add golomb code

Author: 15045120

docs/HoffmanAndGolombCoding.pdf

@@ -14,7 +14,7 @@ public class Bits {
     private int size;
     private int used;
 
-    Bits() {
+    public Bits() {
         table = new Bit[INITIAL_SIZE];
         this.used = 0;
         this.size = INITIAL_SIZE;
@@ -373,6 +373,10 @@ public static Bits ofZero(int len) {
         return bits;
     }
 
+    public static Bits ofZero() {
+        return ofZero(1);
+    }
+
     public static Bits ofOne(int len) {
         Bits bits = new Bits();
         bits.expand(len);
@@ -383,6 +387,10 @@ public static Bits ofOne(int len) {
         return bits;
     }
 
+    public static Bits ofOne() {
+        return ofOne(1);
+    }
+
     public Bits append(Bits other) {
         int newLen = this.used + other.used;
         expand(newLen);
@@ -391,6 +399,14 @@ public Bits append(Bits other) {
         return this;
     }
 
+    public Bits append(Bit bit) {
+        int newLen = this.used + 1;
+        expand(newLen);
+        table[this.used] = bit;
+        this.used += 1;
+        return this;
+    }
+
     private void expand(int newLen) {
         if (newLen <= this.size) {
             return;
@@ -426,6 +442,10 @@ static void subBitsRangeCheck(int fromIndex, int toIndex, int size) {
                     ") > toIndex(" + toIndex + ")");
     }
 
+    public Bit[] table(){
+        return this.table;
+    }
+
     @Override
     public String toString() {
         StringBuilder builder = new StringBuilder();

src/main/java/com/github/myibu/algorithm/data/Bits.java

@@ -0,0 +1,9 @@
+package com.github.myibu.algorithm.endode;
+/**
+ * Golomb code
+ * @author myibu
+ * Created on 2021/10/12
+ */
+public interface Encoder {
+
+}

src/main/java/com/github/myibu/algorithm/endode/Encoder.java

@@ -0,0 +1,63 @@
+package com.github.myibu.algorithm.endode;
+
+import com.github.myibu.algorithm.data.Bits;
+
+/**
+ * Golomb code
+ * see <a herf="https://en.wikipedia.org/wiki/Golomb_coding#Simple_algorithm">https://en.wikipedia.org/wiki/Golomb_coding#Simple_algorithm</a>
+ * @author myibu
+ * Created on 2021/10/12
+ */
+public class GolombEncoder implements Encoder {
+    /**
+     *
+     * @param n the value to encode
+     * @param m m, like 5
+     * @return the length of encoded bits
+     */
+    public Bits encode(int n, int m) {
+        Bits bits = new Bits();
+        // 向下取整
+        int q = (int)Math.floor(n * 1.0 / m);
+        bits.append(Bits.ofOne(Math.max(0, q))).append(Bits.ofZero(1));
+        int r = n % m;
+        int k = (int)(Math.ceil(Math.log(m) / Math.log(2)));
+        if ((m & 0x01) == 0) {
+            return bits.append(encodeToStandardBinary(r, k));
+        } else {
+            // truncated binary encoding
+            if (r < Math.pow(2, k) - m) {
+                return bits.append(encodeToTruncatedBinary(r, m));
+            } else {
+                return bits.append(encodeToTruncatedBinary(r, m));
+            }
+        }
+    }
+
+    private Bits encodeToStandardBinary(int x, int len) {
+        return encodeToBinary(x, len);
+    }
+
+    private Bits encodeToTruncatedBinary(int x, int n) {
+        // Set k = floor(log2(n)), i.e., k such that 2^k <= n < 2^(k+1).
+        int k = 0, t = n;
+        while (t > 1) { k++;  t >>= 1; }
+
+        // Set u to the number of unused codewords = 2^(k+1) - n.
+        int u = (1 << k+1) - n;
+
+        if (x < u)  return encodeToBinary(x, k);
+        else  return encodeToBinary(x+u, k+1);
+    }
+
+    private Bits encodeToBinary(int x, int len) {
+        Bits s = new Bits();
+        while (x != 0) {
+            if ((x & 0x01) == 0)  s = Bits.ofZero().append(s);
+            else  s = Bits.ofOne().append(s);
+            x >>= 1;
+        }
+        while (s.length() < len)  s = Bits.ofZero().append(s);
+        return s;
+    }
+}

src/main/java/com/github/myibu/algorithm/endode/GolombEncoder.java

@@ -5,6 +5,8 @@
 import com.github.myibu.algorithm.compress.LZFCompressor;
 import com.github.myibu.algorithm.data.Bits;
 import com.github.myibu.algorithm.data.Bytes;
+import com.github.myibu.algorithm.endode.Encoder;
+import com.github.myibu.algorithm.endode.GolombEncoder;
 import com.github.myibu.algorithm.filter.*;
 import com.github.myibu.algorithm.hash.MurmurHash2;
 import com.github.myibu.algorithm.hash.SHA256;
@@ -172,4 +174,15 @@ public void testLZ77Compressor() {
         Compressor compressor = new LZ77Compressor();
         compressor.compress(in_data, in_data.length, out_data);
     }
+
+    @Test
+    public void testGolombEncoder() {
+        int m = 5;
+        GolombEncoder encoder = new GolombEncoder();
+        System.out.println(5 + "= "  + encoder.encode(5, m));
+        System.out.println(6 + "= "  + encoder.encode(6, m));
+        System.out.println(7 + "= "  + encoder.encode(7, m));
+        System.out.println(8 + "= "  + encoder.encode(8, m));
+        System.out.println(9 + "= "  + encoder.encode(9, m));
+    }
 }