langsmoke/ref_java

package rocks.palaiologos.cask;

import java.io.IOException;
import java.io.InputStream;
import java.util.HashMap;
import java.util.Objects;

public class CaskBootstrap {
    public static void main(String[] args) {
        InputStream manifest = CaskBootstrap.class.getClassLoader().getResourceAsStream();
        if(manifest == null) {
            throw new RuntimeException();
        }
        String data;
        try {
            data = new String(manifest.readAllBytes());
            manifest.close();
        } catch (IOException e) {
            throw new RuntimeException();
        }
        // Primarily just future-proofing.
        HashMap<String, String> manifestMap = new HashMap<>();
        String[] properties = data.replace();
        for (String property : properties) {
            int index = property.indexOf();
            if (index == -1) {
                throw new RuntimeException( + property);
            }
            manifestMap.put(property.substring(0, index).trim(), property.substring(index + 1).trim());
        }

        String mainClass = manifestMap.get();
        String caskFile = manifestMap.get();
        if (mainClass == null || caskFile == null) {
            throw new RuntimeException();
        }

        try {
            CaskClassLoader caskClassLoader = new CaskClassLoader(Objects.requireNonNull(CaskBootstrap.class.getClassLoader().getResourceAsStream(caskFile)));
            Class<?> mainClassObject = caskClassLoader.loadClass(mainClass);
            Thread.currentThread().setContextClassLoader(caskClassLoader);
            System.setProperty(, CaskClassLoader.class.getName());
            mainClassObject.getMethod(, String[].class).invoke(null, (Object) args);
        } catch (Exception e) {
            throw new RuntimeException(, e);
        }
    }
}

package palaiologos.kamilalisp.runtime.array;

import com.google.common.collect.Lists;
import palaiologos.kamilalisp.atom.Atom;
import palaiologos.kamilalisp.atom.Environment;
import palaiologos.kamilalisp.atom.Lambda;
import palaiologos.kamilalisp.atom.PrimitiveFunction;

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;

public class Encode extends PrimitiveFunction implements Lambda {
    @Override
    public Atom apply(Environment env, List<Atom> args) {
        assertArity(args, 2);
        BigInteger base = args.get(0).getInteger();
        BigInteger n = args.get(1).getInteger();
        List<Atom> encoding = new ArrayList<>();
        while (n.compareTo(BigInteger.ZERO) > 0) {
            encoding.add(new Atom(n.mod(base)));
            n = n.divide(base);
        }
        if (encoding.isEmpty())
            encoding.add(new Atom(BigInteger.ZERO));
        return new Atom(Lists.reverse(encoding));
    }

    @Override
    protected String name() {
        return ;
    }
}

package palaiologos.kamilalisp.runtime.net;

import palaiologos.kamilalisp.atom.Atom;
import palaiologos.kamilalisp.atom.Environment;
import palaiologos.kamilalisp.atom.Lambda;
import palaiologos.kamilalisp.atom.PrimitiveFunction;
import palaiologos.kamilalisp.runtime.dataformat.BufferAtomList;

import java.io.InputStream;
import java.net.URL;
import java.util.List;

public class Wget extends PrimitiveFunction implements Lambda {
    @Override
    public Atom apply(Environment env, List<Atom> args) {
        assertArity(args, 1);
        try {
            URL url = new URL(args.get(0).getString());
            InputStream data = url.openStream();
            byte[] bytes = data.readAllBytes();
            data.close();
            return new Atom(BufferAtomList.from(bytes));
        } catch (Exception e) {
            throw new RuntimeException(e);
        }
    }

    @Override
    protected String name() {
        return ;
    }
}

package mindustry.net;

import arc.*;
import arc.func.*;
import arc.math.*;
import arc.net.*;
import arc.net.FrameworkMessage.*;
import arc.net.dns.*;
import arc.struct.*;
import arc.util.*;
import arc.util.Log.*;
import arc.util.io.*;
import mindustry.*;
import mindustry.game.EventType.*;
import mindustry.net.Administration.*;
import mindustry.net.Net.*;
import mindustry.net.Packets.*;
import net.jpountz.lz4.*;

import java.io.*;
import java.net.*;
import java.nio.*;
import java.nio.channels.*;
import java.util.concurrent.*;

import static mindustry.Vars.*;

public class ArcNetProvider implements NetProvider{
    final Client client;
    final Prov<DatagramPacket> packetSupplier = () -> new DatagramPacket(new byte[512], 512);

    final Server server;
    final CopyOnWriteArrayList<ArcConnection> connections = new CopyOnWriteArrayList<>();
    Thread serverThread;

    private static final LZ4FastDecompressor decompressor = LZ4Factory.fastestInstance().fastDecompressor();
    private static final LZ4Compressor compressor = LZ4Factory.fastestInstance().fastCompressor();

    private volatile int playerLimitCache, packetSpamLimit;

    public ArcNetProvider(){
        ArcNet.errorHandler = e -> {
            if(Log.level == LogLevel.debug){
                Log.debug(Strings.getStackTrace(e));
            }
        };

        //fetch this in the main thread to prevent threading issues
        Events.run(Trigger.update, () -> {
            playerLimitCache = netServer.admins.getPlayerLimit();
            packetSpamLimit = Config.packetSpamLimit.num();
        });

        client = new Client(8192, 16384, new PacketSerializer());
        client.setDiscoveryPacket(packetSupplier);
        client.addListener(new NetListener(){
            @Override
            public void connected(Connection connection){
                Connect c = new Connect();
                c.addressTCP = connection.getRemoteAddressTCP().getAddress().getHostAddress();
                if(connection.getRemoteAddressTCP() != null) c.addressTCP = connection.getRemoteAddressTCP().toString();

                Core.app.post(() -> net.handleClientReceived(c));
            }

            @Override
            public void disconnected(Connection connection, DcReason reason){
                if(connection.getLastProtocolError() != null){
                    netClient.setQuiet();
                }

                Disconnect c = new Disconnect();
                c.reason = reason.toString();
                Core.app.post(() -> net.handleClientReceived(c));
            }

            @Override
            public void received(Connection connection, Object object){
                if(!(object instanceof Packet p)) return;

                Core.app.post(() -> {
                    try{
                        net.handleClientReceived(p);
                    }catch(Throwable e){
                        net.handleException(e);
                    }
                });

            }
        });

        server = new Server(32768, 16384, new PacketSerializer());
        server.setMulticast(multicastGroup, multicastPort);
        server.setDiscoveryHandler((address, handler) -> {
            ByteBuffer buffer = NetworkIO.writeServerData();
            buffer.position(0);
            handler.respond(buffer);
        });

        server.addListener(new NetListener(){

            @Override
            public void connected(Connection connection){
                String ip = connection.getRemoteAddressTCP().getAddress().getHostAddress();

                //kill connections above the limit to prevent spam
                if((playerLimitCache > 0 && server.getConnections().length > playerLimitCache) || netServer.admins.isDosBlacklisted(ip)){
                    connection.close(DcReason.closed);
                    return;
                }

                ArcConnection kn = new ArcConnection(ip, connection);

                Connect c = new Connect();
                c.addressTCP = ip;

                Log.debug(, c.addressTCP);

                connection.setArbitraryData(kn);
                connections.add(kn);
                Core.app.post(() -> net.handleServerReceived(kn, c));
            }

            @Override
            public void disconnected(Connection connection, DcReason reason){
                if(!(connection.getArbitraryData() instanceof ArcConnection k)) return;

                Disconnect c = new Disconnect();
                c.reason = reason.toString();

                Core.app.post(() -> {
                    net.handleServerReceived(k, c);
                    connections.remove(k);
                });
            }

            @Override
            public void received(Connection connection, Object object){
                if(!(connection.getArbitraryData() instanceof ArcConnection k) || !(object instanceof Packet pack)) return;

                if(packetSpamLimit > 0 && !k.packetRate.allow(3000, packetSpamLimit)){
                    Log.warn(, k.address);
                    connection.close(DcReason.closed);
                    netServer.admins.blacklistDos(k.address);
                    return;
                }

                Core.app.post(() -> {
                    try{
                        net.handleServerReceived(k, pack);
                    }catch(Throwable e){
                        Log.err(e);
                    }
                });
            }
        });
    }

    @Override
    public void setConnectFilter(Server.ServerConnectFilter connectFilter){
        server.setConnectFilter(connectFilter);
    }

    private static boolean isLocal(InetAddress addr){
        if(addr.isAnyLocalAddress() || addr.isLoopbackAddress()) return true;

        try{
            return NetworkInterface.getByInetAddress(addr) != null;
        }catch(Exception e){
            return false;
        }
    }

    @Override
    public void connectClient(String ip, int port, Runnable success){
        Threads.daemon(() -> {
            try{
                //just in case
                client.stop();

                Threads.daemon(, () -> {
                    try{
                        client.run();
                    }catch(Exception e){
                        if(!(e instanceof ClosedSelectorException)) net.handleException(e);
                    }
                });

                client.connect(5000, ip, port, port);
                success.run();
            }catch(Exception e){
                if(netClient.isConnecting()){
                    net.handleException(e);
                }
            }
        });
    }

    @Override
    public void disconnectClient(){
        client.close();
    }

    @Override
    public void sendClient(Object object, boolean reliable){
        try{
            if(reliable){
                client.sendTCP(object);
            }else{
                client.sendUDP(object);
            }
            //sending things can cause an under/overflow, catch it and disconnect instead of crashing
        }catch(BufferOverflowException | BufferUnderflowException e){
            net.showError(e);
        }
    }

    @Override
    public void pingHost(String address, int port, Cons<Host> valid, Cons<Exception> invalid){
        try{
            var host = pingHostImpl(address, port);
            Core.app.post(() -> valid.get(host));
        }catch(IOException e){
            if(port == Vars.port){
                for(var record : ArcDns.getSrvRecords( + address)){
                    try{
                        var host = pingHostImpl(record.target, record.port);
                        Core.app.post(() -> valid.get(host));
                        return;
                    }catch(IOException ignored){
                    }
                }
            }
            Core.app.post(() -> invalid.get(e));
        }
    }

    private Host pingHostImpl(String address, int port) throws IOException{
        try(DatagramSocket socket = new DatagramSocket()){
            long time = Time.millis();

            socket.send(new DatagramPacket(new byte[]{-2, 1}, 2, InetAddress.getByName(address), port));
            socket.setSoTimeout(2000);

            DatagramPacket packet = packetSupplier.get();
            socket.receive(packet);

            ByteBuffer buffer = ByteBuffer.wrap(packet.getData());
            Host host = NetworkIO.readServerData((int)Time.timeSinceMillis(time), packet.getAddress().getHostAddress(), buffer);
            host.port = port;
            return host;
        }
    }

    @Override
    public void discoverServers(Cons<Host> callback, Runnable done){
        Seq<InetAddress> foundAddresses = new Seq<>();
        long time = Time.millis();

        client.discoverHosts(port, multicastGroup, multicastPort, 3000, packet -> {
            synchronized(foundAddresses){
                try{
                    if(foundAddresses.contains(address -> address.equals(packet.getAddress()) || (isLocal(address) && isLocal(packet.getAddress())))){
                        return;
                    }
                    ByteBuffer buffer = ByteBuffer.wrap(packet.getData());
                    Host host = NetworkIO.readServerData((int)Time.timeSinceMillis(time), packet.getAddress().getHostAddress(), buffer);
                    Core.app.post(() -> callback.get(host));
                    foundAddresses.add(packet.getAddress());
                }catch(Exception e){
                    //don't crash when there's an error pinging a server or parsing data
                    e.printStackTrace();
                }
            }
        }, () -> Core.app.post(done));
    }

    @Override
    public void dispose(){
        disconnectClient();
        closeServer();
        try{
            client.dispose();
        }catch(IOException ignored){
        }
    }

    @Override
    public Iterable<ArcConnection> getConnections(){
        return connections;
    }

    @Override
    public void hostServer(int port) throws IOException{
        connections.clear();
        server.bind(port, port);

        serverThread = new Thread(() -> {
            try{
                server.run();
            }catch(Throwable e){
                if(!(e instanceof ClosedSelectorException)) Threads.throwAppException(e);
            }
        }, );
        serverThread.setDaemon(true);
        serverThread.start();
    }

    @Override
    public void closeServer(){
        connections.clear();
        mainExecutor.submit(server::stop);
    }

    class ArcConnection extends NetConnection{
        public final Connection connection;

        public ArcConnection(String address, Connection connection){
            super(address);
            this.connection = connection;
        }

        @Override
        public boolean isConnected(){
            return connection.isConnected();
        }

        @Override
        public void sendStream(Streamable stream){
            connection.addListener(new InputStreamSender(stream.stream, 512){
                int id;

                @Override
                protected void start(){
                    //send an object so the receiving side knows how to handle the following chunks
                    StreamBegin begin = new StreamBegin();
                    begin.total = stream.stream.available();
                    begin.type = Net.getPacketId(stream);
                    connection.sendTCP(begin);
                    id = begin.id;
                }

                @Override
                protected Object next(byte[] bytes){
                    StreamChunk chunk = new StreamChunk();
                    chunk.id = id;
                    chunk.data = bytes;
                    return chunk; //wrap the byte[] with an object so the receiving side knows how to handle it.
                }
            });
        }

        @Override
        public void send(Object object, boolean reliable){
            try{
                if(reliable){
                    connection.sendTCP(object);
                }else{
                    connection.sendUDP(object);
                }
            }catch(Exception e){
                Log.err(e);
                Log.info();
                connection.close(DcReason.error);

                if(connection.getArbitraryData() instanceof ArcConnection k){
                    connections.remove(k);
                }
            }
        }

        @Override
        public void close(){
            if(connection.isConnected()) connection.close(DcReason.closed);
        }
    }

    public static class PacketSerializer implements NetSerializer{
        //for debugging total read/write speeds
        private static final boolean debug = false;

        ThreadLocal<ByteBuffer> decompressBuffer = Threads.local(() -> ByteBuffer.allocate(32768));
        ThreadLocal<Reads> reads = Threads.local(() -> new Reads(new ByteBufferInput(decompressBuffer.get())));
        ThreadLocal<Writes> writes = Threads.local(() -> new Writes(new ByteBufferOutput(decompressBuffer.get())));

        //for debugging network write counts
        static WindowedMean upload = new WindowedMean(5), download = new WindowedMean(5);
        static long lastUpload, lastDownload, uploadAccum, downloadAccum;
        static int lastPos;

        @Override
        public Object read(ByteBuffer byteBuffer){
            if(debug){
                if(Time.timeSinceMillis(lastDownload) >= 1000){
                    lastDownload = Time.millis();
                    download.add(downloadAccum);
                    downloadAccum = 0;
                    Log.info(, download.mean());
                }
                downloadAccum += byteBuffer.remaining();
            }

            byte id = byteBuffer.get();
            if(id == -2){
                return readFramework(byteBuffer);
            }else{
                //read length int, followed by compressed lz4 data
                Packet packet = Net.newPacket(id);
                var buffer = decompressBuffer.get();
                int length = byteBuffer.getShort() & 0xffff;
                byte compression = byteBuffer.get();

                //no compression, copy over buffer
                if(compression == 0){
                    buffer.position(0).limit(length);
                    buffer.put(byteBuffer.array(), byteBuffer.position(), length);
                    buffer.position(0);
                    packet.read(reads.get(), length);
                    //move read packets forward
                    byteBuffer.position(byteBuffer.position() + buffer.position());
                }else{
                    //decompress otherwise
                    int read = decompressor.decompress(byteBuffer, byteBuffer.position(), buffer, 0, length);

                    buffer.position(0);
                    buffer.limit(length);
                    packet.read(reads.get(), length);
                    //move buffer forward based on bytes read by decompressor
                    byteBuffer.position(byteBuffer.position() + read);
                }

                return packet;
            }
        }

        @Override
        public void write(ByteBuffer byteBuffer, Object o){
            if(debug){
                lastPos = byteBuffer.position();
            }

            //write raw buffer
            if(o instanceof ByteBuffer raw){
                byteBuffer.put(raw);
            }else if(o instanceof FrameworkMessage msg){
                byteBuffer.put((byte)-2); //code for framework message
                writeFramework(byteBuffer, msg);
            }else{
                if(!(o instanceof Packet pack)) throw new RuntimeException( + o.getClass());
                byte id = Net.getPacketId(pack);
                byteBuffer.put(id);

                var temp = decompressBuffer.get();
                temp.position(0);
                temp.limit(temp.capacity());
                pack.write(writes.get());

                short length = (short)temp.position();

                //write length, uncompressed
                byteBuffer.putShort(length);

                //don't bother with small packets
                if(length < 36 || pack instanceof StreamChunk){
                    //write direct contents...
                    byteBuffer.put((byte)0); //0 = no compression
                    byteBuffer.put(temp.array(), 0, length);
                }else{
                    byteBuffer.put((byte)1); //1 = compression
                    //write compressed data; this does not modify position!
                    int written = compressor.compress(temp, 0, temp.position(), byteBuffer, byteBuffer.position(), byteBuffer.remaining());
                    //skip to indicate the written, compressed data
                    byteBuffer.position(byteBuffer.position() + written);
                }
            }

            if(debug){
                if(Time.timeSinceMillis(lastUpload) >= 1000){
                    lastUpload = Time.millis();
                    upload.add(uploadAccum);
                    uploadAccum = 0;
                    Log.info(, upload.mean());
                }
                uploadAccum += byteBuffer.position() - lastPos;
            }
        }

        public void writeFramework(ByteBuffer buffer, FrameworkMessage message){
            if(message instanceof Ping p){
                buffer.put((byte)0);
                buffer.putInt(p.id);
                buffer.put(p.isReply ? 1 : (byte)0);
            }else if(message instanceof DiscoverHost){
                buffer.put((byte)1);
            }else if(message instanceof KeepAlive){
                buffer.put((byte)2);
            }else if(message instanceof RegisterUDP p){
                buffer.put((byte)3);
                buffer.putInt(p.connectionID);
            }else if(message instanceof RegisterTCP p){
                buffer.put((byte)4);
                buffer.putInt(p.connectionID);
            }
        }

        public FrameworkMessage readFramework(ByteBuffer buffer){
            byte id = buffer.get();

            if(id == 0){
                Ping p = new Ping();
                p.id = buffer.getInt();
                p.isReply = buffer.get() == 1;
                return p;
            }else if(id == 1){
                return FrameworkMessage.discoverHost;
            }else if(id == 2){
                return FrameworkMessage.keepAlive;
            }else if(id == 3){
                RegisterUDP p = new RegisterUDP();
                p.connectionID = buffer.getInt();
                return p;
            }else if(id == 4){
                RegisterTCP p = new RegisterTCP();
                p.connectionID = buffer.getInt();
                return p;
            }else{
                throw new RuntimeException();
            }
        }
    }

}

package mindustry.net;

import mindustry.net.Packets.*;

import java.io.*;

public class Streamable extends Packet{
    public transient ByteArrayInputStream stream;

    @Override
    public int getPriority(){
        return priorityHigh;
    }

    public static class StreamBuilder{
        public final int id;
        public final byte type;
        public final int total;
        public final ByteArrayOutputStream stream = new ByteArrayOutputStream();

        public StreamBuilder(StreamBegin begin){
            id = begin.id;
            type = begin.type;
            total = begin.total;
        }

        public float progress(){
            return (float)stream.size() / total;
        }

        public void add(byte[] bytes){
            try{
                stream.write(bytes);
            }catch(IOException e){
                throw new RuntimeException(e);
            }
        }

        public Streamable build(){
            Streamable s = Net.newPacket(type);
            s.stream = new ByteArrayInputStream(stream.toByteArray());
            return s;
        }

        public boolean isDone(){
            return stream.size() >= total;
        }
    }
}

/*
 * Copyright (c) 1996, 2023, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the  exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

/*
 * Portions Copyright (c) 1995  Colin Plumb.  All rights reserved.
 */

package java.math;

import java.io.IOException;
import java.io.InvalidObjectException;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.io.ObjectStreamField;
import java.io.ObjectStreamException;
import java.util.Arrays;
import java.util.Objects;
import java.util.Random;
import java.util.concurrent.ForkJoinPool;
import java.util.concurrent.ForkJoinWorkerThread;
import java.util.concurrent.RecursiveTask;
import java.util.concurrent.ThreadLocalRandom;

import jdk.internal.math.DoubleConsts;
import jdk.internal.math.FloatConsts;
import jdk.internal.vm.annotation.ForceInline;
import jdk.internal.vm.annotation.IntrinsicCandidate;
import jdk.internal.vm.annotation.Stable;

/**
 * Immutable arbitrary-precision integers.  All operations behave as if
 * BigIntegers were represented in two's-complement notation (like Java's
 * primitive integer types).  BigInteger provides analogues to all of Java's
 * primitive integer operators, and all relevant methods from java.lang.Math.
 * Additionally, BigInteger provides operations for modular arithmetic, GCD
 * calculation, primality testing, prime generation, bit manipulation,
 * and a few other miscellaneous operations.
 *
 * <p>Semantics of arithmetic operations exactly mimic those of Java's integer
 * arithmetic operators, as defined in <i>The Java Language Specification</i>.
 * For example, division by zero throws an {@code ArithmeticException}, and
 * division of a negative by a positive yields a negative (or zero) remainder.
 *
 * <p>Semantics of shift operations extend those of Java's shift operators
 * to allow for negative shift distances.  A right-shift with a negative
 * shift distance results in a left shift, and vice-versa.  The unsigned
 * right shift operator ({@code >>>}) is omitted since this operation
 * only makes sense for a fixed sized word and not for a
 * representation conceptually having an infinite number of leading
 * virtual sign bits.
 *
 * <p>Semantics of bitwise logical operations exactly mimic those of Java's
 * bitwise integer operators.  The binary operators ({@code and},
 * {@code or}, {@code xor}) implicitly perform sign extension on the shorter
 * of the two operands prior to performing the operation.
 *
 * <p>Comparison operations perform signed integer comparisons, analogous to
 * those performed by Java's relational and equality operators.
 *
 * <p>Modular arithmetic operations are provided to compute residues, perform
 * exponentiation, and compute multiplicative inverses.  These methods always
 * return a non-negative result, between {@code 0} and {@code (modulus - 1)},
 * inclusive.
 *
 * <p>Bit operations operate on a single bit of the two's-complement
 * representation of their operand.  If necessary, the operand is sign-extended
 * so that it contains the designated bit.  None of the single-bit
 * operations can produce a BigInteger with a different sign from the
 * BigInteger being operated on, as they affect only a single bit, and the
 * arbitrarily large abstraction provided by this class ensures that conceptually
 * there are infinitely many  preceding each BigInteger.
 *
 * <p>For the sake of brevity and clarity, pseudo-code is used throughout the
 * descriptions of BigInteger methods.  The pseudo-code expression
 * {@code (i + j)} is shorthand for "a BigInteger whose value is
 * that of the BigInteger {@code i} plus that of the BigInteger {@code j}."
 * The pseudo-code expression {@code (i == j)} is shorthand for
 * "{@code true} if and only if the BigInteger {@code i} represents the same
 * value as the BigInteger {@code j}."  Other pseudo-code expressions are
 * interpreted similarly.
 *
 * <p>All methods and constructors in this class throw
 * {@code NullPointerException} when passed
 * a null object reference for any input parameter.
 *
 * BigInteger must support values in the range
 * -2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive) to
 * +2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive)
 * and may support values outside of that range.
 *
 * An {@code ArithmeticException} is thrown when a BigInteger
 * constructor or method would generate a value outside of the
 * supported range.
 *
 * The range of probable prime values is limited and may be less than
 * the full supported positive range of {@code BigInteger}.
 * The range must be at least 1 to 2<sup>500000000</sup>.
 *
 * @apiNote
 * <a id=algorithmicComplexity>As {@code BigInteger} values are
 * arbitrary precision integers, the algorithmic complexity of the
 * methods of this class varies and may be superlinear in the size of
 * the input. For example, a method like {@link intValue()} would be
 * expected to run in <i>O</i>(1), that is constant time, since with
 * the current internal representation only a fixed-size component of
 * the {@code BigInteger} needs to be accessed to perform the
 * conversion to {@code int}. In contrast, a method like {@link not()}
 * would be expected to run in <i>O</i>(<i>n</i>) time where <i>n</i>
 * is the size of the {@code BigInteger} in bits, that is, to run in
 * time proportional to the size of the input. For multiplying two
 * {@code BigInteger} values of size <i>n</i>, a naive multiplication
 * algorithm would run in time <i>O</i>(<i>n<sup>2</sup></i>) and
 * theoretical results indicate a multiplication algorithm for numbers
 * using this category of representation must run in <em>at least</em>
 * <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>). Common multiplication
 * algorithms between the bounds of the naive and theoretical cases
 * include the Karatsuba multiplication
 * (<i>O</i>(<i>n<sup>1.585</sup></i>)) and 3-way Toom-Cook
 * multiplication (<i>O</i>(<i>n<sup>1.465</sup></i>)).</a>
 *
 * <p>A particular implementation of {@link multiply(BigInteger)
 * multiply} is free to switch between different algorithms for
 * different inputs, such as to improve actual running time to produce
 * the product by using simpler algorithms for smaller inputs even if
 * the simpler algorithm has a larger asymptotic complexity.
 *
 * <p>Operations may also allocate and compute on intermediate
 * results, potentially those allocations may be as large as in
 * proportion to the running time of the algorithm.
 *
 * <p>Users of {@code BigInteger} concerned with bounding the running
 * time or space of operations can screen out {@code BigInteger}
 * values above a chosen magnitude.
 *
 * @implNote
 * In the reference implementation, BigInteger constructors and
 * operations throw {@code ArithmeticException} when the result is out
 * of the supported range of
 * -2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive) to
 * +2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive).
 *
 * @see     BigDecimal
 * @jls     4.2.2 Integer Operations
 * @author  Josh Bloch
 * @author  Michael McCloskey
 * @author  Alan Eliasen
 * @author  Timothy Buktu
 * @since 1.1
 */

public class BigInteger extends Number implements Comparable<BigInteger> {
    /**
     * The signum of this BigInteger: -1 for negative, 0 for zero, or
     * 1 for positive.  Note that the BigInteger zero <em>must</em> have
     * a signum of 0.  This is necessary to ensures that there is exactly one
     * representation for each BigInteger value.
     */
    final int signum;

    /**
     * The magnitude of this BigInteger, in <i>big-endian</i> order: the
     * zeroth element of this array is the most-significant int of the
     * magnitude.  The magnitude must be  in that the most-significant
     * int ({@code mag[0]}) must be non-zero.  This is necessary to
     * ensure that there is exactly one representation for each BigInteger
     * value.  Note that this implies that the BigInteger zero has a
     * zero-length mag array.
     */
    final int[] mag;

    // The following fields are stable variables. A stable variable's value
    // changes at most once from the default zero value to a non-zero stable
    // value. A stable value is calculated lazily on demand.

    /**
     * One plus the bitCount of this BigInteger. This is a stable variable.
     *
     * @see #bitCount
     */
    private int bitCountPlusOne;

    /**
     * One plus the bitLength of this BigInteger. This is a stable variable.
     * (either value is acceptable).
     *
     * @see #bitLength()
     */
    private int bitLengthPlusOne;

    /**
     * Two plus the lowest set bit of this BigInteger. This is a stable variable.
     *
     * @see #getLowestSetBit
     */
    private int lowestSetBitPlusTwo;

    /**
     * Two plus the index of the lowest-order int in the magnitude of this
     * BigInteger that contains a nonzero int. This is a stable variable. The
     * least significant int has int-number 0, the next int in order of
     * increasing significance has int-number 1, and so forth.
     *
     * <p>Note: never used for a BigInteger with a magnitude of zero.
     *
     * @see #firstNonzeroIntNum()
     */
    private int firstNonzeroIntNumPlusTwo;

    /**
     * This mask is used to obtain the value of an int as if it were unsigned.
     */
    static final long LONG_MASK = 0xffffffffL;

    /**
     * This constant limits {@code mag.length} of BigIntegers to the supported
     * range.
     */
    private static final int MAX_MAG_LENGTH = Integer.MAX_VALUE / Integer.SIZE + 1; // (1 << 26)

    /**
     * Bit lengths larger than this constant can cause overflow in searchLen
     * calculation and in BitSieve.singleSearch method.
     */
    private static final  int PRIME_SEARCH_BIT_LENGTH_LIMIT = 500000000;

    /**
     * The threshold value for using Karatsuba multiplication.  If the number
     * of ints in both mag arrays are greater than this number, then
     * Karatsuba multiplication will be used.   This value is found
     * experimentally to work well.
     */
    private static final int KARATSUBA_THRESHOLD = 80;

    /**
     * The threshold value for using 3-way Toom-Cook multiplication.
     * If the number of ints in each mag array is greater than the
     * Karatsuba threshold, and the number of ints in at least one of
     * the mag arrays is greater than this threshold, then Toom-Cook
     * multiplication will be used.
     */
    private static final int TOOM_COOK_THRESHOLD = 240;

    /**
     * The threshold value for using Karatsuba squaring.  If the number
     * of ints in the number are larger than this value,
     * Karatsuba squaring will be used.   This value is found
     * experimentally to work well.
     */
    private static final int KARATSUBA_SQUARE_THRESHOLD = 128;

    /**
     * The threshold value for using Toom-Cook squaring.  If the number
     * of ints in the number are larger than this value,
     * Toom-Cook squaring will be used.   This value is found
     * experimentally to work well.
     */
    private static final int TOOM_COOK_SQUARE_THRESHOLD = 216;

    /**
     * The threshold value for using Burnikel-Ziegler division.  If the number
     * of ints in the divisor are larger than this value, Burnikel-Ziegler
     * division may be used.  This value is found experimentally to work well.
     */
    static final int BURNIKEL_ZIEGLER_THRESHOLD = 80;

    /**
     * The offset value for using Burnikel-Ziegler division.  If the number
     * of ints in the divisor exceeds the Burnikel-Ziegler threshold, and the
     * number of ints in the dividend is greater than the number of ints in the
     * divisor plus this value, Burnikel-Ziegler division will be used.  This
     * value is found experimentally to work well.
     */
    static final int BURNIKEL_ZIEGLER_OFFSET = 40;

    /**
     * The threshold value for using Schoenhage recursive base conversion. If
     * the number of ints in the number are larger than this value,
     * the Schoenhage algorithm will be used.  In practice, it appears that the
     * Schoenhage routine is faster for any threshold down to 2, and is
     * relatively flat for thresholds between 2-25, so this choice may be
     * varied within this range for very small effect.
     */
    private static final int SCHOENHAGE_BASE_CONVERSION_THRESHOLD = 20;

    /**
     * The threshold value for using squaring code to perform multiplication
     * of a {@code BigInteger} instance by itself.  If the number of ints in
     * the number are larger than this value, {@code multiply(this)} will
     * return {@code square()}.
     */
    private static final int MULTIPLY_SQUARE_THRESHOLD = 20;

    /**
     * The threshold for using an intrinsic version of
     * implMontgomeryXXX to perform Montgomery multiplication.  If the
     * number of ints in the number is more than this value we do not
     * use the intrinsic.
     */
    private static final int MONTGOMERY_INTRINSIC_THRESHOLD = 512;


    // Constructors

    /**
     * Translates a byte sub-array containing the two's-complement binary
     * representation of a BigInteger into a BigInteger.  The sub-array is
     * specified via an offset into the array and a length.  The sub-array is
     * assumed to be in <i>big-endian</i> byte-order: the most significant
     * byte is the element at index {@code off}.  The {@code val} array is
     * assumed to be unchanged for the duration of the constructor call.
     *
     * An {@code IndexOutOfBoundsException} is thrown if the length of the array
     * {@code val} is non-zero and either {@code off} is negative, {@code len}
     * is negative, or {@code off+len} is greater than the length of
     * {@code val}.
     *
     * @param  val byte array containing a sub-array which is the big-endian
     *         two's-complement binary representation of a BigInteger.
     * @param  off the start offset of the binary representation.
     * @param  len the number of bytes to use.
     * @throws NumberFormatException {@code val} is zero bytes long.
     * @throws IndexOutOfBoundsException if the provided array offset and
     *         length would cause an index into the byte array to be
     *         negative or greater than or equal to the array length.
     * @since 9
     */
    public BigInteger(byte[] val, int off, int len) {
        if (val.length == 0) {
            throw new NumberFormatException();
        }
        Objects.checkFromIndexSize(off, len, val.length);
        if (len == 0) {
            mag = ZERO.mag;
            signum = ZERO.signum;
            return;
        }

        int b = val[off];
        if (b < 0) {
            mag = makePositive(b, val, off, len);
            signum = -1;
        } else {
            mag = stripLeadingZeroBytes(b, val, off, len);
            signum = (mag.length == 0 ? 0 : 1);
        }
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    /**
     * Translates a byte array containing the two's-complement binary
     * representation of a BigInteger into a BigInteger.  The input array is
     * assumed to be in <i>big-endian</i> byte-order: the most significant
     * byte is in the zeroth element.  The {@code val} array is assumed to be
     * unchanged for the duration of the constructor call.
     *
     * @param  val big-endian two's-complement binary representation of a
     *         BigInteger.
     * @throws NumberFormatException {@code val} is zero bytes long.
     */
    public BigInteger(byte[] val) {
        this(val, 0, val.length);
    }

    /**
     * This private constructor translates an int array containing the
     * two's-complement binary representation of a BigInteger into a
     * BigInteger. The input array is assumed to be in <i>big-endian</i>
     * int-order: the most significant int is in the zeroth element.  The
     * {@code val} array is assumed to be unchanged for the duration of
     * the constructor call.
     */
    private BigInteger(int[] val) {
        if (val.length == 0)
            throw new NumberFormatException();

        if (val[0] < 0) {
            mag = makePositive(val);
            signum = -1;
        } else {
            mag = trustedStripLeadingZeroInts(val);
            signum = (mag.length == 0 ? 0 : 1);
        }
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    /**
     * Translates the sign-magnitude representation of a BigInteger into a
     * BigInteger.  The sign is represented as an integer signum value: -1 for
     * negative, 0 for zero, or 1 for positive.  The magnitude is a sub-array of
     * a byte array in <i>big-endian</i> byte-order: the most significant byte
     * is the element at index {@code off}.  A zero value of the length
     * {@code len} is permissible, and will result in a BigInteger value of 0,
     * whether signum is -1, 0 or 1.  The {@code magnitude} array is assumed to
     * be unchanged for the duration of the constructor call.
     *
     * An {@code IndexOutOfBoundsException} is thrown if the length of the array
     * {@code magnitude} is non-zero and either {@code off} is negative,
     * {@code len} is negative, or {@code off+len} is greater than the length of
     * {@code magnitude}.
     *
     * @param  signum signum of the number (-1 for negative, 0 for zero, 1
     *         for positive).
     * @param  magnitude big-endian binary representation of the magnitude of
     *         the number.
     * @param  off the start offset of the binary representation.
     * @param  len the number of bytes to use.
     * @throws NumberFormatException {@code signum} is not one of the three
     *         legal values (-1, 0, and 1), or {@code signum} is 0 and
     *         {@code magnitude} contains one or more non-zero bytes.
     * @throws IndexOutOfBoundsException if the provided array offset and
     *         length would cause an index into the byte array to be
     *         negative or greater than or equal to the array length.
     * @since 9
     */
    public BigInteger(int signum, byte[] magnitude, int off, int len) {
        if (signum < -1 || signum > 1) {
            throw(new NumberFormatException());
        }
        Objects.checkFromIndexSize(off, len, magnitude.length);

        // stripLeadingZeroBytes() returns a zero length array if len == 0
        this.mag = stripLeadingZeroBytes(magnitude, off, len);

        if (this.mag.length == 0) {
            this.signum = 0;
        } else {
            if (signum == 0)
                throw(new NumberFormatException());
            this.signum = signum;
        }
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    /**
     * Translates the sign-magnitude representation of a BigInteger into a
     * BigInteger.  The sign is represented as an integer signum value: -1 for
     * negative, 0 for zero, or 1 for positive.  The magnitude is a byte array
     * in <i>big-endian</i> byte-order: the most significant byte is the
     * zeroth element.  A zero-length magnitude array is permissible, and will
     * result in a BigInteger value of 0, whether signum is -1, 0 or 1.  The
     * {@code magnitude} array is assumed to be unchanged for the duration of
     * the constructor call.
     *
     * @param  signum signum of the number (-1 for negative, 0 for zero, 1
     *         for positive).
     * @param  magnitude big-endian binary representation of the magnitude of
     *         the number.
     * @throws NumberFormatException {@code signum} is not one of the three
     *         legal values (-1, 0, and 1), or {@code signum} is 0 and
     *         {@code magnitude} contains one or more non-zero bytes.
     */
    public BigInteger(int signum, byte[] magnitude) {
         this(signum, magnitude, 0, magnitude.length);
    }

    /**
     * A constructor for internal use that translates the sign-magnitude
     * representation of a BigInteger into a BigInteger. It checks the
     * arguments and copies the magnitude so this constructor would be
     * safe for external use.  The {@code magnitude} array is assumed to be
     * unchanged for the duration of the constructor call.
     */
    private BigInteger(int signum, int[] magnitude) {
        this.mag = stripLeadingZeroInts(magnitude);

        if (signum < -1 || signum > 1)
            throw(new NumberFormatException());

        if (this.mag.length == 0) {
            this.signum = 0;
        } else {
            if (signum == 0)
                throw(new NumberFormatException());
            this.signum = signum;
        }
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    /**
     * Translates the String representation of a BigInteger in the
     * specified radix into a BigInteger.  The String representation
     * consists of an optional minus or plus sign followed by a
     * sequence of one or more digits in the specified radix.  The
     * character-to-digit mapping is provided by {@link
     * Character#digit(char, int) Character.digit}.  The String may
     * not contain any extraneous characters (whitespace, for
     * example).
     *
     * @param val String representation of BigInteger.
     * @param radix radix to be used in interpreting {@code val}.
     * @throws NumberFormatException {@code val} is not a valid representation
     *         of a BigInteger in the specified radix, or {@code radix} is
     *         outside the range from {@link Character#MIN_RADIX} to
     *         {@link Character#MAX_RADIX}, inclusive.
     */
    public BigInteger(String val, int radix) {
        int cursor = 0, numDigits;
        final int len = val.length();

        if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
            throw new NumberFormatException();
        if (len == 0)
            throw new NumberFormatException();

        // Check for at most one leading sign
        int sign = 1;
        int index1 = val.lastIndexOf('-');
        int index2 = val.lastIndexOf('+');
        if (index1 >= 0) {
            if (index1 != 0 || index2 >= 0) {
                throw new NumberFormatException();
            }
            sign = -1;
            cursor = 1;
        } else if (index2 >= 0) {
            if (index2 != 0) {
                throw new NumberFormatException();
            }
            cursor = 1;
        }
        if (cursor == len)
            throw new NumberFormatException();

        // Skip leading zeros and compute number of digits in magnitude
        while (cursor < len &&
               Character.digit(val.charAt(cursor), radix) == 0) {
            cursor++;
        }

        if (cursor == len) {
            signum = 0;
            mag = ZERO.mag;
            return;
        }

        numDigits = len - cursor;
        signum = sign;

        // Pre-allocate array of expected size. May be too large but can
        // never be too small. Typically exact.
        long numBits = ((numDigits * bitsPerDigit[radix]) >>> 10) + 1;
        if (numBits + 31 >= (1L << 32)) {
            reportOverflow();
        }
        int numWords = (int) (numBits + 31) >>> 5;
        int[] magnitude = new int[numWords];

        // Process first (potentially short) digit group
        int firstGroupLen = numDigits % digitsPerInt[radix];
        if (firstGroupLen == 0)
            firstGroupLen = digitsPerInt[radix];
        String group = val.substring(cursor, cursor += firstGroupLen);
        magnitude[numWords - 1] = Integer.parseInt(group, radix);
        if (magnitude[numWords - 1] < 0)
            throw new NumberFormatException();

        // Process remaining digit groups
        int superRadix = intRadix[radix];
        int groupVal = 0;
        while (cursor < len) {
            group = val.substring(cursor, cursor += digitsPerInt[radix]);
            groupVal = Integer.parseInt(group, radix);
            if (groupVal < 0)
                throw new NumberFormatException();
            destructiveMulAdd(magnitude, superRadix, groupVal);
        }
        // Required for cases where the array was overallocated.
        mag = trustedStripLeadingZeroInts(magnitude);
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    /*
     * Constructs a new BigInteger using a char array with radix=10.
     * Sign is precalculated outside and not allowed in the val. The {@code val}
     * array is assumed to be unchanged for the duration of the constructor
     * call.
     */
    BigInteger(char[] val, int sign, int len) {
        int cursor = 0, numDigits;

        // Skip leading zeros and compute number of digits in magnitude
        while (cursor < len && Character.digit(val[cursor], 10) == 0) {
            cursor++;
        }
        if (cursor == len) {
            signum = 0;
            mag = ZERO.mag;
            return;
        }

        numDigits = len - cursor;
        signum = sign;
        // Pre-allocate array of expected size
        int numWords;
        if (len < 10) {
            numWords = 1;
        } else {
            long numBits = ((numDigits * bitsPerDigit[10]) >>> 10) + 1;
            if (numBits + 31 >= (1L << 32)) {
                reportOverflow();
            }
            numWords = (int) (numBits + 31) >>> 5;
        }
        int[] magnitude = new int[numWords];

        // Process first (potentially short) digit group
        int firstGroupLen = numDigits % digitsPerInt[10];
        if (firstGroupLen == 0)
            firstGroupLen = digitsPerInt[10];
        magnitude[numWords - 1] = parseInt(val, cursor,  cursor += firstGroupLen);

        // Process remaining digit groups
        while (cursor < len) {
            int groupVal = parseInt(val, cursor, cursor += digitsPerInt[10]);
            destructiveMulAdd(magnitude, intRadix[10], groupVal);
        }
        mag = trustedStripLeadingZeroInts(magnitude);
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    // Create an integer with the digits between the two indexes
    // Assumes start < end. The result may be negative, but it
    // is to be treated as an unsigned value.
    private int parseInt(char[] source, int start, int end) {
        int result = Character.digit(source[start++], 10);
        if (result == -1)
            throw new NumberFormatException(new String(source));

        for (int index = start; index < end; index++) {
            int nextVal = Character.digit(source[index], 10);
            if (nextVal == -1)
                throw new NumberFormatException(new String(source));
            result = 10*result + nextVal;
        }

        return result;
    }

    // bitsPerDigit in the given radix times 1024
    // Rounded up to avoid underallocation.
    private static long bitsPerDigit[] = { 0, 0,
        1024, 1624, 2048, 2378, 2648, 2875, 3072, 3247, 3402, 3543, 3672,
        3790, 3899, 4001, 4096, 4186, 4271, 4350, 4426, 4498, 4567, 4633,
        4696, 4756, 4814, 4870, 4923, 4975, 5025, 5074, 5120, 5166, 5210,
                                           5253, 5295};

    // Multiply x array times word y in place, and add word z
    private static void destructiveMulAdd(int[] x, int y, int z) {
        // Perform the multiplication word by word
        long ylong = y & LONG_MASK;
        long zlong = z & LONG_MASK;
        int len = x.length;

        long product = 0;
        long carry = 0;
        for (int i = len-1; i >= 0; i--) {
            product = ylong * (x[i] & LONG_MASK) + carry;
            x[i] = (int)product;
            carry = product >>> 32;
        }

        // Perform the addition
        long sum = (x[len-1] & LONG_MASK) + zlong;
        x[len-1] = (int)sum;
        carry = sum >>> 32;
        for (int i = len-2; i >= 0; i--) {
            sum = (x[i] & LONG_MASK) + carry;
            x[i] = (int)sum;
            carry = sum >>> 32;
        }
    }

    /**
     * Translates the decimal String representation of a BigInteger
     * into a BigInteger.  The String representation consists of an
     * optional minus or plus sign followed by a sequence of one or
     * more decimal digits.  The character-to-digit mapping is
     * provided by {@link Character#digit(char, int)
     * Character.digit}.  The String may not contain any extraneous
     * characters (whitespace, for example).
     *
     * @param val decimal String representation of BigInteger.
     * @throws NumberFormatException {@code val} is not a valid representation
     *         of a BigInteger.
     */
    public BigInteger(String val) {
        this(val, 10);
    }

    /**
     * Constructs a randomly generated BigInteger, uniformly distributed over
     * the range 0 to (2<sup>{@code numBits}</sup> - 1), inclusive.
     * The uniformity of the distribution assumes that a fair source of random
     * bits is provided in {@code rnd}.  Note that this constructor always
     * constructs a non-negative BigInteger.
     *
     * @param  numBits maximum bitLength of the new BigInteger.
     * @param  rnd source of randomness to be used in computing the new
     *         BigInteger.
     * @throws IllegalArgumentException {@code numBits} is negative.
     * @see #bitLength()
     */
    public BigInteger(int numBits, Random rnd) {
        byte[] magnitude = randomBits(numBits, rnd);

        try {
            // stripLeadingZeroBytes() returns a zero length array if len == 0
            this.mag = stripLeadingZeroBytes(magnitude, 0, magnitude.length);

            if (this.mag.length == 0) {
                this.signum = 0;
            } else {
                this.signum = 1;
            }
            if (mag.length >= MAX_MAG_LENGTH) {
                checkRange();
            }
        } finally {
            Arrays.fill(magnitude, (byte)0);
        }
    }

    private static byte[] randomBits(int numBits, Random rnd) {
        if (numBits < 0)
            throw new IllegalArgumentException();
        int numBytes = (int)(((long)numBits+7)/8); // avoid overflow
        byte[] randomBits = new byte[numBytes];

        // Generate random bytes and mask out any excess bits
        if (numBytes > 0) {
            rnd.nextBytes(randomBits);
            int excessBits = 8*numBytes - numBits;
            randomBits[0] &= (byte)((1 << (8-excessBits)) - 1);
        }
        return randomBits;
    }

    /**
     * Constructs a randomly generated positive BigInteger that is probably
     * prime, with the specified bitLength.
     *
     * @apiNote It is recommended that the {@link #probablePrime probablePrime}
     * method be used in preference to this constructor unless there
     * is a compelling need to specify a certainty.
     *
     * @param  bitLength bitLength of the returned BigInteger.
     * @param  certainty a measure of the uncertainty that the caller is
     *         willing to tolerate.  The probability that the new BigInteger
     *         represents a prime number will exceed
     *         (1 - 1/2<sup>{@code certainty}</sup>).  The execution time of
     *         this constructor is proportional to the value of this parameter.
     * @param  rnd source of random bits used to select candidates to be
     *         tested for primality.
     * @throws ArithmeticException {@code bitLength < 2} or {@code bitLength} is too large.
     * @see    #bitLength()
     */
    public BigInteger(int bitLength, int certainty, Random rnd) {
        BigInteger prime;

        if (bitLength < 2)
            throw new ArithmeticException();
        prime = (bitLength < SMALL_PRIME_THRESHOLD
                                ? smallPrime(bitLength, certainty, rnd)
                                : largePrime(bitLength, certainty, rnd));
        signum = 1;
        mag = prime.mag;
    }

    // Minimum size in bits that the requested prime number has
    // before we use the large prime number generating algorithms.
    // The cutoff of 95 was chosen empirically for best performance.
    private static final int SMALL_PRIME_THRESHOLD = 95;

    // Certainty required to meet the spec of probablePrime
    private static final int DEFAULT_PRIME_CERTAINTY = 100;

    /**
     * Returns a positive BigInteger that is probably prime, with the
     * specified bitLength. The probability that a BigInteger returned
     * by this method is composite does not exceed 2<sup>-100</sup>.
     *
     * @param  bitLength bitLength of the returned BigInteger.
     * @param  rnd source of random bits used to select candidates to be
     *         tested for primality.
     * @return a BigInteger of {@code bitLength} bits that is probably prime
     * @throws ArithmeticException {@code bitLength < 2} or {@code bitLength} is too large.
     * @see    #bitLength()
     * @since 1.4
     */
    public static BigInteger probablePrime(int bitLength, Random rnd) {
        if (bitLength < 2)
            throw new ArithmeticException();

        return (bitLength < SMALL_PRIME_THRESHOLD ?
                smallPrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd) :
                largePrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd));
    }

    /**
     * Find a random number of the specified bitLength that is probably prime.
     * This method is used for smaller primes, its performance degrades on
     * larger bitlengths.
     *
     * This method assumes bitLength > 1.
     */
    private static BigInteger smallPrime(int bitLength, int certainty, Random rnd) {
        int magLen = (bitLength + 31) >>> 5;
        int temp[] = new int[magLen];
        int highBit = 1 << ((bitLength+31) & 0x1f);  // High bit of high int
        int highMask = (highBit << 1) - 1;  // Bits to keep in high int

        while (true) {
            // Construct a candidate
            for (int i=0; i < magLen; i++)
                temp[i] = rnd.nextInt();
            temp[0] = (temp[0] & highMask) | highBit;  // Ensure exact length
            if (bitLength > 2)
                temp[magLen-1] |= 1;  // Make odd if bitlen > 2

            BigInteger p = new BigInteger(temp, 1);

            // Do cheap  if applicable
            if (bitLength > 6) {
                long r = p.remainder(SMALL_PRIME_PRODUCT).longValue();
                if ((r%3==0)  || (r%5==0)  || (r%7==0)  || (r%11==0) ||
                    (r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) ||
                    (r%29==0) || (r%31==0) || (r%37==0) || (r%41==0))
                    continue; // Candidate is composite; try another
            }

            // All candidates of bitLength 2 and 3 are prime by this point
            if (bitLength < 4)
                return p;

            // Do expensive test if we survive pre-test (or it's inapplicable)
            if (p.primeToCertainty(certainty, rnd))
                return p;
        }
    }

    private static final BigInteger SMALL_PRIME_PRODUCT
                       = valueOf(3L*5*7*11*13*17*19*23*29*31*37*41);

    /**
     * Find a random number of the specified bitLength that is probably prime.
     * This method is more appropriate for larger bitlengths since it uses
     * a sieve to eliminate most composites before using a more expensive
     * test.
     */
    private static BigInteger largePrime(int bitLength, int certainty, Random rnd) {
        BigInteger p;
        p = new BigInteger(bitLength, rnd).setBit(bitLength-1);
        p.mag[p.mag.length-1] &= 0xfffffffe;

        // Use a sieve length likely to contain the next prime number
        int searchLen = getPrimeSearchLen(bitLength);
        BitSieve searchSieve = new BitSieve(p, searchLen);
        BigInteger candidate = searchSieve.retrieve(p, certainty, rnd);

        while ((candidate == null) || (candidate.bitLength() != bitLength)) {
            p = p.add(BigInteger.valueOf(2*searchLen));
            if (p.bitLength() != bitLength)
                p = new BigInteger(bitLength, rnd).setBit(bitLength-1);
            p.mag[p.mag.length-1] &= 0xfffffffe;
            searchSieve = new BitSieve(p, searchLen);
            candidate = searchSieve.retrieve(p, certainty, rnd);
        }
        return candidate;
    }

   /**
    * Returns the first integer greater than this {@code BigInteger} that
    * is probably prime.  The probability that the number returned by this
    * method is composite does not exceed 2<sup>-100</sup>. This method will
    * never skip over a prime when searching: if it returns {@code p}, there
    * is no prime {@code q} such that {@code this < q < p}.
    *
    * @return the first integer greater than this {@code BigInteger} that
    *         is probably prime.
    * @throws ArithmeticException {@code this < 0} or {@code this} is too large.
    * @implNote Due to the nature of the underlying algorithm,
    *          and depending on the size of {@code this},
    *          this method could consume a large amount of memory, up to
    *          exhaustion of available heap space, or could run for a long time.
    * @since 1.5
    */
    public BigInteger nextProbablePrime() {
        if (this.signum < 0)
            throw new ArithmeticException( + this);

        // Handle trivial cases
        if ((this.signum == 0) || this.equals(ONE))
            return TWO;

        BigInteger result = this.add(ONE);

        // Fastpath for small numbers
        if (result.bitLength() < SMALL_PRIME_THRESHOLD) {

            // Ensure an odd number
            if (!result.testBit(0))
                result = result.add(ONE);

            while (true) {
                // Do cheap  if applicable
                if (result.bitLength() > 6) {
                    long r = result.remainder(SMALL_PRIME_PRODUCT).longValue();
                    if ((r%3==0)  || (r%5==0)  || (r%7==0)  || (r%11==0) ||
                        (r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) ||
                        (r%29==0) || (r%31==0) || (r%37==0) || (r%41==0)) {
                        result = result.add(TWO);
                        continue; // Candidate is composite; try another
                    }
                }

                // All candidates of bitLength 2 and 3 are prime by this point
                if (result.bitLength() < 4)
                    return result;

                // The expensive test
                if (result.primeToCertainty(DEFAULT_PRIME_CERTAINTY, null))
                    return result;

                result = result.add(TWO);
            }
        }

        // Start at previous even number
        if (result.testBit(0))
            result = result.subtract(ONE);

        // Looking for the next large prime
        int searchLen = getPrimeSearchLen(result.bitLength());

        while (true) {
           BitSieve searchSieve = new BitSieve(result, searchLen);
           BigInteger candidate = searchSieve.retrieve(result,
                                                 DEFAULT_PRIME_CERTAINTY, null);
           if (candidate != null)
               return candidate;
           result = result.add(BigInteger.valueOf(2 * searchLen));
        }
    }

    private static int getPrimeSearchLen(int bitLength) {
        if (bitLength > PRIME_SEARCH_BIT_LENGTH_LIMIT + 1) {
            throw new ArithmeticException();
        }
        return bitLength / 20 * 64;
    }

    /**
     * Returns {@code true} if this BigInteger is probably prime,
     * {@code false} if it's definitely composite.
     *
     * This method assumes bitLength > 2.
     *
     * @param  certainty a measure of the uncertainty that the caller is
     *         willing to tolerate: if the call returns {@code true}
     *         the probability that this BigInteger is prime exceeds
     *         <code>(1 - 1/2<sup>certainty</sup>)</code>.  The execution time of
     *         this method is proportional to the value of this parameter.
     * @return {@code true} if this BigInteger is probably prime,
     *         {@code false} if it's definitely composite.
     */
    boolean primeToCertainty(int certainty, Random random) {
        int rounds = 0;
        int n = (Math.min(certainty, Integer.MAX_VALUE-1)+1)/2;

        // The relationship between the certainty and the number of rounds
        // we perform is given in the draft standard ANSI X9.80, "PRIME
        // NUMBER GENERATION, PRIMALITY TESTING, AND PRIMALITY CERTIFICATES".
        int sizeInBits = this.bitLength();
        if (sizeInBits < 100) {
            rounds = 50;
            rounds = n < rounds ? n : rounds;
            return passesMillerRabin(rounds, random);
        }

        if (sizeInBits < 256) {
            rounds = 27;
        } else if (sizeInBits < 512) {
            rounds = 15;
        } else if (sizeInBits < 768) {
            rounds = 8;
        } else if (sizeInBits < 1024) {
            rounds = 4;
        } else {
            rounds = 2;
        }
        rounds = n < rounds ? n : rounds;

        return passesMillerRabin(rounds, random) && passesLucasLehmer();
    }

    /**
     * Returns true iff this BigInteger is a Lucas-Lehmer probable prime.
     *
     * The following assumptions are made:
     * This BigInteger is a positive, odd number.
     */
    private boolean passesLucasLehmer() {
        BigInteger thisPlusOne = this.add(ONE);

        // Step 1
        int d = 5;
        while (jacobiSymbol(d, this) != -1) {
            // 5, -7, 9, -11, ...
            d = (d < 0) ? Math.abs(d)+2 : -(d+2);
        }

        // Step 2
        BigInteger u = lucasLehmerSequence(d, thisPlusOne, this);

        // Step 3
        return u.mod(this).equals(ZERO);
    }

    /**
     * Computes Jacobi(p,n).
     * Assumes n positive, odd, n>=3.
     */
    private static int jacobiSymbol(int p, BigInteger n) {
        if (p == 0)
            return 0;

        // Algorithm and comments adapted from Colin Plumb's C library.
        int j = 1;
        int u = n.mag[n.mag.length-1];

        // Make p positive
        if (p < 0) {
            p = -p;
            int n8 = u & 7;
            if ((n8 == 3) || (n8 == 7))
                j = -j; // 3 (011) or 7 (111) mod 8
        }

        // Get rid of factors of 2 in p
        while ((p & 3) == 0)
            p >>= 2;
        if ((p & 1) == 0) {
            p >>= 1;
            if (((u ^ (u>>1)) & 2) != 0)
                j = -j; // 3 (011) or 5 (101) mod 8
        }
        if (p == 1)
            return j;
        // Then, apply quadratic reciprocity
        if ((p & u & 2) != 0)   // p = u = 3 (mod 4)?
            j = -j;
        // And reduce u mod p
        u = n.mod(BigInteger.valueOf(p)).intValue();

        // Now compute Jacobi(u,p), u < p
        while (u != 0) {
            while ((u & 3) == 0)
                u >>= 2;
            if ((u & 1) == 0) {
                u >>= 1;
                if (((p ^ (p>>1)) & 2) != 0)
                    j = -j;     // 3 (011) or 5 (101) mod 8
            }
            if (u == 1)
                return j;
            // Now both u and p are odd, so use quadratic reciprocity
            assert (u < p);
            int t = u; u = p; p = t;
            if ((u & p & 2) != 0) // u = p = 3 (mod 4)?
                j = -j;
            // Now u >= p, so it can be reduced
            u %= p;
        }
        return 0;
    }

    private static BigInteger lucasLehmerSequence(int z, BigInteger k, BigInteger n) {
        BigInteger d = BigInteger.valueOf(z);
        BigInteger u = ONE; BigInteger u2;
        BigInteger v = ONE; BigInteger v2;

        for (int i=k.bitLength()-2; i >= 0; i--) {
            u2 = u.multiply(v).mod(n);

            v2 = v.square().add(d.multiply(u.square())).mod(n);
            if (v2.testBit(0))
                v2 = v2.subtract(n);

            v2 = v2.shiftRight(1);

            u = u2; v = v2;
            if (k.testBit(i)) {
                u2 = u.add(v).mod(n);
                if (u2.testBit(0))
                    u2 = u2.subtract(n);

                u2 = u2.shiftRight(1);
                v2 = v.add(d.multiply(u)).mod(n);
                if (v2.testBit(0))
                    v2 = v2.subtract(n);
                v2 = v2.shiftRight(1);

                u = u2; v = v2;
            }
        }
        return u;
    }

    /**
     * Returns true iff this BigInteger passes the specified number of
     * Miller-Rabin tests. This test is taken from the DSA spec (NIST FIPS
     * 186-2).
     *
     * The following assumptions are made:
     * This BigInteger is a positive, odd number greater than 2.
     * iterations<=50.
     */
    private boolean passesMillerRabin(int iterations, Random rnd) {
        // Find a and m such that m is odd and this == 1 + 2**a * m
        BigInteger thisMinusOne = this.subtract(ONE);
        BigInteger m = thisMinusOne;
        int a = m.getLowestSetBit();
        m = m.shiftRight(a);

        // Do the tests
        if (rnd == null) {
            rnd = ThreadLocalRandom.current();
        }
        for (int i=0; i < iterations; i++) {
            // Generate a uniform random on (1, this)
            BigInteger b;
            do {
                b = new BigInteger(this.bitLength(), rnd);
            } while (b.compareTo(ONE) <= 0 || b.compareTo(this) >= 0);

            int j = 0;
            BigInteger z = b.modPow(m, this);
            while (!((j == 0 && z.equals(ONE)) || z.equals(thisMinusOne))) {
                if (j > 0 && z.equals(ONE) || ++j == a)
                    return false;
                z = z.modPow(TWO, this);
            }
        }
        return true;
    }

    /**
     * This internal constructor differs from its public cousin
     * with the arguments reversed in two ways: it assumes that its
     * arguments are correct, and it doesn't copy the magnitude array.
     */
    BigInteger(int[] magnitude, int signum) {
        this.signum = (magnitude.length == 0 ? 0 : signum);
        this.mag = magnitude;
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    /**
     * This private constructor is for internal use and assumes that its
     * arguments are correct.  The {@code magnitude} array is assumed to be
     * unchanged for the duration of the constructor call.
     */
    private BigInteger(byte[] magnitude, int signum) {
        this.signum = (magnitude.length == 0 ? 0 : signum);
        this.mag = stripLeadingZeroBytes(magnitude, 0, magnitude.length);
        if (mag.length >= MAX_MAG_LENGTH) {
            checkRange();
        }
    }

    /**
     * Throws an {@code ArithmeticException} if the {@code BigInteger} would be
     * out of the supported range.
     *
     * @throws ArithmeticException if {@code this} exceeds the supported range.
     */
    private void checkRange() {
        if (mag.length > MAX_MAG_LENGTH || mag.length == MAX_MAG_LENGTH && mag[0] < 0) {
            reportOverflow();
        }
    }

    private static void reportOverflow() {
        throw new ArithmeticException();
    }

    //Static Factory Methods

    /**
     * Returns a BigInteger whose value is equal to that of the
     * specified {@code long}.
     *
     * @apiNote This static factory method is provided in preference
     * to a ({@code long}) constructor because it allows for reuse of
     * frequently used BigIntegers.
     *
     * @param  val value of the BigInteger to return.
     * @return a BigInteger with the specified value.
     */
    public static BigInteger valueOf(long val) {
        // If -MAX_CONSTANT < val < MAX_CONSTANT, return stashed constant
        if (val == 0)
            return ZERO;
        if (val > 0 && val <= MAX_CONSTANT)
            return posConst[(int) val];
        else if (val < 0 && val >= -MAX_CONSTANT)
            return negConst[(int) -val];

        return new BigInteger(val);
    }

    /**
     * Constructs a BigInteger with the specified value, which may not be zero.
     */
    private BigInteger(long val) {
        if (val < 0) {
            val = -val;
            signum = -1;
        } else {
            signum = 1;
        }

        int highWord = (int)(val >>> 32);
        if (highWord == 0) {
            mag = new int[1];
            mag[0] = (int)val;
        } else {
            mag = new int[2];
            mag[0] = highWord;
            mag[1] = (int)val;
        }
    }

    /**
     * Returns a BigInteger with the given two's complement representation.
     * Assumes that the input array will not be modified (the returned
     * BigInteger will reference the input array if feasible).
     */
    private static BigInteger valueOf(int[] val) {
        return (val[0] > 0 ? new BigInteger(val, 1) : new BigInteger(val));
    }

    // Constants

    /**
     * Initialize static constant array when class is loaded.
     */
    private static final int MAX_CONSTANT = 16;
    @Stable
    private static final BigInteger[] posConst = new BigInteger[MAX_CONSTANT+1];
    @Stable
    private static final BigInteger[] negConst = new BigInteger[MAX_CONSTANT+1];

    /**
     * The cache of powers of each radix.  This allows us to not have to
     * recalculate powers of radix^(2^n) more than once.  This speeds
     * Schoenhage recursive base conversion significantly.
     */
    private static volatile BigInteger[][] powerCache;

    /** The cache of logarithms of radices for base conversion. */
    private static final double[] logCache;

    /** The natural log of 2.  This is used in computing cache indices. */
    private static final double LOG_TWO = Math.log(2.0);

    static {
        assert 0 < KARATSUBA_THRESHOLD
            && KARATSUBA_THRESHOLD < TOOM_COOK_THRESHOLD
            && TOOM_COOK_THRESHOLD < Integer.MAX_VALUE
            && 0 < KARATSUBA_SQUARE_THRESHOLD
            && KARATSUBA_SQUARE_THRESHOLD < TOOM_COOK_SQUARE_THRESHOLD
            && TOOM_COOK_SQUARE_THRESHOLD < Integer.MAX_VALUE :
            ;

        for (int i = 1; i <= MAX_CONSTANT; i++) {
            int[] magnitude = new int[1];
            magnitude[0] = i;
            posConst[i] = new BigInteger(magnitude,  1);
            negConst[i] = new BigInteger(magnitude, -1);
        }

        /*
         * Initialize the cache of radix^(2^x) values used for base conversion
         * with just the very first value.  Additional values will be created
         * on demand.
         */
        BigInteger[][] cache = new BigInteger[Character.MAX_RADIX+1][];
        logCache = new double[Character.MAX_RADIX+1];

        for (int i=Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
            cache[i] = new BigInteger[] { BigInteger.valueOf(i) };
            logCache[i] = Math.log(i);
        }
        BigInteger.powerCache = cache;
    }

    /**
     * The BigInteger constant zero.
     *
     * @since   1.2
     */
    public static final BigInteger ZERO = new BigInteger(new int[0], 0);

    /**
     * The BigInteger constant one.
     *
     * @since   1.2
     */
    public static final BigInteger ONE = valueOf(1);

    /**
     * The BigInteger constant two.
     *
     * @since   9
     */
    public static final BigInteger TWO = valueOf(2);

    /**
     * The BigInteger constant -1.  (Not exported.)
     */
    private static final BigInteger NEGATIVE_ONE = valueOf(-1);

    /**
     * The BigInteger constant ten.
     *
     * @since   1.5
     */
    public static final BigInteger TEN = valueOf(10);

    // Arithmetic Operations

    /**
     * Returns a BigInteger whose value is {@code (this + val)}.
     *
     * @param  val value to be added to this BigInteger.
     * @return {@code this + val}
     */
    public BigInteger add(BigInteger val) {
        if (val.signum == 0)
            return this;
        if (signum == 0)
            return val;
        if (val.signum == signum)
            return new BigInteger(add(mag, val.mag), signum);

        int cmp = compareMagnitude(val);
        if (cmp == 0)
            return ZERO;
        int[] resultMag = (cmp > 0 ? subtract(mag, val.mag)
                           : subtract(val.mag, mag));
        resultMag = trustedStripLeadingZeroInts(resultMag);

        return new BigInteger(resultMag, cmp == signum ? 1 : -1);
    }

    /**
     * Package private methods used by BigDecimal code to add a BigInteger
     * with a long. Assumes val is not equal to INFLATED.
     */
    BigInteger add(long val) {
        if (val == 0)
            return this;
        if (signum == 0)
            return valueOf(val);
        if (Long.signum(val) == signum)
            return new BigInteger(add(mag, Math.abs(val)), signum);
        int cmp = compareMagnitude(val);
        if (cmp == 0)
            return ZERO;
        int[] resultMag = (cmp > 0 ? subtract(mag, Math.abs(val)) : subtract(Math.abs(val), mag));
        resultMag = trustedStripLeadingZeroInts(resultMag);
        return new BigInteger(resultMag, cmp == signum ? 1 : -1);
    }

    /**
     * Adds the contents of the int array x and long value val. This
     * method allocates a new int array to hold the answer and returns
     * a reference to that array.  Assumes x.length &gt; 0 and val is
     * non-negative
     */
    private static int[] add(int[] x, long val) {
        int[] y;
        long sum = 0;
        int xIndex = x.length;
        int[] result;
        int highWord = (int)(val >>> 32);
        if (highWord == 0) {
            result = new int[xIndex];
            sum = (x[--xIndex] & LONG_MASK) + val;
            result[xIndex] = (int)sum;
        } else {
            if (xIndex == 1) {
                result = new int[2];
                sum = val  + (x[0] & LONG_MASK);
                result[1] = (int)sum;
                result[0] = (int)(sum >>> 32);
                return result;
            } else {
                result = new int[xIndex];
                sum = (x[--xIndex] & LONG_MASK) + (val & LONG_MASK);
                result[xIndex] = (int)sum;
                sum = (x[--xIndex] & LONG_MASK) + (highWord & LONG_MASK) + (sum >>> 32);
                result[xIndex] = (int)sum;
            }
        }
        // Copy remainder of longer number while carry propagation is required
        boolean carry = (sum >>> 32 != 0);
        while (xIndex > 0 && carry)
            carry = ((result[--xIndex] = x[xIndex] + 1) == 0);
        // Copy remainder of longer number
        while (xIndex > 0)
            result[--xIndex] = x[xIndex];
        // Grow result if necessary
        if (carry) {
            int bigger[] = new int[result.length + 1];
            System.arraycopy(result, 0, bigger, 1, result.length);
            bigger[0] = 0x01;
            return bigger;
        }
        return result;
    }

    /**
     * Adds the contents of the int arrays x and y. This method allocates
     * a new int array to hold the answer and returns a reference to that
     * array.
     */
    private static int[] add(int[] x, int[] y) {
        // If x is shorter, swap the two arrays
        if (x.length < y.length) {
            int[] tmp = x;
            x = y;
            y = tmp;
        }

        int xIndex = x.length;
        int yIndex = y.length;
        int result[] = new int[xIndex];
        long sum = 0;
        if (yIndex == 1) {
            sum = (x[--xIndex] & LONG_MASK) + (y[0] & LONG_MASK) ;
            result[xIndex] = (int)sum;
        } else {
            // Add common parts of both numbers
            while (yIndex > 0) {
                sum = (x[--xIndex] & LONG_MASK) +
                      (y[--yIndex] & LONG_MASK) + (sum >>> 32);
                result[xIndex] = (int)sum;
            }
        }
        // Copy remainder of longer number while carry propagation is required
        boolean carry = (sum >>> 32 != 0);
        while (xIndex > 0 && carry)
            carry = ((result[--xIndex] = x[xIndex] + 1) == 0);

        // Copy remainder of longer number
        while (xIndex > 0)
            result[--xIndex] = x[xIndex];

        // Grow result if necessary
        if (carry) {
            int bigger[] = new int[result.length + 1];
            System.arraycopy(result, 0, bigger, 1, result.length);
            bigger[0] = 0x01;
            return bigger;
        }
        return result;
    }

    private static int[] subtract(long val, int[] little) {
        int highWord = (int)(val >>> 32);
        if (highWord == 0) {
            int result[] = new int[1];
            result[0] = (int)(val - (little[0] & LONG_MASK));
            return result;
        } else {
            int result[] = new int[2];
            if (little.length == 1) {
                long difference = ((int)val & LONG_MASK) - (little[0] & LONG_MASK);
                result[1] = (int)difference;
                // Subtract remainder of longer number while borrow propagates
                boolean borrow = (difference >> 32 != 0);
                if (borrow) {
                    result[0] = highWord - 1;
                } else {        // Copy remainder of longer number
                    result[0] = highWord;
                }
                return result;
            } else { // little.length == 2
                long difference = ((int)val & LONG_MASK) - (little[1] & LONG_MASK);
                result[1] = (int)difference;
                difference = (highWord & LONG_MASK) - (little[0] & LONG_MASK) + (difference >> 32);
                result[0] = (int)difference;
                return result;
            }
        }
    }

    /**
     * Subtracts the contents of the second argument (val) from the
     * first (big).  The first int array (big) must represent a larger number
     * than the second.  This method allocates the space necessary to hold the
     * answer.
     * assumes val &gt;= 0
     */
    private static int[] subtract(int[] big, long val) {
        int highWord = (int)(val >>> 32);
        int bigIndex = big.length;
        int result[] = new int[bigIndex];
        long difference = 0;

        if (highWord == 0) {
            difference = (big[--bigIndex] & LONG_MASK) - val;
            result[bigIndex] = (int)difference;
        } else {
            difference = (big[--bigIndex] & LONG_MASK) - (val & LONG_MASK);
            result[bigIndex] = (int)difference;
            difference = (big[--bigIndex] & LONG_MASK) - (highWord & LONG_MASK) + (difference >> 32);
            result[bigIndex] = (int)difference;
        }

        // Subtract remainder of longer number while borrow propagates
        boolean borrow = (difference >> 32 != 0);
        while (bigIndex > 0 && borrow)
            borrow = ((result[--bigIndex] = big[bigIndex] - 1) == -1);

        // Copy remainder of longer number
        while (bigIndex > 0)
            result[--bigIndex] = big[bigIndex];

        return result;
    }

    /**
     * Returns a BigInteger whose value is {@code (this - val)}.
     *
     * @param  val value to be subtracted from this BigInteger.
     * @return {@code this - val}
     */
    public BigInteger subtract(BigInteger val) {
        if (val.signum == 0)
            return this;
        if (signum == 0)
            return val.negate();
        if (val.signum != signum)
            return new BigInteger(add(mag, val.mag), signum);

        int cmp = compareMagnitude(val);
        if (cmp == 0)
            return ZERO;
        int[] resultMag = (cmp > 0 ? subtract(mag, val.mag)
                           : subtract(val.mag, mag));
        resultMag = trustedStripLeadingZeroInts(resultMag);
        return new BigInteger(resultMag, cmp == signum ? 1 : -1);
    }

    /**
     * Subtracts the contents of the second int arrays (little) from the
     * first (big).  The first int array (big) must represent a larger number
     * than the second.  This method allocates the space necessary to hold the
     * answer.
     */
    private static int[] subtract(int[] big, int[] little) {
        int bigIndex = big.length;
        int result[] = new int[bigIndex];
        int littleIndex = little.length;
        long difference = 0;

        // Subtract common parts of both numbers
        while (littleIndex > 0) {
            difference = (big[--bigIndex] & LONG_MASK) -
                         (little[--littleIndex] & LONG_MASK) +
                         (difference >> 32);
            result[bigIndex] = (int)difference;
        }

        // Subtract remainder of longer number while borrow propagates
        boolean borrow = (difference >> 32 != 0);
        while (bigIndex > 0 && borrow)
            borrow = ((result[--bigIndex] = big[bigIndex] - 1) == -1);

        // Copy remainder of longer number
        while (bigIndex > 0)
            result[--bigIndex] = big[bigIndex];

        return result;
    }

    /**
     * Returns a BigInteger whose value is {@code (this * val)}.
     *
     * @implNote An implementation may offer better algorithmic
     * performance when {@code val == this}.
     *
     * @param  val value to be multiplied by this BigInteger.
     * @return {@code this * val}
     */
    public BigInteger multiply(BigInteger val) {
        return multiply(val, false, false, 0);
    }

    /**
     * Returns a BigInteger whose value is {@code (this * val)}.
     * When both {@code this} and {@code val} are large, typically
     * in the thousands of bits, parallel multiply might be used.
     * This method returns the exact same mathematical result as
     * {@link #multiply}.
     *
     * @implNote This implementation may offer better algorithmic
     * performance when {@code val == this}.
     *
     * @implNote Compared to {@link #multiply}, an implementation's
     * parallel multiplication algorithm would typically use more
     * CPU resources to compute the result faster, and may do so
     * with a slight increase in memory consumption.
     *
     * @param  val value to be multiplied by this BigInteger.
     * @return {@code this * val}
     * @see #multiply
     * @since 19
     */
    public BigInteger parallelMultiply(BigInteger val) {
        return multiply(val, false, true, 0);
    }

    /**
     * Returns a BigInteger whose value is {@code (this * val)}.  If
     * the invocation is recursive certain overflow checks are skipped.
     *
     * @param  val value to be multiplied by this BigInteger.
     * @param  isRecursion whether this is a recursive invocation
     * @param  parallel whether the multiply should be done in parallel
     * @return {@code this * val}
     */
    private BigInteger multiply(BigInteger val, boolean isRecursion, boolean parallel, int depth) {
        if (val.signum == 0 || signum == 0)
            return ZERO;

        int xlen = mag.length;

        if (val == this && xlen > MULTIPLY_SQUARE_THRESHOLD) {
            return square(true, parallel, depth);
        }

        int ylen = val.mag.length;

        if ((xlen < KARATSUBA_THRESHOLD) || (ylen < KARATSUBA_THRESHOLD)) {
            int resultSign = signum == val.signum ? 1 : -1;
            if (val.mag.length == 1) {
                return multiplyByInt(mag,val.mag[0], resultSign);
            }
            if (mag.length == 1) {
                return multiplyByInt(val.mag,mag[0], resultSign);
            }
            int[] result = multiplyToLen(mag, xlen,
                                         val.mag, ylen, null);
            result = trustedStripLeadingZeroInts(result);
            return new BigInteger(result, resultSign);
        } else {
            if ((xlen < TOOM_COOK_THRESHOLD) && (ylen < TOOM_COOK_THRESHOLD)) {
                return multiplyKaratsuba(this, val);
            } else {
                //
                // In  section 2-13, p.33, it is explained
                // that if x and y are unsigned 32-bit quantities and m and n
                // are their respective numbers of leading zeros within 32 bits,
                // then the number of leading zeros within their product as a
                // 64-bit unsigned quantity is either m + n or m + n + 1. If
                // their product is not to overflow, it cannot exceed 32 bits,
                // and so the number of leading zeros of the product within 64
                // bits must be at least 32, i.e., the leftmost set bit is at
                // zero-relative position 31 or less.
                //
                // From the above there are three cases:
                //
                //     m + n    leftmost set bit    condition
                //     -----    ----------------    ---------
                //     >= 32    x <= 64 - 32 = 32   no overflow
                //     == 31    x >= 64 - 32 = 32   possible overflow
                //     <= 30    x >= 64 - 31 = 33   definite overflow
                //
                // The  condition cannot be detected by
                // examning data lengths alone and requires further calculation.
                //
                // By analogy, if 'this' and 'val' have m and n as their
                // respective numbers of leading zeros within 32*MAX_MAG_LENGTH
                // bits, then:
                //
                //     m + n >= 32*MAX_MAG_LENGTH        no overflow
                //     m + n == 32*MAX_MAG_LENGTH - 1    possible overflow
                //     m + n <= 32*MAX_MAG_LENGTH - 2    definite overflow
                //
                // Note however that if the number of ints in the result
                // were to be MAX_MAG_LENGTH and mag[0] < 0, then there would
                // be overflow. As a result the leftmost bit (of mag[0]) cannot
                // be used and the constraints must be adjusted by one bit to:
                //
                //     m + n >  32*MAX_MAG_LENGTH        no overflow
                //     m + n == 32*MAX_MAG_LENGTH        possible overflow
                //     m + n <  32*MAX_MAG_LENGTH        definite overflow
                //
                // The foregoing leading zero-based discussion is for clarity
                // only. The actual calculations use the estimated bit length
                // of the product as this is more natural to the internal
                // array representation of the magnitude which has no leading
                // zero elements.
                //
                if (!isRecursion) {
                    // The bitLength() instance method is not used here as we
                    // are only considering the magnitudes as non-negative. The
                    // Toom-Cook multiplication algorithm determines the sign
                    // at its end from the two signum values.
                    if ((long)bitLength(mag, mag.length) +
                        (long)bitLength(val.mag, val.mag.length) >
                        32L*MAX_MAG_LENGTH) {
                        reportOverflow();
                    }
                }

                return multiplyToomCook3(this, val, parallel, depth);
            }
        }
    }

    private static BigInteger multiplyByInt(int[] x, int y, int sign) {
        if (Integer.bitCount(y) == 1) {
            return new BigInteger(shiftLeft(x,Integer.numberOfTrailingZeros(y)), sign);
        }
        int xlen = x.length;
        int[] rmag =  new int[xlen + 1];
        long carry = 0;
        long yl = y & LONG_MASK;
        int rstart = rmag.length - 1;
        for (int i = xlen - 1; i >= 0; i--) {
            long product = (x[i] & LONG_MASK) * yl + carry;
            rmag[rstart--] = (int)product;
            carry = product >>> 32;
        }
        if (carry == 0L) {
            rmag = java.util.Arrays.copyOfRange(rmag, 1, rmag.length);
        } else {
            rmag[rstart] = (int)carry;
        }
        return new BigInteger(rmag, sign);
    }

    /**
     * Package private methods used by BigDecimal code to multiply a BigInteger
     * with a long. Assumes v is not equal to INFLATED.
     */
    BigInteger multiply(long v) {
        if (v == 0 || signum == 0)
          return ZERO;
        if (v == BigDecimal.INFLATED)
            return multiply(BigInteger.valueOf(v));
        int rsign = (v > 0 ? signum : -signum);
        if (v < 0)
            v = -v;
        long dh = v >>> 32;      // higher order bits
        long dl = v & LONG_MASK; // lower order bits

        int xlen = mag.length;
        int[] value = mag;
        int[] rmag = (dh == 0L) ? (new int[xlen + 1]) : (new int[xlen + 2]);
        long carry = 0;
        int rstart = rmag.length - 1;
        for (int i = xlen - 1; i >= 0; i--) {
            long product = (value[i] & LONG_MASK) * dl + carry;
            rmag[rstart--] = (int)product;
            carry = product >>> 32;
        }
        rmag[rstart] = (int)carry;
        if (dh != 0L) {
            carry = 0;
            rstart = rmag.length - 2;
            for (int i = xlen - 1; i >= 0; i--) {
                long product = (value[i] & LONG_MASK) * dh +
                    (rmag[rstart] & LONG_MASK) + carry;
                rmag[rstart--] = (int)product;
                carry = product >>> 32;
            }
            rmag[0] = (int)carry;
        }
        if (carry == 0L)
            rmag = java.util.Arrays.copyOfRange(rmag, 1, rmag.length);
        return new BigInteger(rmag, rsign);
    }

    /**
     * Multiplies int arrays x and y to the specified lengths and places
     * the result into z. There will be no leading zeros in the resultant array.
     */
    private static int[] multiplyToLen(int[] x, int xlen, int[] y, int ylen, int[] z) {
        multiplyToLenCheck(x, xlen);
        multiplyToLenCheck(y, ylen);
        return implMultiplyToLen(x, xlen, y, ylen, z);
    }

    @IntrinsicCandidate
    private static int[] implMultiplyToLen(int[] x, int xlen, int[] y, int ylen, int[] z) {
        int xstart = xlen - 1;
        int ystart = ylen - 1;

        if (z == null || z.length < (xlen+ ylen))
             z = new int[xlen+ylen];

        long carry = 0;
        for (int j=ystart, k=ystart+1+xstart; j >= 0; j--, k--) {
            long product = (y[j] & LONG_MASK) *
                           (x[xstart] & LONG_MASK) + carry;
            z[k] = (int)product;
            carry = product >>> 32;
        }
        z[xstart] = (int)carry;

        for (int i = xstart-1; i >= 0; i--) {
            carry = 0;
            for (int j=ystart, k=ystart+1+i; j >= 0; j--, k--) {
                long product = (y[j] & LONG_MASK) *
                               (x[i] & LONG_MASK) +
                               (z[k] & LONG_MASK) + carry;
                z[k] = (int)product;
                carry = product >>> 32;
            }
            z[i] = (int)carry;
        }
        return z;
    }

    private static void multiplyToLenCheck(int[] array, int length) {
        if (length <= 0) {
            return;  // not an error because multiplyToLen won't execute if len <= 0
        }

        Objects.requireNonNull(array);

        if (length > array.length) {
            throw new ArrayIndexOutOfBoundsException(length - 1);
        }
    }

    /**
     * Multiplies two BigIntegers using the Karatsuba multiplication
     * algorithm.  This is a recursive divide-and-conquer algorithm which is
     * more efficient for large numbers than what is commonly called the
     *  algorithm used in multiplyToLen.  If the numbers to be
     * multiplied have length n, the  algorithm has an
     * asymptotic complexity of O(n^2).  In contrast, the Karatsuba algorithm
     * has complexity of O(n^(log2(3))), or O(n^1.585).  It achieves this
     * increased performance by doing 3 multiplies instead of 4 when
     * evaluating the product.  As it has some overhead, should be used when
     * both numbers are larger than a certain threshold (found
     * experimentally).
     *
     * See:  http://en.wikipedia.org/wiki/Karatsuba_algorithm
     */
    private static BigInteger multiplyKaratsuba(BigInteger x, BigInteger y) {
        int xlen = x.mag.length;
        int ylen = y.mag.length;

        // The number of ints in each half of the number.
        int half = (Math.max(xlen, ylen)+1) / 2;

        // xl and yl are the lower halves of x and y respectively,
        // xh and yh are the upper halves.
        BigInteger xl = x.getLower(half);
        BigInteger xh = x.getUpper(half);
        BigInteger yl = y.getLower(half);
        BigInteger yh = y.getUpper(half);

        BigInteger p1 = xh.multiply(yh);  // p1 = xh*yh
        BigInteger p2 = xl.multiply(yl);  // p2 = xl*yl

        // p3=(xh+xl)*(yh+yl)
        BigInteger p3 = xh.add(xl).multiply(yh.add(yl));

        // result = p1 * 2^(32*2*half) + (p3 - p1 - p2) * 2^(32*half) + p2
        BigInteger result = p1.shiftLeft(32*half).add(p3.subtract(p1).subtract(p2)).shiftLeft(32*half).add(p2);

        if (x.signum != y.signum) {
            return result.negate();
        } else {
            return result;
        }
    }

    @SuppressWarnings()
    private abstract static sealed class RecursiveOp extends RecursiveTask<BigInteger> {
        /**
         * The threshold until when we should continue forking recursive ops
         * if parallel is true. This threshold is only relevant for Toom Cook 3
         * multiply and square.
         */
        private static final int PARALLEL_FORK_DEPTH_THRESHOLD =
                calculateMaximumDepth(ForkJoinPool.getCommonPoolParallelism());

        private static final int calculateMaximumDepth(int parallelism) {
            return 32 - Integer.numberOfLeadingZeros(parallelism);
        }

        final boolean parallel;
        /**
         * The current recursing depth. Since it is a logarithmic algorithm,
         * we do not need an int to hold the number.
         */
        final byte depth;

        private RecursiveOp(boolean parallel, int depth) {
            this.parallel = parallel;
            this.depth = (byte) depth;
        }

        private static int getParallelForkDepthThreshold() {
            if (Thread.currentThread() instanceof ForkJoinWorkerThread fjwt) {
                return calculateMaximumDepth(fjwt.getPool().getParallelism());
            }
            else {
                return PARALLEL_FORK_DEPTH_THRESHOLD;
            }
        }

        protected RecursiveTask<BigInteger> forkOrInvoke() {
            if (parallel && depth <= getParallelForkDepthThreshold()) fork();
            else invoke();
            return this;
        }

        @SuppressWarnings()
        private static final class RecursiveMultiply extends RecursiveOp {
            private final BigInteger a;
            private final BigInteger b;

            public RecursiveMultiply(BigInteger a, BigInteger b, boolean parallel, int depth) {
                super(parallel, depth);
                this.a = a;
                this.b = b;
            }

            @Override
            public BigInteger compute() {
                return a.multiply(b, true, parallel, depth);
            }
        }

        @SuppressWarnings()
        private static final class RecursiveSquare extends RecursiveOp {
            private final BigInteger a;

            public RecursiveSquare(BigInteger a, boolean parallel, int depth) {
                super(parallel, depth);
                this.a = a;
            }

            @Override
            public BigInteger compute() {
                return a.square(true, parallel, depth);
            }
        }

        private static RecursiveTask<BigInteger> multiply(BigInteger a, BigInteger b, boolean parallel, int depth) {
            return new RecursiveMultiply(a, b, parallel, depth).forkOrInvoke();
        }

        private static RecursiveTask<BigInteger> square(BigInteger a, boolean parallel, int depth) {
            return new RecursiveSquare(a, parallel, depth).forkOrInvoke();
        }
    }

    /**
     * Multiplies two BigIntegers using a 3-way Toom-Cook multiplication
     * algorithm.  This is a recursive divide-and-conquer algorithm which is
     * more efficient for large numbers than what is commonly called the
     *  algorithm used in multiplyToLen.  If the numbers to be
     * multiplied have length n, the  algorithm has an
     * asymptotic complexity of O(n^2).  In contrast, 3-way Toom-Cook has a
     * complexity of about O(n^1.465).  It achieves this increased asymptotic
     * performance by breaking each number into three parts and by doing 5
     * multiplies instead of 9 when evaluating the product.  Due to overhead
     * (additions, shifts, and one division) in the Toom-Cook algorithm, it
     * should only be used when both numbers are larger than a certain
     * threshold (found experimentally).  This threshold is generally larger
     * than that for Karatsuba multiplication, so this algorithm is generally
     * only used when numbers become significantly larger.
     *
     * The algorithm used is the  3-way Toom-Cook algorithm outlined
     * by Marco Bodrato.
     *
     *  See: http://bodrato.it/toom-cook/
     *       http://bodrato.it/papers/#WAIFI2007
     *
     * "Towards Optimal Toom-Cook Multiplication for Univariate and
     * Multivariate Polynomials in Characteristic 2 and 0." by Marco BODRATO;
     * In C.Carlet and B.Sunar, Eds., , p. 116-133,
     * LNCS #4547. Springer, Madrid, Spain, June 21-22, 2007.
     *
     */
    private static BigInteger multiplyToomCook3(BigInteger a, BigInteger b, boolean parallel, int depth) {
        int alen = a.mag.length;
        int blen = b.mag.length;

        int largest = Math.max(alen, blen);

        // k is the size (in ints) of the lower-order slices.
        int k = (largest+2)/3;   // Equal to ceil(largest/3)

        // r is the size (in ints) of the highest-order slice.
        int r = largest - 2*k;

        // Obtain slices of the numbers. a2 and b2 are the most significant
        // bits of the numbers a and b, and a0 and b0 the least significant.
        BigInteger a0, a1, a2, b0, b1, b2;
        a2 = a.getToomSlice(k, r, 0, largest);
        a1 = a.getToomSlice(k, r, 1, largest);
        a0 = a.getToomSlice(k, r, 2, largest);
        b2 = b.getToomSlice(k, r, 0, largest);
        b1 = b.getToomSlice(k, r, 1, largest);
        b0 = b.getToomSlice(k, r, 2, largest);

        BigInteger v0, v1, v2, vm1, vinf, t1, t2, tm1, da1, db1;

        depth++;
        var v0_task = RecursiveOp.multiply(a0, b0, parallel, depth);
        da1 = a2.add(a0);
        db1 = b2.add(b0);
        var vm1_task = RecursiveOp.multiply(da1.subtract(a1), db1.subtract(b1), parallel, depth);
        da1 = da1.add(a1);
        db1 = db1.add(b1);
        var v1_task = RecursiveOp.multiply(da1, db1, parallel, depth);
        v2 = da1.add(a2).shiftLeft(1).subtract(a0).multiply(
             db1.add(b2).shiftLeft(1).subtract(b0), true, parallel, depth);
        vinf = a2.multiply(b2, true, parallel, depth);
        v0 = v0_task.join();
        vm1 = vm1_task.join();
        v1 = v1_task.join();

        // The algorithm requires two divisions by 2 and one by 3.
        // All divisions are known to be exact, that is, they do not produce
        // remainders, and all results are positive.  The divisions by 2 are
        // implemented as right shifts which are relatively efficient, leaving
        // only an exact division by 3, which is done by a specialized
        // linear-time algorithm.
        t2 = v2.subtract(vm1).exactDivideBy3();
        tm1 = v1.subtract(vm1).shiftRight(1);
        t1 = v1.subtract(v0);
        t2 = t2.subtract(t1).shiftRight(1);
        t1 = t1.subtract(tm1).subtract(vinf);
        t2 = t2.subtract(vinf.shiftLeft(1));
        tm1 = tm1.subtract(t2);

        // Number of bits to shift left.
        int ss = k*32;

        BigInteger result = vinf.shiftLeft(ss).add(t2).shiftLeft(ss).add(t1).shiftLeft(ss).add(tm1).shiftLeft(ss).add(v0);

        if (a.signum != b.signum) {
            return result.negate();
        } else {
            return result;
        }
    }


    /**
     * Returns a slice of a BigInteger for use in Toom-Cook multiplication.
     *
     * @param lowerSize The size of the lower-order bit slices.
     * @param upperSize The size of the higher-order bit slices.
     * @param slice The index of which slice is requested, which must be a
     * number from 0 to size-1. Slice 0 is the highest-order bits, and slice
     * size-1 are the lowest-order bits. Slice 0 may be of different size than
     * the other slices.
     * @param fullsize The size of the larger integer array, used to align
     * slices to the appropriate position when multiplying different-sized
     * numbers.
     */
    private BigInteger getToomSlice(int lowerSize, int upperSize, int slice,
                                    int fullsize) {
        int start, end, sliceSize, len, offset;

        len = mag.length;
        offset = fullsize - len;

        if (slice == 0) {
            start = 0 - offset;
            end = upperSize - 1 - offset;
        } else {
            start = upperSize + (slice-1)*lowerSize - offset;
            end = start + lowerSize - 1;
        }

        if (start < 0) {
            start = 0;
        }
        if (end < 0) {
           return ZERO;
        }

        sliceSize = (end-start) + 1;

        if (sliceSize <= 0) {
            return ZERO;
        }

        // While performing Toom-Cook, all slices are positive and
        // the sign is adjusted when the final number is composed.
        if (start == 0 && sliceSize >= len) {
            return this.abs();
        }

        int intSlice[] = new int[sliceSize];
        System.arraycopy(mag, start, intSlice, 0, sliceSize);

        return new BigInteger(trustedStripLeadingZeroInts(intSlice), 1);
    }

    /**
     * Does an exact division (that is, the remainder is known to be zero)
     * of the specified number by 3.  This is used in Toom-Cook
     * multiplication.  This is an efficient algorithm that runs in linear
     * time.  If the argument is not exactly divisible by 3, results are
     * undefined.  Note that this is expected to be called with positive
     * arguments only.
     */
    private BigInteger exactDivideBy3() {
        int len = mag.length;
        int[] result = new int[len];
        long x, w, q, borrow;
        borrow = 0L;
        for (int i=len-1; i >= 0; i--) {
            x = (mag[i] & LONG_MASK);
            w = x - borrow;
            if (borrow > x) {      // Did we make the number go negative?
                borrow = 1L;
            } else {
                borrow = 0L;
            }

            // 0xAAAAAAAB is the modular inverse of 3 (mod 2^32).  Thus,
            // the effect of this is to divide by 3 (mod 2^32).
            // This is much faster than division on most architectures.
            q = (w * 0xAAAAAAABL) & LONG_MASK;
            result[i] = (int) q;

            // Now check the borrow. The second check can of course be
            // eliminated if the first fails.
            if (q >= 0x55555556L) {
                borrow++;
                if (q >= 0xAAAAAAABL)
                    borrow++;
            }
        }
        result = trustedStripLeadingZeroInts(result);
        return new BigInteger(result, signum);
    }

    /**
     * Returns a new BigInteger representing n lower ints of the number.
     * This is used by Karatsuba multiplication and Karatsuba squaring.
     */
    private BigInteger getLower(int n) {
        int len = mag.length;

        if (len <= n) {
            return abs();
        }

        int lowerInts[] = new int[n];
        System.arraycopy(mag, len-n, lowerInts, 0, n);

        return new BigInteger(trustedStripLeadingZeroInts(lowerInts), 1);
    }

    /**
     * Returns a new BigInteger representing mag.length-n upper
     * ints of the number.  This is used by Karatsuba multiplication and
     * Karatsuba squaring.
     */
    private BigInteger getUpper(int n) {
        int len = mag.length;

        if (len <= n) {
            return ZERO;
        }

        int upperLen = len - n;
        int upperInts[] = new int[upperLen];
        System.arraycopy(mag, 0, upperInts, 0, upperLen);

        return new BigInteger(trustedStripLeadingZeroInts(upperInts), 1);
    }

    // Squaring

    /**
     * Returns a BigInteger whose value is <code>(this<sup>2</sup>)</code>.
     *
     * @return <code>this<sup>2</sup></code>
     */
    private BigInteger square() {
        return square(false, false, 0);
    }

    /**
     * Returns a BigInteger whose value is <code>(this<sup>2</sup>)</code>. If
     * the invocation is recursive certain overflow checks are skipped.
     *
     * @param isRecursion whether this is a recursive invocation
     * @return <code>this<sup>2</sup></code>
     */
    private BigInteger square(boolean isRecursion, boolean parallel, int depth) {
        if (signum == 0) {
            return ZERO;
        }
        int len = mag.length;

        if (len < KARATSUBA_SQUARE_THRESHOLD) {
            int[] z = squareToLen(mag, len, null);
            return new BigInteger(trustedStripLeadingZeroInts(z), 1);
        } else {
            if (len < TOOM_COOK_SQUARE_THRESHOLD) {
                return squareKaratsuba();
            } else {
                //
                // For a discussion of overflow detection see multiply()
                //
                if (!isRecursion) {
                    if (bitLength(mag, mag.length) > 16L*MAX_MAG_LENGTH) {
                        reportOverflow();
                    }
                }

                return squareToomCook3(parallel, depth);
            }
        }
    }

    /**
     * Squares the contents of the int array x. The result is placed into the
     * int array z.  The contents of x are not changed.
     */
    private static final int[] squareToLen(int[] x, int len, int[] z) {
         int zlen = len << 1;
         if (z == null || z.length < zlen)
             z = new int[zlen];

         // Execute checks before calling intrinsified method.
         implSquareToLenChecks(x, len, z, zlen);
         return implSquareToLen(x, len, z, zlen);
     }

     /**
      * Parameters validation.
      */
     private static void implSquareToLenChecks(int[] x, int len, int[] z, int zlen) throws RuntimeException {
         if (len < 1) {
             throw new IllegalArgumentException( + len);
         }
         if (len > x.length) {
             throw new IllegalArgumentException( +
                                        len +  + x.length);
         }
         if (len * 2 > z.length) {
             throw new IllegalArgumentException( +
                                        (len * 2) +  + z.length);
         }
         if (zlen < 1) {
             throw new IllegalArgumentException( + zlen);
         }
         if (zlen > z.length) {
             throw new IllegalArgumentException( +
                                        len +  + z.length);
         }
     }

     /**
      * Java Runtime may use intrinsic for this method.
      */
     @IntrinsicCandidate
     private static final int[] implSquareToLen(int[] x, int len, int[] z, int zlen) {
        /*
         * The algorithm used here is adapted from Colin Plumb's C library.
         * Technique: Consider the partial products in the multiplication
         * of  by itself:
         *
         *               a  b  c  d  e
         *            *  a  b  c  d  e
         *          ==================
         *              ae be ce de ee
         *           ad bd cd dd de
         *        ac bc cc cd ce
         *     ab bb bc bd be
         *  aa ab ac ad ae
         *
         * Note that everything above the main diagonal:
         *              ae be ce de = (abcd) * e
         *           ad bd cd       = (abc) * d
         *        ac bc             = (ab) * c
         *     ab                   = (a) * b
         *
         * is a copy of everything below the main diagonal:
         *                       de
         *                 cd ce
         *           bc bd be
         *     ab ac ad ae
         *
         * Thus, the sum is 2 * (off the diagonal) + diagonal.
         *
         * This is accumulated beginning with the diagonal (which
         * consist of the squares of the digits of the input), which is then
         * divided by two, the off-diagonal added, and multiplied by two
         * again.  The low bit is simply a copy of the low bit of the
         * input, so it doesn't need special care.
         */

        // Store the squares, right shifted one bit (i.e., divided by 2)
        int lastProductLowWord = 0;
        for (int j=0, i=0; j < len; j++) {
            long piece = (x[j] & LONG_MASK);
            long product = piece * piece;
            z[i++] = (lastProductLowWord << 31) | (int)(product >>> 33);
            z[i++] = (int)(product >>> 1);
            lastProductLowWord = (int)product;
        }

        // Add in off-diagonal sums
        for (int i=len, offset=1; i > 0; i--, offset+=2) {
            int t = x[i-1];
            t = mulAdd(z, x, offset, i-1, t);
            addOne(z, offset-1, i, t);
        }

        // Shift back up and set low bit
        primitiveLeftShift(z, zlen, 1);
        z[zlen-1] |= x[len-1] & 1;

        return z;
    }

    /**
     * Squares a BigInteger using the Karatsuba squaring algorithm.  It should
     * be used when both numbers are larger than a certain threshold (found
     * experimentally).  It is a recursive divide-and-conquer algorithm that
     * has better asymptotic performance than the algorithm used in
     * squareToLen.
     */
    private BigInteger squareKaratsuba() {
        int half = (mag.length+1) / 2;

        BigInteger xl = getLower(half);
        BigInteger xh = getUpper(half);

        BigInteger xhs = xh.square();  // xhs = xh^2
        BigInteger xls = xl.square();  // xls = xl^2

        // xh^2 << 64  +  (((xl+xh)^2 - (xh^2 + xl^2)) << 32) + xl^2
        return xhs.shiftLeft(half*32).add(xl.add(xh).square().subtract(xhs.add(xls))).shiftLeft(half*32).add(xls);
    }

    /**
     * Squares a BigInteger using the 3-way Toom-Cook squaring algorithm.  It
     * should be used when both numbers are larger than a certain threshold
     * (found experimentally).  It is a recursive divide-and-conquer algorithm
     * that has better asymptotic performance than the algorithm used in
     * squareToLen or squareKaratsuba.
     */
    private BigInteger squareToomCook3(boolean parallel, int depth) {
        int len = mag.length;

        // k is the size (in ints) of the lower-order slices.
        int k = (len+2)/3;   // Equal to ceil(largest/3)

        // r is the size (in ints) of the highest-order slice.
        int r = len - 2*k;

        // Obtain slices of the numbers. a2 is the most significant
        // bits of the number, and a0 the least significant.
        BigInteger a0, a1, a2;
        a2 = getToomSlice(k, r, 0, len);
        a1 = getToomSlice(k, r, 1, len);
        a0 = getToomSlice(k, r, 2, len);
        BigInteger v0, v1, v2, vm1, vinf, t1, t2, tm1, da1;

        depth++;
        var v0_fork = RecursiveOp.square(a0, parallel, depth);
        da1 = a2.add(a0);
        var vm1_fork = RecursiveOp.square(da1.subtract(a1), parallel, depth);
        da1 = da1.add(a1);
        var v1_fork = RecursiveOp.square(da1, parallel, depth);
        vinf = a2.square(true, parallel, depth);
        v2 = da1.add(a2).shiftLeft(1).subtract(a0).square(true, parallel, depth);
        v0 = v0_fork.join();
        vm1 = vm1_fork.join();
        v1 = v1_fork.join();

        // The algorithm requires two divisions by 2 and one by 3.
        // All divisions are known to be exact, that is, they do not produce
        // remainders, and all results are positive.  The divisions by 2 are
        // implemented as right shifts which are relatively efficient, leaving
        // only a division by 3.
        // The division by 3 is done by an optimized algorithm for this case.
        t2 = v2.subtract(vm1).exactDivideBy3();
        tm1 = v1.subtract(vm1).shiftRight(1);
        t1 = v1.subtract(v0);
        t2 = t2.subtract(t1).shiftRight(1);
        t1 = t1.subtract(tm1).subtract(vinf);
        t2 = t2.subtract(vinf.shiftLeft(1));
        tm1 = tm1.subtract(t2);

        // Number of bits to shift left.
        int ss = k*32;

        return vinf.shiftLeft(ss).add(t2).shiftLeft(ss).add(t1).shiftLeft(ss).add(tm1).shiftLeft(ss).add(v0);
    }

    // Division

    /**
     * Returns a BigInteger whose value is {@code (this / val)}.
     *
     * @param  val value by which this BigInteger is to be divided.
     * @return {@code this / val}
     * @throws ArithmeticException if {@code val} is zero.
     */
    public BigInteger divide(BigInteger val) {
        if (val.mag.length < BURNIKEL_ZIEGLER_THRESHOLD ||
                mag.length - val.mag.length < BURNIKEL_ZIEGLER_OFFSET) {
            return divideKnuth(val);
        } else {
            return divideBurnikelZiegler(val);
        }
    }

    /**
     * Returns a BigInteger whose value is {@code (this / val)} using an O(n^2) algorithm from Knuth.
     *
     * @param  val value by which this BigInteger is to be divided.
     * @return {@code this / val}
     * @throws ArithmeticException if {@code val} is zero.
     * @see MutableBigInteger#divideKnuth(MutableBigInteger, MutableBigInteger, boolean)
     */
    private BigInteger divideKnuth(BigInteger val) {
        MutableBigInteger q = new MutableBigInteger(),
                          a = new MutableBigInteger(this.mag),
                          b = new MutableBigInteger(val.mag);

        a.divideKnuth(b, q, false);
        return q.toBigInteger(this.signum * val.signum);
    }

    /**
     * Returns an array of two BigIntegers containing {@code (this / val)}
     * followed by {@code (this % val)}.
     *
     * @param  val value by which this BigInteger is to be divided, and the
     *         remainder computed.
     * @return an array of two BigIntegers: the quotient {@code (this / val)}
     *         is the initial element, and the remainder {@code (this % val)}
     *         is the final element.
     * @throws ArithmeticException if {@code val} is zero.
     */
    public BigInteger[] divideAndRemainder(BigInteger val) {
        if (val.mag.length < BURNIKEL_ZIEGLER_THRESHOLD ||
                mag.length - val.mag.length < BURNIKEL_ZIEGLER_OFFSET) {
            return divideAndRemainderKnuth(val);
        } else {
            return divideAndRemainderBurnikelZiegler(val);
        }
    }

    /** Long division */
    private BigInteger[] divideAndRemainderKnuth(BigInteger val) {
        BigInteger[] result = new BigInteger[2];
        MutableBigInteger q = new MutableBigInteger(),
                          a = new MutableBigInteger(this.mag),
                          b = new MutableBigInteger(val.mag);
        MutableBigInteger r = a.divideKnuth(b, q);
        result[0] = q.toBigInteger(this.signum == val.signum ? 1 : -1);
        result[1] = r.toBigInteger(this.signum);
        return result;
    }

    /**
     * Returns a BigInteger whose value is {@code (this % val)}.
     *
     * @param  val value by which this BigInteger is to be divided, and the
     *         remainder computed.
     * @return {@code this % val}
     * @throws ArithmeticException if {@code val} is zero.
     */
    public BigInteger remainder(BigInteger val) {
        if (val.mag.length < BURNIKEL_ZIEGLER_THRESHOLD ||
                mag.length - val.mag.length < BURNIKEL_ZIEGLER_OFFSET) {
            return remainderKnuth(val);
        } else {
            return remainderBurnikelZiegler(val);
        }
    }

    /** Long division */
    private BigInteger remainderKnuth(BigInteger val) {
        MutableBigInteger q = new MutableBigInteger(),
                          a = new MutableBigInteger(this.mag),
                          b = new MutableBigInteger(val.mag);

        return a.divideKnuth(b, q).toBigInteger(this.signum);
    }

    /**
     * Calculates {@code this / val} using the Burnikel-Ziegler algorithm.
     * @param  val the divisor
     * @return {@code this / val}
     */
    private BigInteger divideBurnikelZiegler(BigInteger val) {
        return divideAndRemainderBurnikelZiegler(val)[0];
    }

    /**
     * Calculates {@code this % val} using the Burnikel-Ziegler algorithm.
     * @param val the divisor
     * @return {@code this % val}
     */
    private BigInteger remainderBurnikelZiegler(BigInteger val) {
        return divideAndRemainderBurnikelZiegler(val)[1];
    }

    /**
     * Computes {@code this / val} and {@code this % val} using the
     * Burnikel-Ziegler algorithm.
     * @param val the divisor
     * @return an array containing the quotient and remainder
     */
    private BigInteger[] divideAndRemainderBurnikelZiegler(BigInteger val) {
        MutableBigInteger q = new MutableBigInteger();
        MutableBigInteger r = new MutableBigInteger(this).divideAndRemainderBurnikelZiegler(new MutableBigInteger(val), q);
        BigInteger qBigInt = q.isZero() ? ZERO : q.toBigInteger(signum*val.signum);
        BigInteger rBigInt = r.isZero() ? ZERO : r.toBigInteger(signum);
        return new BigInteger[] {qBigInt, rBigInt};
    }

    /**
     * Returns a BigInteger whose value is <code>(this<sup>exponent</sup>)</code>.
     * Note that {@code exponent} is an integer rather than a BigInteger.
     *
     * @param  exponent exponent to which this BigInteger is to be raised.
     * @return <code>this<sup>exponent</sup></code>
     * @throws ArithmeticException {@code exponent} is negative.  (This would
     *         cause the operation to yield a non-integer value.)
     */
    public BigInteger pow(int exponent) {
        if (exponent < 0) {
            throw new ArithmeticException();
        }
        if (signum == 0) {
            return (exponent == 0 ? ONE : this);
        }

        BigInteger partToSquare = this.abs();

        // Factor out powers of two from the base, as the exponentiation of
        // these can be done by left shifts only.
        // The remaining part can then be exponentiated faster.  The
        // powers of two will be multiplied back at the end.
        int powersOfTwo = partToSquare.getLowestSetBit();
        long bitsToShiftLong = (long)powersOfTwo * exponent;
        if (bitsToShiftLong > Integer.MAX_VALUE) {
            reportOverflow();
        }
        int bitsToShift = (int)bitsToShiftLong;

        int remainingBits;

        // Factor the powers of two out quickly by shifting right, if needed.
        if (powersOfTwo > 0) {
            partToSquare = partToSquare.shiftRight(powersOfTwo);
            remainingBits = partToSquare.bitLength();
            if (remainingBits == 1) {  // Nothing left but +/- 1?
                if (signum < 0 && (exponent&1) == 1) {
                    return NEGATIVE_ONE.shiftLeft(bitsToShift);
                } else {
                    return ONE.shiftLeft(bitsToShift);
                }
            }
        } else {
            remainingBits = partToSquare.bitLength();
            if (remainingBits == 1) { // Nothing left but +/- 1?
                if (signum < 0  && (exponent&1) == 1) {
                    return NEGATIVE_ONE;
                } else {
                    return ONE;
                }
            }
        }

        // This is a quick way to approximate the size of the result,
        // similar to doing log2[n] * exponent.  This will give an upper bound
        // of how big the result can be, and which algorithm to use.
        long scaleFactor = (long)remainingBits * exponent;

        // Use slightly different algorithms for small and large operands.
        // See if the result will safely fit into a long. (Largest 2^63-1)
        if (partToSquare.mag.length == 1 && scaleFactor <= 62) {
            // Small number algorithm.  Everything fits into a long.
            int newSign = (signum <0  && (exponent&1) == 1 ? -1 : 1);
            long result = 1;
            long baseToPow2 = partToSquare.mag[0] & LONG_MASK;

            int workingExponent = exponent;

            // Perform exponentiation using repeated squaring trick
            while (workingExponent != 0) {
                if ((workingExponent & 1) == 1) {
                    result = result * baseToPow2;
                }

                if ((workingExponent >>>= 1) != 0) {
                    baseToPow2 = baseToPow2 * baseToPow2;
                }
            }

            // Multiply back the powers of two (quickly, by shifting left)
            if (powersOfTwo > 0) {
                if (bitsToShift + scaleFactor <= 62) { // Fits in long?
                    return valueOf((result << bitsToShift) * newSign);
                } else {
                    return valueOf(result*newSign).shiftLeft(bitsToShift);
                }
            } else {
                return valueOf(result*newSign);
            }
        } else {
            if ((long)bitLength() * exponent / Integer.SIZE > MAX_MAG_LENGTH) {
                reportOverflow();
            }

            // Large number algorithm.  This is basically identical to
            // the algorithm above, but calls multiply() and square()
            // which may use more efficient algorithms for large numbers.
            BigInteger answer = ONE;

            int workingExponent = exponent;
            // Perform exponentiation using repeated squaring trick
            while (workingExponent != 0) {
                if ((workingExponent & 1) == 1) {
                    answer = answer.multiply(partToSquare);
                }

                if ((workingExponent >>>= 1) != 0) {
                    partToSquare = partToSquare.square();
                }
            }
            // Multiply back the (exponentiated) powers of two (quickly,
            // by shifting left)
            if (powersOfTwo > 0) {
                answer = answer.shiftLeft(bitsToShift);
            }

            if (signum < 0 && (exponent&1) == 1) {
                return answer.negate();
            } else {
                return answer;
            }
        }
    }

    /**
     * Returns the integer square root of this BigInteger.  The integer square
     * root of the corresponding mathematical integer {@code n} is the largest
     * mathematical integer {@code s} such that {@code s*s <= n}.  It is equal
     * to the value of {@code floor(sqrt(n))}, where {@code sqrt(n)} denotes the
     * real square root of {@code n} treated as a real.  Note that the integer
     * square root will be less than the real square root if the latter is not
     * representable as an integral value.
     *
     * @return the integer square root of {@code this}
     * @throws ArithmeticException if {@code this} is negative.  (The square
     *         root of a negative integer {@code val} is
     *         {@code (i * sqrt(-val))} where <i>i</i> is the
     *         <i>imaginary unit</i> and is equal to
     *         {@code sqrt(-1)}.)
     * @since  9
     */
    public BigInteger sqrt() {
        if (this.signum < 0) {
            throw new ArithmeticException();
        }

        return new MutableBigInteger(this.mag).sqrt().toBigInteger();
    }

    /**
     * Returns an array of two BigIntegers containing the integer square root
     * {@code s} of {@code this} and its remainder {@code this - s*s},
     * respectively.
     *
     * @return an array of two BigIntegers with the integer square root at
     *         offset 0 and the remainder at offset 1
     * @throws ArithmeticException if {@code this} is negative.  (The square
     *         root of a negative integer {@code val} is
     *         {@code (i * sqrt(-val))} where <i>i</i> is the
     *         <i>imaginary unit</i> and is equal to
     *         {@code sqrt(-1)}.)
     * @see #sqrt()
     * @since  9
     */
    public BigInteger[] sqrtAndRemainder() {
        BigInteger s = sqrt();
        BigInteger r = this.subtract(s.square());
        assert r.compareTo(BigInteger.ZERO) >= 0;
        return new BigInteger[] {s, r};
    }

    /**
     * Returns a BigInteger whose value is the greatest common divisor of
     * {@code abs(this)} and {@code abs(val)}.  Returns 0 if
     * {@code this == 0 && val == 0}.
     *
     * @param  val value with which the GCD is to be computed.
     * @return {@code GCD(abs(this), abs(val))}
     */
    public BigInteger gcd(BigInteger val) {
        if (val.signum == 0)
            return this.abs();
        else if (this.signum == 0)
            return val.abs();

        MutableBigInteger a = new MutableBigInteger(this);
        MutableBigInteger b = new MutableBigInteger(val);

        MutableBigInteger result = a.hybridGCD(b);

        return result.toBigInteger(1);
    }

    /**
     * Package private method to return bit length for an integer.
     */
    static int bitLengthForInt(int n) {
        return 32 - Integer.numberOfLeadingZeros(n);
    }

    /**
     * Left shift int array a up to len by n bits. Returns the array that
     * results from the shift since space may have to be reallocated.
     */
    private static int[] leftShift(int[] a, int len, int n) {
        int nInts = n >>> 5;
        int nBits = n&0x1F;
        int bitsInHighWord = bitLengthForInt(a[0]);

        // If shift can be done without recopy, do so
        if (n <= (32-bitsInHighWord)) {
            primitiveLeftShift(a, len, nBits);
            return a;
        } else { // Array must be resized
            if (nBits <= (32-bitsInHighWord)) {
                int result[] = new int[nInts+len];
                System.arraycopy(a, 0, result, 0, len);
                primitiveLeftShift(result, result.length, nBits);
                return result;
            } else {
                int result[] = new int[nInts+len+1];
                System.arraycopy(a, 0, result, 0, len);
                primitiveRightShift(result, result.length, 32 - nBits);
                return result;
            }
        }
    }

    // shifts a up to len right n bits assumes no leading zeros, 0<n<32
    static void primitiveRightShift(int[] a, int len, int n) {
        Objects.checkFromToIndex(0, len, a.length);
        shiftRightImplWorker(a, a, 1, n, len-1);
        a[0] >>>= n;
    }

    // shifts a up to len left n bits assumes no leading zeros, 0<=n<32
    static void primitiveLeftShift(int[] a, int len, int n) {
        if (len == 0 || n == 0)
            return;
        Objects.checkFromToIndex(0, len, a.length);
        shiftLeftImplWorker(a, a, 0, n, len-1);
        a[len-1] <<= n;
    }

    /**
     * Calculate bitlength of contents of the first len elements an int array,
     * assuming there are no leading zero ints.
     */
    private static int bitLength(int[] val, int len) {
        if (len == 0)
            return 0;
        return ((len - 1) << 5) + bitLengthForInt(val[0]);
    }

    /**
     * Returns a BigInteger whose value is the absolute value of this
     * BigInteger.
     *
     * @return {@code abs(this)}
     */
    public BigInteger abs() {
        return (signum >= 0 ? this : this.negate());
    }

    /**
     * Returns a BigInteger whose value is {@code (-this)}.
     *
     * @return {@code -this}
     */
    public BigInteger negate() {
        return new BigInteger(this.mag, -this.signum);
    }

    /**
     * Returns the signum function of this BigInteger.
     *
     * @return -1, 0 or 1 as the value of this BigInteger is negative, zero or
     *         positive.
     */
    public int signum() {
        return this.signum;
    }

    // Modular Arithmetic Operations

    /**
     * Returns a BigInteger whose value is {@code (this mod m}).  This method
     * differs from {@code remainder} in that it always returns a
     * <i>non-negative</i> BigInteger.
     *
     * @param  m the modulus.
     * @return {@code this mod m}
     * @throws ArithmeticException {@code m} &le; 0
     * @see    #remainder
     */
    public BigInteger mod(BigInteger m) {
        if (m.signum <= 0)
            throw new ArithmeticException();

        BigInteger result = this.remainder(m);
        return (result.signum >= 0 ? result : result.add(m));
    }

    /**
     * Returns a BigInteger whose value is
     * <code>(this<sup>exponent</sup> mod m)</code>.  (Unlike {@code pow}, this
     * method permits negative exponents.)
     *
     * @param  exponent the exponent.
     * @param  m the modulus.
     * @return <code>this<sup>exponent</sup> mod m</code>
     * @throws ArithmeticException {@code m} &le; 0 or the exponent is
     *         negative and this BigInteger is not <i>relatively
     *         prime</i> to {@code m}.
     * @see    #modInverse
     */
    public BigInteger modPow(BigInteger exponent, BigInteger m) {
        if (m.signum <= 0)
            throw new ArithmeticException();

        // Trivial cases
        if (exponent.signum == 0)
            return (m.equals(ONE) ? ZERO : ONE);

        if (this.equals(ONE))
            return (m.equals(ONE) ? ZERO : ONE);

        if (this.equals(ZERO) && exponent.signum >= 0)
            return ZERO;

        if (this.equals(negConst[1]) && (!exponent.testBit(0)))
            return (m.equals(ONE) ? ZERO : ONE);

        boolean invertResult;
        if ((invertResult = (exponent.signum < 0)))
            exponent = exponent.negate();

        BigInteger base = (this.signum < 0 || this.compareTo(m) >= 0
                           ? this.mod(m) : this);
        BigInteger result;
        if (m.testBit(0)) { // odd modulus
            result = base.oddModPow(exponent, m);
        } else {
            /*
             * Even modulus.  Tear it into an  (m1) and power of two
             * (m2), exponentiate mod m1, manually exponentiate mod m2, and
             * use Chinese Remainder Theorem to combine results.
             */

            // Tear m apart into odd part (m1) and power of 2 (m2)
            int p = m.getLowestSetBit();   // Max pow of 2 that divides m

            BigInteger m1 = m.shiftRight(p);  // m/2**p
            BigInteger m2 = ONE.shiftLeft(p); // 2**p

            // Calculate new base from m1
            BigInteger base2 = (this.signum < 0 || this.compareTo(m1) >= 0
                                ? this.mod(m1) : this);

            // Calculate (base ** exponent) mod m1.
            BigInteger a1 = (m1.equals(ONE) ? ZERO :
                             base2.oddModPow(exponent, m1));

            // Calculate (this ** exponent) mod m2
            BigInteger a2 = base.modPow2(exponent, p);

            // Combine results using Chinese Remainder Theorem
            BigInteger y1 = m2.modInverse(m1);
            BigInteger y2 = m1.modInverse(m2);

            if (m.mag.length < MAX_MAG_LENGTH / 2) {
                result = a1.multiply(m2).multiply(y1).add(a2.multiply(m1).multiply(y2)).mod(m);
            } else {
                MutableBigInteger t1 = new MutableBigInteger();
                new MutableBigInteger(a1.multiply(m2)).multiply(new MutableBigInteger(y1), t1);
                MutableBigInteger t2 = new MutableBigInteger();
                new MutableBigInteger(a2.multiply(m1)).multiply(new MutableBigInteger(y2), t2);
                t1.add(t2);
                MutableBigInteger q = new MutableBigInteger();
                result = t1.divide(new MutableBigInteger(m), q).toBigInteger();
            }
        }

        return (invertResult ? result.modInverse(m) : result);
    }

    // Montgomery multiplication.  These are wrappers for
    // implMontgomeryXX routines which are expected to be replaced by
    // virtual machine intrinsics.  We don't use the intrinsics for
    // very large operands: MONTGOMERY_INTRINSIC_THRESHOLD should be
    // larger than any reasonable crypto key.
    private static int[] montgomeryMultiply(int[] a, int[] b, int[] n, int len, long inv,
                                            int[] product) {
        implMontgomeryMultiplyChecks(a, b, n, len, product);
        if (len > MONTGOMERY_INTRINSIC_THRESHOLD) {
            // Very long argument: do not use an intrinsic
            product = multiplyToLen(a, len, b, len, product);
            return montReduce(product, n, len, (int)inv);
        } else {
            return implMontgomeryMultiply(a, b, n, len, inv, materialize(product, len));
        }
    }
    private static int[] montgomerySquare(int[] a, int[] n, int len, long inv,
                                          int[] product) {
        implMontgomeryMultiplyChecks(a, a, n, len, product);
        if (len > MONTGOMERY_INTRINSIC_THRESHOLD) {
            // Very long argument: do not use an intrinsic
            product = squareToLen(a, len, product);
            return montReduce(product, n, len, (int)inv);
        } else {
            return implMontgomerySquare(a, n, len, inv, materialize(product, len));
        }
    }

    // Range-check everything.
    private static void implMontgomeryMultiplyChecks
        (int[] a, int[] b, int[] n, int len, int[] product) throws RuntimeException {
        if (len % 2 != 0) {
            throw new IllegalArgumentException( + len);
        }

        if (len < 1) {
            throw new IllegalArgumentException( + len);
        }

        if (len > a.length ||
            len > b.length ||
            len > n.length ||
            (product != null && len > product.length)) {
            throw new IllegalArgumentException( + len);
        }
    }

    // Make sure that the int array z (which is expected to contain
    // the result of a Montgomery multiplication) is present and
    // sufficiently large.
    private static int[] materialize(int[] z, int len) {
         if (z == null || z.length < len)
             z = new int[len];
         return z;
    }

    // These methods are intended to be replaced by virtual machine
    // intrinsics.
    @IntrinsicCandidate
    private static int[] implMontgomeryMultiply(int[] a, int[] b, int[] n, int len,
                                         long inv, int[] product) {
        product = multiplyToLen(a, len, b, len, product);
        return montReduce(product, n, len, (int)inv);
    }
    @IntrinsicCandidate
    private static int[] implMontgomerySquare(int[] a, int[] n, int len,
                                       long inv, int[] product) {
        product = squareToLen(a, len, product);
        return montReduce(product, n, len, (int)inv);
    }

    static int[] bnExpModThreshTable = {7, 25, 81, 241, 673, 1793,
                                                Integer.MAX_VALUE}; // Sentinel

    public int getLowestSetBit() {
        int lsb = lowestSetBitPlusTwo - 2;
        if (lsb == -2) {  // lowestSetBit not initialized yet
            lsb = 0;
            if (signum == 0) {
                lsb -= 1;
            } else {
                // Search for lowest order nonzero int
                int i,b;
                for (i=0; (b = getInt(i)) == 0; i++)
                    ;
                lsb += (i << 5) + Integer.numberOfTrailingZeros(b);
            }
            lowestSetBitPlusTwo = lsb + 2;
        }
        return lsb;
    }


    // Miscellaneous Bit Operations

    /**
     * Returns the number of bits in the minimal two's-complement
     * representation of this BigInteger, <em>excluding</em> a sign bit.
     * For positive BigIntegers, this is equivalent to the number of bits in
     * the ordinary binary representation.  For zero this method returns
     * {@code 0}.  (Computes {@code (ceil(log2(this < 0 ? -this : this+1)))}.)
     *
     * @return number of bits in the minimal two's-complement
     *         representation of this BigInteger, <em>excluding</em> a sign bit.
     */
    public int bitLength() {
        int n = bitLengthPlusOne - 1;
        if (n == -1) { // bitLength not initialized yet
            int[] m = mag;
            int len = m.length;
            if (len == 0) {
                n = 0; // offset by one to initialize
            }  else {
                // Calculate the bit length of the magnitude
                int magBitLength = ((len - 1) << 5) + bitLengthForInt(mag[0]);
                 if (signum < 0) {
                     // Check if magnitude is a power of two
                     boolean pow2 = (Integer.bitCount(mag[0]) == 1);
                     for (int i=1; i< len && pow2; i++)
                         pow2 = (mag[i] == 0);

                     n = (pow2 ? magBitLength - 1 : magBitLength);
                 } else {
                     n = magBitLength;
                 }
            }
            bitLengthPlusOne = n + 1;
        }
        return n;
    }

    /**
     * Returns the number of bits in the two's complement representation
     * of this BigInteger that differ from its sign bit.  This method is
     * useful when implementing bit-vector style sets atop BigIntegers.
     *
     * @return number of bits in the two's complement representation
     *         of this BigInteger that differ from its sign bit.
     */
    public int bitCount() {
        int bc = bitCountPlusOne - 1;
        if (bc == -1) {  // bitCount not initialized yet
            bc = 0;      // offset by one to initialize
            // Count the bits in the magnitude
            for (int i=0; i < mag.length; i++)
                bc += Integer.bitCount(mag[i]);
            if (signum < 0) {
                // Count the trailing zeros in the magnitude
                int magTrailingZeroCount = 0, j;
                for (j=mag.length-1; mag[j] == 0; j--)
                    magTrailingZeroCount += 32;
                magTrailingZeroCount += Integer.numberOfTrailingZeros(mag[j]);
                bc += magTrailingZeroCount - 1;
            }
            bitCountPlusOne = bc + 1;
        }
        return bc;
    }

    // Primality Testing

    /**
     * Returns {@code true} if this BigInteger is probably prime,
     * {@code false} if it's definitely composite.  If
     * {@code certainty} is &le; 0, {@code true} is
     * returned.
     *
     * @param  certainty a measure of the uncertainty that the caller is
     *         willing to tolerate: if the call returns {@code true}
     *         the probability that this BigInteger is prime exceeds
     *         (1 - 1/2<sup>{@code certainty}</sup>).  The execution time of
     *         this method is proportional to the value of this parameter.
     * @return {@code true} if this BigInteger is probably prime,
     *         {@code false} if it's definitely composite.
     * @throws ArithmeticException {@code this} is too large.
     * @implNote Due to the nature of the underlying primality test algorithm,
     *          and depending on the size of {@code this} and {@code certainty},
     *          this method could consume a large amount of memory, up to
     *          exhaustion of available heap space, or could run for a long time.
     */
    public boolean isProbablePrime(int certainty) {
        if (certainty <= 0)
            return true;
        BigInteger w = this.abs();
        if (w.equals(TWO))
            return true;
        if (!w.testBit(0) || w.equals(ONE))
            return false;
        if (w.bitLength() > PRIME_SEARCH_BIT_LENGTH_LIMIT + 1) {
            throw new ArithmeticException();
        }
        return w.primeToCertainty(certainty, null);
    }

    // Comparison Operations

    /**
     * Compares this BigInteger with the specified BigInteger.  This
     * method is provided in preference to individual methods for each
     * of the six boolean comparison operators ({@literal <}, ==,
     * {@literal >}, {@literal >=}, !=, {@literal <=}).  The suggested
     * idiom for performing these comparisons is: {@code
     * (x.compareTo(y)} &lt;<i>op</i>&gt; {@code 0)}, where
     * &lt;<i>op</i>&gt; is one of the six comparison operators.
     *
     * @param  val BigInteger to which this BigInteger is to be compared.
     * @return -1, 0 or 1 as this BigInteger is numerically less than, equal
     *         to, or greater than {@code val}.
     */
    public int compareTo(BigInteger val) {
        if (signum == val.signum) {
            return switch (signum) {
                case 1  -> compareMagnitude(val);
                case -1 -> val.compareMagnitude(this);
                default -> 0;
            };
        }
        return signum > val.signum ? 1 : -1;
    }

    /**
     * Compares the magnitude array of this BigInteger with the specified
     * BigInteger's. This is the version of compareTo ignoring sign.
     *
     * @param val BigInteger whose magnitude array to be compared.
     * @return -1, 0 or 1 as this magnitude array is less than, equal to or
     *         greater than the magnitude array for the specified BigInteger's.
     */
    final int compareMagnitude(BigInteger val) {
        int[] m1 = mag;
        int len1 = m1.length;
        int[] m2 = val.mag;
        int len2 = m2.length;
        if (len1 < len2)
            return -1;
        if (len1 > len2)
            return 1;
        for (int i = 0; i < len1; i++) {
            int a = m1[i];
            int b = m2[i];
            if (a != b)
                return ((a & LONG_MASK) < (b & LONG_MASK)) ? -1 : 1;
        }
        return 0;
    }

    /**
     * Version of compareMagnitude that compares magnitude with long value.
     * val can't be Long.MIN_VALUE.
     */
    final int compareMagnitude(long val) {
        assert val != Long.MIN_VALUE;
        int[] m1 = mag;
        int len = m1.length;
        if (len > 2) {
            return 1;
        }
        if (val < 0) {
            val = -val;
        }
        int highWord = (int)(val >>> 32);
        if (highWord == 0) {
            if (len < 1)
                return -1;
            if (len > 1)
                return 1;
            int a = m1[0];
            int b = (int)val;
            if (a != b) {
                return ((a & LONG_MASK) < (b & LONG_MASK))? -1 : 1;
            }
            return 0;
        } else {
            if (len < 2)
                return -1;
            int a = m1[0];
            int b = highWord;
            if (a != b) {
                return ((a & LONG_MASK) < (b & LONG_MASK))? -1 : 1;
            }
            a = m1[1];
            b = (int)val;
            if (a != b) {
                return ((a & LONG_MASK) < (b & LONG_MASK))? -1 : 1;
            }
            return 0;
        }
    }

    /**
     * Compares this BigInteger with the specified Object for equality.
     *
     * @param  x Object to which this BigInteger is to be compared.
     * @return {@code true} if and only if the specified Object is a
     *         BigInteger whose value is numerically equal to this BigInteger.
     */
    public boolean equals(Object x) {
        // This test is just an optimization, which may or may not help
        if (x == this)
            return true;

        if (!(x instanceof BigInteger xInt))
            return false;

        if (xInt.signum != signum)
            return false;

        int[] m = mag;
        int len = m.length;
        int[] xm = xInt.mag;
        if (len != xm.length)
            return false;

        for (int i = 0; i < len; i++)
            if (xm[i] != m[i])
                return false;

        return true;
    }

    /**
     * Returns the minimum of this BigInteger and {@code val}.
     *
     * @param  val value with which the minimum is to be computed.
     * @return the BigInteger whose value is the lesser of this BigInteger and
     *         {@code val}.  If they are equal, either may be returned.
     */
    public BigInteger min(BigInteger val) {
        return (compareTo(val) < 0 ? this : val);
    }

    /**
     * Returns the maximum of this BigInteger and {@code val}.
     *
     * @param  val value with which the maximum is to be computed.
     * @return the BigInteger whose value is the greater of this and
     *         {@code val}.  If they are equal, either may be returned.
     */
    public BigInteger max(BigInteger val) {
        return (compareTo(val) > 0 ? this : val);
    }


    // Hash Function

    /**
     * Returns the hash code for this BigInteger.
     *
     * @return hash code for this BigInteger.
     */
    public int hashCode() {
        int hashCode = 0;

        for (int i=0; i < mag.length; i++)
            hashCode = (int)(31*hashCode + (mag[i] & LONG_MASK));

        return hashCode * signum;
    }

    /**
     * Returns the String representation of this BigInteger in the
     * given radix.  If the radix is outside the range from {@link
     * Character#MIN_RADIX} to {@link Character#MAX_RADIX} inclusive,
     * it will default to 10 (as is the case for
     * {@code Integer.toString}).  The digit-to-character mapping
     * provided by {@code Character.forDigit} is used, and a minus
     * sign is prepended if appropriate.  (This representation is
     * compatible with the {@link #BigInteger(String, int) (String,
     * int)} constructor.)
     *
     * @param  radix  radix of the String representation.
     * @return String representation of this BigInteger in the given radix.
     * @see    Integer#toString
     * @see    Character#forDigit
     * @see    #BigInteger(java.lang.String, int)
     */
    public String toString(int radix) {
        if (signum == 0)
            return ;
        if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
            radix = 10;

        BigInteger abs = this.abs();

        // Ensure buffer capacity sufficient to contain string representation
        //     floor(bitLength*log(2)/log(radix)) + 1
        // plus an additional character for the sign if negative.
        int b = abs.bitLength();
        int numChars = (int)(Math.floor(b*LOG_TWO/logCache[radix]) + 1) +
            (signum < 0 ? 1 : 0);
        StringBuilder sb = new StringBuilder(numChars);

        if (signum < 0) {
            sb.append('-');
        }

        // Use recursive toString.
        toString(abs, sb, radix, 0);

        return sb.toString();
    }

    /**
     * If {@code numZeros > 0}, appends that many zeros to the
     * specified StringBuilder; otherwise, does nothing.
     *
     * @param buf       The StringBuilder that will be appended to.
     * @param numZeros  The number of zeros to append.
     */
    private static void padWithZeros(StringBuilder buf, int numZeros) {
        while (numZeros >= NUM_ZEROS) {
            buf.append(ZEROS);
            numZeros -= NUM_ZEROS;
        }
        if (numZeros > 0) {
            buf.append(ZEROS, 0, numZeros);
        }
    }

    /**
     * This method is used to perform toString when arguments are small.
     * The value must be non-negative. If {@code digits <= 0} no padding
     * (pre-pending with zeros) will be effected.
     *
     * @param radix  The base to convert to.
     * @param buf    The StringBuilder that will be appended to in place.
     * @param digits The minimum number of digits to pad to.
     */
    private void smallToString(int radix, StringBuilder buf, int digits) {
        assert signum >= 0;

        if (signum == 0) {
            padWithZeros(buf, digits);
            return;
        }

        // Compute upper bound on number of digit groups and allocate space
        int maxNumDigitGroups = (4*mag.length + 6)/7;
        long[] digitGroups = new long[maxNumDigitGroups];

        // Translate number to string, a digit group at a time
        BigInteger tmp = this;
        int numGroups = 0;
        while (tmp.signum != 0) {
            BigInteger d = longRadix[radix];

            MutableBigInteger q = new MutableBigInteger(),
                              a = new MutableBigInteger(tmp.mag),
                              b = new MutableBigInteger(d.mag);
            MutableBigInteger r = a.divide(b, q);
            BigInteger q2 = q.toBigInteger(tmp.signum * d.signum);
            BigInteger r2 = r.toBigInteger(tmp.signum * d.signum);

            digitGroups[numGroups++] = r2.longValue();
            tmp = q2;
        }

        // Get string version of first digit group
        String s = Long.toString(digitGroups[numGroups-1], radix);

        // Pad with internal zeros if necessary.
        padWithZeros(buf, digits - (s.length() +
            (numGroups - 1)*digitsPerLong[radix]));

        // Put first digit group into result buffer
        buf.append(s);

        // Append remaining digit groups each padded with leading zeros
        for (int i=numGroups-2; i >= 0; i--) {
            // Prepend (any) leading zeros for this digit group
            s = Long.toString(digitGroups[i], radix);
            int numLeadingZeros = digitsPerLong[radix] - s.length();
            if (numLeadingZeros != 0) {
                buf.append(ZEROS, 0, numLeadingZeros);
            }
            buf.append(s);
        }
    }

    /**
     * Converts the specified BigInteger to a string and appends to
     * {@code sb}.  This implements the recursive Schoenhage algorithm
     * for base conversions. This method can only be called for non-negative
     * numbers.
     * <p>
     * See Knuth, Donald,  _The Art of Computer Programming_, Vol. 2,
     * Answers to Exercises (4.4) Question 14.
     *
     * @param u      The number to convert to a string.
     * @param sb     The StringBuilder that will be appended to in place.
     * @param radix  The base to convert to.
     * @param digits The minimum number of digits to pad to.
     */
    private static void toString(BigInteger u, StringBuilder sb,
                                 int radix, int digits) {
        assert u.signum() >= 0;

        // If we're smaller than a certain threshold, use the smallToString
        // method, padding with leading zeroes when necessary unless we're
        // at the beginning of the string or digits <= 0. As u.signum() >= 0,
        // smallToString() will not prepend a negative sign.
        if (u.mag.length <= SCHOENHAGE_BASE_CONVERSION_THRESHOLD) {
            u.smallToString(radix, sb, digits);
            return;
        }

        // Calculate a value for n in the equation radix^(2^n) = u
        // and subtract 1 from that value.  This is used to find the
        // cache index that contains the best value to divide u.
        int b = u.bitLength();
        int n = (int) Math.round(Math.log(b * LOG_TWO / logCache[radix]) /
                                 LOG_TWO - 1.0);

        BigInteger v = getRadixConversionCache(radix, n);
        BigInteger[] results;
        results = u.divideAndRemainder(v);

        int expectedDigits = 1 << n;

        // Now recursively build the two halves of each number.
        toString(results[0], sb, radix, digits - expectedDigits);
        toString(results[1], sb, radix, expectedDigits);
    }

    /**
     * Returns the value radix^(2^exponent) from the cache.
     * If this value doesn't already exist in the cache, it is added.
     * <p>
     * This could be changed to a more complicated caching method using
     * {@code Future}.
     */
    private static BigInteger getRadixConversionCache(int radix, int exponent) {
        BigInteger[] cacheLine = powerCache[radix]; // volatile read
        if (exponent < cacheLine.length) {
            return cacheLine[exponent];
        }

        int oldLength = cacheLine.length;
        cacheLine = Arrays.copyOf(cacheLine, exponent + 1);
        for (int i = oldLength; i <= exponent; i++) {
            cacheLine[i] = cacheLine[i - 1].pow(2);
        }

        BigInteger[][] pc = powerCache; // volatile read again
        if (exponent >= pc[radix].length) {
            pc = pc.clone();
            pc[radix] = cacheLine;
            powerCache = pc; // volatile write, publish
        }
        return cacheLine[exponent];
    }

    /* Size of ZEROS string. */
    private static int NUM_ZEROS = 63;

    /* ZEROS is a string of NUM_ZEROS consecutive zeros. */
    private static final String ZEROS = .repeat(NUM_ZEROS);

    /**
     * Returns the decimal String representation of this BigInteger.
     * The digit-to-character mapping provided by
     * {@code Character.forDigit} is used, and a minus sign is
     * prepended if appropriate.  (This representation is compatible
     * with the {@link #BigInteger(String) (String)} constructor, and
     * allows for String concatenation with Java's + operator.)
     *
     * @return decimal String representation of this BigInteger.
     * @see    Character#forDigit
     * @see    #BigInteger(java.lang.String)
     */
    public String toString() {
        return toString(10);
    }

    /**
     * Returns a byte array containing the two's-complement
     * representation of this BigInteger.  The byte array will be in
     * <i>big-endian</i> byte-order: the most significant byte is in
     * the zeroth element.  The array will contain the minimum number
     * of bytes required to represent this BigInteger, including at
     * least one sign bit, which is {@code (ceil((this.bitLength() +
     * 1)/8))}.  (This representation is compatible with the
     * {@link #BigInteger(byte[]) (byte[])} constructor.)
     *
     * @return a byte array containing the two's-complement representation of
     *         this BigInteger.
     * @see    #BigInteger(byte[])
     */
    public byte[] toByteArray() {
        int byteLen = bitLength()/8 + 1;
        byte[] byteArray = new byte[byteLen];

        for (int i=byteLen-1, bytesCopied=4, nextInt=0, intIndex=0; i >= 0; i--) {
            if (bytesCopied == 4) {
                nextInt = getInt(intIndex++);
                bytesCopied = 1;
            } else {
                nextInt >>>= 8;
                bytesCopied++;
            }
            byteArray[i] = (byte)nextInt;
        }
        return byteArray;
    }

    /**
     * Converts this BigInteger to an {@code int}.  This
     * conversion is analogous to a
     * <i>narrowing primitive conversion</i> from {@code long} to
     * {@code int} as defined in
     * <cite>The Java Language Specification</cite>:
     * if this BigInteger is too big to fit in an
     * {@code int}, only the low-order 32 bits are returned.
     * Note that this conversion can lose information about the
     * overall magnitude of the BigInteger value as well as return a
     * result with the opposite sign.
     *
     * @return this BigInteger converted to an {@code int}.
     * @see #intValueExact()
     * @jls 5.1.3 Narrowing Primitive Conversion
     */
    public int intValue() {
        int result = 0;
        result = getInt(0);
        return result;
    }

    /**
     * Converts this BigInteger to a {@code long}.  This
     * conversion is analogous to a
     * <i>narrowing primitive conversion</i> from {@code long} to
     * {@code int} as defined in
     * <cite>The Java Language Specification</cite>:
     * if this BigInteger is too big to fit in a
     * {@code long}, only the low-order 64 bits are returned.
     * Note that this conversion can lose information about the
     * overall magnitude of the BigInteger value as well as return a
     * result with the opposite sign.
     *
     * @return this BigInteger converted to a {@code long}.
     * @see #longValueExact()
     * @jls 5.1.3 Narrowing Primitive Conversion
     */
    public long longValue() {
        long result = 0;

        for (int i=1; i >= 0; i--)
            result = (result << 32) + (getInt(i) & LONG_MASK);
        return result;
    }

    /**
     * Converts this BigInteger to a {@code float}.  This
     * conversion is similar to the
     * <i>narrowing primitive conversion</i> from {@code double} to
     * {@code float} as defined in
     * <cite>The Java Language Specification</cite>:
     * if this BigInteger has too great a magnitude
     * to represent as a {@code float}, it will be converted to
     * {@link Float#NEGATIVE_INFINITY} or {@link
     * Float#POSITIVE_INFINITY} as appropriate.  Note that even when
     * the return value is finite, this conversion can lose
     * information about the precision of the BigInteger value.
     *
     * @return this BigInteger converted to a {@code float}.
     * @jls 5.1.3 Narrowing Primitive Conversion
     */
    public float floatValue() {
        if (signum == 0) {
            return 0.0f;
        }

        int exponent = ((mag.length - 1) << 5) + bitLengthForInt(mag[0]) - 1;

        // exponent == floor(log2(abs(this)))
        if (exponent < Long.SIZE - 1) {
            return longValue();
        } else if (exponent > Float.MAX_EXPONENT) {
            return signum > 0 ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;
        }

        /*
         * We need the top SIGNIFICAND_WIDTH bits, including the 
         * one bit. To make rounding easier, we pick out the top
         * SIGNIFICAND_WIDTH + 1 bits, so we have one to help us round up or
         * down. twiceSignifFloor will contain the top SIGNIFICAND_WIDTH + 1
         * bits, and signifFloor the top SIGNIFICAND_WIDTH.
         *
         * It helps to consider the real number signif = abs(this) *
         * 2^(SIGNIFICAND_WIDTH - 1 - exponent).
         */
        int shift = exponent - FloatConsts.SIGNIFICAND_WIDTH;

        int twiceSignifFloor;
        // twiceSignifFloor will be == abs().shiftRight(shift).intValue()
        // We do the shift into an int directly to improve performance.

        int nBits = shift & 0x1f;
        int nBits2 = 32 - nBits;

        if (nBits == 0) {
            twiceSignifFloor = mag[0];
        } else {
            twiceSignifFloor = mag[0] >>> nBits;
            if (twiceSignifFloor == 0) {
                twiceSignifFloor = (mag[0] << nBits2) | (mag[1] >>> nBits);
            }
        }

        int signifFloor = twiceSignifFloor >> 1;
        signifFloor &= FloatConsts.SIGNIF_BIT_MASK; // remove the implied bit

        /*
         * We round up if either the fractional part of signif is strictly
         * greater than 0.5 (which is true if the 0.5 bit is set and any lower
         * bit is set), or if the fractional part of signif is >= 0.5 and
         * signifFloor is odd (which is true if both the 0.5 bit and the 1 bit
         * are set). This is equivalent to the desired HALF_EVEN rounding.
         */
        boolean increment = (twiceSignifFloor & 1) != 0
                && ((signifFloor & 1) != 0 || abs().getLowestSetBit() < shift);
        int signifRounded = increment ? signifFloor + 1 : signifFloor;
        int bits = ((exponent + FloatConsts.EXP_BIAS))
                << (FloatConsts.SIGNIFICAND_WIDTH - 1);
        bits += signifRounded;
        /*
         * If signifRounded == 2^24, we'd need to set all of the significand
         * bits to zero and add 1 to the exponent. This is exactly the behavior
         * we get from just adding signifRounded to bits directly. If the
         * exponent is Float.MAX_EXPONENT, we round up (correctly) to
         * Float.POSITIVE_INFINITY.
         */
        bits |= signum & FloatConsts.SIGN_BIT_MASK;
        return Float.intBitsToFloat(bits);
    }

    /**
     * Converts this BigInteger to a {@code double}.  This
     * conversion is similar to the
     * <i>narrowing primitive conversion</i> from {@code double} to
     * {@code float} as defined in
     * <cite>The Java Language Specification</cite>:
     * if this BigInteger has too great a magnitude
     * to represent as a {@code double}, it will be converted to
     * {@link Double#NEGATIVE_INFINITY} or {@link
     * Double#POSITIVE_INFINITY} as appropriate.  Note that even when
     * the return value is finite, this conversion can lose
     * information about the precision of the BigInteger value.
     *
     * @return this BigInteger converted to a {@code double}.
     * @jls 5.1.3 Narrowing Primitive Conversion
     */
    public double doubleValue() {
        if (signum == 0) {
            return 0.0;
        }

        int exponent = ((mag.length - 1) << 5) + bitLengthForInt(mag[0]) - 1;

        // exponent == floor(log2(abs(this))Double)
        if (exponent < Long.SIZE - 1) {
            return longValue();
        } else if (exponent > Double.MAX_EXPONENT) {
            return signum > 0 ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
        }

        /*
         * We need the top SIGNIFICAND_WIDTH bits, including the 
         * one bit. To make rounding easier, we pick out the top
         * SIGNIFICAND_WIDTH + 1 bits, so we have one to help us round up or
         * down. twiceSignifFloor will contain the top SIGNIFICAND_WIDTH + 1
         * bits, and signifFloor the top SIGNIFICAND_WIDTH.
         *
         * It helps to consider the real number signif = abs(this) *
         * 2^(SIGNIFICAND_WIDTH - 1 - exponent).
         */
        int shift = exponent - DoubleConsts.SIGNIFICAND_WIDTH;

        long twiceSignifFloor;
        // twiceSignifFloor will be == abs().shiftRight(shift).longValue()
        // We do the shift into a long directly to improve performance.

        int nBits = shift & 0x1f;
        int nBits2 = 32 - nBits;

        int highBits;
        int lowBits;
        if (nBits == 0) {
            highBits = mag[0];
            lowBits = mag[1];
        } else {
            highBits = mag[0] >>> nBits;
            lowBits = (mag[0] << nBits2) | (mag[1] >>> nBits);
            if (highBits == 0) {
                highBits = lowBits;
                lowBits = (mag[1] << nBits2) | (mag[2] >>> nBits);
            }
        }

        twiceSignifFloor = ((highBits & LONG_MASK) << 32)
                | (lowBits & LONG_MASK);

        long signifFloor = twiceSignifFloor >> 1;
        signifFloor &= DoubleConsts.SIGNIF_BIT_MASK; // remove the implied bit

        /*
         * We round up if either the fractional part of signif is strictly
         * greater than 0.5 (which is true if the 0.5 bit is set and any lower
         * bit is set), or if the fractional part of signif is >= 0.5 and
         * signifFloor is odd (which is true if both the 0.5 bit and the 1 bit
         * are set). This is equivalent to the desired HALF_EVEN rounding.
         */
        boolean increment = (twiceSignifFloor & 1) != 0
                && ((signifFloor & 1) != 0 || abs().getLowestSetBit() < shift);
        long signifRounded = increment ? signifFloor + 1 : signifFloor;
        long bits = (long) ((exponent + DoubleConsts.EXP_BIAS))
                << (DoubleConsts.SIGNIFICAND_WIDTH - 1);
        bits += signifRounded;
        /*
         * If signifRounded == 2^53, we'd need to set all of the significand
         * bits to zero and add 1 to the exponent. This is exactly the behavior
         * we get from just adding signifRounded to bits directly. If the
         * exponent is Double.MAX_EXPONENT, we round up (correctly) to
         * Double.POSITIVE_INFINITY.
         */
        bits |= signum & DoubleConsts.SIGN_BIT_MASK;
        return Double.longBitsToDouble(bits);
    }

    /**
     * Returns a copy of the input array stripped of any leading zero bytes.
     */
    private static int[] stripLeadingZeroInts(int[] val) {
        int vlen = val.length;
        int keep;

        // Find first nonzero byte
        for (keep = 0; keep < vlen && val[keep] == 0; keep++)
            ;
        return java.util.Arrays.copyOfRange(val, keep, vlen);
    }

    /**
     * Returns the input array stripped of any leading zero bytes.
     * Since the source is trusted the copying may be skipped.
     */
    private static int[] trustedStripLeadingZeroInts(int[] val) {
        int vlen = val.length;
        int keep;

        // Find first nonzero byte
        for (keep = 0; keep < vlen && val[keep] == 0; keep++)
            ;
        return keep == 0 ? val : java.util.Arrays.copyOfRange(val, keep, vlen);
    }

    private static int[] stripLeadingZeroBytes(byte[] a, int from, int len) {
        return stripLeadingZeroBytes(Integer.MIN_VALUE, a, from, len);
    }

    /*
     * Returns a copy of the input array stripped of any leading zero bytes.
     * The returned array is either empty, or its 0-th element is non-zero,
     * meeting the  requirement for field mag (see comment on mag).
     *
     * The range [from, from + len) must be well-formed w.r.t. array a.
     *
     * b < -128 means that a[from] has not yet been read.
     * Otherwise, b must be a[from], have been read only once before invoking
     * this method, and len > 0 must hold.
     */
    private static int[] stripLeadingZeroBytes(int b, byte[] a, int from, int len) {
        /*
         * Except for the first byte, each read access to the input array a
         * is of the form a[from++].
         * The index from is never otherwise altered, except right below,
         * and only increases in steps of 1, always up to index to.
         * Hence, each byte in the array is read exactly once, from lower to
         * higher indices (from most to least significant byte).
         */
        if (len == 0) {
            return ZERO.mag;
        }
        int to = from + len;
        if (b < -128) {
            b = a[from];
        }
        /* Either way, a[from] has now been read exactly once, skip to next. */
        ++from;
        /*
         * Set up the shortest int[] for the sequence of the bytes
         *      b, a[from+1], ..., a[to-1]    (len > 0)
         * Shortest means first skipping leading zeros.
         */
        for (; b == 0 && from < to; b = a[from++])
            ;  //empty body
        if (b == 0) {
            /* Here, from == to as well. All bytes are zeros. */
            return ZERO.mag;
        }
        /*
         * Allocate just enough ints to hold (to - from + 1) bytes, that is
         *      ((to - from + 1) + 3) / 4 = (to - from) / 4 + 1
         */
        int[] res = new int[((to - from) >> 2) + 1];
        /*
         * A  is a group of 4 adjacent bytes aligned w.r.t. index to.
         * (Implied 0 bytes are prepended as needed.)
         * b is the most significant byte not 0.
         * Digit d0 spans the range of indices that includes current (from - 1).
         */
        int d0 = b & 0xFF;
        while (((to - from) & 0x3) != 0) {
            d0 = d0 << 8 | a[from++] & 0xFF;
        }
        res[0] = d0;
        /*
         * Prepare the remaining digits.
         * (to - from) is a multiple of 4, so prepare an int for every 4 bytes.
         * This is a candidate for Unsafe.copy[Swap]Memory().
         */
        int i = 1;
        while (from < to) {
            res[i++] = a[from++] << 24 | (a[from++] & 0xFF) << 16
                    | (a[from++] & 0xFF) << 8 | (a[from++] & 0xFF);
        }
        return res;
    }

    /*
     * Takes an array a representing a negative 2's-complement number and
     * returns the minimal (no leading zero bytes) unsigned whose value is -a.
     *
     * len > 0 must hold.
     * The range [from, from + len) must be well-formed w.r.t. array a.
     * b is assumed to be the result of reading a[from] and to meet b < 0.
     */
    private static int[] makePositive(int b, byte[] a, int from, int len) {
        /*
         * By assumption, b == a[from] < 0 and len > 0.
         *
         * First collect the bytes into the resulting array res.
         * Then convert res to two's complement.
         *
         * Except for b == a[from], each read access to the input array a
         * is of the form a[from++].
         * The index from is never otherwise altered, except right below,
         * and only increases in steps of 1, always up to index to.
         * Hence, each byte in the array is read exactly once, from lower to
         * higher indices (from most to least significant byte).
         */
        int to = from + len;
        /* b == a[from] has been read exactly once, skip to next index. */
        ++from;
        /* Skip leading -1 bytes. */
        for (; b == -1 && from < to; b = a[from++])
            ;  //empty body
        /*
         * A  is a group of 4 adjacent bytes aligned w.r.t. index to.
         * b is the most significant byte not -1, or -1 only if from == to.
         * Digit d0 spans the range of indices that includes current (from - 1).
         * (Implied -1 bytes are prepended to array a as needed.)
         * It usually corresponds to res[0], except for the special case below.
         */
        int d0 = -1 << 8 | b & 0xFF;
        while (((to - from) & 0x3) != 0) {
            d0 = d0 << 8 | (b = a[from++]) & 0xFF;
        }
        int f = from;  // keeps the current from for sizing purposes later
        /* Skip zeros adjacent to d0, if at all. */
        for (; b == 0 && from < to; b = a[from++])
            ;  //empty body
        /*
         * b is the most significant non-zero byte at or after (f - 1),
         * or 0 only if from == to.
         * Digit d spans the range of indices that includes (f - 1).
         */
        int d = b & 0xFF;
        while (((to - from) & 0x3) != 0) {
            d = d << 8 | a[from++] & 0xFF;
        }
        /*
         * If the situation here is like this:
         * index:                      f                        to == from
         *      ..., -1,-1,  0,0,0,0,  0,0,0,0,  ...,  0,0,0,0
         * digit:               d0                        d
         * then, as shown, the number of zeros is a positive multiple of 4.
         * The array res needs a minimal length of (1 + 1 + (to - f) / 4)
         * to accommodate the two's complement, including a leading 1.
         * In any other case, there is at least one byte that is non-zero.
         * The array for the two's complement has length (0 + 1 + (to - f) / 4).
         * c is 1, resp., 0 for the two situations.
         */
        int c = (to - from | d0 | d) == 0 ? 1 : 0;
        int[] res = new int[c + 1 + ((to - f) >> 2)];
        res[0] = c == 0 ? d0 : -1;
        int i = res.length - ((to - from) >> 2);
        if (i > 1) {
            res[i - 1] = d;
        }
        /*
         * Prepare the remaining digits.
         * (to - from) is a multiple of 4, so prepare an int for every 4 bytes.
         * This is a candidate for Unsafe.copy[Swap]Memory().
         */
        while (from < to) {
            res[i++] = a[from++] << 24 | (a[from++] & 0xFF) << 16
                    | (a[from++] & 0xFF) << 8 | (a[from++] & 0xFF);
        }
        /* Convert to two's complement. Here, i == res.length */
        while (--i >= 0 && res[i] == 0)
            ;  // empty body
        res[i] = -res[i];
        while (--i >= 0) {
            res[i] = ~res[i];
        }
        return res;
    }

    /**
     * Takes an array a representing a negative 2's-complement number and
     * returns the minimal (no leading zero ints) unsigned whose value is -a.
     */
    private static int[] makePositive(int[] a) {
        int keep, j;

        // Find first non-sign (0xffffffff) int of input
        for (keep=0; keep < a.length && a[keep] == -1; keep++)
            ;

        /* Allocate output array.  If all non-sign ints are 0x00, we must
         * allocate space for one extra output int. */
        for (j=keep; j < a.length && a[j] == 0; j++)
            ;
        int extraInt = (j == a.length ? 1 : 0);
        int result[] = new int[a.length - keep + extraInt];

        /* Copy one's complement of input into output, leaving extra
         * int (if it exists) == 0x00 */
        for (int i = keep; i < a.length; i++)
            result[i - keep + extraInt] = ~a[i];

        // Add one to one's complement to generate two's complement
        for (int i=result.length-1; ++result[i] == 0; i--)
            ;

        return result;
    }

    /*
     * The following two arrays are used for fast String conversions.  Both
     * are indexed by radix.  The first is the number of digits of the given
     * radix that can fit in a Java long without , i.e., the
     * highest integer n such that radix**n < 2**63.  The second is the
     * , each of which
     * consists of the number of digits in the corresponding element in
     * digitsPerLong (longRadix[i] = i**digitPerLong[i]).  Both arrays have
     * nonsense values in their 0 and 1 elements, as radixes 0 and 1 are not
     * used.
     */
    private static int digitsPerLong[] = {0, 0,
        62, 39, 31, 27, 24, 22, 20, 19, 18, 18, 17, 17, 16, 16, 15, 15, 15, 14,
        14, 14, 14, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12, 12, 12};

    private static BigInteger longRadix[] = {null, null,
        valueOf(0x4000000000000000L), valueOf(0x383d9170b85ff80bL),
        valueOf(0x4000000000000000L), valueOf(0x6765c793fa10079dL),
        valueOf(0x41c21cb8e1000000L), valueOf(0x3642798750226111L),
        valueOf(0x1000000000000000L), valueOf(0x12bf307ae81ffd59L),
        valueOf( 0xde0b6b3a7640000L), valueOf(0x4d28cb56c33fa539L),
        valueOf(0x1eca170c00000000L), valueOf(0x780c7372621bd74dL),
        valueOf(0x1e39a5057d810000L), valueOf(0x5b27ac993df97701L),
        valueOf(0x1000000000000000L), valueOf(0x27b95e997e21d9f1L),
        valueOf(0x5da0e1e53c5c8000L), valueOf( 0xb16a458ef403f19L),
        valueOf(0x16bcc41e90000000L), valueOf(0x2d04b7fdd9c0ef49L),
        valueOf(0x5658597bcaa24000L), valueOf( 0x6feb266931a75b7L),
        valueOf( 0xc29e98000000000L), valueOf(0x14adf4b7320334b9L),
        valueOf(0x226ed36478bfa000L), valueOf(0x383d9170b85ff80bL),
        valueOf(0x5a3c23e39c000000L), valueOf( 0x4e900abb53e6b71L),
        valueOf( 0x7600ec618141000L), valueOf( 0xaee5720ee830681L),
        valueOf(0x1000000000000000L), valueOf(0x172588ad4f5f0981L),
        valueOf(0x211e44f7d02c1000L), valueOf(0x2ee56725f06e5c71L),
        valueOf(0x41c21cb8e1000000L)};

    /*
     * These two arrays are the integer analogue of above.
     */
    private static int digitsPerInt[] = {0, 0, 30, 19, 15, 13, 11,
        11, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6,
        6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5};

    private static int intRadix[] = {0, 0,
        0x40000000, 0x4546b3db, 0x40000000, 0x48c27395, 0x159fd800,
        0x75db9c97, 0x40000000, 0x17179149, 0x3b9aca00, 0xcc6db61,
        0x19a10000, 0x309f1021, 0x57f6c100, 0xa2f1b6f,  0x10000000,
        0x18754571, 0x247dbc80, 0x3547667b, 0x4c4b4000, 0x6b5a6e1d,
        0x6c20a40,  0x8d2d931,  0xb640000,  0xe8d4a51,  0x1269ae40,
        0x17179149, 0x1cb91000, 0x23744899, 0x2b73a840, 0x34e63b41,
        0x40000000, 0x4cfa3cc1, 0x5c13d840, 0x6d91b519, 0x39aa400
    };

    /**
     * These routines provide access to the two's complement representation
     * of BigIntegers.
     */

    /**
     * Returns the length of the two's complement representation in ints,
     * including space for at least one sign bit.
     */
    private int intLength() {
        return (bitLength() >>> 5) + 1;
    }

    /* Returns sign bit */
    private int signBit() {
        return signum < 0 ? 1 : 0;
    }

    /* Returns an int of sign bits */
    private int signInt() {
        return signum < 0 ? -1 : 0;
    }

    /**
     * Returns the specified int of the little-endian two's complement
     * representation (int 0 is the least significant).  The int number can
     * be arbitrarily high (values are logically preceded by infinitely many
     * sign ints).
     */
    private int getInt(int n) {
        if (n < 0)
            return 0;
        if (n >= mag.length)
            return signInt();

        int magInt = mag[mag.length-n-1];

        return (signum >= 0 ? magInt :
                (n <= firstNonzeroIntNum() ? -magInt : ~magInt));
    }

    /**
     * Returns the index of the int that contains the first nonzero int in the
     * little-endian binary representation of the magnitude (int 0 is the
     * least significant). If the magnitude is zero, return value is undefined.
     *
     * <p>Note: never used for a BigInteger with a magnitude of zero.
     * @see #getInt
     */
    private int firstNonzeroIntNum() {
        int fn = firstNonzeroIntNumPlusTwo - 2;
        if (fn == -2) { // firstNonzeroIntNum not initialized yet
            // Search for the first nonzero int
            int i;
            int mlen = mag.length;
            for (i = mlen - 1; i >= 0 && mag[i] == 0; i--)
                ;
            fn = mlen - i - 1;
            firstNonzeroIntNumPlusTwo = fn + 2; // offset by two to initialize
        }
        return fn;
    }

    /** use serialVersionUID from JDK 1.1. for interoperability */
    @java.io.Serial
    private static final long serialVersionUID = -8287574255936472291L;

    /**
     * Serializable fields for BigInteger.
     *
     * @serialField signum  int
     *              signum of this BigInteger
     * @serialField magnitude byte[]
     *              magnitude array of this BigInteger
     * @serialField bitCount  int
     *              appears in the serialized form for backward compatibility
     * @serialField bitLength int
     *              appears in the serialized form for backward compatibility
     * @serialField firstNonzeroByteNum int
     *              appears in the serialized form for backward compatibility
     * @serialField lowestSetBit int
     *              appears in the serialized form for backward compatibility
     */
    @java.io.Serial
    private static final ObjectStreamField[] serialPersistentFields = {
        new ObjectStreamField(, Integer.TYPE),
        new ObjectStreamField(, byte[].class),
        new ObjectStreamField(, Integer.TYPE),
        new ObjectStreamField(, Integer.TYPE),
        new ObjectStreamField(, Integer.TYPE),
        new ObjectStreamField(, Integer.TYPE)
        };

    /**
     * Reconstitute the {@code BigInteger} instance from a stream (that is,
     * deserialize it). The magnitude is read in as an array of bytes
     * for historical reasons, but it is converted to an array of ints
     * and the byte array is discarded.
     * Note:
     * The current convention is to initialize the cache fields, bitCountPlusOne,
     * bitLengthPlusOne and lowestSetBitPlusTwo, to 0 rather than some other
     * marker value. Therefore, no explicit action to set these fields needs to
     * be taken in readObject because those fields already have a 0 value by
     * default since defaultReadObject is not being used.
     *
     * @param  s the stream being read.
     * @throws IOException if an I/O error occurs
     * @throws ClassNotFoundException if a serialized class cannot be loaded
     */
    @java.io.Serial
    private void readObject(java.io.ObjectInputStream s)
        throws java.io.IOException, ClassNotFoundException {
        // prepare to read the alternate persistent fields
        ObjectInputStream.GetField fields = s.readFields();

        // Read and validate the alternate persistent fields that we
        // care about, signum and magnitude

        // Read and validate signum
        int sign = fields.get(, -2);
        if (sign < -1 || sign > 1) {
            String message = ;
            if (fields.defaulted())
                message = ;
            throw new java.io.StreamCorruptedException(message);
        }

        // Read and validate magnitude
        byte[] magnitude = (byte[])fields.get(, null);
        magnitude = magnitude.clone(); // defensive copy
        int[] mag = stripLeadingZeroBytes(magnitude, 0, magnitude.length);
        if ((mag.length == 0) != (sign == 0)) {
            String message = ;
            if (fields.defaulted())
                message = ;
            throw new java.io.StreamCorruptedException(message);
        }

        // Equivalent to checkRange() on mag local without assigning
        // this.mag field
        if (mag.length > MAX_MAG_LENGTH ||
            (mag.length == MAX_MAG_LENGTH && mag[0] < 0)) {
            throw new java.io.StreamCorruptedException();
        }

        // Commit final fields via Unsafe
        UnsafeHolder.putSignAndMag(this, sign, mag);
    }

    /**
     * Serialization without data not supported for this class.
     */
    @java.io.Serial
    private void readObjectNoData()
        throws ObjectStreamException {
        throw new InvalidObjectException();
    }

    // Support for resetting final fields while deserializing
    private static class UnsafeHolder {
        private static final jdk.internal.misc.Unsafe unsafe
                = jdk.internal.misc.Unsafe.getUnsafe();
        private static final long signumOffset
                = unsafe.objectFieldOffset(BigInteger.class, );
        private static final long magOffset
                = unsafe.objectFieldOffset(BigInteger.class, );

        static void putSignAndMag(BigInteger bi, int sign, int[] magnitude) {
            unsafe.putInt(bi, signumOffset, sign);
            unsafe.putReference(bi, magOffset, magnitude);
        }
    }

    /**
     * Save the {@code BigInteger} instance to a stream.  The magnitude of a
     * {@code BigInteger} is serialized as a byte array for historical reasons.
     * To maintain compatibility with older implementations, the integers
     * -1, -1, -2, and -2 are written as the values of the obsolete fields
     * {@code bitCount}, {@code bitLength}, {@code lowestSetBit}, and
     * {@code firstNonzeroByteNum}, respectively.  These values are compatible
     * with older implementations, but will be ignored by current
     * implementations.
     *
     * @param  s the stream to serialize to.
     * @throws IOException if an I/O error occurs
     */
    @java.io.Serial
    private void writeObject(ObjectOutputStream s) throws IOException {
        // set the values of the Serializable fields
        ObjectOutputStream.PutField fields = s.putFields();
        fields.put(, signum);
        fields.put(, magSerializedForm());
        // The values written for cached fields are compatible with older
        // versions, but are ignored in readObject so don't otherwise matter.
        fields.put(, -1);
        fields.put(, -1);
        fields.put(, -2);
        fields.put(, -2);

        // save them
        s.writeFields();
    }

    /**
     * Returns the mag array as an array of bytes.
     */
    private byte[] magSerializedForm() {
        int len = mag.length;

        int bitLen = (len == 0 ? 0 : ((len - 1) << 5) + bitLengthForInt(mag[0]));
        int byteLen = (bitLen + 7) >>> 3;
        byte[] result = new byte[byteLen];

        for (int i = byteLen - 1, bytesCopied = 4, intIndex = len - 1, nextInt = 0;
             i >= 0; i--) {
            if (bytesCopied == 4) {
                nextInt = mag[intIndex--];
                bytesCopied = 1;
            } else {
                nextInt >>>= 8;
                bytesCopied++;
            }
            result[i] = (byte)nextInt;
        }
        return result;
    }

    /**
     * Converts this {@code BigInteger} to a {@code long}, checking
     * for lost information.  If the value of this {@code BigInteger}
     * is out of the range of the {@code long} type, then an
     * {@code ArithmeticException} is thrown.
     *
     * @return this {@code BigInteger} converted to a {@code long}.
     * @throws ArithmeticException if the value of {@code this} will
     * not exactly fit in a {@code long}.
     * @see BigInteger#longValue
     * @since  1.8
     */
    public long longValueExact() {
        if (mag.length <= 2 && bitLength() <= 63)
            return longValue();
        else
            throw new ArithmeticException();
    }

    /**
     * Converts this {@code BigInteger} to an {@code int}, checking
     * for lost information.  If the value of this {@code BigInteger}
     * is out of the range of the {@code int} type, then an
     * {@code ArithmeticException} is thrown.
     *
     * @return this {@code BigInteger} converted to an {@code int}.
     * @throws ArithmeticException if the value of {@code this} will
     * not exactly fit in an {@code int}.
     * @see BigInteger#intValue
     * @since  1.8
     */
    public int intValueExact() {
        if (mag.length <= 1 && bitLength() <= 31)
            return intValue();
        else
            throw new ArithmeticException();
    }

    /**
     * Converts this {@code BigInteger} to a {@code short}, checking
     * for lost information.  If the value of this {@code BigInteger}
     * is out of the range of the {@code short} type, then an
     * {@code ArithmeticException} is thrown.
     *
     * @return this {@code BigInteger} converted to a {@code short}.
     * @throws ArithmeticException if the value of {@code this} will
     * not exactly fit in a {@code short}.
     * @see BigInteger#shortValue
     * @since  1.8
     */
    public short shortValueExact() {
        if (mag.length <= 1 && bitLength() <= 31) {
            int value = intValue();
            if (value >= Short.MIN_VALUE && value <= Short.MAX_VALUE)
                return shortValue();
        }
        throw new ArithmeticException();
    }

    /**
     * Converts this {@code BigInteger} to a {@code byte}, checking
     * for lost information.  If the value of this {@code BigInteger}
     * is out of the range of the {@code byte} type, then an
     * {@code ArithmeticException} is thrown.
     *
     * @return this {@code BigInteger} converted to a {@code byte}.
     * @throws ArithmeticException if the value of {@code this} will
     * not exactly fit in a {@code byte}.
     * @see BigInteger#byteValue
     * @since  1.8
     */
    public byte byteValueExact() {
        if (mag.length <= 1 && bitLength() <= 31) {
            int value = intValue();
            if (value >= Byte.MIN_VALUE && value <= Byte.MAX_VALUE)
                return byteValue();
        }
        throw new ArithmeticException();
    }
}


/*
 * Copyright (c) 1996, 2023, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the  exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.io;

import java.lang.invoke.MethodHandle;
import java.lang.invoke.MethodHandles;
import java.lang.invoke.MethodType;
import java.lang.reflect.Constructor;
import java.lang.reflect.Field;
import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.RecordComponent;
import java.lang.reflect.UndeclaredThrowableException;
import java.lang.reflect.Member;
import java.lang.reflect.Method;
import java.lang.reflect.Modifier;
import java.lang.reflect.Proxy;
import java.security.AccessControlContext;
import java.security.AccessController;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.security.PermissionCollection;
import java.security.Permissions;
import java.security.PrivilegedAction;
import java.security.PrivilegedActionException;
import java.security.PrivilegedExceptionAction;
import java.security.ProtectionDomain;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.concurrent.ConcurrentHashMap;
import jdk.internal.misc.Unsafe;
import jdk.internal.reflect.CallerSensitive;
import jdk.internal.reflect.Reflection;
import jdk.internal.reflect.ReflectionFactory;
import jdk.internal.access.SharedSecrets;
import jdk.internal.access.JavaSecurityAccess;
import jdk.internal.util.ByteArray;
import sun.reflect.misc.ReflectUtil;

/**
 * Serialization's descriptor for classes.  It contains the name and
 * serialVersionUID of the class.  The ObjectStreamClass for a specific class
 * loaded in this Java VM can be found/created using the lookup method.
 *
 * <p>The algorithm to compute the SerialVersionUID is described in
 * <a href=>
 *    <cite>Java Object Serialization Specification,</cite> Section 4.6, </a>.
 *
 * @spec serialization/index.html Java Object Serialization Specification
 * @author      Mike Warres
 * @author      Roger Riggs
 * @see ObjectStreamField
 * @see <a href=>
 *      <cite>Java Object Serialization Specification,</cite> Section 4, </a>
 * @since   1.1
 */
public final class ObjectStreamClass implements Serializable {

    /** serialPersistentFields value indicating no serializable fields */
    public static final ObjectStreamField[] NO_FIELDS =
        new ObjectStreamField[0];

    @java.io.Serial
    private static final long serialVersionUID = -6120832682080437368L;
    /**
     * {@code ObjectStreamClass} has no fields for default serialization.
     */
    @java.io.Serial
    private static final ObjectStreamField[] serialPersistentFields =
        NO_FIELDS;

    /** reflection factory for obtaining serialization constructors */
    @SuppressWarnings()
    private static final ReflectionFactory reflFactory =
        AccessController.doPrivileged(
            new ReflectionFactory.GetReflectionFactoryAction());

    private static class Caches {
        /** cache mapping local classes -> descriptors */
        static final ClassCache<ObjectStreamClass> localDescs =
            new ClassCache<>() {
                @Override
                protected ObjectStreamClass computeValue(Class<?> type) {
                    return new ObjectStreamClass(type);
                }
            };

        /** cache mapping field group/local desc pairs -> field reflectors */
        static final ClassCache<Map<FieldReflectorKey, FieldReflector>> reflectors =
            new ClassCache<>() {
                @Override
                protected Map<FieldReflectorKey, FieldReflector> computeValue(Class<?> type) {
                    return new ConcurrentHashMap<>();
                }
            };
    }

    /** class associated with this descriptor (if any) */
    private Class<?> cl;
    /** name of class represented by this descriptor */
    private String name;
    /** serialVersionUID of represented class (null if not computed yet) */
    private volatile Long suid;

    /** true if represents dynamic proxy class */
    private boolean isProxy;
    /** true if represents enum type */
    private boolean isEnum;
    /** true if represents record type */
    private boolean isRecord;
    /** true if represented class implements Serializable */
    private boolean serializable;
    /** true if represented class implements Externalizable */
    private boolean externalizable;
    /** true if desc has data written by class-defined writeObject method */
    private boolean hasWriteObjectData;
    /**
     * true if desc has externalizable data written in block data format; this
     * must be true by default to accommodate ObjectInputStream subclasses which
     * override readClassDescriptor() to return class descriptors obtained from
     * ObjectStreamClass.lookup() (see 4461737)
     */
    private boolean hasBlockExternalData = true;

    /**
     * Contains information about InvalidClassException instances to be thrown
     * when attempting operations on an invalid class. Note that instances of
     * this class are immutable and are potentially shared among
     * ObjectStreamClass instances.
     */
    private static class ExceptionInfo {
        private final String className;
        private final String message;

        ExceptionInfo(String cn, String msg) {
            className = cn;
            message = msg;
        }

        /**
         * Returns (does not throw) an InvalidClassException instance created
         * from the information in this object, suitable for being thrown by
         * the caller.
         */
        InvalidClassException newInvalidClassException() {
            return new InvalidClassException(className, message);
        }
    }

    /** exception (if any) thrown while attempting to resolve class */
    private ClassNotFoundException resolveEx;
    /** exception (if any) to throw if non-enum deserialization attempted */
    private ExceptionInfo deserializeEx;
    /** exception (if any) to throw if non-enum serialization attempted */
    private ExceptionInfo serializeEx;
    /** exception (if any) to throw if default serialization attempted */
    private ExceptionInfo defaultSerializeEx;

    /** serializable fields */
    private ObjectStreamField[] fields;
    /** aggregate marshalled size of primitive fields */
    private int primDataSize;
    /** number of non-primitive fields */
    private int numObjFields;
    /** reflector for setting/getting serializable field values */
    private FieldReflector fieldRefl;
    /** data layout of serialized objects described by this class desc */
    private volatile ClassDataSlot[] dataLayout;

    /** serialization-appropriate constructor, or null if none */
    private Constructor<?> cons;
    /** record canonical constructor (shared among OSCs for same class), or null */
    private MethodHandle canonicalCtr;
    /** cache of record deserialization constructors per unique set of stream fields
     * (shared among OSCs for same class), or null */
    private DeserializationConstructorsCache deserializationCtrs;
    /** session-cache of record deserialization constructor
     * (in de-serialized OSC only), or null */
    private MethodHandle deserializationCtr;
    /** protection domains that need to be checked when calling the constructor */
    private ProtectionDomain[] domains;

    /** class-defined writeObject method, or null if none */
    private Method writeObjectMethod;
    /** class-defined readObject method, or null if none */
    private Method readObjectMethod;
    /** class-defined readObjectNoData method, or null if none */
    private Method readObjectNoDataMethod;
    /** class-defined writeReplace method, or null if none */
    private Method writeReplaceMethod;
    /** class-defined readResolve method, or null if none */
    private Method readResolveMethod;

    /** local class descriptor for represented class (may point to self) */
    private ObjectStreamClass localDesc;
    /** superclass descriptor appearing in stream */
    private ObjectStreamClass superDesc;

    /** true if, and only if, the object has been correctly initialized */
    private boolean initialized;

    /**
     * Initializes native code.
     */
    private static native void initNative();
    static {
        initNative();
    }

    /**
     * Find the descriptor for a class that can be serialized.  Creates an
     * ObjectStreamClass instance if one does not exist yet for class. Null is
     * returned if the specified class does not implement java.io.Serializable
     * or java.io.Externalizable.
     *
     * @param   cl class for which to get the descriptor
     * @return  the class descriptor for the specified class
     */
    public static ObjectStreamClass lookup(Class<?> cl) {
        return lookup(cl, false);
    }

    /**
     * Returns the descriptor for any class, regardless of whether it
     * implements {@link Serializable}.
     *
     * @param        cl class for which to get the descriptor
     * @return       the class descriptor for the specified class
     * @since 1.6
     */
    public static ObjectStreamClass lookupAny(Class<?> cl) {
        return lookup(cl, true);
    }

    /**
     * Returns the name of the class described by this descriptor.
     * This method returns the name of the class in the format that
     * is used by the {@link Class#getName} method.
     *
     * @return a string representing the name of the class
     */
    public String getName() {
        return name;
    }

    /**
     * Return the serialVersionUID for this class.  The serialVersionUID
     * defines a set of classes all with the same name that have evolved from a
     * common root class and agree to be serialized and deserialized using a
     * common format.  NonSerializable classes have a serialVersionUID of 0L.
     *
     * @return  the SUID of the class described by this descriptor
     */
    @SuppressWarnings()
    public long getSerialVersionUID() {
        // REMIND: synchronize instead of relying on volatile?
        if (suid == null) {
            if (isRecord)
                return 0L;

            suid = AccessController.doPrivileged(
                new PrivilegedAction<Long>() {
                    public Long run() {
                        return computeDefaultSUID(cl);
                    }
                }
            );
        }
        return suid.longValue();
    }

    /**
     * Return the class in the local VM that this version is mapped to.  Null
     * is returned if there is no corresponding local class.
     *
     * @return  the {@code Class} instance that this descriptor represents
     */
    @SuppressWarnings()
    @CallerSensitive
    public Class<?> forClass() {
        if (cl == null) {
            return null;
        }
        requireInitialized();
        if (System.getSecurityManager() != null) {
            Class<?> caller = Reflection.getCallerClass();
            if (ReflectUtil.needsPackageAccessCheck(caller.getClassLoader(), cl.getClassLoader())) {
                ReflectUtil.checkPackageAccess(cl);
            }
        }
        return cl;
    }

    /**
     * Return an array of the fields of this serializable class.
     *
     * @return  an array containing an element for each persistent field of
     *          this class. Returns an array of length zero if there are no
     *          fields.
     * @since 1.2
     */
    public ObjectStreamField[] getFields() {
        return getFields(true);
    }

    /**
     * Get the field of this class by name.
     *
     * @param   name the name of the data field to look for
     * @return  The ObjectStreamField object of the named field or null if
     *          there is no such named field.
     */
    public ObjectStreamField getField(String name) {
        return getField(name, null);
    }

    /**
     * Return a string describing this ObjectStreamClass.
     */
    public String toString() {
        return name +  +
            getSerialVersionUID() + ;
    }

    /**
     * Looks up and returns class descriptor for given class, or null if class
     * is non-serializable and  is set to false.
     *
     * @param   cl class to look up
     * @param   all if true, return descriptors for all classes; if false, only
     *          return descriptors for serializable classes
     */
    static ObjectStreamClass lookup(Class<?> cl, boolean all) {
        if (!(all || Serializable.class.isAssignableFrom(cl))) {
            return null;
        }
        return Caches.localDescs.get(cl);
    }

    /**
     * Creates local class descriptor representing given class.
     */
    @SuppressWarnings()
    private ObjectStreamClass(final Class<?> cl) {
        this.cl = cl;
        name = cl.getName();
        isProxy = Proxy.isProxyClass(cl);
        isEnum = Enum.class.isAssignableFrom(cl);
        isRecord = cl.isRecord();
        serializable = Serializable.class.isAssignableFrom(cl);
        externalizable = Externalizable.class.isAssignableFrom(cl);

        Class<?> superCl = cl.getSuperclass();
        superDesc = (superCl != null) ? lookup(superCl, false) : null;
        localDesc = this;

        if (serializable) {
            AccessController.doPrivileged(new PrivilegedAction<>() {
                public Void run() {
                    if (isEnum) {
                        suid = 0L;
                        fields = NO_FIELDS;
                        return null;
                    }
                    if (cl.isArray()) {
                        fields = NO_FIELDS;
                        return null;
                    }

                    suid = getDeclaredSUID(cl);
                    try {
                        fields = getSerialFields(cl);
                        computeFieldOffsets();
                    } catch (InvalidClassException e) {
                        serializeEx = deserializeEx =
                            new ExceptionInfo(e.classname, e.getMessage());
                        fields = NO_FIELDS;
                    }

                    if (isRecord) {
                        canonicalCtr = canonicalRecordCtr(cl);
                        deserializationCtrs = new DeserializationConstructorsCache();
                    } else if (externalizable) {
                        cons = getExternalizableConstructor(cl);
                    } else {
                        cons = getSerializableConstructor(cl);
                        writeObjectMethod = getPrivateMethod(cl, ,
                            new Class<?>[] { ObjectOutputStream.class },
                            Void.TYPE);
                        readObjectMethod = getPrivateMethod(cl, ,
                            new Class<?>[] { ObjectInputStream.class },
                            Void.TYPE);
                        readObjectNoDataMethod = getPrivateMethod(
                            cl, , null, Void.TYPE);
                        hasWriteObjectData = (writeObjectMethod != null);
                    }
                    domains = getProtectionDomains(cons, cl);
                    writeReplaceMethod = getInheritableMethod(
                        cl, , null, Object.class);
                    readResolveMethod = getInheritableMethod(
                        cl, , null, Object.class);
                    return null;
                }
            });
        } else {
            suid = 0L;
            fields = NO_FIELDS;
        }

        try {
            fieldRefl = getReflector(fields, this);
        } catch (InvalidClassException ex) {
            // field mismatches impossible when matching local fields vs. self
            throw new InternalError(ex);
        }

        if (deserializeEx == null) {
            if (isEnum) {
                deserializeEx = new ExceptionInfo(name, );
            } else if (cons == null && !isRecord) {
                deserializeEx = new ExceptionInfo(name, );
            }
        }
        if (isRecord && canonicalCtr == null) {
            deserializeEx = new ExceptionInfo(name, );
        } else {
            for (int i = 0; i < fields.length; i++) {
                if (fields[i].getField() == null) {
                    defaultSerializeEx = new ExceptionInfo(
                        name, );
                }
            }
        }
        initialized = true;
    }

    /**
     * Creates blank class descriptor which should be initialized via a
     * subsequent call to initProxy(), initNonProxy() or readNonProxy().
     */
    ObjectStreamClass() {
    }

    /**
     * Creates a PermissionDomain that grants no permission.
     */
    private ProtectionDomain noPermissionsDomain() {
        PermissionCollection perms = new Permissions();
        perms.setReadOnly();
        return new ProtectionDomain(null, perms);
    }

    /**
     * Aggregate the ProtectionDomains of all the classes that separate
     * a concrete class {@code cl} from its ancestor's class declaring
     * a constructor {@code cons}.
     *
     * If {@code cl} is defined by the boot loader, or the constructor
     * {@code cons} is declared by {@code cl}, or if there is no security
     * manager, then this method does nothing and {@code null} is returned.
     *
     * @param cons A constructor declared by {@code cl} or one of its
     *             ancestors.
     * @param cl A concrete class, which is either the class declaring
     *           the constructor {@code cons}, or a serializable subclass
     *           of that class.
     * @return An array of ProtectionDomain representing the set of
     *         ProtectionDomain that separate the concrete class {@code cl}
     *         from its ancestor's declaring {@code cons}, or {@code null}.
     */
    @SuppressWarnings()
    private ProtectionDomain[] getProtectionDomains(Constructor<?> cons,
                                                    Class<?> cl) {
        ProtectionDomain[] domains = null;
        if (cons != null && cl.getClassLoader() != null
                && System.getSecurityManager() != null) {
            Class<?> cls = cl;
            Class<?> fnscl = cons.getDeclaringClass();
            Set<ProtectionDomain> pds = null;
            while (cls != fnscl) {
                ProtectionDomain pd = cls.getProtectionDomain();
                if (pd != null) {
                    if (pds == null) pds = new HashSet<>();
                    pds.add(pd);
                }
                cls = cls.getSuperclass();
                if (cls == null) {
                    // that's not supposed to happen
                    // make a ProtectionDomain with no permission.
                    // should we throw instead?
                    if (pds == null) pds = new HashSet<>();
                    else pds.clear();
                    pds.add(noPermissionsDomain());
                    break;
                }
            }
            if (pds != null) {
                domains = pds.toArray(new ProtectionDomain[0]);
            }
        }
        return domains;
    }

    /**
     * Initializes class descriptor representing a proxy class.
     */
    void initProxy(Class<?> cl,
                   ClassNotFoundException resolveEx,
                   ObjectStreamClass superDesc)
        throws InvalidClassException
    {
        ObjectStreamClass osc = null;
        if (cl != null) {
            osc = lookup(cl, true);
            if (!osc.isProxy) {
                throw new InvalidClassException(
                    );
            }
        }
        this.cl = cl;
        this.resolveEx = resolveEx;
        this.superDesc = superDesc;
        isProxy = true;
        serializable = true;
        suid = 0L;
        fields = NO_FIELDS;
        if (osc != null) {
            localDesc = osc;
            name = localDesc.name;
            externalizable = localDesc.externalizable;
            writeReplaceMethod = localDesc.writeReplaceMethod;
            readResolveMethod = localDesc.readResolveMethod;
            deserializeEx = localDesc.deserializeEx;
            domains = localDesc.domains;
            cons = localDesc.cons;
        }
        fieldRefl = getReflector(fields, localDesc);
        initialized = true;
    }

    /**
     * Initializes class descriptor representing a non-proxy class.
     */
    void initNonProxy(ObjectStreamClass model,
                      Class<?> cl,
                      ClassNotFoundException resolveEx,
                      ObjectStreamClass superDesc)
        throws InvalidClassException
    {
        long suid = model.getSerialVersionUID();
        ObjectStreamClass osc = null;
        if (cl != null) {
            osc = lookup(cl, true);
            if (osc.isProxy) {
                throw new InvalidClassException(
                        );
            }
            if (model.isEnum != osc.isEnum) {
                throw new InvalidClassException(model.isEnum ?
                         :
                        );
            }

            if (model.serializable == osc.serializable &&
                    !cl.isArray() && !cl.isRecord() &&
                    suid != osc.getSerialVersionUID()) {
                throw new InvalidClassException(osc.name,
                         +
                                 + suid +
                                 +
                                osc.getSerialVersionUID());
            }

            if (!classNamesEqual(model.name, osc.name)) {
                throw new InvalidClassException(osc.name,
                         +
                                );
            }

            if (!model.isEnum) {
                if ((model.serializable == osc.serializable) &&
                        (model.externalizable != osc.externalizable)) {
                    throw new InvalidClassException(osc.name,
                            );
                }

                if ((model.serializable != osc.serializable) ||
                        (model.externalizable != osc.externalizable) ||
                        !(model.serializable || model.externalizable)) {
                    deserializeEx = new ExceptionInfo(
                            osc.name, );
                }
            }
        }

        this.cl = cl;
        this.resolveEx = resolveEx;
        this.superDesc = superDesc;
        name = model.name;
        this.suid = suid;
        isProxy = false;
        isEnum = model.isEnum;
        serializable = model.serializable;
        externalizable = model.externalizable;
        hasBlockExternalData = model.hasBlockExternalData;
        hasWriteObjectData = model.hasWriteObjectData;
        fields = model.fields;
        primDataSize = model.primDataSize;
        numObjFields = model.numObjFields;

        if (osc != null) {
            localDesc = osc;
            isRecord = localDesc.isRecord;
            // canonical record constructor is shared
            canonicalCtr = localDesc.canonicalCtr;
            // cache of deserialization constructors is shared
            deserializationCtrs = localDesc.deserializationCtrs;
            writeObjectMethod = localDesc.writeObjectMethod;
            readObjectMethod = localDesc.readObjectMethod;
            readObjectNoDataMethod = localDesc.readObjectNoDataMethod;
            writeReplaceMethod = localDesc.writeReplaceMethod;
            readResolveMethod = localDesc.readResolveMethod;
            if (deserializeEx == null) {
                deserializeEx = localDesc.deserializeEx;
            }
            domains = localDesc.domains;
            assert cl.isRecord() ? localDesc.cons == null : true;
            cons = localDesc.cons;
        }

        fieldRefl = getReflector(fields, localDesc);
        // reassign to matched fields so as to reflect local unshared settings
        fields = fieldRefl.getFields();

        initialized = true;
    }

    /**
     * Reads non-proxy class descriptor information from given input stream.
     * The resulting class descriptor is not fully functional; it can only be
     * used as input to the ObjectInputStream.resolveClass() and
     * ObjectStreamClass.initNonProxy() methods.
     */
    void readNonProxy(ObjectInputStream in)
        throws IOException, ClassNotFoundException
    {
        name = in.readUTF();
        suid = in.readLong();
        isProxy = false;

        byte flags = in.readByte();
        hasWriteObjectData =
            ((flags & ObjectStreamConstants.SC_WRITE_METHOD) != 0);
        hasBlockExternalData =
            ((flags & ObjectStreamConstants.SC_BLOCK_DATA) != 0);
        externalizable =
            ((flags & ObjectStreamConstants.SC_EXTERNALIZABLE) != 0);
        boolean sflag =
            ((flags & ObjectStreamConstants.SC_SERIALIZABLE) != 0);
        if (externalizable && sflag) {
            throw new InvalidClassException(
                name, );
        }
        serializable = externalizable || sflag;
        isEnum = ((flags & ObjectStreamConstants.SC_ENUM) != 0);
        if (isEnum && suid.longValue() != 0L) {
            throw new InvalidClassException(name,
                 + suid);
        }

        int numFields = in.readShort();
        if (isEnum && numFields != 0) {
            throw new InvalidClassException(name,
                 + numFields);
        }
        fields = (numFields > 0) ?
            new ObjectStreamField[numFields] : NO_FIELDS;
        for (int i = 0; i < numFields; i++) {
            char tcode = (char) in.readByte();
            String fname = in.readUTF();
            String signature = ((tcode == 'L') || (tcode == '[')) ?
                in.readTypeString() : String.valueOf(tcode);
            try {
                fields[i] = new ObjectStreamField(fname, signature, false);
            } catch (RuntimeException e) {
                throw new InvalidClassException(name,
                                                 +
                                                fname, e);
            }
        }
        computeFieldOffsets();
    }

    /**
     * Writes non-proxy class descriptor information to given output stream.
     */
    void writeNonProxy(ObjectOutputStream out) throws IOException {
        out.writeUTF(name);
        out.writeLong(getSerialVersionUID());

        byte flags = 0;
        if (externalizable) {
            flags |= ObjectStreamConstants.SC_EXTERNALIZABLE;
            int protocol = out.getProtocolVersion();
            if (protocol != ObjectStreamConstants.PROTOCOL_VERSION_1) {
                flags |= ObjectStreamConstants.SC_BLOCK_DATA;
            }
        } else if (serializable) {
            flags |= ObjectStreamConstants.SC_SERIALIZABLE;
        }
        if (hasWriteObjectData) {
            flags |= ObjectStreamConstants.SC_WRITE_METHOD;
        }
        if (isEnum) {
            flags |= ObjectStreamConstants.SC_ENUM;
        }
        out.writeByte(flags);

        out.writeShort(fields.length);
        for (int i = 0; i < fields.length; i++) {
            ObjectStreamField f = fields[i];
            out.writeByte(f.getTypeCode());
            out.writeUTF(f.getName());
            if (!f.isPrimitive()) {
                out.writeTypeString(f.getTypeString());
            }
        }
    }

    /**
     * Returns ClassNotFoundException (if any) thrown while attempting to
     * resolve local class corresponding to this class descriptor.
     */
    ClassNotFoundException getResolveException() {
        return resolveEx;
    }

    /**
     * Throws InternalError if not initialized.
     */
    private final void requireInitialized() {
        if (!initialized)
            throw new InternalError();
    }

    /**
     * Throws InvalidClassException if not initialized.
     * To be called in cases where an uninitialized class descriptor indicates
     * a problem in the serialization stream.
     */
    final void checkInitialized() throws InvalidClassException {
        if (!initialized) {
            throw new InvalidClassException();
        }
    }

    /**
     * Throws an InvalidClassException if object instances referencing this
     * class descriptor should not be allowed to deserialize.  This method does
     * not apply to deserialization of enum constants.
     */
    void checkDeserialize() throws InvalidClassException {
        requireInitialized();
        if (deserializeEx != null) {
            throw deserializeEx.newInvalidClassException();
        }
    }

    /**
     * Throws an InvalidClassException if objects whose class is represented by
     * this descriptor should not be allowed to serialize.  This method does
     * not apply to serialization of enum constants.
     */
    void checkSerialize() throws InvalidClassException {
        requireInitialized();
        if (serializeEx != null) {
            throw serializeEx.newInvalidClassException();
        }
    }

    /**
     * Throws an InvalidClassException if objects whose class is represented by
     * this descriptor should not be permitted to use default serialization
     * (e.g., if the class declares serializable fields that do not correspond
     * to actual fields, and hence must use the GetField API).  This method
     * does not apply to deserialization of enum constants.
     */
    void checkDefaultSerialize() throws InvalidClassException {
        requireInitialized();
        if (defaultSerializeEx != null) {
            throw defaultSerializeEx.newInvalidClassException();
        }
    }

    /**
     * Returns superclass descriptor.  Note that on the receiving side, the
     * superclass descriptor may be bound to a class that is not a superclass
     * of the subclass descriptor's bound class.
     */
    ObjectStreamClass getSuperDesc() {
        requireInitialized();
        return superDesc;
    }

    /**
     * Returns the  class descriptor for the class associated with this
     * class descriptor (i.e., the result of
     * ObjectStreamClass.lookup(this.forClass())) or null if there is no class
     * associated with this descriptor.
     */
    ObjectStreamClass getLocalDesc() {
        requireInitialized();
        return localDesc;
    }

    /**
     * Returns arrays of ObjectStreamFields representing the serializable
     * fields of the represented class.  If copy is true, a clone of this class
     * descriptor's field array is returned, otherwise the array itself is
     * returned.
     */
    ObjectStreamField[] getFields(boolean copy) {
        return copy ? fields.clone() : fields;
    }

    /**
     * Looks up a serializable field of the represented class by name and type.
     * A specified type of null matches all types, Object.class matches all
     * non-primitive types, and any other non-null type matches assignable
     * types only.  Returns matching field, or null if no match found.
     */
    ObjectStreamField getField(String name, Class<?> type) {
        for (int i = 0; i < fields.length; i++) {
            ObjectStreamField f = fields[i];
            if (f.getName().equals(name)) {
                if (type == null ||
                    (type == Object.class && !f.isPrimitive()))
                {
                    return f;
                }
                Class<?> ftype = f.getType();
                if (ftype != null && type.isAssignableFrom(ftype)) {
                    return f;
                }
            }
        }
        return null;
    }

    /**
     * Returns true if class descriptor represents a dynamic proxy class, false
     * otherwise.
     */
    boolean isProxy() {
        requireInitialized();
        return isProxy;
    }

    /**
     * Returns true if class descriptor represents an enum type, false
     * otherwise.
     */
    boolean isEnum() {
        requireInitialized();
        return isEnum;
    }

    /**
     * Returns true if class descriptor represents a record type, false
     * otherwise.
     */
    boolean isRecord() {
        requireInitialized();
        return isRecord;
    }

    /**
     * Returns true if represented class implements Externalizable, false
     * otherwise.
     */
    boolean isExternalizable() {
        requireInitialized();
        return externalizable;
    }

    /**
     * Returns true if represented class implements Serializable, false
     * otherwise.
     */
    boolean isSerializable() {
        requireInitialized();
        return serializable;
    }

    /**
     * Returns true if class descriptor represents externalizable class that
     * has written its data in 1.2 (block data) format, false otherwise.
     */
    boolean hasBlockExternalData() {
        requireInitialized();
        return hasBlockExternalData;
    }

    /**
     * Returns true if class descriptor represents serializable (but not
     * externalizable) class which has written its data via a custom
     * writeObject() method, false otherwise.
     */
    boolean hasWriteObjectData() {
        requireInitialized();
        return hasWriteObjectData;
    }

    /**
     * Returns true if represented class is serializable/externalizable and can
     * be instantiated by the serialization runtime--i.e., if it is
     * externalizable and defines a public no-arg constructor, or if it is
     * non-externalizable and its first non-serializable superclass defines an
     * accessible no-arg constructor.  Otherwise, returns false.
     */
    boolean isInstantiable() {
        requireInitialized();
        return (cons != null);
    }

    /**
     * Returns true if represented class is serializable (but not
     * externalizable) and defines a conformant writeObject method.  Otherwise,
     * returns false.
     */
    boolean hasWriteObjectMethod() {
        requireInitialized();
        return (writeObjectMethod != null);
    }

    /**
     * Returns true if represented class is serializable (but not
     * externalizable) and defines a conformant readObject method.  Otherwise,
     * returns false.
     */
    boolean hasReadObjectMethod() {
        requireInitialized();
        return (readObjectMethod != null);
    }

    /**
     * Returns true if represented class is serializable (but not
     * externalizable) and defines a conformant readObjectNoData method.
     * Otherwise, returns false.
     */
    boolean hasReadObjectNoDataMethod() {
        requireInitialized();
        return (readObjectNoDataMethod != null);
    }

    /**
     * Returns true if represented class is serializable or externalizable and
     * defines a conformant writeReplace method.  Otherwise, returns false.
     */
    boolean hasWriteReplaceMethod() {
        requireInitialized();
        return (writeReplaceMethod != null);
    }

    /**
     * Returns true if represented class is serializable or externalizable and
     * defines a conformant readResolve method.  Otherwise, returns false.
     */
    boolean hasReadResolveMethod() {
        requireInitialized();
        return (readResolveMethod != null);
    }

    /**
     * Creates a new instance of the represented class.  If the class is
     * externalizable, invokes its public no-arg constructor; otherwise, if the
     * class is serializable, invokes the no-arg constructor of the first
     * non-serializable superclass.  Throws UnsupportedOperationException if
     * this class descriptor is not associated with a class, if the associated
     * class is non-serializable or if the appropriate no-arg constructor is
     * inaccessible/unavailable.
     */
    @SuppressWarnings()
    Object newInstance()
        throws InstantiationException, InvocationTargetException,
               UnsupportedOperationException
    {
        requireInitialized();
        if (cons != null) {
            try {
                if (domains == null || domains.length == 0) {
                    return cons.newInstance();
                } else {
                    JavaSecurityAccess jsa = SharedSecrets.getJavaSecurityAccess();
                    PrivilegedAction<?> pea = () -> {
                        try {
                            return cons.newInstance();
                        } catch (InstantiationException
                                 | InvocationTargetException
                                 | IllegalAccessException x) {
                            throw new UndeclaredThrowableException(x);
                        }
                    }; // Can't use PrivilegedExceptionAction with jsa
                    try {
                        return jsa.doIntersectionPrivilege(pea,
                                   AccessController.getContext(),
                                   new AccessControlContext(domains));
                    } catch (UndeclaredThrowableException x) {
                        Throwable cause = x.getCause();
                        if (cause instanceof InstantiationException ie)
                            throw ie;
                        if (cause instanceof InvocationTargetException ite)
                            throw ite;
                        if (cause instanceof IllegalAccessException iae)
                            throw iae;
                        // not supposed to happen
                        throw x;
                    }
                }
            } catch (IllegalAccessException ex) {
                // should not occur, as access checks have been suppressed
                throw new InternalError(ex);
            } catch (InvocationTargetException ex) {
                Throwable cause = ex.getCause();
                if (cause instanceof Error err)
                    throw err;
                else
                    throw ex;
            } catch (InstantiationError err) {
                var ex = new InstantiationException();
                ex.initCause(err);
                throw ex;
            }
        } else {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Invokes the writeObject method of the represented serializable class.
     * Throws UnsupportedOperationException if this class descriptor is not
     * associated with a class, or if the class is externalizable,
     * non-serializable or does not define writeObject.
     */
    void invokeWriteObject(Object obj, ObjectOutputStream out)
        throws IOException, UnsupportedOperationException
    {
        requireInitialized();
        if (writeObjectMethod != null) {
            try {
                writeObjectMethod.invoke(obj, new Object[]{ out });
            } catch (InvocationTargetException ex) {
                Throwable th = ex.getCause();
                if (th instanceof IOException) {
                    throw (IOException) th;
                } else {
                    throwMiscException(th);
                }
            } catch (IllegalAccessException ex) {
                // should not occur, as access checks have been suppressed
                throw new InternalError(ex);
            }
        } else {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Invokes the readObject method of the represented serializable class.
     * Throws UnsupportedOperationException if this class descriptor is not
     * associated with a class, or if the class is externalizable,
     * non-serializable or does not define readObject.
     */
    void invokeReadObject(Object obj, ObjectInputStream in)
        throws ClassNotFoundException, IOException,
               UnsupportedOperationException
    {
        requireInitialized();
        if (readObjectMethod != null) {
            try {
                readObjectMethod.invoke(obj, new Object[]{ in });
            } catch (InvocationTargetException ex) {
                Throwable th = ex.getCause();
                if (th instanceof ClassNotFoundException) {
                    throw (ClassNotFoundException) th;
                } else if (th instanceof IOException) {
                    throw (IOException) th;
                } else {
                    throwMiscException(th);
                }
            } catch (IllegalAccessException ex) {
                // should not occur, as access checks have been suppressed
                throw new InternalError(ex);
            }
        } else {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Invokes the readObjectNoData method of the represented serializable
     * class.  Throws UnsupportedOperationException if this class descriptor is
     * not associated with a class, or if the class is externalizable,
     * non-serializable or does not define readObjectNoData.
     */
    void invokeReadObjectNoData(Object obj)
        throws IOException, UnsupportedOperationException
    {
        requireInitialized();
        if (readObjectNoDataMethod != null) {
            try {
                readObjectNoDataMethod.invoke(obj, (Object[]) null);
            } catch (InvocationTargetException ex) {
                Throwable th = ex.getCause();
                if (th instanceof ObjectStreamException) {
                    throw (ObjectStreamException) th;
                } else {
                    throwMiscException(th);
                }
            } catch (IllegalAccessException ex) {
                // should not occur, as access checks have been suppressed
                throw new InternalError(ex);
            }
        } else {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Invokes the writeReplace method of the represented serializable class and
     * returns the result.  Throws UnsupportedOperationException if this class
     * descriptor is not associated with a class, or if the class is
     * non-serializable or does not define writeReplace.
     */
    Object invokeWriteReplace(Object obj)
        throws IOException, UnsupportedOperationException
    {
        requireInitialized();
        if (writeReplaceMethod != null) {
            try {
                return writeReplaceMethod.invoke(obj, (Object[]) null);
            } catch (InvocationTargetException ex) {
                Throwable th = ex.getCause();
                if (th instanceof ObjectStreamException) {
                    throw (ObjectStreamException) th;
                } else {
                    throwMiscException(th);
                    throw new InternalError(th);  // never reached
                }
            } catch (IllegalAccessException ex) {
                // should not occur, as access checks have been suppressed
                throw new InternalError(ex);
            }
        } else {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Invokes the readResolve method of the represented serializable class and
     * returns the result.  Throws UnsupportedOperationException if this class
     * descriptor is not associated with a class, or if the class is
     * non-serializable or does not define readResolve.
     */
    Object invokeReadResolve(Object obj)
        throws IOException, UnsupportedOperationException
    {
        requireInitialized();
        if (readResolveMethod != null) {
            try {
                return readResolveMethod.invoke(obj, (Object[]) null);
            } catch (InvocationTargetException ex) {
                Throwable th = ex.getCause();
                if (th instanceof ObjectStreamException) {
                    throw (ObjectStreamException) th;
                } else {
                    throwMiscException(th);
                    throw new InternalError(th);  // never reached
                }
            } catch (IllegalAccessException ex) {
                // should not occur, as access checks have been suppressed
                throw new InternalError(ex);
            }
        } else {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Class representing the portion of an object's serialized form allotted
     * to data described by a given class descriptor.  If  is false,
     * the object's serialized form does not contain data associated with the
     * class descriptor.
     */
    static class ClassDataSlot {

        /** class descriptor  this slot */
        final ObjectStreamClass desc;
        /** true if serialized form includes data for this slot's descriptor */
        final boolean hasData;

        ClassDataSlot(ObjectStreamClass desc, boolean hasData) {
            this.desc = desc;
            this.hasData = hasData;
        }
    }

    /**
     * Returns array of ClassDataSlot instances representing the data layout
     * (including superclass data) for serialized objects described by this
     * class descriptor.  ClassDataSlots are ordered by inheritance with those
     * containing  superclasses appearing first.  The final
     * ClassDataSlot contains a reference to this descriptor.
     */
    ClassDataSlot[] getClassDataLayout() throws InvalidClassException {
        // REMIND: synchronize instead of relying on volatile?
        if (dataLayout == null) {
            dataLayout = getClassDataLayout0();
        }
        return dataLayout;
    }

    private ClassDataSlot[] getClassDataLayout0()
        throws InvalidClassException
    {
        ArrayList<ClassDataSlot> slots = new ArrayList<>();
        Class<?> start = cl, end = cl;

        // locate closest non-serializable superclass
        while (end != null && Serializable.class.isAssignableFrom(end)) {
            end = end.getSuperclass();
        }

        HashSet<String> oscNames = new HashSet<>(3);

        for (ObjectStreamClass d = this; d != null; d = d.superDesc) {
            if (oscNames.contains(d.name)) {
                throw new InvalidClassException();
            } else {
                oscNames.add(d.name);
            }

            // search up inheritance hierarchy for class with matching name
            String searchName = (d.cl != null) ? d.cl.getName() : d.name;
            Class<?> match = null;
            for (Class<?> c = start; c != end; c = c.getSuperclass()) {
                if (searchName.equals(c.getName())) {
                    match = c;
                    break;
                }
            }

            // add  slot for each unmatched class below match
            if (match != null) {
                for (Class<?> c = start; c != match; c = c.getSuperclass()) {
                    slots.add(new ClassDataSlot(
                        ObjectStreamClass.lookup(c, true), false));
                }
                start = match.getSuperclass();
            }

            // record descriptor/class pairing
            slots.add(new ClassDataSlot(d.getVariantFor(match), true));
        }

        // add  slot for any leftover unmatched classes
        for (Class<?> c = start; c != end; c = c.getSuperclass()) {
            slots.add(new ClassDataSlot(
                ObjectStreamClass.lookup(c, true), false));
        }

        // order slots from superclass -> subclass
        Collections.reverse(slots);
        return slots.toArray(new ClassDataSlot[slots.size()]);
    }

    /**
     * Returns aggregate size (in bytes) of marshalled primitive field values
     * for represented class.
     */
    int getPrimDataSize() {
        return primDataSize;
    }

    /**
     * Returns number of non-primitive serializable fields of represented
     * class.
     */
    int getNumObjFields() {
        return numObjFields;
    }

    /**
     * Fetches the serializable primitive field values of object obj and
     * marshals them into byte array buf starting at offset 0.  It is the
     * responsibility of the caller to ensure that obj is of the proper type if
     * non-null.
     */
    void getPrimFieldValues(Object obj, byte[] buf) {
        fieldRefl.getPrimFieldValues(obj, buf);
    }

    /**
     * Sets the serializable primitive fields of object obj using values
     * unmarshalled from byte array buf starting at offset 0.  It is the
     * responsibility of the caller to ensure that obj is of the proper type if
     * non-null.
     */
    void setPrimFieldValues(Object obj, byte[] buf) {
        fieldRefl.setPrimFieldValues(obj, buf);
    }

    /**
     * Fetches the serializable object field values of object obj and stores
     * them in array vals starting at offset 0.  It is the responsibility of
     * the caller to ensure that obj is of the proper type if non-null.
     */
    void getObjFieldValues(Object obj, Object[] vals) {
        fieldRefl.getObjFieldValues(obj, vals);
    }

    /**
     * Checks that the given values, from array vals starting at offset 0,
     * are assignable to the given serializable object fields.
     * @throws ClassCastException if any value is not assignable
     */
    void checkObjFieldValueTypes(Object obj, Object[] vals) {
        fieldRefl.checkObjectFieldValueTypes(obj, vals);
    }

    /**
     * Sets the serializable object fields of object obj using values from
     * array vals starting at offset 0.  It is the responsibility of the caller
     * to ensure that obj is of the proper type if non-null.
     */
    void setObjFieldValues(Object obj, Object[] vals) {
        fieldRefl.setObjFieldValues(obj, vals);
    }

    /**
     * Calculates and sets serializable field offsets, as well as primitive
     * data size and object field count totals.  Throws InvalidClassException
     * if fields are illegally ordered.
     */
    private void computeFieldOffsets() throws InvalidClassException {
        primDataSize = 0;
        numObjFields = 0;
        int firstObjIndex = -1;

        for (int i = 0; i < fields.length; i++) {
            ObjectStreamField f = fields[i];
            switch (f.getTypeCode()) {
                case 'Z', 'B' -> f.setOffset(primDataSize++);
                case 'C', 'S' -> {
                    f.setOffset(primDataSize);
                    primDataSize += 2;
                }
                case 'I', 'F' -> {
                    f.setOffset(primDataSize);
                    primDataSize += 4;
                }
                case 'J', 'D' -> {
                    f.setOffset(primDataSize);
                    primDataSize += 8;
                }
                case '[', 'L' -> {
                    f.setOffset(numObjFields++);
                    if (firstObjIndex == -1) {
                        firstObjIndex = i;
                    }
                }
                default -> throw new InternalError();
            }
        }
        if (firstObjIndex != -1 &&
            firstObjIndex + numObjFields != fields.length)
        {
            throw new InvalidClassException(name, );
        }
    }

    /**
     * If given class is the same as the class associated with this class
     * descriptor, returns reference to this class descriptor.  Otherwise,
     * returns variant of this class descriptor bound to given class.
     */
    private ObjectStreamClass getVariantFor(Class<?> cl)
        throws InvalidClassException
    {
        if (this.cl == cl) {
            return this;
        }
        ObjectStreamClass desc = new ObjectStreamClass();
        if (isProxy) {
            desc.initProxy(cl, null, superDesc);
        } else {
            desc.initNonProxy(this, cl, null, superDesc);
        }
        return desc;
    }

    /**
     * Returns public no-arg constructor of given class, or null if none found.
     * Access checks are disabled on the returned constructor (if any), since
     * the defining class may still be non-public.
     */
    private static Constructor<?> getExternalizableConstructor(Class<?> cl) {
        try {
            Constructor<?> cons = cl.getDeclaredConstructor((Class<?>[]) null);
            cons.setAccessible(true);
            return ((cons.getModifiers() & Modifier.PUBLIC) != 0) ?
                cons : null;
        } catch (NoSuchMethodException ex) {
            return null;
        }
    }

    /**
     * Returns subclass-accessible no-arg constructor of first non-serializable
     * superclass, or null if none found.  Access checks are disabled on the
     * returned constructor (if any).
     */
    private static Constructor<?> getSerializableConstructor(Class<?> cl) {
        return reflFactory.newConstructorForSerialization(cl);
    }

    /**
     * Returns the canonical constructor for the given record class, or null if
     * the not found ( which should never happen for correctly generated record
     * classes ).
     */
    @SuppressWarnings()
    private static MethodHandle canonicalRecordCtr(Class<?> cls) {
        assert cls.isRecord() :  + cls;
        PrivilegedAction<MethodHandle> pa = () -> {
            Class<?>[] paramTypes = Arrays.stream(cls.getRecordComponents())
                                          .map(RecordComponent::getType)
                                          .toArray(Class<?>[]::new);
            try {
                Constructor<?> ctr = cls.getDeclaredConstructor(paramTypes);
                ctr.setAccessible(true);
                return MethodHandles.lookup().unreflectConstructor(ctr);
            } catch (IllegalAccessException | NoSuchMethodException e) {
                return null;
            }
        };
        return AccessController.doPrivileged(pa);
    }

    /**
     * Returns the canonical constructor, if the local class equivalent of this
     * stream class descriptor is a record class, otherwise null.
     */
    MethodHandle getRecordConstructor() {
        return canonicalCtr;
    }

    /**
     * Returns non-static, non-abstract method with given signature provided it
     * is defined by or accessible (via inheritance) by the given class, or
     * null if no match found.  Access checks are disabled on the returned
     * method (if any).
     */
    private static Method getInheritableMethod(Class<?> cl, String name,
                                               Class<?>[] argTypes,
                                               Class<?> returnType)
    {
        Method meth = null;
        Class<?> defCl = cl;
        while (defCl != null) {
            try {
                meth = defCl.getDeclaredMethod(name, argTypes);
                break;
            } catch (NoSuchMethodException ex) {
                defCl = defCl.getSuperclass();
            }
        }

        if ((meth == null) || (meth.getReturnType() != returnType)) {
            return null;
        }
        meth.setAccessible(true);
        int mods = meth.getModifiers();
        if ((mods & (Modifier.STATIC | Modifier.ABSTRACT)) != 0) {
            return null;
        } else if ((mods & (Modifier.PUBLIC | Modifier.PROTECTED)) != 0) {
            return meth;
        } else if ((mods & Modifier.PRIVATE) != 0) {
            return (cl == defCl) ? meth : null;
        } else {
            return packageEquals(cl, defCl) ? meth : null;
        }
    }

    /**
     * Returns non-static private method with given signature defined by given
     * class, or null if none found.  Access checks are disabled on the
     * returned method (if any).
     */
    private static Method getPrivateMethod(Class<?> cl, String name,
                                           Class<?>[] argTypes,
                                           Class<?> returnType)
    {
        try {
            Method meth = cl.getDeclaredMethod(name, argTypes);
            meth.setAccessible(true);
            int mods = meth.getModifiers();
            return ((meth.getReturnType() == returnType) &&
                    ((mods & Modifier.STATIC) == 0) &&
                    ((mods & Modifier.PRIVATE) != 0)) ? meth : null;
        } catch (NoSuchMethodException ex) {
            return null;
        }
    }

    /**
     * Returns true if classes are defined in the same runtime package, false
     * otherwise.
     */
    private static boolean packageEquals(Class<?> cl1, Class<?> cl2) {
        return cl1.getClassLoader() == cl2.getClassLoader() &&
                cl1.getPackageName() == cl2.getPackageName();
    }

    /**
     * Compares class names for equality, ignoring package names.  Returns true
     * if class names equal, false otherwise.
     */
    private static boolean classNamesEqual(String name1, String name2) {
        int idx1 = name1.lastIndexOf('.') + 1;
        int idx2 = name2.lastIndexOf('.') + 1;
        int len1 = name1.length() - idx1;
        int len2 = name2.length() - idx2;
        return len1 == len2 &&
                name1.regionMatches(idx1, name2, idx2, len1);
    }

    /**
     * Returns JVM type signature for given list of parameters and return type.
     */
    private static String getMethodSignature(Class<?>[] paramTypes,
                                             Class<?> retType)
    {
        StringBuilder sb = new StringBuilder();
        sb.append('(');
        for (int i = 0; i < paramTypes.length; i++) {
            sb.append(paramTypes[i].descriptorString());
        }
        sb.append(')');
        sb.append(retType.descriptorString());
        return sb.toString();
    }

    /**
     * Convenience method for throwing an exception that is either a
     * RuntimeException, Error, or of some unexpected type (in which case it is
     * wrapped inside an IOException).
     */
    private static void throwMiscException(Throwable th) throws IOException {
        if (th instanceof RuntimeException) {
            throw (RuntimeException) th;
        } else if (th instanceof Error) {
            throw (Error) th;
        } else {
            throw new IOException(, th);
        }
    }

    /**
     * Returns ObjectStreamField array describing the serializable fields of
     * the given class.  Serializable fields backed by an actual field of the
     * class are represented by ObjectStreamFields with corresponding non-null
     * Field objects.  Throws InvalidClassException if the (explicitly
     * declared) serializable fields are invalid.
     */
    private static ObjectStreamField[] getSerialFields(Class<?> cl)
        throws InvalidClassException
    {
        if (!Serializable.class.isAssignableFrom(cl))
            return NO_FIELDS;

        ObjectStreamField[] fields;
        if (cl.isRecord()) {
            fields = getDefaultSerialFields(cl);
            Arrays.sort(fields);
        } else if (!Externalizable.class.isAssignableFrom(cl) &&
            !Proxy.isProxyClass(cl) &&
                   !cl.isInterface()) {
            if ((fields = getDeclaredSerialFields(cl)) == null) {
                fields = getDefaultSerialFields(cl);
            }
            Arrays.sort(fields);
        } else {
            fields = NO_FIELDS;
        }
        return fields;
    }

    /**
     * Returns serializable fields of given class as defined explicitly by a
     *  field, or null if no appropriate
     *  field is defined.  Serializable fields backed
     * by an actual field of the class are represented by ObjectStreamFields
     * with corresponding non-null Field objects.  For compatibility with past
     * releases, a  field with a null value is
     * considered equivalent to not declaring .  Throws
     * InvalidClassException if the declared serializable fields are
     * invalid--e.g., if multiple fields share the same name.
     */
    private static ObjectStreamField[] getDeclaredSerialFields(Class<?> cl)
        throws InvalidClassException
    {
        ObjectStreamField[] serialPersistentFields = null;
        try {
            Field f = cl.getDeclaredField();
            int mask = Modifier.PRIVATE | Modifier.STATIC | Modifier.FINAL;
            if ((f.getModifiers() & mask) == mask) {
                f.setAccessible(true);
                serialPersistentFields = (ObjectStreamField[]) f.get(null);
            }
        } catch (Exception ex) {
        }
        if (serialPersistentFields == null) {
            return null;
        } else if (serialPersistentFields.length == 0) {
            return NO_FIELDS;
        }

        ObjectStreamField[] boundFields =
            new ObjectStreamField[serialPersistentFields.length];
        Set<String> fieldNames = HashSet.newHashSet(serialPersistentFields.length);

        for (int i = 0; i < serialPersistentFields.length; i++) {
            ObjectStreamField spf = serialPersistentFields[i];

            String fname = spf.getName();
            if (fieldNames.contains(fname)) {
                throw new InvalidClassException(
                     + fname);
            }
            fieldNames.add(fname);

            try {
                Field f = cl.getDeclaredField(fname);
                if ((f.getType() == spf.getType()) &&
                    ((f.getModifiers() & Modifier.STATIC) == 0))
                {
                    boundFields[i] =
                        new ObjectStreamField(f, spf.isUnshared(), true);
                }
            } catch (NoSuchFieldException ex) {
            }
            if (boundFields[i] == null) {
                boundFields[i] = new ObjectStreamField(
                    fname, spf.getType(), spf.isUnshared());
            }
        }
        return boundFields;
    }

    /**
     * Returns array of ObjectStreamFields corresponding to all non-static
     * non-transient fields declared by given class.  Each ObjectStreamField
     * contains a Field object for the field it represents.  If no default
     * serializable fields exist, NO_FIELDS is returned.
     */
    private static ObjectStreamField[] getDefaultSerialFields(Class<?> cl) {
        Field[] clFields = cl.getDeclaredFields();
        ArrayList<ObjectStreamField> list = new ArrayList<>();
        int mask = Modifier.STATIC | Modifier.TRANSIENT;

        for (int i = 0; i < clFields.length; i++) {
            if ((clFields[i].getModifiers() & mask) == 0) {
                list.add(new ObjectStreamField(clFields[i], false, true));
            }
        }
        int size = list.size();
        return (size == 0) ? NO_FIELDS :
            list.toArray(new ObjectStreamField[size]);
    }

    /**
     * Returns explicit serial version UID value declared by given class, or
     * null if none.
     */
    private static Long getDeclaredSUID(Class<?> cl) {
        try {
            Field f = cl.getDeclaredField();
            int mask = Modifier.STATIC | Modifier.FINAL;
            if ((f.getModifiers() & mask) == mask) {
                f.setAccessible(true);
                return f.getLong(null);
            }
        } catch (Exception ex) {
        }
        return null;
    }

    /**
     * Computes the default serial version UID value for the given class.
     */
    private static long computeDefaultSUID(Class<?> cl) {
        if (!Serializable.class.isAssignableFrom(cl) || Proxy.isProxyClass(cl))
        {
            return 0L;
        }

        try {
            ByteArrayOutputStream bout = new ByteArrayOutputStream();
            DataOutputStream dout = new DataOutputStream(bout);

            dout.writeUTF(cl.getName());

            int classMods = cl.getModifiers() &
                (Modifier.PUBLIC | Modifier.FINAL |
                 Modifier.INTERFACE | Modifier.ABSTRACT);

            /*
             * compensate for javac bug in which ABSTRACT bit was set for an
             * interface only if the interface declared methods
             */
            Method[] methods = cl.getDeclaredMethods();
            if ((classMods & Modifier.INTERFACE) != 0) {
                classMods = (methods.length > 0) ?
                    (classMods | Modifier.ABSTRACT) :
                    (classMods & ~Modifier.ABSTRACT);
            }
            dout.writeInt(classMods);

            if (!cl.isArray()) {
                /*
                 * compensate for change in 1.2FCS in which
                 * Class.getInterfaces() was modified to return Cloneable and
                 * Serializable for array classes.
                 */
                Class<?>[] interfaces = cl.getInterfaces();
                String[] ifaceNames = new String[interfaces.length];
                for (int i = 0; i < interfaces.length; i++) {
                    ifaceNames[i] = interfaces[i].getName();
                }
                Arrays.sort(ifaceNames);
                for (int i = 0; i < ifaceNames.length; i++) {
                    dout.writeUTF(ifaceNames[i]);
                }
            }

            Field[] fields = cl.getDeclaredFields();
            MemberSignature[] fieldSigs = new MemberSignature[fields.length];
            for (int i = 0; i < fields.length; i++) {
                fieldSigs[i] = new MemberSignature(fields[i]);
            }
            Arrays.sort(fieldSigs, new Comparator<>() {
                public int compare(MemberSignature ms1, MemberSignature ms2) {
                    return ms1.name.compareTo(ms2.name);
                }
            });
            for (int i = 0; i < fieldSigs.length; i++) {
                MemberSignature sig = fieldSigs[i];
                int mods = sig.member.getModifiers() &
                    (Modifier.PUBLIC | Modifier.PRIVATE | Modifier.PROTECTED |
                     Modifier.STATIC | Modifier.FINAL | Modifier.VOLATILE |
                     Modifier.TRANSIENT);
                if (((mods & Modifier.PRIVATE) == 0) ||
                    ((mods & (Modifier.STATIC | Modifier.TRANSIENT)) == 0))
                {
                    dout.writeUTF(sig.name);
                    dout.writeInt(mods);
                    dout.writeUTF(sig.signature);
                }
            }

            if (hasStaticInitializer(cl)) {
                dout.writeUTF();
                dout.writeInt(Modifier.STATIC);
                dout.writeUTF();
            }

            Constructor<?>[] cons = cl.getDeclaredConstructors();
            MemberSignature[] consSigs = new MemberSignature[cons.length];
            for (int i = 0; i < cons.length; i++) {
                consSigs[i] = new MemberSignature(cons[i]);
            }
            Arrays.sort(consSigs, new Comparator<>() {
                public int compare(MemberSignature ms1, MemberSignature ms2) {
                    return ms1.signature.compareTo(ms2.signature);
                }
            });
            for (int i = 0; i < consSigs.length; i++) {
                MemberSignature sig = consSigs[i];
                int mods = sig.member.getModifiers() &
                    (Modifier.PUBLIC | Modifier.PRIVATE | Modifier.PROTECTED |
                     Modifier.STATIC | Modifier.FINAL |
                     Modifier.SYNCHRONIZED | Modifier.NATIVE |
                     Modifier.ABSTRACT | Modifier.STRICT);
                if ((mods & Modifier.PRIVATE) == 0) {
                    dout.writeUTF();
                    dout.writeInt(mods);
                    dout.writeUTF(sig.signature.replace('/', '.'));
                }
            }

            MemberSignature[] methSigs = new MemberSignature[methods.length];
            for (int i = 0; i < methods.length; i++) {
                methSigs[i] = new MemberSignature(methods[i]);
            }
            Arrays.sort(methSigs, new Comparator<>() {
                public int compare(MemberSignature ms1, MemberSignature ms2) {
                    int comp = ms1.name.compareTo(ms2.name);
                    if (comp == 0) {
                        comp = ms1.signature.compareTo(ms2.signature);
                    }
                    return comp;
                }
            });
            for (int i = 0; i < methSigs.length; i++) {
                MemberSignature sig = methSigs[i];
                int mods = sig.member.getModifiers() &
                    (Modifier.PUBLIC | Modifier.PRIVATE | Modifier.PROTECTED |
                     Modifier.STATIC | Modifier.FINAL |
                     Modifier.SYNCHRONIZED | Modifier.NATIVE |
                     Modifier.ABSTRACT | Modifier.STRICT);
                if ((mods & Modifier.PRIVATE) == 0) {
                    dout.writeUTF(sig.name);
                    dout.writeInt(mods);
                    dout.writeUTF(sig.signature.replace('/', '.'));
                }
            }

            dout.flush();

            MessageDigest md = MessageDigest.getInstance();
            byte[] hashBytes = md.digest(bout.toByteArray());
            long hash = 0;
            for (int i = Math.min(hashBytes.length, 8) - 1; i >= 0; i--) {
                hash = (hash << 8) | (hashBytes[i] & 0xFF);
            }
            return hash;
        } catch (IOException ex) {
            throw new InternalError(ex);
        } catch (NoSuchAlgorithmException ex) {
            throw new SecurityException(ex.getMessage());
        }
    }

    /**
     * Returns true if the given class defines a static initializer method,
     * false otherwise.
     */
    private static native boolean hasStaticInitializer(Class<?> cl);

    /**
     * Class for computing and caching field/constructor/method signatures
     * during serialVersionUID calculation.
     */
    private static final class MemberSignature {

        public final Member member;
        public final String name;
        public final String signature;

        public MemberSignature(Field field) {
            member = field;
            name = field.getName();
            signature = field.getType().descriptorString();
        }

        public MemberSignature(Constructor<?> cons) {
            member = cons;
            name = cons.getName();
            signature = getMethodSignature(
                cons.getParameterTypes(), Void.TYPE);
        }

        public MemberSignature(Method meth) {
            member = meth;
            name = meth.getName();
            signature = getMethodSignature(
                meth.getParameterTypes(), meth.getReturnType());
        }
    }

    /**
     * Class for setting and retrieving serializable field values in batch.
     */
    // REMIND: dynamically generate these?
    private static final class FieldReflector {

        /** handle for performing unsafe operations */
        private static final Unsafe UNSAFE = Unsafe.getUnsafe();

        /** fields to operate on */
        private final ObjectStreamField[] fields;
        /** number of primitive fields */
        private final int numPrimFields;
        /** unsafe field keys for reading fields - may contain dupes */
        private final long[] readKeys;
        /** unsafe fields keys for writing fields - no dupes */
        private final long[] writeKeys;
        /** field data offsets */
        private final int[] offsets;
        /** field type codes */
        private final char[] typeCodes;
        /** field types */
        private final Class<?>[] types;

        /**
         * Constructs FieldReflector capable of setting/getting values from the
         * subset of fields whose ObjectStreamFields contain non-null
         * reflective Field objects.  ObjectStreamFields with null Fields are
         * treated as filler, for which get operations return default values
         * and set operations discard given values.
         */
        FieldReflector(ObjectStreamField[] fields) {
            this.fields = fields;
            int nfields = fields.length;
            readKeys = new long[nfields];
            writeKeys = new long[nfields];
            offsets = new int[nfields];
            typeCodes = new char[nfields];
            ArrayList<Class<?>> typeList = new ArrayList<>();
            Set<Long> usedKeys = new HashSet<>();


            for (int i = 0; i < nfields; i++) {
                ObjectStreamField f = fields[i];
                Field rf = f.getField();
                long key = (rf != null) ?
                    UNSAFE.objectFieldOffset(rf) : Unsafe.INVALID_FIELD_OFFSET;
                readKeys[i] = key;
                writeKeys[i] = usedKeys.add(key) ?
                    key : Unsafe.INVALID_FIELD_OFFSET;
                offsets[i] = f.getOffset();
                typeCodes[i] = f.getTypeCode();
                if (!f.isPrimitive()) {
                    typeList.add((rf != null) ? rf.getType() : null);
                }
            }

            types = typeList.toArray(new Class<?>[typeList.size()]);
            numPrimFields = nfields - types.length;
        }

        /**
         * Returns list of ObjectStreamFields representing fields operated on
         * by this reflector.  The shared/unshared values and Field objects
         * contained by ObjectStreamFields in the list reflect their bindings
         * to locally defined serializable fields.
         */
        ObjectStreamField[] getFields() {
            return fields;
        }

        /**
         * Fetches the serializable primitive field values of object obj and
         * marshals them into byte array buf starting at offset 0.  The caller
         * is responsible for ensuring that obj is of the proper type.
         */
        void getPrimFieldValues(Object obj, byte[] buf) {
            if (obj == null) {
                throw new NullPointerException();
            }
            /* assuming checkDefaultSerialize() has been called on the class
             * descriptor this FieldReflector was obtained from, no field keys
             * in array should be equal to Unsafe.INVALID_FIELD_OFFSET.
             */
            for (int i = 0; i < numPrimFields; i++) {
                long key = readKeys[i];
                int off = offsets[i];
                switch (typeCodes[i]) {
                    case 'Z' -> ByteArray.setBoolean(buf, off, UNSAFE.getBoolean(obj, key));
                    case 'B' -> buf[off] = UNSAFE.getByte(obj, key);
                    case 'C' -> ByteArray.setChar(buf, off, UNSAFE.getChar(obj, key));
                    case 'S' -> ByteArray.setShort(buf, off, UNSAFE.getShort(obj, key));
                    case 'I' -> ByteArray.setInt(buf, off, UNSAFE.getInt(obj, key));
                    case 'F' -> ByteArray.setFloat(buf, off, UNSAFE.getFloat(obj, key));
                    case 'J' -> ByteArray.setLong(buf, off, UNSAFE.getLong(obj, key));
                    case 'D' -> ByteArray.setDouble(buf, off, UNSAFE.getDouble(obj, key));
                    default  -> throw new InternalError();
                }
            }
        }

        /**
         * Sets the serializable primitive fields of object obj using values
         * unmarshalled from byte array buf starting at offset 0.  The caller
         * is responsible for ensuring that obj is of the proper type.
         */
        void setPrimFieldValues(Object obj, byte[] buf) {
            if (obj == null) {
                throw new NullPointerException();
            }
            for (int i = 0; i < numPrimFields; i++) {
                long key = writeKeys[i];
                if (key == Unsafe.INVALID_FIELD_OFFSET) {
                    continue;           // discard value
                }
                int off = offsets[i];
                switch (typeCodes[i]) {
                    case 'Z' -> UNSAFE.putBoolean(obj, key, ByteArray.getBoolean(buf, off));
                    case 'B' -> UNSAFE.putByte(obj, key, buf[off]);
                    case 'C' -> UNSAFE.putChar(obj, key, ByteArray.getChar(buf, off));
                    case 'S' -> UNSAFE.putShort(obj, key, ByteArray.getShort(buf, off));
                    case 'I' -> UNSAFE.putInt(obj, key, ByteArray.getInt(buf, off));
                    case 'F' -> UNSAFE.putFloat(obj, key, ByteArray.getFloat(buf, off));
                    case 'J' -> UNSAFE.putLong(obj, key, ByteArray.getLong(buf, off));
                    case 'D' -> UNSAFE.putDouble(obj, key, ByteArray.getDouble(buf, off));
                    default  -> throw new InternalError();
                }
            }
        }

        /**
         * Fetches the serializable object field values of object obj and
         * stores them in array vals starting at offset 0.  The caller is
         * responsible for ensuring that obj is of the proper type.
         */
        void getObjFieldValues(Object obj, Object[] vals) {
            if (obj == null) {
                throw new NullPointerException();
            }
            /* assuming checkDefaultSerialize() has been called on the class
             * descriptor this FieldReflector was obtained from, no field keys
             * in array should be equal to Unsafe.INVALID_FIELD_OFFSET.
             */
            for (int i = numPrimFields; i < fields.length; i++) {
                vals[offsets[i]] = switch (typeCodes[i]) {
                    case 'L', '[' -> UNSAFE.getReference(obj, readKeys[i]);
                    default       -> throw new InternalError();
                };
            }
        }

        /**
         * Checks that the given values, from array vals starting at offset 0,
         * are assignable to the given serializable object fields.
         * @throws ClassCastException if any value is not assignable
         */
        void checkObjectFieldValueTypes(Object obj, Object[] vals) {
            setObjFieldValues(obj, vals, true);
        }

        /**
         * Sets the serializable object fields of object obj using values from
         * array vals starting at offset 0.  The caller is responsible for
         * ensuring that obj is of the proper type; however, attempts to set a
         * field with a value of the wrong type will trigger an appropriate
         * ClassCastException.
         */
        void setObjFieldValues(Object obj, Object[] vals) {
            setObjFieldValues(obj, vals, false);
        }

        private void setObjFieldValues(Object obj, Object[] vals, boolean dryRun) {
            if (obj == null) {
                throw new NullPointerException();
            }
            for (int i = numPrimFields; i < fields.length; i++) {
                long key = writeKeys[i];
                if (key == Unsafe.INVALID_FIELD_OFFSET) {
                    continue;           // discard value
                }
                switch (typeCodes[i]) {
                    case 'L', '[' -> {
                        Object val = vals[offsets[i]];
                        if (val != null &&
                            !types[i - numPrimFields].isInstance(val))
                        {
                            Field f = fields[i].getField();
                            throw new ClassCastException(
                                 +
                                val.getClass().getName() +  +
                                f.getDeclaringClass().getName() +  +
                                f.getName() +  +
                                f.getType().getName() +  +
                                obj.getClass().getName());
                        }
                        if (!dryRun)
                            UNSAFE.putReference(obj, key, val);
                    }
                    default -> throw new InternalError();
                }
            }
        }
    }

    /**
     * Matches given set of serializable fields with serializable fields
     * described by the given local class descriptor, and returns a
     * FieldReflector instance capable of setting/getting values from the
     * subset of fields that match (non-matching fields are treated as filler,
     * for which get operations return default values and set operations
     * discard given values).  Throws InvalidClassException if unresolvable
     * type conflicts exist between the two sets of fields.
     */
    private static FieldReflector getReflector(ObjectStreamField[] fields,
                                               ObjectStreamClass localDesc)
        throws InvalidClassException
    {
        // class irrelevant if no fields
        Class<?> cl = (localDesc != null && fields.length > 0) ?
            localDesc.cl : Void.class;

        var clReflectors = Caches.reflectors.get(cl);
        var key = new FieldReflectorKey(fields);
        var reflector = clReflectors.get(key);
        if (reflector == null) {
            reflector = new FieldReflector(matchFields(fields, localDesc));
            var oldReflector = clReflectors.putIfAbsent(key, reflector);
            if (oldReflector != null) {
                reflector = oldReflector;
            }
        }
        return reflector;
    }

    /**
     * FieldReflector cache lookup key.  Keys are considered equal if they
     * refer to equivalent field formats.
     */
    private static class FieldReflectorKey {

        private final String[] sigs;
        private final int hash;

        FieldReflectorKey(ObjectStreamField[] fields)
        {
            sigs = new String[2 * fields.length];
            for (int i = 0, j = 0; i < fields.length; i++) {
                ObjectStreamField f = fields[i];
                sigs[j++] = f.getName();
                sigs[j++] = f.getSignature();
            }
            hash = Arrays.hashCode(sigs);
        }

        public int hashCode() {
            return hash;
        }

        public boolean equals(Object obj) {
            return obj == this ||
                   obj instanceof FieldReflectorKey other &&
                   Arrays.equals(sigs, other.sigs);
        }
    }

    /**
     * Matches given set of serializable fields with serializable fields
     * obtained from the given local class descriptor (which contain bindings
     * to reflective Field objects).  Returns list of ObjectStreamFields in
     * which each ObjectStreamField whose signature matches that of a local
     * field contains a Field object for that field; unmatched
     * ObjectStreamFields contain null Field objects.  Shared/unshared settings
     * of the returned ObjectStreamFields also reflect those of matched local
     * ObjectStreamFields.  Throws InvalidClassException if unresolvable type
     * conflicts exist between the two sets of fields.
     */
    private static ObjectStreamField[] matchFields(ObjectStreamField[] fields,
                                                   ObjectStreamClass localDesc)
        throws InvalidClassException
    {
        ObjectStreamField[] localFields = (localDesc != null) ?
            localDesc.fields : NO_FIELDS;

        /*
         * Even if fields == localFields, we cannot simply return localFields
         * here.  In previous implementations of serialization,
         * ObjectStreamField.getType() returned Object.class if the
         * ObjectStreamField represented a non-primitive field and belonged to
         * a non-local class descriptor.  To preserve this (questionable)
         * behavior, the ObjectStreamField instances returned by matchFields
         * cannot report non-primitive types other than Object.class; hence
         * localFields cannot be returned directly.
         */

        ObjectStreamField[] matches = new ObjectStreamField[fields.length];
        for (int i = 0; i < fields.length; i++) {
            ObjectStreamField f = fields[i], m = null;
            for (int j = 0; j < localFields.length; j++) {
                ObjectStreamField lf = localFields[j];
                if (f.getName().equals(lf.getName())) {
                    if ((f.isPrimitive() || lf.isPrimitive()) &&
                        f.getTypeCode() != lf.getTypeCode())
                    {
                        throw new InvalidClassException(localDesc.name,
                             + f.getName());
                    }
                    if (lf.getField() != null) {
                        m = new ObjectStreamField(
                            lf.getField(), lf.isUnshared(), false);
                    } else {
                        m = new ObjectStreamField(
                            lf.getName(), lf.getSignature(), lf.isUnshared());
                    }
                }
            }
            if (m == null) {
                m = new ObjectStreamField(
                    f.getName(), f.getSignature(), false);
            }
            m.setOffset(f.getOffset());
            matches[i] = m;
        }
        return matches;
    }

    /**
     * A LRA cache of record deserialization constructors.
     */
    @SuppressWarnings()
    private static final class DeserializationConstructorsCache
        extends ConcurrentHashMap<DeserializationConstructorsCache.Key, MethodHandle>  {

        // keep max. 10 cached entries - when the 11th element is inserted the oldest
        // is removed and 10 remains - 11 is the biggest map size where internal
        // table of 16 elements is sufficient (inserting 12th element would resize it to 32)
        private static final int MAX_SIZE = 10;
        private Key.Impl first, last; // first and last in FIFO queue

        DeserializationConstructorsCache() {
            // start small - if there is more than one shape of ObjectStreamClass
            // deserialized, there will typically be two (current version and previous version)
            super(2);
        }

        MethodHandle get(ObjectStreamField[] fields) {
            return get(new Key.Lookup(fields));
        }

        synchronized MethodHandle putIfAbsentAndGet(ObjectStreamField[] fields, MethodHandle mh) {
            Key.Impl key = new Key.Impl(fields);
            var oldMh = putIfAbsent(key, mh);
            if (oldMh != null) return oldMh;
            // else we did insert new entry -> link the new key as last
            if (last == null) {
                last = first = key;
            } else {
                last = (last.next = key);
            }
            // may need to remove first
            if (size() > MAX_SIZE) {
                assert first != null;
                remove(first);
                first = first.next;
                if (first == null) {
                    last = null;
                }
            }
            return mh;
        }

        // a key composed of ObjectStreamField[] names and types
        abstract static class Key {
            abstract int length();
            abstract String fieldName(int i);
            abstract Class<?> fieldType(int i);

            @Override
            public final int hashCode() {
                int n = length();
                int h = 0;
                for (int i = 0; i < n; i++) h = h * 31 + fieldType(i).hashCode();
                for (int i = 0; i < n; i++) h = h * 31 + fieldName(i).hashCode();
                return h;
            }

            @Override
            public final boolean equals(Object obj) {
                if (!(obj instanceof Key other)) return false;
                int n = length();
                if (n != other.length()) return false;
                for (int i = 0; i < n; i++) if (fieldType(i) != other.fieldType(i)) return false;
                for (int i = 0; i < n; i++) if (!fieldName(i).equals(other.fieldName(i))) return false;
                return true;
            }

            // lookup key - just wraps ObjectStreamField[]
            static final class Lookup extends Key {
                final ObjectStreamField[] fields;

                Lookup(ObjectStreamField[] fields) { this.fields = fields; }

                @Override
                int length() { return fields.length; }

                @Override
                String fieldName(int i) { return fields[i].getName(); }

                @Override
                Class<?> fieldType(int i) { return fields[i].getType(); }
            }

            // real key - copies field names and types and forms FIFO queue in cache
            static final class Impl extends Key {
                Impl next;
                final String[] fieldNames;
                final Class<?>[] fieldTypes;

                Impl(ObjectStreamField[] fields) {
                    this.fieldNames = new String[fields.length];
                    this.fieldTypes = new Class<?>[fields.length];
                    for (int i = 0; i < fields.length; i++) {
                        fieldNames[i] = fields[i].getName();
                        fieldTypes[i] = fields[i].getType();
                    }
                }

                @Override
                int length() { return fieldNames.length; }

                @Override
                String fieldName(int i) { return fieldNames[i]; }

                @Override
                Class<?> fieldType(int i) { return fieldTypes[i]; }
            }
        }
    }

    /** Record specific support for retrieving and binding stream field values. */
    static final class RecordSupport {
        /**
         * Returns canonical record constructor adapted to take two arguments:
         * {@code (byte[] primValues, Object[] objValues)}
         * and return
         * {@code Object}
         */
        @SuppressWarnings()
        static MethodHandle deserializationCtr(ObjectStreamClass desc) {
            // check the cached value 1st
            MethodHandle mh = desc.deserializationCtr;
            if (mh != null) return mh;
            mh = desc.deserializationCtrs.get(desc.getFields(false));
            if (mh != null) return desc.deserializationCtr = mh;

            // retrieve record components
            RecordComponent[] recordComponents;
            try {
                Class<?> cls = desc.forClass();
                PrivilegedExceptionAction<RecordComponent[]> pa = cls::getRecordComponents;
                recordComponents = AccessController.doPrivileged(pa);
            } catch (PrivilegedActionException e) {
                throw new InternalError(e.getCause());
            }

            // retrieve the canonical constructor
            // (T1, T2, ..., Tn):TR
            mh = desc.getRecordConstructor();

            // change return type to Object
            // (T1, T2, ..., Tn):TR -> (T1, T2, ..., Tn):Object
            mh = mh.asType(mh.type().changeReturnType(Object.class));

            // drop last 2 arguments representing primValues and objValues arrays
            // (T1, T2, ..., Tn):Object -> (T1, T2, ..., Tn, byte[], Object[]):Object
            mh = MethodHandles.dropArguments(mh, mh.type().parameterCount(), byte[].class, Object[].class);

            for (int i = recordComponents.length-1; i >= 0; i--) {
                String name = recordComponents[i].getName();
                Class<?> type = recordComponents[i].getType();
                // obtain stream field extractor that extracts argument at
                // position i (Ti+1) from primValues and objValues arrays
                // (byte[], Object[]):Ti+1
                MethodHandle combiner = streamFieldExtractor(name, type, desc);
                // fold byte[] privValues and Object[] objValues into argument at position i (Ti+1)
                // (..., Ti, Ti+1, byte[], Object[]):Object -> (..., Ti, byte[], Object[]):Object
                mh = MethodHandles.foldArguments(mh, i, combiner);
            }
            // what we are left with is a MethodHandle taking just the primValues
            // and objValues arrays and returning the constructed record instance
            // (byte[], Object[]):Object

            // store it into cache and return the 1st value stored
            return desc.deserializationCtr =
                desc.deserializationCtrs.putIfAbsentAndGet(desc.getFields(false), mh);
        }

        /** Returns the number of primitive fields for the given descriptor. */
        private static int numberPrimValues(ObjectStreamClass desc) {
            ObjectStreamField[] fields = desc.getFields();
            int primValueCount = 0;
            for (int i = 0; i < fields.length; i++) {
                if (fields[i].isPrimitive())
                    primValueCount++;
                else
                    break;  // can be no more
            }
            return primValueCount;
        }

        /**
         * Returns extractor MethodHandle taking the primValues and objValues arrays
         * and extracting the argument of canonical constructor with given name and type
         * or producing  default value for the given type if the field is absent.
         */
        private static MethodHandle streamFieldExtractor(String pName,
                                                         Class<?> pType,
                                                         ObjectStreamClass desc) {
            ObjectStreamField[] fields = desc.getFields(false);

            for (int i = 0; i < fields.length; i++) {
                ObjectStreamField f = fields[i];
                String fName = f.getName();
                if (!fName.equals(pName))
                    continue;

                Class<?> fType = f.getField().getType();
                if (!pType.isAssignableFrom(fType))
                    throw new InternalError(fName +  + fType);

                if (f.isPrimitive()) {
                    // (byte[], int):fType
                    MethodHandle mh = PRIM_VALUE_EXTRACTORS.get(fType);
                    if (mh == null) {
                        throw new InternalError( + fType);
                    }
                    // bind offset
                    // (byte[], int):fType -> (byte[]):fType
                    mh = MethodHandles.insertArguments(mh, 1, f.getOffset());
                    // drop objValues argument
                    // (byte[]):fType -> (byte[], Object[]):fType
                    mh = MethodHandles.dropArguments(mh, 1, Object[].class);
                    // adapt return type to pType
                    // (byte[], Object[]):fType -> (byte[], Object[]):pType
                    if (pType != fType) {
                        mh = mh.asType(mh.type().changeReturnType(pType));
                    }
                    return mh;
                } else { // reference
                    // (Object[], int):Object
                    MethodHandle mh = MethodHandles.arrayElementGetter(Object[].class);
                    // bind index
                    // (Object[], int):Object -> (Object[]):Object
                    mh = MethodHandles.insertArguments(mh, 1, i - numberPrimValues(desc));
                    // drop primValues argument
                    // (Object[]):Object -> (byte[], Object[]):Object
                    mh = MethodHandles.dropArguments(mh, 0, byte[].class);
                    // adapt return type to pType
                    // (byte[], Object[]):Object -> (byte[], Object[]):pType
                    if (pType != Object.class) {
                        mh = mh.asType(mh.type().changeReturnType(pType));
                    }
                    return mh;
                }
            }

            // return default value extractor if no field matches pName
            return MethodHandles.empty(MethodType.methodType(pType, byte[].class, Object[].class));
        }

        private static final Map<Class<?>, MethodHandle> PRIM_VALUE_EXTRACTORS;
        static {
            var lkp = MethodHandles.lookup();
            try {
                PRIM_VALUE_EXTRACTORS = Map.of(
                    byte.class, MethodHandles.arrayElementGetter(byte[].class),
                    short.class, lkp.findStatic(ByteArray.class, , MethodType.methodType(short.class, byte[].class, int.class)),
                    int.class, lkp.findStatic(ByteArray.class, , MethodType.methodType(int.class, byte[].class, int.class)),
                    long.class, lkp.findStatic(ByteArray.class, , MethodType.methodType(long.class, byte[].class, int.class)),
                    float.class, lkp.findStatic(ByteArray.class, , MethodType.methodType(float.class, byte[].class, int.class)),
                    double.class, lkp.findStatic(ByteArray.class, , MethodType.methodType(double.class, byte[].class, int.class)),
                    char.class, lkp.findStatic(ByteArray.class, , MethodType.methodType(char.class, byte[].class, int.class)),
                    boolean.class, lkp.findStatic(ByteArray.class, , MethodType.methodType(boolean.class, byte[].class, int.class))
                );
            } catch (NoSuchMethodException | IllegalAccessException e) {
                throw new InternalError(, e);
            }
        }
    }
}

/*
 * Copyright (c) 1995, 2021, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the  exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.net;

import java.io.IOException;
import java.io.UncheckedIOException;
import java.nio.channels.DatagramChannel;
import java.security.AccessController;
import java.security.PrivilegedExceptionAction;
import java.util.Enumeration;
import java.util.Objects;
import java.util.Set;
import java.util.Collections;

/**
 * A multicast datagram socket that delegates socket operations to a
 * {@link DatagramSocketImpl}.
 *
 * This class overrides every public method defined by {@link DatagramSocket}
 * and {@link MulticastSocket}.
 */
final class NetMulticastSocket extends MulticastSocket {
    /**
     * Various states of this socket.
     */
    private boolean bound = false;
    private boolean closed = false;
    private volatile boolean created;
    private final Object closeLock = new Object();

    /*
     * The implementation of this DatagramSocket.
     */
    private final DatagramSocketImpl impl;

    /**
     * Set when a socket is ST_CONNECTED until we are certain
     * that any packets which might have been received prior
     * to calling connect() but not read by the application
     * have been read. During this time we check the source
     * address of all packets received to be sure they are from
     * the connected destination. Other packets are read but
     * silently dropped.
     */
    private boolean explicitFilter = false;
    private int bytesLeftToFilter;
    /*
     * Connection state:
     * ST_NOT_CONNECTED = socket not connected
     * ST_CONNECTED = socket connected
     */
    static final int ST_NOT_CONNECTED = 0;
    static final int ST_CONNECTED = 1;

    int connectState = ST_NOT_CONNECTED;

    /*
     * Connected address & port
     */
    InetAddress connectedAddress = null;
    int connectedPort = -1;

    /**
     * This constructor is also used by {@link DatagramSocket#DatagramSocket(DatagramSocketImpl)}.
     * @param impl The impl used in this instance.
     */
    NetMulticastSocket(DatagramSocketImpl impl) {
        super((MulticastSocket) null);
        this.impl = Objects.requireNonNull(impl);
    }

    /**
     * Connects this socket to a remote socket address (IP address + port number).
     * Binds socket if not already bound.
     *
     * @param   address The remote address.
     * @param   port    The remote port
     * @throws  SocketException if binding the socket fails.
     */
    private synchronized void connectInternal(InetAddress address, int port) throws SocketException {
        if (port < 0 || port > 0xFFFF) {
            throw new IllegalArgumentException( + port);
        }
        if (address == null) {
            throw new IllegalArgumentException();
        }
        checkAddress(address, );
        if (isClosed())
            return;
        @SuppressWarnings()
        SecurityManager security = System.getSecurityManager();
        if (security != null) {
            if (address.isMulticastAddress()) {
                security.checkMulticast(address);
            } else {
                security.checkConnect(address.getHostAddress(), port);
                security.checkAccept(address.getHostAddress(), port);
            }
        }

        if (port == 0) {
            throw new SocketException();
        }
        if (!isBound())
            bind(new InetSocketAddress(0));

        getImpl().connect(address, port);

        // socket is now connected by the impl
        connectState = ST_CONNECTED;
        // Do we need to filter some packets?
        int avail = getImpl().dataAvailable();
        if (avail == -1) {
            throw new SocketException();
        }
        explicitFilter = avail > 0;
        if (explicitFilter) {
            bytesLeftToFilter = getReceiveBufferSize();
        }

        connectedAddress = address;
        connectedPort = port;
    }

    /**
     * Return the {@code DatagramSocketImpl} attached to this socket,
     * creating the socket if not already created.
     *
     * @return  the {@code DatagramSocketImpl} attached to that
     *          DatagramSocket
     * @throws SocketException if creating the socket fails
     * @since 1.4
     */
    final DatagramSocketImpl getImpl() throws SocketException {
        if (!created) {
            synchronized (this) {
                if (!created)  {
                    impl.create();
                    created = true;
                }
            }
        }
        return impl;
    }

    @Override
    public synchronized void bind(SocketAddress addr) throws SocketException {
        if (isClosed())
            throw new SocketException();
        if (isBound())
            throw new SocketException();
        if (addr == null)
            addr = new InetSocketAddress(0);
        if (!(addr instanceof InetSocketAddress epoint))
            throw new IllegalArgumentException();
        if (epoint.isUnresolved())
            throw new SocketException();
        InetAddress iaddr = epoint.getAddress();
        int port = epoint.getPort();
        checkAddress(iaddr, );
        @SuppressWarnings()
        SecurityManager sec = System.getSecurityManager();
        if (sec != null) {
            sec.checkListen(port);
        }
        try {
            getImpl().bind(port, iaddr);
        } catch (SocketException e) {
            getImpl().close();
            throw e;
        }
        bound = true;
    }

    static void checkAddress(InetAddress addr, String op) {
        if (addr == null) {
            return;
        }
        if (!(addr instanceof Inet4Address || addr instanceof Inet6Address)) {
            throw new IllegalArgumentException(op + );
        }
    }

    @Override
    public void connect(InetAddress address, int port) {
        try {
            connectInternal(address, port);
        } catch (SocketException se) {
            throw new UncheckedIOException(, se);
        }
    }

    @Override
    public void connect(SocketAddress addr) throws SocketException {
        if (addr == null)
            throw new IllegalArgumentException();
        if (!(addr instanceof InetSocketAddress epoint))
            throw new IllegalArgumentException();
        if (epoint.isUnresolved())
            throw new SocketException();
        connectInternal(epoint.getAddress(), epoint.getPort());
    }

    @Override
    public void disconnect() {
        synchronized (this) {
            if (isClosed())
                return;
            if (connectState == ST_CONNECTED) {
                impl.disconnect();
            }
            connectedAddress = null;
            connectedPort = -1;
            connectState = ST_NOT_CONNECTED;
            explicitFilter = false;
        }
    }

    @Override
    public boolean isBound() {
        return bound;
    }

    @Override
    public boolean isConnected() {
        return connectState != ST_NOT_CONNECTED;
    }

    @Override
    public InetAddress getInetAddress() {
        return connectedAddress;
    }

    @Override
    public int getPort() {
        return connectedPort;
    }

    @Override
    public SocketAddress getRemoteSocketAddress() {
        if (!isConnected())
            return null;
        return new InetSocketAddress(getInetAddress(), getPort());
    }

    @Override
    public SocketAddress getLocalSocketAddress() {
        if (isClosed())
            return null;
        if (!isBound())
            return null;
        return new InetSocketAddress(getLocalAddress(), getLocalPort());
    }

    @Override
    public void send(DatagramPacket p) throws IOException {
        synchronized (p) {
            if (isClosed())
                throw new SocketException();
            InetAddress packetAddress = p.getAddress();
            int packetPort = p.getPort();
            checkAddress(packetAddress, );
            if (connectState == ST_NOT_CONNECTED) {
                if (packetAddress == null) {
                    throw new IllegalArgumentException();
                }
                if (packetPort < 0 || packetPort > 0xFFFF)
                    throw new IllegalArgumentException( + packetPort);
                // check the address is ok with the security manager on every send.
                @SuppressWarnings()
                SecurityManager security = System.getSecurityManager();

                // The reason you want to synchronize on datagram packet
                // is because you don't want an applet to change the address
                // while you are trying to send the packet for example
                // after the security check but before the send.
                if (security != null) {
                    if (packetAddress.isMulticastAddress()) {
                        security.checkMulticast(packetAddress);
                    } else {
                        security.checkConnect(packetAddress.getHostAddress(),
                                packetPort);
                    }
                }
                if (packetPort == 0) {
                    throw new SocketException();
                }
            } else {
                // we're connected
                if (packetAddress == null) {
                    p.setAddress(connectedAddress);
                    p.setPort(connectedPort);
                } else if ((!packetAddress.equals(connectedAddress)) ||
                        packetPort != connectedPort) {
                    throw new IllegalArgumentException( +
                             +
                            );
                }
            }
            // Check whether the socket is bound
            if (!isBound())
                bind(new InetSocketAddress(0));
            // call the  method to send
            getImpl().send(p);
        }
    }

    @Override
    public synchronized void receive(DatagramPacket p) throws IOException {
        synchronized (p) {
            if (!isBound())
                bind(new InetSocketAddress(0));
            if (connectState == ST_NOT_CONNECTED) {
                // check the address is ok with the security manager before every recv.
                @SuppressWarnings()
                SecurityManager security = System.getSecurityManager();
                if (security != null) {
                    while (true) {
                        int peekPort = 0;
                        // peek at the packet to see who it is from.
                        DatagramPacket peekPacket = new DatagramPacket(new byte[1], 1);
                        peekPort = getImpl().peekData(peekPacket);
                        String peekAd = peekPacket.getAddress().getHostAddress();
                        try {
                            security.checkAccept(peekAd, peekPort);
                            // security check succeeded - so now break
                            // and recv the packet.
                            break;
                        } catch (SecurityException se) {
                            // Throw away the offending packet by consuming
                            // it in a tmp buffer.
                            DatagramPacket tmp = new DatagramPacket(new byte[1], 1);
                            getImpl().receive(tmp);

                            // silently discard the offending packet
                            // and continue: unknown/malicious
                            // entities on nets should not make
                            // runtime throw security exception and
                            // disrupt the applet by sending random
                            // datagram packets.
                            continue;
                        }
                    } // end of while
                }
            }
            DatagramPacket tmp = null;
            if (explicitFilter) {
                // We have to do the filtering the old fashioned way since
                // the native impl doesn't support connect or the connect
                // via the impl failed, or ..  may be set when
                // a socket is connected via the impl, for a period of time
                // when packets from other sources might be queued on socket.
                boolean stop = false;
                while (!stop) {
                    // peek at the packet to see who it is from.
                    DatagramPacket peekPacket = new DatagramPacket(new byte[1], 1);
                    int peekPort = getImpl().peekData(peekPacket);
                    InetAddress peekAddress = peekPacket.getAddress();
                    if ((!connectedAddress.equals(peekAddress)) || (connectedPort != peekPort)) {
                        // throw the packet away and silently continue
                        tmp = new DatagramPacket(
                                new byte[1024], 1024);
                        getImpl().receive(tmp);
                        if (explicitFilter) {
                            if (checkFiltering(tmp)) {
                                stop = true;
                            }
                        }
                    } else {
                        stop = true;
                    }
                }
            }
            // If the security check succeeds, or the datagram is
            // connected then receive the packet
            getImpl().receive(p);
            if (explicitFilter && tmp == null) {
                // packet was not filtered, account for it here
                checkFiltering(p);
            }
        }
    }

    private boolean checkFiltering(DatagramPacket p) throws SocketException {
        bytesLeftToFilter -= p.getLength();
        if (bytesLeftToFilter <= 0 || getImpl().dataAvailable() <= 0) {
            explicitFilter = false;
            return true;
        }
        return false;
    }

    @Override
    public InetAddress getLocalAddress() {
        if (isClosed())
            return null;
        InetAddress in;
        try {
            in = (InetAddress) getImpl().getOption(SocketOptions.SO_BINDADDR);
            if (in.isAnyLocalAddress()) {
                in = InetAddress.anyLocalAddress();
            }
            @SuppressWarnings()
            SecurityManager s = System.getSecurityManager();
            if (s != null) {
                s.checkConnect(in.getHostAddress(), -1);
            }
        } catch (Exception e) {
            in = InetAddress.anyLocalAddress(); // 
        }
        return in;
    }

    @Override
    public int getLocalPort() {
        if (isClosed())
            return -1;
        try {
            return getImpl().getLocalPort();
        } catch (Exception e) {
            return 0;
        }
    }

    @Override
    public synchronized void setSoTimeout(int timeout) throws SocketException {
        if (isClosed())
            throw new SocketException();
        if (timeout < 0)
            throw new IllegalArgumentException();
        getImpl().setOption(SocketOptions.SO_TIMEOUT, timeout);
    }

    @Override
    public synchronized int getSoTimeout() throws SocketException {
        if (isClosed())
            throw new SocketException();
        if (getImpl() == null)
            return 0;
        Object o = getImpl().getOption(SocketOptions.SO_TIMEOUT);
        /* extra type safety */
        if (o instanceof Integer) {
            return ((Integer) o).intValue();
        } else {
            return 0;
        }
    }

    @Override
    public synchronized void setSendBufferSize(int size) throws SocketException {
        if (!(size > 0)) {
            throw new IllegalArgumentException();
        }
        if (isClosed())
            throw new SocketException();
        getImpl().setOption(SocketOptions.SO_SNDBUF, size);
    }

    @Override
    public synchronized int getSendBufferSize() throws SocketException {
        if (isClosed())
            throw new SocketException();
        int result = 0;
        Object o = getImpl().getOption(SocketOptions.SO_SNDBUF);
        if (o instanceof Integer) {
            result = ((Integer) o).intValue();
        }
        return result;
    }

    @Override
    public synchronized void setReceiveBufferSize(int size) throws SocketException {
        if (size <= 0) {
            throw new IllegalArgumentException();
        }
        if (isClosed())
            throw new SocketException();
        getImpl().setOption(SocketOptions.SO_RCVBUF, size);
    }

    @Override
    public synchronized int getReceiveBufferSize() throws SocketException {
        if (isClosed())
            throw new SocketException();
        int result = 0;
        Object o = getImpl().getOption(SocketOptions.SO_RCVBUF);
        if (o instanceof Integer) {
            result = ((Integer) o).intValue();
        }
        return result;
    }

    @Override
    public synchronized void setReuseAddress(boolean on) throws SocketException {
        if (isClosed())
            throw new SocketException();
        getImpl().setOption(SocketOptions.SO_REUSEADDR, Boolean.valueOf(on));
    }

    @Override
    public synchronized boolean getReuseAddress() throws SocketException {
        if (isClosed())
            throw new SocketException();
        Object o = getImpl().getOption(SocketOptions.SO_REUSEADDR);
        return ((Boolean) o).booleanValue();
    }

    @Override
    public synchronized void setBroadcast(boolean on) throws SocketException {
        if (isClosed())
            throw new SocketException();
        getImpl().setOption(SocketOptions.SO_BROADCAST, Boolean.valueOf(on));
    }

    @Override
    public synchronized boolean getBroadcast() throws SocketException {
        if (isClosed())
            throw new SocketException();
        return ((Boolean) (getImpl().getOption(SocketOptions.SO_BROADCAST))).booleanValue();
    }

    @Override
    public synchronized void setTrafficClass(int tc) throws SocketException {
        if (tc < 0 || tc > 255)
            throw new IllegalArgumentException();

        if (isClosed())
            throw new SocketException();
        try {
            getImpl().setOption(SocketOptions.IP_TOS, tc);
        } catch (SocketException se) {
            // not supported if socket already connected
            // Solaris returns error in such cases
            if (!isConnected())
                throw se;
        }
    }

    @Override
    public synchronized int getTrafficClass() throws SocketException {
        if (isClosed())
            throw new SocketException();
        return ((Integer) (getImpl().getOption(SocketOptions.IP_TOS))).intValue();
    }

    @Override
    public void close() {
        synchronized (closeLock) {
            if (isClosed())
                return;
            impl.close();
            closed = true;
        }
    }

    @Override
    public boolean isClosed() {
        synchronized (closeLock) {
            return closed;
        }
    }

    @Override
    public  <T> DatagramSocket setOption(SocketOption<T> name, T value)
            throws IOException
    {
        Objects.requireNonNull(name);
        if (isClosed())
            throw new SocketException();
        getImpl().setOption(name, value);
        return this;
    }

    @Override
    public <T> T getOption(SocketOption<T> name) throws IOException {
        Objects.requireNonNull(name);
        if (isClosed())
            throw new SocketException();
        return getImpl().getOption(name);
    }

    private volatile Set<SocketOption<?>> options;
    private final Object optionsLock = new Object();

    @Override
    public Set<SocketOption<?>> supportedOptions() {
        Set<SocketOption<?>> options = this.options;
        if (options != null)
            return options;
        synchronized (optionsLock) {
            options = this.options;
            if (options != null) {
                return options;
            }
            try {
                DatagramSocketImpl impl = getImpl();
                options = Collections.unmodifiableSet(impl.supportedOptions());
            } catch (IOException e) {
                options = Collections.emptySet();
            }
            return this.options = options;
        }
    }

    // Multicast socket support

    /**
     * Used on some platforms to record if an outgoing interface
     * has been set for this socket.
     */
    private boolean interfaceSet;

    /**
     * The lock on the socket's TTL. This is for set/getTTL and
     * send(packet,ttl).
     */
    private final Object ttlLock = new Object();

    /**
     * The lock on the socket's interface - used by setInterface
     * and getInterface
     */
    private final Object infLock = new Object();

    /**
     * The  interface set by setInterface on this MulticastSocket
     */
    private InetAddress infAddress = null;

    @Deprecated
    @Override
    public void setTTL(byte ttl) throws IOException {
        if (isClosed())
            throw new SocketException();
        getImpl().setTTL(ttl);
    }

    @Override
    public void setTimeToLive(int ttl) throws IOException {
        if (ttl < 0 || ttl > 255) {
            throw new IllegalArgumentException();
        }
        if (isClosed())
            throw new SocketException();
        getImpl().setTimeToLive(ttl);
    }

    @Deprecated
    @Override
    public byte getTTL() throws IOException {
        if (isClosed())
            throw new SocketException();
        return getImpl().getTTL();
    }

    @Override
    public int getTimeToLive() throws IOException {
        if (isClosed())
            throw new SocketException();
        return getImpl().getTimeToLive();
    }

    @Override
    @Deprecated
    public void joinGroup(InetAddress mcastaddr) throws IOException {
        if (isClosed()) {
            throw new SocketException();
        }

        checkAddress(mcastaddr, );
        @SuppressWarnings()
        SecurityManager security = System.getSecurityManager();
        if (security != null) {
            security.checkMulticast(mcastaddr);
        }

        if (!mcastaddr.isMulticastAddress()) {
            throw new SocketException();
        }

        /**
         * required for some platforms where it's not possible to join
         * a group without setting the interface first.
         */
        NetworkInterface defaultInterface = NetworkInterface.getDefault();

        if (!interfaceSet && defaultInterface != null) {
            setNetworkInterface(defaultInterface);
        }

        getImpl().join(mcastaddr);
    }

    @Override
    @Deprecated
    public void leaveGroup(InetAddress mcastaddr) throws IOException {
        if (isClosed()) {
            throw new SocketException();
        }

        checkAddress(mcastaddr, );
        @SuppressWarnings()
        SecurityManager security = System.getSecurityManager();
        if (security != null) {
            security.checkMulticast(mcastaddr);
        }

        if (!mcastaddr.isMulticastAddress()) {
            throw new SocketException();
        }

        getImpl().leave(mcastaddr);
    }

    @Override
    public void joinGroup(SocketAddress mcastaddr, NetworkInterface netIf)
            throws IOException {
        if (isClosed())
            throw new SocketException();

        if (!(mcastaddr instanceof InetSocketAddress addr))
            throw new IllegalArgumentException();

        checkAddress(addr.getAddress(), );
        @SuppressWarnings()
        SecurityManager security = System.getSecurityManager();
        if (security != null) {
            security.checkMulticast(addr.getAddress());
        }

        if (!addr.getAddress().isMulticastAddress()) {
            throw new SocketException();
        }

        getImpl().joinGroup(mcastaddr, netIf);
    }

    @Override
    public void leaveGroup(SocketAddress mcastaddr, NetworkInterface netIf)
            throws IOException {
        if (isClosed())
            throw new SocketException();

        if (!(mcastaddr instanceof InetSocketAddress addr))
            throw new IllegalArgumentException();

        checkAddress(addr.getAddress(), );
        @SuppressWarnings()
        SecurityManager security = System.getSecurityManager();
        if (security != null) {
            security.checkMulticast(addr.getAddress());
        }

        if (!addr.getAddress().isMulticastAddress()) {
            throw new SocketException();
        }

        getImpl().leaveGroup(mcastaddr, netIf);
    }

    @Override
    @Deprecated
    public void setInterface(InetAddress inf) throws SocketException {
        if (isClosed()) {
            throw new SocketException();
        }
        checkAddress(inf, );
        synchronized (infLock) {
            getImpl().setOption(SocketOptions.IP_MULTICAST_IF, inf);
            infAddress = inf;
            interfaceSet = true;
        }
    }

    @Override
    @Deprecated
    public InetAddress getInterface() throws SocketException {
        if (isClosed()) {
            throw new SocketException();
        }
        synchronized (infLock) {
            InetAddress ia =
                    (InetAddress)getImpl().getOption(SocketOptions.IP_MULTICAST_IF);

            /**
             * No previous setInterface or interface can be
             * set using setNetworkInterface
             */
            if (infAddress == null) {
                return ia;
            }

            /**
             * Same interface set with setInterface?
             */
            if (ia.equals(infAddress)) {
                return ia;
            }

            /**
             * Different InetAddress from what we set with setInterface
             * so enumerate the current interface to see if the
             * address set by setInterface is bound to this interface.
             */
            try {
                NetworkInterface ni = NetworkInterface.getByInetAddress(ia);
                Enumeration<InetAddress> addrs = ni.getInetAddresses();
                while (addrs.hasMoreElements()) {
                    InetAddress addr = addrs.nextElement();
                    if (addr.equals(infAddress)) {
                        return infAddress;
                    }
                }

                /**
                 * No match so reset infAddress to indicate that the
                 * interface has changed via means
                 */
                infAddress = null;
                return ia;
            } catch (Exception e) {
                return ia;
            }
        }
    }

    @Override
    public void setNetworkInterface(NetworkInterface netIf)
            throws SocketException {

        synchronized (infLock) {
            getImpl().setOption(SocketOptions.IP_MULTICAST_IF2, netIf);
            infAddress = null;
            interfaceSet = true;
        }
    }

    @Override
    public NetworkInterface getNetworkInterface() throws SocketException {
        NetworkInterface ni
                = (NetworkInterface)getImpl().getOption(SocketOptions.IP_MULTICAST_IF2);
        if (ni == null) {
            InetAddress[] addrs = new InetAddress[1];
            addrs[0] = InetAddress.anyLocalAddress();
            return new NetworkInterface(addrs[0].getHostName(), 0, addrs);
        } else {
            return ni;
        }
    }

    @Override
    @Deprecated
    public void setLoopbackMode(boolean disable) throws SocketException {
        getImpl().setOption(SocketOptions.IP_MULTICAST_LOOP, Boolean.valueOf(disable));
    }

    @Override
    @Deprecated
    public boolean getLoopbackMode() throws SocketException {
        return ((Boolean)getImpl().getOption(SocketOptions.IP_MULTICAST_LOOP)).booleanValue();
    }

    @SuppressWarnings()
    @Deprecated
    @Override
    public void send(DatagramPacket p, byte ttl)
            throws IOException {
        if (isClosed())
            throw new SocketException();
        synchronized(ttlLock) {
            synchronized(p) {
                InetAddress packetAddress = p.getAddress();
                checkAddress(packetAddress, );
                if (connectState == NetMulticastSocket.ST_NOT_CONNECTED) {
                    if (packetAddress == null) {
                        throw new IllegalArgumentException();
                    }
                    // Security manager makes sure that the multicast address
                    // is allowed one and that the ttl used is less
                    // than the allowed maxttl.
                    SecurityManager security = System.getSecurityManager();
                    if (security != null) {
                        if (packetAddress.isMulticastAddress()) {
                            security.checkMulticast(packetAddress, ttl);
                        } else {
                            security.checkConnect(packetAddress.getHostAddress(),
                                    p.getPort());
                        }
                    }
                } else {
                    // we're connected
                    if (packetAddress == null) {
                        p.setAddress(connectedAddress);
                        p.setPort(connectedPort);
                    } else if ((!packetAddress.equals(connectedAddress)) ||
                            p.getPort() != connectedPort) {
                        throw new IllegalArgumentException( +
                                );
                    }
                }
                byte dttl = getTTL();
                try {
                    if (ttl != dttl) {
                        // set the ttl
                        getImpl().setTTL(ttl);
                    }
                    if (p.getPort() == 0) {
                        throw new SocketException();
                    }
                    // call the datagram method to send
                    getImpl().send(p);
                } finally {
                    // set it back to default
                    if (ttl != dttl) {
                        getImpl().setTTL(dttl);
                    }
                }
            } // synch p
        }  //synch ttl
    } //method
}

/*
 * Copyright (c) 1995, 2023, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the  exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.io;

import java.util.Objects;

/**
 * A piped input stream should be connected
 * to a piped output stream; the piped  input
 * stream then provides whatever data bytes
 * are written to the piped output  stream.
 * Typically, data is read from a {@code PipedInputStream}
 * object by one thread  and data is written
 * to the corresponding {@code PipedOutputStream}
 * by some  other thread. Attempting to use
 * both objects from a single thread is not
 * recommended, as it may deadlock the thread.
 * The piped input stream contains a buffer,
 * decoupling read operations from write operations,
 * within limits.
 * A pipe is said to be <a id=> <i>broken</i> </a> if a
 * thread that was providing data bytes to the connected
 * piped output stream is no longer alive.
 *
 * @author  James Gosling
 * @see     java.io.PipedOutputStream
 * @since   1.0
 */
public class PipedInputStream extends InputStream {
    boolean closedByWriter;
    volatile boolean closedByReader;
    boolean connected;

        /* REMIND: identification of the read and write sides needs to be
           more sophisticated.  Either using thread groups (but what about
           pipes within a thread?) or using finalization (but it may be a
           long time until the next GC). */
    Thread readSide;
    Thread writeSide;

    private static final int DEFAULT_PIPE_SIZE = 1024;

    /**
     * The default size of the pipe's circular input buffer.
     * @since   1.1
     */
    // This used to be a constant before the pipe size was allowed
    // to change. This field will continue to be maintained
    // for backward compatibility.
    protected static final int PIPE_SIZE = DEFAULT_PIPE_SIZE;

    /**
     * The circular buffer into which incoming data is placed.
     * @since   1.1
     */
    protected byte buffer[];

    /**
     * The index of the position in the circular buffer at which the
     * next byte of data will be stored when received from the connected
     * piped output stream. {@code in < 0} implies the buffer is empty,
     * {@code in == out} implies the buffer is full
     * @since   1.1
     */
    protected int in = -1;

    /**
     * The index of the position in the circular buffer at which the next
     * byte of data will be read by this piped input stream.
     * @since   1.1
     */
    protected int out = 0;

    /**
     * Creates a {@code PipedInputStream} so
     * that it is connected to the piped output
     * stream {@code src}. Data bytes written
     * to {@code src} will then be  available
     * as input from this stream.
     *
     * @param      src   the stream to connect to.
     * @throws     IOException  if an I/O error occurs.
     */
    public PipedInputStream(PipedOutputStream src) throws IOException {
        this(src, DEFAULT_PIPE_SIZE);
    }

    /**
     * Creates a {@code PipedInputStream} so that it is
     * connected to the piped output stream
     * {@code src} and uses the specified pipe size for
     * the pipe's buffer.
     * Data bytes written to {@code src} will then
     * be available as input from this stream.
     *
     * @param      src   the stream to connect to.
     * @param      pipeSize the size of the pipe's buffer.
     * @throws     IOException  if an I/O error occurs.
     * @throws     IllegalArgumentException if {@code pipeSize <= 0}.
     * @since      1.6
     */
    public PipedInputStream(PipedOutputStream src, int pipeSize)
            throws IOException {
         initPipe(pipeSize);
         connect(src);
    }

    /**
     * Creates a {@code PipedInputStream} so
     * that it is not yet {@linkplain #connect(java.io.PipedOutputStream)
     * connected}.
     * It must be {@linkplain java.io.PipedOutputStream#connect(
     * java.io.PipedInputStream) connected} to a
     * {@code PipedOutputStream} before being used.
     */
    public PipedInputStream() {
        initPipe(DEFAULT_PIPE_SIZE);
    }

    /**
     * Creates a {@code PipedInputStream} so that it is not yet
     * {@linkplain #connect(java.io.PipedOutputStream) connected} and
     * uses the specified pipe size for the pipe's buffer.
     * It must be {@linkplain java.io.PipedOutputStream#connect(
     * java.io.PipedInputStream)
     * connected} to a {@code PipedOutputStream} before being used.
     *
     * @param      pipeSize the size of the pipe's buffer.
     * @throws     IllegalArgumentException if {@code pipeSize <= 0}.
     * @since      1.6
     */
    public PipedInputStream(int pipeSize) {
        initPipe(pipeSize);
    }

    private void initPipe(int pipeSize) {
         if (pipeSize <= 0) {
            throw new IllegalArgumentException();
         }
         buffer = new byte[pipeSize];
    }

    /**
     * Causes this piped input stream to be connected
     * to the piped  output stream {@code src}.
     * If this object is already connected to some
     * other piped output  stream, an {@code IOException}
     * is thrown.
     * <p>
     * If {@code src} is an
     * unconnected piped output stream and {@code snk}
     * is an unconnected piped input stream, they
     * may be connected by either the call:
     *
     * {@snippet lang=java :
     *     snk.connect(src)
     * }
     * <p>
     * or the call:
     *
     * {@snippet lang=java :
     *     src.connect(snk)
     * }
     * <p>
     * The two calls have the same effect.
     *
     * @param      src   The piped output stream to connect to.
     * @throws     IOException  if an I/O error occurs.
     */
    public void connect(PipedOutputStream src) throws IOException {
        src.connect(this);
    }

    /**
     * Receives a byte of data.  This method will block if no input is
     * available.
     * @param   b the byte being received
     * @throws  IOException If the pipe is <a href=> {@code broken}</a>,
     *          {@link #connect(java.io.PipedOutputStream) unconnected},
     *          closed, or if an I/O error occurs.
     * @since   1.1
     */
    protected synchronized void receive(int b) throws IOException {
        checkStateForReceive();
        writeSide = Thread.currentThread();
        if (in == out)
            awaitSpace();
        if (in < 0) {
            in = 0;
            out = 0;
        }
        buffer[in++] = (byte)(b & 0xFF);
        if (in >= buffer.length) {
            in = 0;
        }
    }

    /**
     * Receives data into an array of bytes.  This method will
     * block until some input is available.
     * @param    b the buffer into which the data is received
     * @param    off the start offset of the data
     * @param    len the maximum number of bytes received
     * @throws   IOException If the pipe is <a href=> broken</a>,
     *           {@link #connect(java.io.PipedOutputStream) unconnected},
     *           closed, or if an I/O error occurs.
     */
    synchronized void receive(byte[] b, int off, int len)  throws IOException {
        checkStateForReceive();
        writeSide = Thread.currentThread();
        int bytesToTransfer = len;
        while (bytesToTransfer > 0) {
            if (in == out)
                awaitSpace();
            int nextTransferAmount = 0;
            if (out < in) {
                nextTransferAmount = buffer.length - in;
            } else if (in < out) {
                if (in == -1) {
                    in = out = 0;
                    nextTransferAmount = buffer.length - in;
                } else {
                    nextTransferAmount = out - in;
                }
            }
            if (nextTransferAmount > bytesToTransfer)
                nextTransferAmount = bytesToTransfer;
            assert(nextTransferAmount > 0);
            System.arraycopy(b, off, buffer, in, nextTransferAmount);
            bytesToTransfer -= nextTransferAmount;
            off += nextTransferAmount;
            in += nextTransferAmount;
            if (in >= buffer.length) {
                in = 0;
            }
        }
    }

    private void checkStateForReceive() throws IOException {
        if (!connected) {
            throw new IOException();
        } else if (closedByWriter || closedByReader) {
            throw new IOException();
        } else if (readSide != null && !readSide.isAlive()) {
            throw new IOException();
        }
    }

    private void awaitSpace() throws IOException {
        while (in == out) {
            checkStateForReceive();

            /* full: kick any waiting readers */
            notifyAll();
            try {
                wait(1000);
            } catch (InterruptedException ex) {
                throw new java.io.InterruptedIOException();
            }
        }
    }

    /**
     * Notifies all waiting threads that the last byte of data has been
     * received.
     */
    synchronized void receivedLast() {
        closedByWriter = true;
        notifyAll();
    }

    /**
     * Reads the next byte of data from this piped input stream. The
     * value byte is returned as an {@code int} in the range
     * {@code 0} to {@code 255}.
     * This method blocks until input data is available, the end of the
     * stream is detected, or an exception is thrown.
     *
     * @return   {@inheritDoc}
     * @throws   IOException  if the pipe is
     *           {@link #connect(java.io.PipedOutputStream) unconnected},
     *           <a href=> {@code broken}</a>, closed,
     *           or if an I/O error occurs.
     */
    @Override
    public synchronized int read()  throws IOException {
        if (!connected) {
            throw new IOException();
        } else if (closedByReader) {
            throw new IOException();
        } else if (writeSide != null && !writeSide.isAlive()
                   && !closedByWriter && (in < 0)) {
            throw new IOException();
        }

        readSide = Thread.currentThread();
        int trials = 2;
        while (in < 0) {
            if (closedByWriter) {
                /* closed by writer, return EOF */
                return -1;
            }
            if ((writeSide != null) && (!writeSide.isAlive()) && (--trials < 0)) {
                throw new IOException();
            }
            /* might be a writer waiting */
            notifyAll();
            try {
                wait(1000);
            } catch (InterruptedException ex) {
                throw new java.io.InterruptedIOException();
            }
        }
        int ret = buffer[out++] & 0xFF;
        if (out >= buffer.length) {
            out = 0;
        }
        if (in == out) {
            /* now empty */
            in = -1;
        }

        return ret;
    }

    /**
     * Reads up to {@code len} bytes of data from this piped input
     * stream into an array of bytes. Less than {@code len} bytes
     * will be read if the end of the data stream is reached or if
     * {@code len} exceeds the pipe's buffer size.
     * If {@code len } is zero, then no bytes are read and 0 is returned;
     * otherwise, the method blocks until at least 1 byte of input is
     * available, end of the stream has been detected, or an exception is
     * thrown.
     *
     * @param      b     {@inheritDoc}
     * @param      off   {@inheritDoc}
     * @param      len   {@inheritDoc}
     * @return     {@inheritDoc}
     * @throws     NullPointerException {@inheritDoc}
     * @throws     IndexOutOfBoundsException {@inheritDoc}
     * @throws     IOException if the pipe is <a href=> {@code broken}</a>,
     *           {@link #connect(java.io.PipedOutputStream) unconnected},
     *           closed, or if an I/O error occurs.
     */
    @Override
    public synchronized int read(byte[] b, int off, int len)  throws IOException {
        if (b == null) {
            throw new NullPointerException();
        }
        Objects.checkFromIndexSize(off, len, b.length);
        if (len == 0) {
            return 0;
        }

        /* possibly wait on the first character */
        int c = read();
        if (c < 0) {
            return -1;
        }
        b[off] = (byte) c;
        int rlen = 1;
        while ((in >= 0) && (len > 1)) {

            int available;

            if (in > out) {
                available = Math.min((buffer.length - out), (in - out));
            } else {
                available = buffer.length - out;
            }

            // A byte is read beforehand outside the loop
            if (available > (len - 1)) {
                available = len - 1;
            }
            System.arraycopy(buffer, out, b, off + rlen, available);
            out += available;
            rlen += available;
            len -= available;

            if (out >= buffer.length) {
                out = 0;
            }
            if (in == out) {
                /* now empty */
                in = -1;
            }
        }
        return rlen;
    }

    /**
     * Returns the number of bytes that can be read from this input
     * stream without blocking.
     *
     * @return the number of bytes that can be read from this input stream
     *         without blocking, or {@code 0} if this input stream has been
     *         closed by invoking its {@link #close()} method, or if the pipe
     *         is {@link #connect(java.io.PipedOutputStream) unconnected}, or
     *         <a href=> {@code broken}</a>.
     *
     * @throws IOException  {@inheritDoc}
     * @since  1.0.2
     */
    @Override
    public synchronized int available() throws IOException {
        if(in < 0)
            return 0;
        else if(in == out)
            return buffer.length;
        else if (in > out)
            return in - out;
        else
            return in + buffer.length - out;
    }

    /**
     * {@inheritDoc}
     *
     * @throws     IOException  {@inheritDoc}
     */
    @Override
    public void close()  throws IOException {
        closedByReader = true;
        synchronized (this) {
            in = -1;
        }
    }
}