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QR-Code-generator/java/io/nayuki/qrcodegen/QrCode.java

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/*
* QR Code generator library (Java)
*
* Copyright (c) Project Nayuki. (MIT License)
* https://www.nayuki.io/page/qr-code-generator-library
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
* - The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
* - The Software is provided "as is", without warranty of any kind, express or
* implied, including but not limited to the warranties of merchantability,
* fitness for a particular purpose and noninfringement. In no event shall the
* authors or copyright holders be liable for any claim, damages or other
* liability, whether in an action of contract, tort or otherwise, arising from,
* out of or in connection with the Software or the use or other dealings in the
* Software.
*/
package io.nayuki.qrcodegen;
import java.awt.image.BufferedImage;
import java.util.Arrays;
import java.util.List;
import java.util.Objects;
/**
* Represents an immutable square grid of black and white cells for a QR Code symbol, and
* provides static functions to create a QR Code from user-supplied textual or binary data.
* <p>This class covers the QR Code Model 2 specification, supporting all versions (sizes)
* from 1 to 40, all 4 error correction levels, and 4 character encoding modes.</p>
*/
public final class QrCode {
/*---- Static factory functions (high level) ----*/
/**
* Returns a QR Code representing the specified Unicode text string at the specified error correction level.
* As a conservative upper bound, this function is guaranteed to succeed for strings that have 738 or fewer
* Unicode code points (not UTF-16 code units) if the low error correction level is used. The smallest possible
* QR Code version is automatically chosen for the output. The ECC level of the result may be higher than the
* ecl argument if it can be done without increasing the version.
* @param text the text to be encoded, which can be any Unicode string
* @param ecl the error correction level to use (will be boosted)
* @return a QR Code representing the text
* @throws NullPointerException if the text or error correction level is {@code null}
* @throws IllegalArgumentException if the text fails to fit in the
* largest version QR Code at the ECL, which means it is too long
*/
public static QrCode encodeText(String text, Ecc ecl) {
Objects.requireNonNull(text);
Objects.requireNonNull(ecl);
List<QrSegment> segs = QrSegment.makeSegments(text);
return encodeSegments(segs, ecl);
}
/**
* Returns a QR Code representing the specified binary data string at the specified error correction level.
* This function always encodes using the binary segment mode, not any text mode. The maximum number of
* bytes allowed is 2953. The smallest possible QR Code version is automatically chosen for the output.
* The ECC level of the result may be higher than the ecl argument if it can be done without increasing the version.
* @param data the binary data to encode
* @param ecl the error correction level to use (will be boosted)
* @return a QR Code representing the binary data
* @throws NullPointerException if the data or error correction level is {@code null}
* @throws IllegalArgumentException if the data fails to fit in the
* largest version QR Code at the ECL, which means it is too long
*/
public static QrCode encodeBinary(byte[] data, Ecc ecl) {
Objects.requireNonNull(data);
Objects.requireNonNull(ecl);
QrSegment seg = QrSegment.makeBytes(data);
return encodeSegments(Arrays.asList(seg), ecl);
}
/*---- Static factory functions (mid level) ----*/
/**
* Returns a QR Code representing the specified segments at the specified error correction
* level. The smallest possible QR Code version is automatically chosen for the output. The ECC level
* of the result may be higher than the ecl argument if it can be done without increasing the version.
* <p>This function allows the user to create a custom sequence of segments that switches
* between modes (such as alphanumeric and binary) to encode text more efficiently.
* This function is considered to be lower level than simply encoding text or binary data.</p>
* @param segs the segments to encode
* @param ecl the error correction level to use (will be boosted)
* @return a QR Code representing the segments
* @throws NullPointerException if the list of segments, any segment, or the error correction level is {@code null}
* @throws IllegalArgumentException if the segments fail to fit in the
* largest version QR Code at the ECL, which means they are too long
*/
public static QrCode encodeSegments(List<QrSegment> segs, Ecc ecl) {
return encodeSegments(segs, ecl, MIN_VERSION, MAX_VERSION, -1, true);
}
/**
* Returns a QR Code representing the specified segments with the specified encoding parameters.
* The smallest possible QR Code version within the specified range is automatically chosen for the output.
* <p>This function allows the user to create a custom sequence of segments that switches
* between modes (such as alphanumeric and binary) to encode text more efficiently.
* This function is considered to be lower level than simply encoding text or binary data.</p>
* @param segs the segments to encode
* @param ecl the error correction level to use (may be boosted)
* @param minVersion the minimum allowed version of the QR symbol (at least 1)
* @param maxVersion the maximum allowed version of the QR symbol (at most 40)
* @param mask the mask pattern to use, which is either -1 for automatic choice or from 0 to 7 for fixed choice
* @param boostEcl increases the error correction level if it can be done without increasing the version number
* @return a QR Code representing the segments
* @throws NullPointerException if the list of segments, any segment, or the error correction level is {@code null}
* @throws IllegalArgumentException if 1 &#x2264; minVersion &#x2264; maxVersion &#x2264; 40
* is violated, or if mask &lt; &#x2212;1 or mask &gt; 7, or if the segments fail
* to fit in the maxVersion QR Code at the ECL, which means they are too long
*/
public static QrCode encodeSegments(List<QrSegment> segs, Ecc ecl, int minVersion, int maxVersion, int mask, boolean boostEcl) {
Objects.requireNonNull(segs);
Objects.requireNonNull(ecl);
if (!(MIN_VERSION <= minVersion && minVersion <= maxVersion && maxVersion <= MAX_VERSION) || mask < -1 || mask > 7)
throw new IllegalArgumentException("Invalid value");
// Find the minimal version number to use
int version, dataUsedBits;
for (version = minVersion; ; version++) {
int dataCapacityBits = getNumDataCodewords(version, ecl) * 8; // Number of data bits available
dataUsedBits = QrSegment.getTotalBits(segs, version);
if (dataUsedBits != -1 && dataUsedBits <= dataCapacityBits)
break; // This version number is found to be suitable
if (version >= maxVersion) // All versions in the range could not fit the given data
throw new IllegalArgumentException("Data too long");
}
assert dataUsedBits != -1;
// Increase the error correction level while the data still fits in the current version number
for (Ecc newEcl : Ecc.values()) { // From low to high
if (boostEcl && dataUsedBits <= getNumDataCodewords(version, newEcl) * 8)
ecl = newEcl;
}
// Concatenate all segments to create the data bit string
BitBuffer bb = new BitBuffer();
for (QrSegment seg : segs) {
bb.appendBits(seg.mode.modeBits, 4);
bb.appendBits(seg.numChars, seg.mode.numCharCountBits(version));
bb.appendData(seg.data);
}
assert bb.bitLength() == dataUsedBits;
// Add terminator and pad up to a byte if applicable
int dataCapacityBits = getNumDataCodewords(version, ecl) * 8;
assert bb.bitLength() <= dataCapacityBits;
bb.appendBits(0, Math.min(4, dataCapacityBits - bb.bitLength()));
bb.appendBits(0, (8 - bb.bitLength() % 8) % 8);
assert bb.bitLength() % 8 == 0;
// Pad with alternating bytes until data capacity is reached
for (int padByte = 0xEC; bb.bitLength() < dataCapacityBits; padByte ^= 0xEC ^ 0x11)
bb.appendBits(padByte, 8);
// Create the QR Code object
return new QrCode(version, ecl, bb.getBytes(), mask);
}
/*---- Instance fields ----*/
// Public immutable scalar parameters:
/** The version number of this QR Code, which is between 1 and 40 (inclusive).
* This determines the size of this barcode. */
public final int version;
/** The width and height of this QR Code, measured in modules, between
* 21 and 177 (inclusive). This is equal to version &#xD7; 4 + 17. */
public final int size;
/** The error correction level used in this QR Code, which is not {@code null}. */
public final Ecc errorCorrectionLevel;
/** The index of the mask pattern used in this QR Code, which is between 0 and 7 (inclusive).
* <p>Even if a QR Code is created with automatic masking requested (mask =
* &#x2212;1), the resulting object still has a mask value between 0 and 7. */
public final int mask;
// Private grids of modules/pixels, with dimensions of size*size:
// The modules of this QR Code (false = white, true = black). Immutable after constructor finishes.
private boolean[][] modules;
// Indicates function modules that are not subjected to masking. Discarded when constructor finishes.
private boolean[][] isFunction;
/*---- Constructor (low level) ----*/
/**
* Constructs a QR Code with the specified version number, error correction level, binary data array, and mask number.
* <p>This is a cumbersome low-level constructor that should not be invoked directly by the user.
* To go one level up, see the {@link #encodeSegments(List,Ecc,int,int,int,boolean)} function.</p>
* @param ver the version number to use, which must be in the range 1 to 40 (inclusive)
* @param ecl the error correction level to use
* @param dataCodewords the bytes representing segments to encode (without ECC)
* @param mask the mask pattern to use, which is either &#x2212;1 for automatic choice or from 0 to 7 for fixed choice
* @throws NullPointerException if the byte array or error correction level is {@code null}
* @throws IllegalArgumentException if the version or mask value is out of range,
* or if the data is the wrong length for the specified version and error correction level
*/
public QrCode(int ver, Ecc ecl, byte[] dataCodewords, int mask) {
// Check arguments and initialize fields
if (ver < MIN_VERSION || ver > MAX_VERSION)
throw new IllegalArgumentException("Version value out of range");
if (mask < -1 || mask > 7)
throw new IllegalArgumentException("Mask value out of range");
version = ver;
size = ver * 4 + 17;
errorCorrectionLevel = Objects.requireNonNull(ecl);
Objects.requireNonNull(dataCodewords);
modules = new boolean[size][size]; // Initially all white
isFunction = new boolean[size][size];
// Compute ECC, draw modules, do masking
drawFunctionPatterns();
byte[] allCodewords = addEccAndInterleave(dataCodewords);
drawCodewords(allCodewords);
this.mask = handleConstructorMasking(mask);
isFunction = null;
}
/*---- Public instance methods ----*/
/**
* Returns the color of the module (pixel) at the specified coordinates, which is either
* false for white or true for black. The top left corner has the coordinates (x=0, y=0).
* If the specified coordinates are out of bounds, then false (white) is returned.
* @param x the x coordinate, where 0 is the left edge and size&#x2212;1 is the right edge
* @param y the y coordinate, where 0 is the top edge and size&#x2212;1 is the bottom edge
* @return the module's color, which is either false (white) or true (black)
*/
public boolean getModule(int x, int y) {
return 0 <= x && x < size && 0 <= y && y < size && modules[y][x];
}
/**
* Returns a new image object representing this QR Code, with the specified module scale and number
* of border modules. For example, the arguments scale=10, border=4 means to pad the QR Code
* with 4 white border modules on all four edges, then use 10*10 pixels to represent each module.
* The resulting image only contains the hex colors 000000 and FFFFFF.
* @param scale the module scale factor, which must be positive
* @param border the number of border modules to add, which must be non-negative
* @return an image representing this QR Code, with padding and scaling
* @throws IllegalArgumentException if the scale or border is out of range, or if
* {scale, border, size} cause the image dimensions to exceed Integer.MAX_VALUE
*/
public BufferedImage toImage(int scale, int border) {
if (scale <= 0 || border < 0)
throw new IllegalArgumentException("Value out of range");
if (border > Integer.MAX_VALUE / 2 || size + border * 2L > Integer.MAX_VALUE / scale)
throw new IllegalArgumentException("Scale or border too large");
BufferedImage result = new BufferedImage((size + border * 2) * scale, (size + border * 2) * scale, BufferedImage.TYPE_INT_RGB);
for (int y = 0; y < result.getHeight(); y++) {
for (int x = 0; x < result.getWidth(); x++) {
boolean color = getModule(x / scale - border, y / scale - border);
result.setRGB(x, y, color ? 0x000000 : 0xFFFFFF);
}
}
return result;
}
/**
* Returns a string of SVG XML code representing an image of this QR Code with the specified
* number of border modules. Note that Unix newlines (\n) are always used, regardless of the platform.
* @param border the number of border modules to add, which must be non-negative
* @return a string representing this QR Code as an SVG document
* @throws IllegalArgumentException if the border is negative
*/
public String toSvgString(int border) {
if (border < 0)
throw new IllegalArgumentException("Border must be non-negative");
long brd = border;
StringBuilder sb = new StringBuilder()
.append("<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n")
.append("<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n")
.append(String.format("<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\" viewBox=\"0 0 %1$d %1$d\" stroke=\"none\">\n",
size + brd * 2))
.append("\t<rect width=\"100%\" height=\"100%\" fill=\"#FFFFFF\"/>\n")
.append("\t<path d=\"");
for (int y = 0; y < size; y++) {
for (int x = 0; x < size; x++) {
if (getModule(x, y)) {
if (x != 0 || y != 0)
sb.append(" ");
sb.append(String.format("M%d,%dh1v1h-1z", x + brd, y + brd));
}
}
}
return sb
.append("\" fill=\"#000000\"/>\n")
.append("</svg>\n")
.toString();
}
/*---- Private helper methods for constructor: Drawing function modules ----*/
// Reads this object's version field, and draws and marks all function modules.
private void drawFunctionPatterns() {
// Draw horizontal and vertical timing patterns
for (int i = 0; i < size; i++) {
setFunctionModule(6, i, i % 2 == 0);
setFunctionModule(i, 6, i % 2 == 0);
}
// Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules)
drawFinderPattern(3, 3);
drawFinderPattern(size - 4, 3);
drawFinderPattern(3, size - 4);
// Draw numerous alignment patterns
int[] alignPatPos = getAlignmentPatternPositions();
int numAlign = alignPatPos.length;
for (int i = 0; i < numAlign; i++) {
for (int j = 0; j < numAlign; j++) {
// Don't draw on the three finder corners
if (!(i == 0 && j == 0 || i == 0 && j == numAlign - 1 || i == numAlign - 1 && j == 0))
drawAlignmentPattern(alignPatPos[i], alignPatPos[j]);
}
}
// Draw configuration data
drawFormatBits(0); // Dummy mask value; overwritten later in the constructor
drawVersion();
}
// Draws two copies of the format bits (with its own error correction code)
// based on the given mask and this object's error correction level field.
private void drawFormatBits(int mask) {
// Calculate error correction code and pack bits
int data = errorCorrectionLevel.formatBits << 3 | mask; // errCorrLvl is uint2, mask is uint3
int rem = data;
for (int i = 0; i < 10; i++)
rem = (rem << 1) ^ ((rem >>> 9) * 0x537);
int bits = (data << 10 | rem) ^ 0x5412; // uint15
assert bits >>> 15 == 0;
// Draw first copy
for (int i = 0; i <= 5; i++)
setFunctionModule(8, i, getBit(bits, i));
setFunctionModule(8, 7, getBit(bits, 6));
setFunctionModule(8, 8, getBit(bits, 7));
setFunctionModule(7, 8, getBit(bits, 8));
for (int i = 9; i < 15; i++)
setFunctionModule(14 - i, 8, getBit(bits, i));
// Draw second copy
for (int i = 0; i <= 7; i++)
setFunctionModule(size - 1 - i, 8, getBit(bits, i));
for (int i = 8; i < 15; i++)
setFunctionModule(8, size - 15 + i, getBit(bits, i));
setFunctionModule(8, size - 8, true); // Always black
}
// Draws two copies of the version bits (with its own error correction code),
// based on this object's version field, iff 7 <= version <= 40.
private void drawVersion() {
if (version < 7)
return;
// Calculate error correction code and pack bits
int rem = version; // version is uint6, in the range [7, 40]
for (int i = 0; i < 12; i++)
rem = (rem << 1) ^ ((rem >>> 11) * 0x1F25);
int bits = version << 12 | rem; // uint18
assert bits >>> 18 == 0;
// Draw two copies
for (int i = 0; i < 18; i++) {
boolean bit = getBit(bits, i);
int a = size - 11 + i % 3;
int b = i / 3;
setFunctionModule(a, b, bit);
setFunctionModule(b, a, bit);
}
}
// Draws a 9*9 finder pattern including the border separator,
// with the center module at (x, y). Modules can be out of bounds.
private void drawFinderPattern(int x, int y) {
for (int dy = -4; dy <= 4; dy++) {
for (int dx = -4; dx <= 4; dx++) {
int dist = Math.max(Math.abs(dx), Math.abs(dy)); // Chebyshev/infinity norm
int xx = x + dx, yy = y + dy;
if (0 <= xx && xx < size && 0 <= yy && yy < size)
setFunctionModule(xx, yy, dist != 2 && dist != 4);
}
}
}
// Draws a 5*5 alignment pattern, with the center module
// at (x, y). All modules must be in bounds.
private void drawAlignmentPattern(int x, int y) {
for (int dy = -2; dy <= 2; dy++) {
for (int dx = -2; dx <= 2; dx++)
setFunctionModule(x + dx, y + dy, Math.max(Math.abs(dx), Math.abs(dy)) != 1);
}
}
// Sets the color of a module and marks it as a function module.
// Only used by the constructor. Coordinates must be in bounds.
private void setFunctionModule(int x, int y, boolean isBlack) {
modules[y][x] = isBlack;
isFunction[y][x] = true;
}
/*---- Private helper methods for constructor: Codewords and masking ----*/
// Returns a new byte string representing the given data with the appropriate error correction
// codewords appended to it, based on this object's version and error correction level.
private byte[] addEccAndInterleave(byte[] data) {
Objects.requireNonNull(data);
if (data.length != getNumDataCodewords(version, errorCorrectionLevel))
throw new IllegalArgumentException();
// Calculate parameter numbers
int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[errorCorrectionLevel.ordinal()][version];
int blockEccLen = ECC_CODEWORDS_PER_BLOCK [errorCorrectionLevel.ordinal()][version];
int rawCodewords = getNumRawDataModules(version) / 8;
int numShortBlocks = numBlocks - rawCodewords % numBlocks;
int shortBlockLen = rawCodewords / numBlocks;
// Split data into blocks and append ECC to each block
byte[][] blocks = new byte[numBlocks][];
ReedSolomonGenerator rs = new ReedSolomonGenerator(blockEccLen);
for (int i = 0, k = 0; i < numBlocks; i++) {
byte[] dat = Arrays.copyOfRange(data, k, k + shortBlockLen - blockEccLen + (i < numShortBlocks ? 0 : 1));
k += dat.length;
byte[] block = Arrays.copyOf(dat, shortBlockLen + 1);
byte[] ecc = rs.getRemainder(dat);
System.arraycopy(ecc, 0, block, block.length - blockEccLen, ecc.length);
blocks[i] = block;
}
// Interleave (not concatenate) the bytes from every block into a single sequence
byte[] result = new byte[rawCodewords];
for (int i = 0, k = 0; i < blocks[0].length; i++) {
for (int j = 0; j < blocks.length; j++) {
// Skip the padding byte in short blocks
if (i != shortBlockLen - blockEccLen || j >= numShortBlocks) {
result[k] = blocks[j][i];
k++;
}
}
}
return result;
}
// Draws the given sequence of 8-bit codewords (data and error correction) onto the entire
// data area of this QR Code. Function modules need to be marked off before this is called.
private void drawCodewords(byte[] data) {
Objects.requireNonNull(data);
if (data.length != getNumRawDataModules(version) / 8)
throw new IllegalArgumentException();
int i = 0; // Bit index into the data
// Do the funny zigzag scan
for (int right = size - 1; right >= 1; right -= 2) { // Index of right column in each column pair
if (right == 6)
right = 5;
for (int vert = 0; vert < size; vert++) { // Vertical counter
for (int j = 0; j < 2; j++) {
int x = right - j; // Actual x coordinate
boolean upward = ((right + 1) & 2) == 0;
int y = upward ? size - 1 - vert : vert; // Actual y coordinate
if (!isFunction[y][x] && i < data.length * 8) {
modules[y][x] = getBit(data[i >>> 3], 7 - (i & 7));
i++;
}
// If this QR Code has any remainder bits (0 to 7), they were assigned as
// 0/false/white by the constructor and are left unchanged by this method
}
}
}
assert i == data.length * 8;
}
// XORs the codeword modules in this QR Code with the given mask pattern.
// The function modules must be marked and the codeword bits must be drawn
// before masking. Due to the arithmetic of XOR, calling applyMask() with
// the same mask value a second time will undo the mask. A final well-formed
// QR Code needs exactly one (not zero, two, etc.) mask applied.
private void applyMask(int mask) {
if (mask < 0 || mask > 7)
throw new IllegalArgumentException("Mask value out of range");
for (int y = 0; y < size; y++) {
for (int x = 0; x < size; x++) {
boolean invert;
switch (mask) {
case 0: invert = (x + y) % 2 == 0; break;
case 1: invert = y % 2 == 0; break;
case 2: invert = x % 3 == 0; break;
case 3: invert = (x + y) % 3 == 0; break;
case 4: invert = (x / 3 + y / 2) % 2 == 0; break;
case 5: invert = x * y % 2 + x * y % 3 == 0; break;
case 6: invert = (x * y % 2 + x * y % 3) % 2 == 0; break;
case 7: invert = ((x + y) % 2 + x * y % 3) % 2 == 0; break;
default: throw new AssertionError();
}
modules[y][x] ^= invert & !isFunction[y][x];
}
}
}
// A messy helper function for the constructor. This QR Code must be in an unmasked state when this
// method is called. The given argument is the requested mask, which is -1 for auto or 0 to 7 for fixed.
// This method applies and returns the actual mask chosen, from 0 to 7.
private int handleConstructorMasking(int mask) {
if (mask == -1) { // Automatically choose best mask
int minPenalty = Integer.MAX_VALUE;
for (int i = 0; i < 8; i++) {
drawFormatBits(i);
applyMask(i);
int penalty = getPenaltyScore();
if (penalty < minPenalty) {
mask = i;
minPenalty = penalty;
}
applyMask(i); // Undoes the mask due to XOR
}
}
assert 0 <= mask && mask <= 7;
drawFormatBits(mask); // Overwrite old format bits
applyMask(mask); // Apply the final choice of mask
return mask; // The caller shall assign this value to the final-declared field
}
// Calculates and returns the penalty score based on state of this QR Code's current modules.
// This is used by the automatic mask choice algorithm to find the mask pattern that yields the lowest score.
private int getPenaltyScore() {
int result = 0;
// Adjacent modules in row having same color
for (int y = 0; y < size; y++) {
boolean colorX = false;
for (int x = 0, runX = 0; x < size; x++) {
if (x == 0 || modules[y][x] != colorX) {
colorX = modules[y][x];
runX = 1;
} else {
runX++;
if (runX == 5)
result += PENALTY_N1;
else if (runX > 5)
result++;
}
}
}
// Adjacent modules in column having same color
for (int x = 0; x < size; x++) {
boolean colorY = false;
for (int y = 0, runY = 0; y < size; y++) {
if (y == 0 || modules[y][x] != colorY) {
colorY = modules[y][x];
runY = 1;
} else {
runY++;
if (runY == 5)
result += PENALTY_N1;
else if (runY > 5)
result++;
}
}
}
// 2*2 blocks of modules having same color
for (int y = 0; y < size - 1; y++) {
for (int x = 0; x < size - 1; x++) {
boolean color = modules[y][x];
if ( color == modules[y][x + 1] &&
color == modules[y + 1][x] &&
color == modules[y + 1][x + 1])
result += PENALTY_N2;
}
}
// Finder-like pattern in rows
for (int y = 0; y < size; y++) {
for (int x = 0, bits = 0; x < size; x++) {
bits = ((bits << 1) & 0b11111111111) | (modules[y][x] ? 1 : 0);
if (x >= 10 && (bits == 0b00001011101 || bits == 0b10111010000)) // Needs 11 bits accumulated
result += PENALTY_N3;
}
}
// Finder-like pattern in columns
for (int x = 0; x < size; x++) {
for (int y = 0, bits = 0; y < size; y++) {
bits = ((bits << 1) & 0b11111111111) | (modules[y][x] ? 1 : 0);
if (y >= 10 && (bits == 0b00001011101 || bits == 0b10111010000)) // Needs 11 bits accumulated
result += PENALTY_N3;
}
}
// Balance of black and white modules
int black = 0;
for (boolean[] row : modules) {
for (boolean color : row) {
if (color)
black++;
}
}
int total = size * size; // Note that size is odd, so black/total != 1/2
// Compute the smallest integer k >= 0 such that (45-5k)% <= black/total <= (55+5k)%
int k = (Math.abs(black * 20 - total * 10) + total - 1) / total - 1;
result += k * PENALTY_N4;
return result;
}
/*---- Private helper functions ----*/
// Returns an ascending list of positions of alignment patterns for this version number.
// Each position is in the range [0,177), and are used on both the x and y axes.
// This could be implemented as lookup table of 40 variable-length lists of unsigned bytes.
private int[] getAlignmentPatternPositions() {
if (version == 1)
return new int[]{};
else {
int numAlign = version / 7 + 2;
int step;
if (version == 32) // Special snowflake
step = 26;
else // step = ceil[(size - 13) / (numAlign*2 - 2)] * 2
step = (version*4 + numAlign*2 + 1) / (numAlign*2 - 2) * 2;
int[] result = new int[numAlign];
result[0] = 6;
for (int i = result.length - 1, pos = size - 7; i >= 1; i--, pos -= step)
result[i] = pos;
return result;
}
}
// Returns the number of data bits that can be stored in a QR Code of the given version number, after
// all function modules are excluded. This includes remainder bits, so it might not be a multiple of 8.
// The result is in the range [208, 29648]. This could be implemented as a 40-entry lookup table.
private static int getNumRawDataModules(int ver) {
if (ver < MIN_VERSION || ver > MAX_VERSION)
throw new IllegalArgumentException("Version number out of range");
int size = ver * 4 + 17;
int result = size * size; // Number of modules in the whole QR Code square
result -= 8 * 8 * 3; // Subtract the three finders with separators
result -= 15 * 2 + 1; // Subtract the format information and black module
result -= (size - 16) * 2; // Subtract the timing patterns (excluding finders)
// The five lines above are equivalent to: int result = (16 * ver + 128) * ver + 64;
if (ver >= 2) {
int numAlign = ver / 7 + 2;
result -= (numAlign - 1) * (numAlign - 1) * 25; // Subtract alignment patterns not overlapping with timing patterns
result -= (numAlign - 2) * 2 * 20; // Subtract alignment patterns that overlap with timing patterns
// The two lines above are equivalent to: result -= (25 * numAlign - 10) * numAlign - 55;
if (ver >= 7)
result -= 6 * 3 * 2; // Subtract version information
}
return result;
}
// Returns the number of 8-bit data (i.e. not error correction) codewords contained in any
// QR Code of the given version number and error correction level, with remainder bits discarded.
// This stateless pure function could be implemented as a (40*4)-cell lookup table.
static int getNumDataCodewords(int ver, Ecc ecl) {
return getNumRawDataModules(ver) / 8
- ECC_CODEWORDS_PER_BLOCK [ecl.ordinal()][ver]
* NUM_ERROR_CORRECTION_BLOCKS[ecl.ordinal()][ver];
}
// Returns true iff the i'th bit of x is set to 1.
static boolean getBit(int x, int i) {
return ((x >>> i) & 1) != 0;
}
/*---- Constants and tables ----*/
/** The minimum version number (1) supported in the QR Code Model 2 standard. */
public static final int MIN_VERSION = 1;
/** The maximum version number (40) supported in the QR Code Model 2 standard. */
public static final int MAX_VERSION = 40;
// For use in getPenaltyScore(), when evaluating which mask is best.
private static final int PENALTY_N1 = 3;
private static final int PENALTY_N2 = 3;
private static final int PENALTY_N3 = 40;
private static final int PENALTY_N4 = 10;
private static final byte[][] ECC_CODEWORDS_PER_BLOCK = {
// Version: (note that index 0 is for padding, and is set to an illegal value)
//0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level
{-1, 7, 10, 15, 20, 26, 18, 20, 24, 30, 18, 20, 24, 26, 30, 22, 24, 28, 30, 28, 28, 28, 28, 30, 30, 26, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30}, // Low
{-1, 10, 16, 26, 18, 24, 16, 18, 22, 22, 26, 30, 22, 22, 24, 24, 28, 28, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28}, // Medium
{-1, 13, 22, 18, 26, 18, 24, 18, 22, 20, 24, 28, 26, 24, 20, 30, 24, 28, 28, 26, 30, 28, 30, 30, 30, 30, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30}, // Quartile
{-1, 17, 28, 22, 16, 22, 28, 26, 26, 24, 28, 24, 28, 22, 24, 24, 30, 28, 28, 26, 28, 30, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30}, // High
};
private static final byte[][] NUM_ERROR_CORRECTION_BLOCKS = {
// Version: (note that index 0 is for padding, and is set to an illegal value)
//0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level
{-1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 7, 8, 8, 9, 9, 10, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 21, 22, 24, 25}, // Low
{-1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 5, 8, 9, 9, 10, 10, 11, 13, 14, 16, 17, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 35, 37, 38, 40, 43, 45, 47, 49}, // Medium
{-1, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 12, 16, 12, 17, 16, 18, 21, 20, 23, 23, 25, 27, 29, 34, 34, 35, 38, 40, 43, 45, 48, 51, 53, 56, 59, 62, 65, 68}, // Quartile
{-1, 1, 1, 2, 4, 4, 4, 5, 6, 8, 8, 11, 11, 16, 16, 18, 16, 19, 21, 25, 25, 25, 34, 30, 32, 35, 37, 40, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 77, 81}, // High
};
/*---- Public helper enumeration ----*/
/**
* The error correction level in a QR Code symbol.
*/
public enum Ecc {
// Must be declared in ascending order of error protection
// so that the implicit ordinal() and values() work properly
/** The QR Code can tolerate about 7% erroneous codewords. */ LOW(1),
/** The QR Code can tolerate about 15% erroneous codewords. */ MEDIUM(0),
/** The QR Code can tolerate about 25% erroneous codewords. */ QUARTILE(3),
/** The QR Code can tolerate about 30% erroneous codewords. */ HIGH(2);
// In the range 0 to 3 (unsigned 2-bit integer).
final int formatBits;
// Constructor.
private Ecc(int fb) {
formatBits = fb;
}
}
/*---- Private helper class ----*/
/**
* Computes the Reed-Solomon error correction codewords for a sequence of data codewords
* at a given degree. Objects are immutable, and the state only depends on the degree.
* This class exists because each data block in a QR Code shares the same the divisor polynomial.
*/
private static final class ReedSolomonGenerator {
/*-- Field --*/
// 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 final byte[] coefficients;
/*-- Constructor --*/
/**
* Constructs a Reed-Solomon ECC generator for the specified degree. This could be implemented
* as a lookup table over all possible parameter values, instead of as an algorithm.
* @param degree the divisor polynomial degree, which must be between 1 and 255 (inclusive)
* @throws IllegalArgumentException if degree &lt; 1 or degree > 255
*/
public ReedSolomonGenerator(int degree) {
if (degree < 1 || degree > 255)
throw new IllegalArgumentException("Degree out of range");
// Start with the monomial x^0
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);
}
}
/*-- Method --*/
/**
* Computes and returns the Reed-Solomon error correction codewords for the specified
* sequence of data codewords. The returned object is always a new byte array.
* This method does not alter this object's state (because it is immutable).
* @param data the sequence of data codewords
* @return the Reed-Solomon error correction codewords
* @throws NullPointerException if the data is {@code null}
*/
public byte[] getRemainder(byte[] data) {
Objects.requireNonNull(data);
// Compute the remainder by performing polynomial division
byte[] result = new byte[coefficients.length];
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] ^= multiply(coefficients[i] & 0xFF, factor);
}
return result;
}
/*-- Static function --*/
// 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) {
assert x >>> 8 == 0 && y >>> 8 == 0;
// Russian peasant multiplication
int z = 0;
for (int i = 7; i >= 0; i--) {
z = (z << 1) ^ ((z >>> 7) * 0x11D);
z ^= ((y >>> i) & 1) * x;
}
assert z >>> 8 == 0;
return z;
}
}
}
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