From ccd7f3e9e89a83b6c4ad5c3067f5f50fb6a91f4f Mon Sep 17 00:00:00 2001 From: Project Nayuki Date: Tue, 28 Aug 2018 04:25:48 +0000 Subject: [PATCH] Simplified Reed-Solomon generator algorithms, without changing behavior. --- .../fastqrcodegen/ReedSolomonGenerator.java | 27 ++++++++++--------- 1 file changed, 15 insertions(+), 12 deletions(-) diff --git a/src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java b/src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java index 979faec..99ba41b 100644 --- a/src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java +++ b/src/io/nayuki/fastqrcodegen/ReedSolomonGenerator.java @@ -85,7 +85,11 @@ final class ReedSolomonGenerator { /*---- Instance members ----*/ - private byte[][] multiplies; + // A table of size 256 * degree, where polynomialMultiply[i][j] = multiply(i, coefficients[j]). + // 'coefficients' is the temporary array representing the coefficients of the divisor polynomial, + // stored from highest to lowest power, excluding the leading term which is always 1. + // For example the polynomial x^3 + 255x^2 + 8x + 93 is stored as the uint8 array {255, 8, 93}. + private byte[][] polynomialMultiply; private ReedSolomonGenerator(int degree) { @@ -110,10 +114,10 @@ final class ReedSolomonGenerator { root = multiply(root, 0x02); } - multiplies = new byte[degree][256]; - for (int i = 0; i < multiplies.length; i++) { - for (int j = 0; j < 256; j++) - multiplies[i][j] = (byte)multiply(coefficients[i] & 0xFF, j); + polynomialMultiply = new byte[256][degree]; + for (int i = 0; i < polynomialMultiply.length; i++) { + for (int j = 0; j < degree; j++) + polynomialMultiply[i][j] = (byte)multiply(i, coefficients[j] & 0xFF); } } @@ -123,15 +127,14 @@ final class ReedSolomonGenerator { Objects.requireNonNull(result); // Compute the remainder by performing polynomial division - int resultEnd = resultOff + multiplies.length; + int degree = polynomialMultiply[0].length; + int resultEnd = resultOff + degree; Arrays.fill(result, resultOff, resultEnd, (byte)0); for (int i = dataOff, dataEnd = dataOff + dataLen; i < dataEnd; i++) { - byte b = data[i]; - int factor = (b ^ result[resultOff]) & 0xFF; - System.arraycopy(result, resultOff + 1, result, resultOff, multiplies.length - 1); - result[resultEnd - 1] = 0; - for (int j = 0; j < multiplies.length; j++) - result[resultOff + j] ^= multiplies[j][factor]; + byte[] table = polynomialMultiply[(data[i] ^ result[resultOff]) & 0xFF]; + for (int j = 0; j < degree - 1; j++) + result[resultOff + j] = (byte)(result[resultOff + j + 1] ^ table[j]); + result[resultOff + degree - 1] = table[degree - 1]; } }