script system state");
		if (!loadScriptState(pSaveName))
		{
			debug(LOG_ERROR, "Failed loadScriptState(%s)!", pSaveName);
			return false;
		}
	}

	if (!stageThreeInitialise())
	{
		debug(LOG_ERROR, "Failed stageThreeInitialise()!");
		return false;
	}

	dataClearSaveFlag();

	//this enables us to to start cam2/cam3 without going via a save game and get the extra droids
	//in from the script-controlled Transporters
	if (!pSaveName && psNewLevel->type == LDS_CAMSTART)
	{
		eventFireCallbackTrigger((TRIGGER_TYPE)CALL_NO_REINFORCEMENTS_LEFT);
	}

	//restore the level name for comparisons on next mission load up
	if (psChangeLevel == nullptr)
	{
		psCurrLevel = psNewLevel;
	}
	else
	{
		psCurrLevel = psChangeLevel;
	}

	// Copy this info to be used by the crash handler for the dump file
	char buf[256];

	ssprintf(buf, "Current Level/map is %s", psCurrLevel->pName);
	addDumpInfo(buf);

	triggerEvent(TRIGGER_GAME_LOADED);

	if (autogame_enabled())
	{
		gameTimeSetMod(Rational(500));
		if (hostlaunch != 2) // tests will specify the AI manually
		{
			jsAutogameSpecific("multiplay/skirmish/semperfi.js", selectedPlayer);
		}
	}

	return true;
}

Tsubtitle* TsubtitleParserSSA::parse(Tstream &fd, int flags, REFERENCE_TIME start, REFERENCE_TIME stop)
{
    /*
     * Sub Station Alpha v4 (and v2?) scripts have 9 commas before subtitle
     * other Sub Station Alpha scripts have only 8 commas before subtitle
     * Reading the "ScriptType:" field is not reliable since many scripts appear
     * w/o it
     *
     * http://www.scriptclub.org is a good place to find more examples
     * http://www.eswat.demon.co.uk is where the SSA specs can be found
     */
    wchar_t line0[this->LINE_LEN + 1];
    wchar_t *line = line0;
    int playResXscript = 0, playResYscript = 0;
    while (fd.fgets(line, this->LINE_LEN)) {
#if 0
        DPRINTF(L"%s", line);
#endif
        lineID++;
        if (line[0] == ';') {
            continue;
        }
        wchar_t *cr = strrchr(line, '\n');
        if (cr) {
            *cr = '\0';
        }
        cr = strrchr(line, '\r');
        if (cr) {
            *cr = '\0';
        }
        if (strnicmp(line, L"[Script Info]", 13) == 0) {
            inV4styles = 0;
            inEvents = 0;
            inInfo = 1;
        } else if (inInfo && strnicmp(line, L"PlayResX:", 8) == 0) {
            nmTextSubtitles::strToInt(line + 9, &playResXscript);
        } else if (inInfo && strnicmp(line, L"PlayResY:", 8) == 0) {
            nmTextSubtitles::strToInt(line + 9, &playResYscript);
        } else if (inInfo && strnicmp(line, L"Timer:", 6) == 0) {
            wchar_t *end;
            double t = strtod(line + 7, &end);
            if (*end == '\0' && t != 0) {
                timer = Rational(t / 100.0, _I32_MAX);
            }
        } else if (inInfo && strnicmp(line, L"WrapStyle:", 9) == 0) {
            nmTextSubtitles::strToInt(line + 10, &wrapStyle);
        } else if (inInfo && strnicmp(line, L"ScaledBorderAndShadow:", 21) == 0) {
            nmTextSubtitles::strToInt(line + 22, &scaleBorderAndShadow);
        } else if (strnicmp(line, L"[V4 Styles]", 11) == 0) {
            version = nmTextSubtitles::SSA;
            inV4styles = 2;
            inEvents = 0;
            inInfo = 0;
        } else if (strnicmp(line, L"[V4+ Styles]", 11) == 0) {
            version = nmTextSubtitles::ASS;
            inV4styles = 2;
            inEvents = 0;
            inInfo = 0;
        } else if (strnicmp(line, L"[V4++ Styles]", 11) == 0) {
            version = nmTextSubtitles::ASS2;
            inV4styles = 2;
            inEvents = 0;
            inInfo = 0;
        } else if (strnicmp(line, L"[Events]", 8) == 0) {
            inV4styles = 0;
            inEvents = 2;
            inInfo = 0;
        } else if (inV4styles == 2 && strnicmp(line, L"Format:", 7) == 0) {
            strlwr(line);
            strrmchar(line, L' ');
            typedef std::vector<Tstrpart > Tparts;
            Tparts fields;
            const wchar_t *l = line + 7;
            strtok(l, L",", fields);
            styleFormat.clear();
            for (Tparts::const_iterator f = fields.begin(); f != fields.end(); f++) {
                if (strnicmp(f->first, L"name", 4) == 0) {
                    styleFormat.push_back(&TSSAstyle::name);
                } else if (strnicmp(f->first, L"layer", 5) == 0) {
                    styleFormat.push_back(&TSSAstyle::layer);
                } else if (strnicmp(f->first, L"fontname", 8) == 0) {
                    styleFormat.push_back(&TSSAstyle::fontname);
                } else if (strnicmp(f->first, L"fontsize", 8) == 0) {
                    styleFormat.push_back(&TSSAstyle::fontsize);
                } else if (strnicmp(f->first, L"primaryColour", 13) == 0) {
                    styleFormat.push_back(&TSSAstyle::primaryColour);
                } else if (strnicmp(f->first, L"SecondaryColour", 15) == 0) {
                    styleFormat.push_back(&TSSAstyle::secondaryColour);
                } else if (strnicmp(f->first, L"TertiaryColour", 14) == 0) {
                    styleFormat.push_back(&TSSAstyle::tertiaryColour);
                } else if (strnicmp(f->first, L"OutlineColour", 13) == 0) {
                    styleFormat.push_back(&TSSAstyle::outlineColour);
                } else if (strnicmp(f->first, L"BackColour", 10) == 0) {
                    styleFormat.push_back(&TSSAstyle::backgroundColour);
                } else if (strnicmp(f->first, L"bold", 4) == 0) {
                    styleFormat.push_back(&TSSAstyle::bold);
                } else if (strnicmp(f->first, L"italic", 6) == 0) {
                    styleFormat.push_back(&TSSAstyle::italic);
                } else if (strnicmp(f->first, L"Underline", 9) == 0) {
                    styleFormat.push_back(&TSSAstyle::underline);
//.........这里部分代码省略.........

Rational StateGraph::getWeight(int i) const {
	return Rational(1);
}

 Rational inverse() const
 {
     return Rational(denominator, numerator);
 }

Rational operator-(Rational num1, Rational num2)
{
    int c = LCM(num1.getB(), num2.getB());
    int d = (c / num1.getB())*num1.getA() - (c / num2.getB())*num2.getA();
    return Rational(d, c);
}