From 6be9684df4cf1561e062024b1de8123da6e8b7a3 Mon Sep 17 00:00:00 2001
From: Project Nayuki <me@nayuki.io>
Date: Thu, 23 Nov 2017 03:06:55 +0000
Subject: [PATCH] Started this "Fast QR Code generator library" project, added
 Reed-Solomon ECC generator.

---
 .../fastqrcodegen/ReedSolomonGenerator.java   | 141 ++++++++++++++++++
 1 file changed, 141 insertions(+)
 create mode 100644 src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java

diff --git a/src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java b/src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java
new file mode 100644
index 0000000..8be42e7
--- /dev/null
+++ b/src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java
@@ -0,0 +1,141 @@
+package io.nayuki.fastqrcodegen;
+
+import java.lang.ref.SoftReference;
+import java.util.Arrays;
+import java.util.Objects;
+
+
+final class ReedSolomonGenerator {
+	
+	/*---- Factory members ----*/
+	
+	public static ReedSolomonGenerator getInstance(int degree) {
+		if (degree < 1 || degree > MAX_DEGREE)
+			throw new IllegalArgumentException("Degree out of range");
+		
+		while (true) {
+			synchronized(cache) {
+				SoftReference<ReedSolomonGenerator> ref = cache[degree];
+				if (ref != null) {
+					ReedSolomonGenerator result = ref.get();
+					if (result != null)
+						return result;
+					cache[degree] = null;
+				}
+				
+				if (!isPending[degree]) {
+					isPending[degree] = true;
+					break;
+				}
+				
+				try {
+					cache.wait();
+				} catch (InterruptedException e) {
+					throw new RuntimeException(e);
+				}
+			}
+		}
+		
+		ReedSolomonGenerator rs = new ReedSolomonGenerator(degree);
+		synchronized(cache) {
+			cache[degree] = new SoftReference<>(rs);
+			isPending[degree] = false;
+			cache.notifyAll();
+		}
+		return rs;
+	}
+	
+	
+	private static final int MAX_DEGREE = 30;
+	
+	@SuppressWarnings("unchecked")
+	private static final SoftReference<ReedSolomonGenerator>[] cache = new SoftReference[MAX_DEGREE + 1];
+	
+	private static final boolean[] isPending = new boolean[MAX_DEGREE + 1];
+	
+	
+	
+	/*---- Instance members ----*/
+	
+	private byte[][] multiplies;
+	
+	
+	private ReedSolomonGenerator(int degree) {
+		if (degree < 1 || degree > 255)
+			throw new IllegalArgumentException("Degree out of range");
+		
+		// Start with the monomial x^0
+		byte[] coefficients = new byte[degree];
+		coefficients[degree - 1] = 1;
+		
+		// Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}),
+		// drop the highest term, and store the rest of the coefficients in order of descending powers.
+		// Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D).
+		int root = 1;
+		for (int i = 0; i < degree; i++) {
+			// Multiply the current product by (x - r^i)
+			for (int j = 0; j < coefficients.length; j++) {
+				coefficients[j] = (byte)multiply(coefficients[j] & 0xFF, root);
+				if (j + 1 < coefficients.length)
+					coefficients[j] ^= coefficients[j + 1];
+			}
+			root = multiply(root, 0x02);
+		}
+		
+		multiplies = new byte[degree][];
+		for (int i = 0; i < multiplies.length; i++)
+			multiplies[i] = MULTIPLICATION_TABLE[coefficients[i] & 0xFF];
+	}
+	
+	
+	public void getRemainder(byte[] data, byte[] result) {
+		Objects.requireNonNull(data);
+		Objects.requireNonNull(result);
+		if (result.length != multiplies.length)
+			throw new IllegalArgumentException("Array length mismatch");
+		
+		// Compute the remainder by performing polynomial division
+		Arrays.fill(result, (byte)0);
+		for (byte b : data) {
+			int factor = (b ^ result[0]) & 0xFF;
+			System.arraycopy(result, 1, result, 0, result.length - 1);
+			result[result.length - 1] = 0;
+			for (int i = 0; i < result.length; i++)
+				result[i] ^= multiplies[i][factor];
+		}
+	}
+	
+	
+	
+	/*---- Constant members ----*/
+	
+	// Returns the product of the two given field elements modulo GF(2^8/0x11D). The arguments and result
+	// are unsigned 8-bit integers. This could be implemented as a lookup table of 256*256 entries of uint8.
+	private static int multiply(int x, int y) {
+		if (x >>> 8 != 0 || y >>> 8 != 0)
+			throw new IllegalArgumentException("Byte out of range");
+		// Russian peasant multiplication
+		int z = 0;
+		for (int i = 7; i >= 0; i--) {
+			z = (z << 1) ^ ((z >>> 7) * 0x11D);
+			z ^= ((y >>> i) & 1) * x;
+		}
+		if (z >>> 8 != 0)
+			throw new AssertionError();
+		return z;
+	}
+	
+	
+	private static final byte[][] MULTIPLICATION_TABLE = new byte[256][256];
+	
+	static {
+		for (int i = 0; i < MULTIPLICATION_TABLE.length; i++) {
+			for (int j = 0; j <= i; j++) {
+				byte k = (byte)multiply(i, j);
+				MULTIPLICATION_TABLE[i][j] = k;
+				MULTIPLICATION_TABLE[j][i] = k;
+			}
+		}
+	}
+	
+}