Today’s Thought


import 'dart:math';

class PseudoRandom {
  int a;
  int c;
  int m = 1 << 32;
  int s;
  int i;

  PseudoRandom([int prod = 1664525, int add = 1013904223]) {
    a = prod;
    c = add;
    s = Random().nextInt(m) * 2 + 1;//odd
    next();// a fast round
    i = a.modInverse(m);//4276115653 as inverse of 1664525
  }

  int next() {
    return s = (a * s + c) % m;
  }

  int prev() {
    return s = (s - c) * i % m;
  }
}

class RingNick {
  List<double> walls = [ 0.25, 0.5, 0.75 ];
  int position = 0;
  int mostEscaped = 1;//the lowest pair of walls 0.25 and 0.5
  int leastEscaped = 2;//the highest walls 0.5 and 0.75
  int theThird = 0;//the 0.75 and 0.25 walls
  bool right = true;
  PseudoRandom pr = PseudoRandom();

  int _getPosition() => position;

  int _asMod(int pos) {
    return pos % walls.length;
  }

  void _setPosition(int pos) {
    position = _asMod(pos);
  }

  void _next() {
    int direction = right ? 0 : walls.length - 1;//truncate to 2
    double wall = walls[_asMod(_getPosition() + direction)];
    if(pr.next() > (wall * pr.m).toInt()) {
      //jumped
      _setPosition(position + (right ? 1 : walls.length - 1));
    } else {
      //not jumped
      right = !right;//bounce
    }
  }

  void _prev() {
    int direction = !right ? 0 : walls.length - 1;//truncate to 2
    double wall = walls[_asMod(_getPosition() + direction)];
    if(pr.s > (wall * pr.m).toInt()) {// the jump over before sync
      //jumped
      _setPosition(position + (!right ? 1 : walls.length - 1));
    } else {
      //not jumped
      right = !right;//bounce -- double bounce and scale before sync
    }
    pr.prev();//exact inverse
  }

  void next() {
    _next();
    while(_getPosition() == mostEscaped) _next();
  }

  void prev() {
    _prev();
    while(_getPosition() == mostEscaped) _prev();
  }
}

class GroupHandler {
  List<RingNick> rn;

  GroupHandler(int size) {
    if(size % 2 == 0) size++;
    rn = List<RingNick>(size);
  }

  void next() {
    for(RingNick r in rn) r.next();
  }

  void prev() {
    for(RingNick r in rn.reversed) r.prev();
  }

  bool majority() {
    int count = 0;
    for(RingNick r in rn) if(r._getPosition() == r.leastEscaped) count++;//a main cumulative
    return (2 * count > rn.length);// the > 2/3rd state is true
  }

  void modulate() {
    for(RingNick r in rn) if(r._getPosition() == r.leastEscaped) {
      r._setPosition(r.theThird);
    } else {
      //mostEscaped eliminated by not being used
      r._setPosition(r.leastEscaped);
    }
  }
}

class Modulator {
  GroupHandler gh = GroupHandler(55);

  int putBit(bool bitToAbsorb) {//returns absorption status
    gh.next();
    if(gh.majority()) {//main zero state
      if(bitToAbsorb) {
        gh.modulate();
        return 0;//a zero yet to absorb
      } else {
        return 1;//absorbed zero
      }
    } else {
      return -1;//no absorption emitted 1
    }
  }

  int getBit(bool bitLastEmitted) {
    if(gh.majority()) {//zero
      gh.prev();
      return 1;//last bit not needed emit zero
    } else {
      if(bitLastEmitted) {
        gh.prev();
        return -1;//last bit needed and nothing to emit
      } else {
        gh.modulate();
        gh.prev();
        return 0;//last bit needed, emit 1
      }
    }
  }
}

class StackHandler {
  List<bool> data = [];
  Modulator m = Modulator();

  int putBits() {
    int count = 0;
    while(data.length > 0) {
      bool v = data.removeLast();
      switch(m.putBit(v)) {
        case -1:
          data.add(v);
          data.add(true);
          break;
        case 0:
          data.add(false);
          break;
        case 1:
          break;//absorbed zero
        default: break;
      }
      count++;
    }
    return count;
  }

  void getBits(int count) {
    while(count > 0) {
      bool v;
      v = (data.length == 0 ? false : data.removeLast());//zeros out
      switch(m.getBit(v)) {
        case 1:
          data.add(v);//not needed
          data.add(false);//emitted zero
          break;
        case 0:
          data.add(true);//emitted 1 used zero
          break;
        case -1:
          break;//bad skip, ...
        default: break;
      }
      count--;
    }
  }
}

Statistics and Damn Lies

I was wondering over the statistics problem I call the ABC problem. Say you have 3 walls in a circular path, of different heights, and between them are points marked A, B and C. If in any ‘turn’ the ‘climber’ attempts to scale the wall in the current clockwise or anti-clockwise direction. The chances of success are proportional to the wall height. If the climber fails to get over a wall, they reverse direction. A simple thing, but what are the chances of the climber will be found facing clockwise just before scaling or not a wall? Is it close to 0.5 as the problem is not symmetric?

More interestingly the climber will be in a very real sense captured more often in the cell with the highest pair of walls. If the cell with the lowest pair of walls is just considered as consumption of time, then what is the ratio of the containment time over the total time not in the least inescapable wall cell?

So the binomial distribution of the elimination of the ’emptiest’ when repeating this pattern as an array with co-prime ‘dice’ (if all occupancy has to be in either of the most secure cells in each ‘ring nick’), the rate depends on the number of ring nicks. The considered security majority state is the state (selected from the two most secure cell states) which more of the ring nicks are in, given none are in the least secure state of the three states.

For the ring nick array to be majority most secure more than two thirds the time is another binomial or two away. If there are more than two-thirds of the time (excluding gaping minimal occupancy cells) the most secure state majority and less than two-thirds (by unitary summation) of the middle-security cells in majority, there exists a Jaxon Modulation coding to place data on the Prisoners by reversing all their directions at once where necessary, to invert the majority into a minority rarer state with more Shannon information. Note that the pseudo-random dice and other quantifying information remains constant in bits.

Dedicated to Kurt Godel … I am number 6. 😀

BLZW Compression Java

Uses Sais.java with dictionary persist, and initialisation corrections. Also with alignment fix and unused function removed. A 32 bucket context provides an effective 17 bit dictionary key, using just 12 bits, along with the BWT redundancy model. This should provide superior compression of text. Now includes the faster skip decode. Feel free to donate to grow some open source based on data compression and related codecs.





/* BWT/LZW fast wide dictionary. (C)2016-2017 K Ring Technologies Ltd.
The context is used to make 32 dictionary spaces for 128k symbols max.
This then givez 12 bit tokens for an almost effective 16 bit dictionary.
For an approximate 20% data saving above regular LZW.

The process is optimized for L2 cache sizea.

A mod 16 gives DT and EU collisions on hash.
A mod 32 is ASCII proof, and hence good for text.

The count compaction includes a skip code for efficient storage.
The dictionary persists over the stream for good running compression.
64k blocks are used for fast BWT. Larger blocks would give better
compression, but be slower. The main loss is the count compactio storage.

An arithmetic coder post may be effective but would be slow. Dictonary
acceleration would not necessarily be useful, and problematic after the
stream start. A 12 bit code is easy to pack, keeps the dictionary small
and has the sweet spot of redundancy in while not making large rare or
single use symbols.
*/

package uk.co.kring.net;

import java.io.EOFException;
import java.io.Externalizable;
import java.io.FilterInputStream;
import java.io.FilterOutputStream;
import java.io.IOException;
import java.io.ObjectInput;
import java.io.ObjectOutput;
import java.util.HashMap;

/**
 * Created by user on 06/06/2016.
 */
public class Packer {

    public static class OutputStream extends FilterOutputStream implements Externalizable {

        byte[] buf = new byte[4096 * 16];//64K block max
        int cnt = 0;//pointer to end
        int[] dmax = new int[32];
        HashMap<String, Integer> dict;

        public OutputStream(java.io.OutputStream out) {
            super(out);
        }

        @Override
        public void readExternal(ObjectInput input) throws IOException, ClassNotFoundException {
            out = (java.io.OutputStream)input.readObject();
            input.read(buf);
            cnt = input.readChar();
            dict = (HashMap<String, Integer>)input.readObject();
        }

        @Override
        public void writeExternal(ObjectOutput output) throws IOException {
            output.writeObject(out);
            output.write(buf);
            output.writeChar(cnt);
            output.writeObject(dict);
        }

        @Override
        public void close() throws IOException {
            flush();
            out.close();
        }

        private byte pair = 0;
        private boolean two = false;

        private void outputCount(int num, boolean small, boolean tiny) throws IOException {
            if(tiny) {
                out.write((byte)num);
                return;
            }
            if(small) {
                out.write((byte)num);
                pair = (byte)((pair << 4) + (num >> 8));
                if(two) {
                    two = false;
                    out.write(pair);
                } else {
                    two = true;
                }
                return;
            }
            out.write((byte)(num >> 8));
            out.write((byte)num);
        }

        @Override
        public void flush() throws IOException {
            outputCount(cnt, false, false);//just in case length
            char[] count = new char[256];
            if(dict == null) {
                dict = new HashMap<>();
                for(int i = 0; i < 32; i++) {
                    dmax[i] = 256;//dictionary max
                }
            }
            for(int i = 0; i < cnt; i++) {
                count[buf[i]]++;
            }
            char skip = 0;
            boolean first = true;
            char acc = 0;
            char[] start = new char[256];
            for(int j = 0; j < 2; j++) {
                for (int i = 0; i < 256; i++) {
                    if(j == 0) {
                        acc += count[i];
                        start[i] = acc;
                    }
                    if (count[i] == 0) {
                        skip++;
                        if (first) {
                            outputCount(0, false, true);
                            first = false;
                        }
                    } else {
                        if (skip != 0) {
                            outputCount(skip, false, true);
                            skip = 0;
                            first = true;
                        }
                        outputCount(count[i], false, true);
                        count[i] >>= 8;
                    }
                }
                if(skip != 0) outputCount(skip, false, true);//final skip
            }
            int[] ptr = new int[buf.length];
            byte[] bwt = new byte[buf.length];

            outputCount(Sais.bwtransform(buf, bwt, ptr, cnt), false, false);

            //now an lzw
            String sym = "";
            char context = 0;
            char lastContext = 0;
            int test = 0;
            for(int j = 0; j < cnt; j++) {
                while(j >= start[context]) context++;
                if(lastContext == context) {
                    sym += bwt[j];//add a char
                } else {
                    lastContext = context;
                    outputCount(test, true, false);
                    sym = "" + bwt[j];//new char
                }
                if(sym.length() == 1) {
                    test = (int)sym.charAt(0);
                } else {
                    if(dict.containsKey(context + sym)) {
                        test = dict.get(context + sym);
                    } else {
                        outputCount(test, true, false);
                        if (dmax[context & 0x1f] < 0x1000) {//context limit
                            dict.put(context + sym, dmax[context & 0x1f]);
                            dmax[context & 0x1f]++;
                        }
                        sym = "" + bwt[j];//new symbol
                    }
                }
            }
            outputCount(test, true, false);//last match
            if(!two) outputCount(0, true, false);//aligned data
            out.flush();
            cnt = 0;//fill next buffer
        }

        @Override
        public void write(int oneByte) throws IOException {
            if(cnt == buf.length) flush();
            buf[cnt++] = (byte)oneByte;
        }
    }

    public static class InputStream extends FilterInputStream implements Externalizable {

        @Override
        public void readExternal(ObjectInput input) throws IOException, ClassNotFoundException {
            in = (java.io.InputStream)input.readObject();
            input.read(buf);
            idx = input.readChar();
            cnt = input.readChar();
            dict = (HashMap<Integer, String>)input.readObject();
        }

        @Override
        public void writeExternal(ObjectOutput output) throws IOException {
            output.writeObject(in);
            output.write(buf);
            output.writeChar(idx);
            output.writeChar(cnt);
            output.writeObject(dict);
        }

        //SEE MIT LICENCE OF Sais.java

        private static void unbwt(byte[] T, byte[] U, int[] LF, int n, int pidx) {
            int[] C = new int[256];
            int i, t;
            //for(i = 0; i < 256; ++i) { C[i] = 0; }//Java
            for(i = 0; i < n; ++i) { LF[i] = C[(int)(T[i] & 0xff)]++; }
            for(i = 0, t = 0; i < 256; ++i) { t += C[i]; C[i] = t - C[i]; }
            for(i = n - 1, t = 0; 0 <= i; --i) {
                t = LF[t] + C[(int)((U[i] = T[t]) & 0xff)];
                t += (t < pidx) ? 1 : 0;
            }
        }

        byte[] buf = new byte[4096 * 16];//64K block max
        int cnt = 0;//pointer to end
        int idx = 0;
        int[] dmax = new int[32];
        HashMap<Integer, String> dict;

        private boolean two = false;
        private int vala = 0;
        private int valb = 0;

        private int reader() throws IOException {
            int i = in.read();
            if(i == -1) throw new EOFException("End Of Stream");
            return i;
        }

        private char inCount(boolean small, boolean tiny) throws IOException {
            if(tiny) return (char)reader();
            if(small) {
                if(!two) {
                    vala = reader();
                    valb = reader();
                    int valc = reader();
                    vala += (valc << 4) & 0xf00;
                    valb += (valc << 8) & 0xf00;
                    two = true;
                } else {
                    vala = valb;
                    two = false;
                }
                return (char)vala;
            }
            int val = reader() << 8;
            val += reader();
            return (char)val;
        }

        public InputStream(java.io.InputStream in) {
            super(in);
        }

        @Override
        public int available() throws IOException {
            return cnt - idx;
        }

        @Override
        public void close() throws IOException {
            in.close();
        }

        private void doReads() throws IOException {
            if(available() == 0) {
                two = false;//align
                if(dict == null) {
                    dict = new HashMap<>();
                    for(int i = 0; i < 32; i++) {
                        dmax[i] = 256;
                    }
                }
                cnt = inCount(false, false);
                char[] count = new char[256];
                char tmp;
                for(int j = 0; j < 2; j++) {
                    for (int i = 0; i < 256; i++) {
                        count[i] += tmp = (char)(inCount(false, true) << (j == 1?8:0));
                        if (tmp == 0) {
                            i += inCount(false, true) - 1;
                        }
                    }
                }
                for(int i = 1; i < 256; i++) {
                    count[i] += count[i - 1];//accumulate
                }
                if(cnt != count[255]) throw new IOException("Bad Input Check (character count)");
                int choose = inCount(false, false);//read index
                if(cnt < choose) throw new IOException("Bad Input Check (selected row)");
                byte[] build;//make this
                //then lzw
                //rosetta code
                int context = 0;
                int lastContext = 0;
                String w = "" + inCount(true, false);
                StringBuilder result = new StringBuilder(w);
                while (result.length() < cnt) {//not yet complete
                    char k = inCount(true, false);
                    String entry;
                    while(result.length() > count[context]) {
                        context++;//do first
                        if (context > 255)
                            throw new IOException("Bad Input Check (character count)");
                    }
                    if(k < 256)
                        entry = "" + k;
                    else if (dict.containsKey(((context & 0x1f) << 16) + k))
                        entry = dict.get(((context & 0x1f) << 16) + k);
                    else if (k == dmax[context & 0x1f])
                        entry = w + w.charAt(0);
                    else
                        throw new IOException("Bad Input Check (token: " + k + ")");
                    result.append(entry);
                    // Add w+entry[0] to the dictionary.
                    if(lastContext == context) {
                        if (dmax[context & 0x1f] < 0x1000) {
                            dict.put(((context & 0x1f) << 16) +
                                    (dmax[context & 0x1f]++),
                                    w + entry.charAt(0));
                        }
                        w = entry;
                    } else {
                        //context change
                        context = lastContext;
                        //and following context should be a <256 ...
                        if(result.length() < cnt) {
                            w = "" + inCount(true, false);
                            result.append(w);
                        }
                    }
                }
                build = result.toString().getBytes();
                //working buffers
                int[] wrk = new int[buf.length];
                unbwt(build, buf, wrk, buf.length, choose);
                idx = 0;//ready for reads
                if(!two) inCount(true, false);//aligned data
            }
        }

        @Override
        public int read() throws IOException {
            try {
                doReads();
                int x = buf[idx++];
                doReads();//to prevent avail = 0 never access
                return x;
            } catch(EOFException e) {
                return -1;
            }
        }

        @Override
        public long skip(long byteCount) throws IOException {
            long i;
            for(i = 0; i < byteCount; i++)
                if(read() == -1) break;
            return i;
        }

        @Override
        public boolean markSupported() {
            return false;
        }

        @Override
        public synchronized void reset() throws IOException {
            throw new IOException("Mark Not Supported");
        }
    }
}