diff --git a/QrCode.java b/QrCode.java index 16ec193..14bc03d 100644 --- a/QrCode.java +++ b/QrCode.java @@ -53,14 +53,27 @@ public final class QrCode { public static QrCode encodeText(String text, Ecc ecl) { if (text == null || ecl == null) throw new NullPointerException(); - QrSegment seg; // Select the most efficient segment encoding automatically + QrSegment seg = encodeTextToSegment(text); + return encodeSegments(Arrays.asList(seg), ecl); + } + + + /** + * Returns a QR Code segment representing the specified Unicode text string. + * @param text the text to be encoded, which can be any Unicode string + * @return a QR Code representing the text + * @throws NullPointerException if the text is {@code null} + */ + public static QrSegment encodeTextToSegment(String text) { + if (text == null) + throw new NullPointerException(); + // Select the most efficient segment encoding automatically if (QrSegment.NUMERIC_REGEX.matcher(text).matches()) - seg = QrSegment.makeNumeric(text); + return QrSegment.makeNumeric(text); else if (QrSegment.ALPHANUMERIC_REGEX.matcher(text).matches()) - seg = QrSegment.makeAlphanumeric(text); + return QrSegment.makeAlphanumeric(text); else - seg = QrSegment.makeBytes(text.getBytes(StandardCharsets.UTF_8)); - return encodeSegments(Arrays.asList(seg), ecl); + return QrSegment.makeBytes(text.getBytes(StandardCharsets.UTF_8)); } @@ -255,10 +268,10 @@ public final class QrCode { * @return the module's color, which is either 0 (white) or 1 (black) */ public int getModule(int x, int y) { - if (x < 0 || x >= size || y < 0 || y >= size) - return 0; // Infinite white border - else + if (0 <= x && x < size && 0 <= y && y < size) return modules[y][x] ? 1 : 0; + else + return 0; // Infinite white border } @@ -353,7 +366,7 @@ public final class QrCode { // Draws two copies of the format bits (with its own error correction code) - // based on this object's error correction level and mask fields. + // 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 @@ -400,8 +413,9 @@ public final class QrCode { // Draw two copies for (int i = 0; i < 18; i++) { boolean bit = ((data >>> i) & 1) != 0; - setFunctionModule(size - 11 + i % 3, i / 3, bit); - setFunctionModule(i / 3, size - 11 + i % 3, bit); + int a = size - 11 + i % 3, b = i / 3; + setFunctionModule(a, b, bit); + setFunctionModule(b, a, bit); } } @@ -411,8 +425,7 @@ public final class QrCode { for (int i = -4; i <= 4; i++) { for (int j = -4; j <= 4; j++) { int dist = Math.max(Math.abs(i), Math.abs(j)); // Chebyshev/infinity norm - int xx = x + j; - int yy = y + i; + int xx = x + j, yy = y + i; if (0 <= xx && xx < size && 0 <= yy && yy < size) setFunctionModule(xx, yy, dist != 2 && dist != 4); } @@ -495,7 +508,7 @@ public final class QrCode { boolean upwards = ((right & 2) == 0) ^ (x < 6); int y = upwards ? size - 1 - vert : vert; // Actual y coordinate if (!isFunction[y][x] && i < data.length * 8) { - modules[y][x] = (data[i >>> 3] >>> (7 - (i & 7)) & 1) != 0; + modules[y][x] = ((data[i >>> 3] >>> (7 - (i & 7))) & 1) != 0; i++; } } diff --git a/qrcodegen-demo.py b/qrcodegen-demo.py new file mode 100644 index 0000000..7978c94 --- /dev/null +++ b/qrcodegen-demo.py @@ -0,0 +1,125 @@ +# +# QR Code generator demo (Python 2, 3) +# +# Copyright (c) 2016 Project Nayuki +# https://www.nayuki.io/page/qr-code-generator-library +# +# (MIT License) +# 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. +# + +from __future__ import print_function +import qrcodegen + + +# ---- Main program ---- + +def main(): + """The main application program.""" + do_basic_demo() + do_variety_demo() + do_segment_demo() + + +def do_basic_demo(): + """Creates a single QR Code, then prints it to the console.""" + text = u"Hello, world!" # User-supplied Unicode text + errcorlvl = qrcodegen.QrCode.Ecc.LOW # Error correction level + qr = qrcodegen.encode_text(text, errcorlvl) + print_qr(qr) + + +def do_variety_demo(): + """Creates a variety of QR Codes that exercise different features of the library, and prints each one to the console.""" + + # Project Nayuki URL + qr = qrcodegen.encode_text("https://www.nayuki.io/", qrcodegen.QrCode.Ecc.HIGH) + qr = qrcodegen.QrCode(qrcode=qr, mask=3) # Change mask, forcing to mask #3 + print_qr(qr) + + # Numeric mode encoding (3.33 bits per digit) + qr = qrcodegen.encode_text("314159265358979323846264338327950288419716939937510", qrcodegen.QrCode.Ecc.MEDIUM) + print_qr(qr) + + # Alphanumeric mode encoding (5.5 bits per character) + qr = qrcodegen.encode_text("DOLLAR-AMOUNT:$39.87 PERCENTAGE:100.00% OPERATIONS:+-*/", qrcodegen.QrCode.Ecc.HIGH) + print_qr(qr) + + # Unicode text as UTF-8, and different masks + qr = qrcodegen.encode_text(u"\u3053\u3093\u306B\u3061\u0077\u0061\u3001\u4E16\u754C\uFF01\u0020\u03B1\u03B2\u03B3\u03B4", qrcodegen.QrCode.Ecc.QUARTILE) + print_qr(qrcodegen.QrCode(qrcode=qr, mask=0)) + print_qr(qrcodegen.QrCode(qrcode=qr, mask=1)) + print_qr(qrcodegen.QrCode(qrcode=qr, mask=5)) + print_qr(qrcodegen.QrCode(qrcode=qr, mask=7)) + + # Moderately large QR Code using longer text (from Lewis Carroll's Alice in Wonderland) + qr = qrcodegen.encode_text("Alice was beginning to get very tired of sitting by her sister on the bank, " + "and of having nothing to do: once or twice she had peeped into the book her sister was reading, " + "but it had no pictures or conversations in it, 'and what is the use of a book,' thought Alice " + "'without pictures or conversations?' So she was considering in her own mind (as well as she could, " + "for the hot day made her feel very sleepy and stupid), whether the pleasure of making a " + "daisy-chain would be worth the trouble of getting up and picking the daisies, when suddenly " + "a White Rabbit with pink eyes ran close by her.", qrcodegen.QrCode.Ecc.HIGH) + print_qr(qr) + + +def do_segment_demo(): + """Creates QR Codes with manually specified segments for better compactness.""" + + # Illustration "silver" + silver0 = "THE SQUARE ROOT OF 2 IS 1." + silver1 = "41421356237309504880168872420969807856967187537694807317667973799" + qr = qrcodegen.encode_text(silver0 + silver1, qrcodegen.QrCode.Ecc.LOW) + print_qr(qr) + + segs = [ + qrcodegen.QrSegment.make_alphanumeric(silver0), + qrcodegen.QrSegment.make_numeric(silver1)] + qr = qrcodegen.encode_segments(segs, qrcodegen.QrCode.Ecc.LOW) + print_qr(qr) + + # Illustration "golden" + golden0 = u"Golden ratio \u03C6 = 1." + golden1 = u"6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374" + golden2 = u"......" + qr = qrcodegen.encode_text(golden0 + golden1 + golden2, qrcodegen.QrCode.Ecc.LOW) + print_qr(qr) + + segs = [ + qrcodegen.QrSegment.make_bytes(golden0.encode("UTF-8")), + qrcodegen.QrSegment.make_numeric(golden1), + qrcodegen.QrSegment.make_alphanumeric(golden2)] + qr = qrcodegen.encode_segments(segs, qrcodegen.QrCode.Ecc.LOW) + print_qr(qr) + + + +# ---- Utilities ---- + +def print_qr(qrcode): + """Prints the given QrCode object to the console.""" + border = 4 + for y in range(-border, qrcode.get_size() + border): + for x in range(-border, qrcode.get_size() + border): + print(u"\u2588 "[qrcode.get_module(x,y)] * 2, end="") + print() + print() + + +# Run the main program +if __name__ == "__main__": + main() diff --git a/qrcodegen.js b/qrcodegen.js index 8dacbe1..81b6a6d 100644 --- a/qrcodegen.js +++ b/qrcodegen.js @@ -27,16 +27,16 @@ /* * Module "qrcodegen". Public members inside this namespace: - * - Function encodeText(str text, Ecc ecl) -> QrCode + * - Function encodeText(str text, QrCode.Ecc ecl) -> QrCode * - Function encodeTextToSegment(str text) -> QrSegment - * - Function encodeBinary(list data, Ecc ecl) -> QrCode - * - Function encodeSegments(list segs, Ecc ecl) -> QrCode + * - Function encodeBinary(list data, QrCode.Ecc ecl) -> QrCode + * - Function encodeSegments(list segs, QrCode.Ecc ecl) -> QrCode * - Class QrCode: * - Constructor QrCode(QrCode qr, int mask) - * - Constructor QrCode(list bytes, int mask, int version, Ecc ecl) + * - Constructor QrCode(list bytes, int mask, int version, QrCode.Ecc ecl) * - Method getVersion() -> int * - Method getSize() -> int - * - Method getErrorCorrectionLevel() -> Ecc + * - Method getErrorCorrectionLevel() -> QrCode.Ecc * - Method getMask() -> int * - Method getModule(int x, int y) -> int * - Method isFunctionModule(int x, int y) -> bool @@ -48,8 +48,8 @@ * - Function makeBytes(list data) -> QrSegment * - Function makeNumeric(str data) -> QrSegment * - Function makeAlphanumeric(str data) -> QrSegment - * - Constructor QrSegment(Mode mode, int numChars, list bitData) - * - Method getMode() -> Mode + * - Constructor QrSegment(QrSegment.Mode mode, int numChars, list bitData) + * - Method getMode() -> QrSegment.Mode * - Method getNumChars() -> int * - Method getBits() -> list * - Enum Mode: @@ -155,11 +155,13 @@ var qrcodegen = new function() { + /*---- QR Code symbol class ----*/ + /* * A class that represents an immutable square grid of black and white cells for a QR Code symbol, * with associated static functions to create a QR Code from user-supplied textual or binary data. * This class covers the QR Code model 2 specification, supporting all versions (sizes) - * from 1 to 40, all 4 error correction levels, and only 3 character encoding modes. + * from 1 to 40, all 4 error correction levels. * * This constructor can be called in one of two ways: * - new QrCode(bytes, mask, version, errCorLvl): @@ -179,17 +181,15 @@ var qrcodegen = new function() { // Handle simple scalar fields if (mask < -1 || mask > 7) throw "Mask value out of range"; - var size; if (initData instanceof Array) { if (version < 1 || version > 40) throw "Version value out of range"; - size = version * 4 + 17; } else if (initData instanceof qrcodegen.QrCode) { version = initData.getVersion(); - size = initData.getSize(); errCorLvl = initData.getErrorCorrectionLevel(); } else throw "Invalid initial data"; + var size = version * 4 + 17; // Initialize both grids to be size*size arrays of Boolean false var row = []; @@ -204,7 +204,7 @@ var qrcodegen = new function() { // Handle grid fields if (initData instanceof Array) { - // Draw function patterns, draw all codewords, do masking + // Draw function patterns, draw all codewords drawFunctionPatterns(); var allCodewords = appendErrorCorrection(initData); drawCodewords(allCodewords); @@ -267,19 +267,19 @@ var qrcodegen = new function() { // Returns the color of the module (pixel) at the given coordinates, which is either 0 for white or 1 for black. The top // left corner has the coordinates (x=0, y=0). If the given coordinates are out of bounds, then 0 (white) is returned. this.getModule = function(x, y) { - if (x < 0 || x >= size || y < 0 || y >= size) - return 0; // Infinite white border - else + if (0 <= x && x < size && 0 <= y && y < size) return modules[y][x] ? 1 : 0; + else + return 0; // Infinite white border }; // Tests whether the module at the given coordinates is a function module (true) or not (false). The top left // corner has the coordinates (x=0, y=0). If the given coordinates are out of bounds, then false is returned. this.isFunctionModule = function(x, y) { - if (x < 0 || x >= size || y < 0 || y >= size) - return false; // Infinite border - else + if (0 <= x && x < size && 0 <= y && y < size) return isFunction[y][x]; + else + return false; // Infinite border }; @@ -345,7 +345,7 @@ var qrcodegen = new function() { // Draws two copies of the format bits (with its own error correction code) - // based on this object's error correction level and mask fields. + // based on the given mask and this object's error correction level field. function drawFormatBits(mask) { // Calculate error correction code and pack bits var data = errCorLvl.formatBits << 3 | mask; // errCorrLvl is uint2, mask is uint3 @@ -392,8 +392,7 @@ var qrcodegen = new function() { // Draw two copies for (var i = 0; i < 18; i++) { var bit = ((data >>> i) & 1) != 0; - var a = size - 11 + i % 3; - var b = Math.floor(i / 3); + var a = size - 11 + i % 3, b = Math.floor(i / 3); setFunctionModule(a, b, bit); setFunctionModule(b, a, bit); } @@ -405,8 +404,7 @@ var qrcodegen = new function() { for (var i = -4; i <= 4; i++) { for (var j = -4; j <= 4; j++) { var dist = Math.max(Math.abs(i), Math.abs(j)); // Chebyshev/infinity norm - var xx = x + j; - var yy = y + i; + var xx = x + j, yy = y + i; if (0 <= xx && xx < size && 0 <= yy && yy < size) setFunctionModule(xx, yy, dist != 2 && dist != 4); } @@ -489,7 +487,7 @@ var qrcodegen = new function() { var upwards = ((right & 2) == 0) ^ (x < 6); var y = upwards ? size - 1 - vert : vert; // Actual y coordinate if (!isFunction[y][x] && i < data.length * 8) { - modules[y][x] = (data[i >>> 3] >>> (7 - (i & 7)) & 1) != 0; + modules[y][x] = ((data[i >>> 3] >>> (7 - (i & 7))) & 1) != 0; i++; } } @@ -614,9 +612,9 @@ var qrcodegen = new function() { var QrCode = {}; // Private object to assign properties to - // Returns a set of positions of the alignment patterns in ascending order. These positions are - // used on both the x and y axes. Each value in the resulting array is in the range [0, 177). - // This stateless pure function could be implemented as table of 40 variable-length lists of unsigned bytes. + // Returns a sequence of positions of the alignment patterns in ascending order. These positions are + // used on both the x and y axes. Each value in the resulting sequence is in the range [0, 177). + // This stateless pure function could be implemented as table of 40 variable-length lists of integers. QrCode.getAlignmentPatternPositions = function(ver) { if (ver < 1 || ver > 40) throw "Version number out of range"; @@ -705,6 +703,8 @@ var qrcodegen = new function() { + /*---- Data segment class ----*/ + /* * A public class that represents a character string to be encoded in a QR Code symbol. * Each segment has a mode, and a sequence of characters that is already encoded as @@ -714,6 +714,9 @@ var qrcodegen = new function() { * Any segment longer than this is meaningless for the purpose of generating QR Codes. */ this.QrSegment = function(mode, numChars, bitData) { + if (numChars < 0 || !(mode instanceof Mode)) + throw "Invalid argument"; + /*-- Accessor methods --*/ this.getMode = function() { return mode; @@ -726,7 +729,7 @@ var qrcodegen = new function() { }; }; - /*-- Static factory functions --*/ + /*-- Public static factory functions --*/ // Returns a segment representing the given binary data encoded in byte mode. this.QrSegment.makeBytes = function(data) { @@ -819,36 +822,15 @@ var qrcodegen = new function() { // Returns a new array of bytes representing the given string encoded in UTF-8. function toUtf8ByteArray(str) { + str = encodeURI(str); var result = []; for (var i = 0; i < str.length; i++) { - var c = str.charCodeAt(i); - if (c < 0x80) - result.push(c); - else if (c < 0x800) { - result.push(0xC0 | ((c >>> 6) & 0x1F)); - result.push(0x80 | ((c >>> 0) & 0x3F)); - } else if (0xD800 <= c && c < 0xDC00) { // High surrogate - i++; - if (i < str.length) { - var d = str.charCodeAt(i); - if (0xDC00 <= d && d < 0xE000) { // Low surrogate - c = ((c & 0x3FF) << 10 | (d & 0x3FF)) + 0x10000; - result.push(0xF0 | ((c >>> 18) & 0x07)); - result.push(0x80 | ((c >>> 12) & 0x3F)); - result.push(0x80 | ((c >>> 6) & 0x3F)); - result.push(0x80 | ((c >>> 0) & 0x3F)); - continue; - } - } - throw "Invalid UTF-16 string"; - } else if (0xDC00 <= c && c < 0xE000) // Low surrogate - throw "Invalid UTF-16 string"; - else if (c < 0x10000) { - result.push(0xE0 | ((c >>> 12) & 0x0F)); - result.push(0x80 | ((c >>> 6) & 0x3F)); - result.push(0x80 | ((c >>> 0) & 0x3F)); - } else - throw "Assertion error"; + if (str.charAt(i) != "%") + result.push(str.charCodeAt(i)); + else { + result.push(parseInt(str.substr(i + 1, 2), 16)); + i += 2; + } } return result; } diff --git a/qrcodegen.py b/qrcodegen.py new file mode 100644 index 0000000..5e858d0 --- /dev/null +++ b/qrcodegen.py @@ -0,0 +1,813 @@ +# +# QR Code generator library (Python 2, 3) +# +# Copyright (c) 2016 Project Nayuki +# https://www.nayuki.io/page/qr-code-generator-library +# +# (MIT License) +# 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. +# + +import itertools, re, sys + + +""" +Public members inside this module "qrcodegen": +- Function encode_text(str text, QrCode.Ecc ecl) -> QrCode +- Function encode_text_to_segment(str text) -> QrSegment +- Function encode_binary(bytes data, QrCode.Ecc ecl) -> QrCode +- Function encode_segments(list segs, QrCode.Ecc ecl) -> QrCode +- Class QrCode: + - Constructor QrCode(QrCode qr, int mask) + - Constructor QrCode(bytes bytes, int mask, int version, QrCode.Ecc ecl) + - Method get_version() -> int + - Method get_size() -> int + - Method get_error_correction_level() -> QrCode.Ecc + - Method get_mask() -> int + - Method get_module(int x, int y) -> int + - Method to_svg_str(int border) -> str + - Enum Ecc: + - Constants LOW, MEDIUM, QUARTILE, HIGH + - Fields int ordinal, formatbits +- Class QrSegment: + - Function make_bytes(bytes data) -> QrSegment + - Function make_numeric(str digits) -> QrSegment + - Function make_alphanumeric(str text) -> QrSegment + - Constructor QrSegment(QrSegment.Mode mode, int numch, list bitdata) + - Method get_mode() -> QrSegment.Mode + - Method get_num_chars() -> int + - Method get_bits() -> list + - Enum Mode: + - Constants NUMERIC, ALPHANUMERIC, BYTE, KANJI + - Method get_mode_bits() -> int + - Method num_char_count_bits(int ver) -> int +""" + + +# ---- Public static factory functions for QrCode ---- + +def encode_text(text, ecl): + """Returns a QR Code symbol representing the given Unicode text string at the given 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). The smallest possible QR Code version is automatically chosen for the output.""" + seg = encode_text_to_segment(text) + return encode_segments([seg], ecl) + + +def encode_text_to_segment(text): + """Returns a QR Code segment representing the given Unicode text string.""" + if not isinstance(text, str) and (sys.version_info[0] >= 3 or not isinstance(text, unicode)): + raise TypeError("Text string expected") + # Select the most efficient segment encoding automatically + if QrSegment.NUMERIC_REGEX.match(text) is not None: + return QrSegment.make_numeric(text) + elif QrSegment.ALPHANUMERIC_REGEX.match(text) is not None: + return QrSegment.make_alphanumeric(text) + else: + return QrSegment.make_bytes(text.encode("UTF-8")) + + +def encode_binary(data, ecl): + """Returns a QR Code symbol representing the given binary data string at the given 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.""" + if not isinstance(data, bytes): + raise TypeError("Binary array expected") + return QrCode.encode_segments([QrSegment.make_bytes(data)], ecl) + + +def encode_segments(segs, ecl): + """Returns a QR Code symbol representing the given data segments at the given error + correction level. The smallest possible QR Code version is automatically chosen for the output. + 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.""" + + # Find the minimal version number to use + for version in itertools.count(1): # Increment until the data fits in the QR Code + if version > 40: # All versions could not fit the given data + raise ValueError("Data too long") + datacapacitybits = QrCode._get_num_data_codewords(version, ecl) * 8 # Number of data bits available + + # Calculate the total number of bits needed at this version number + # to encode all the segments (i.e. segment metadata and payloads) + datausedbits = 0 + for seg in segs: + if seg.get_num_chars() < 0: + raise AssertionError() + ccbits = seg.get_mode().num_char_count_bits(version) + if seg.get_num_chars() >= (1 << ccbits): + # Segment length value doesn't fit in the length field's bit-width, so fail immediately + break + datausedbits += 4 + ccbits + len(seg.get_bits()) + else: # If the loop above did not break + if datausedbits <= datacapacitybits: + break # This version number is found to be suitable + + # Create the data bit string by concatenating all segments + bb = _BitBuffer() + for seg in segs: + bb.append_bits(seg.get_mode().get_mode_bits(), 4) + bb.append_bits(seg.get_num_chars(), seg.get_mode().num_char_count_bits(version)) + bb.append_all(seg) + + # Add terminator and pad up to a byte if applicable + bb.append_bits(0, min(4, datacapacitybits - bb.bit_length())) + bb.append_bits(0, -bb.bit_length() % 8) + + # Pad with alternate bytes until data capacity is reached + for padbyte in itertools.cycle((0xEC, 0x11)): + if bb.bit_length() >= datacapacitybits: + break + bb.append_bits(padbyte, 8) + assert bb.bit_length() % 8 == 0 + + # Create the QR Code symbol + return QrCode(datacodewords=bb.get_bytes(), mask=-1, version=version, errcorlvl=ecl) + + + +# ---- QR Code symbol class ---- + +class QrCode(object): + """Represents an immutable square grid of black or white cells for a QR Code symbol. This class covers the + QR Code model 2 specification, supporting all versions (sizes) from 1 to 40, all 4 error correction levels.""" + + # ---- Constructor ---- + + def __init__(self, qrcode=None, datacodewords=None, mask=None, version=None, errcorlvl=None): + """This constructor can be called in one of two ways: + - QrCode(datacodewords=list, mask=int, version=int, errcorlvl=QrCode.Ecc): + Creates a new QR Code symbol with the given version number, error correction level, binary data array, + and mask number. This cumbersome constructor can be invoked directly by the user, but is considered + to be even lower level than qrcodegen.encode_segments(). + - QrCode(qrcode=QrCode, mask=int): + Creates a new QR Code symbol based on the given existing object, but with a potentially different + mask pattern. The version, error correction level, codewords, etc. of the newly created object are + all identical to the argument object; only the mask may differ. + In both cases, mask = -1 is for automatic choice or 0 to 7 for fixed choice.""" + + # Handle simple scalar fields + if not -1 <= mask <= 7: + raise ValueError("Mask value out of range") + if datacodewords is not None and qrcode is None: + if not 1 <= version <= 40: + raise ValueError("Version value out of range") + if not isinstance(errcorlvl, QrCode.Ecc): + raise TypeError("QrCode.Ecc expected") + elif qrcode is not None and datacodewords is None: + version = qrcode._version + errcorlvl = qrcode._errcorlvl + else: + raise ValueError("Exactly one of datacodewords or qrcode must be not None") + self._version = version + self._errcorlvl = errcorlvl + self._size = version * 4 + 17 + + if datacodewords is not None: # Render from scratch a QR Code based on data codewords + if len(datacodewords) != QrCode._get_num_data_codewords(version, errcorlvl): + raise ValueError("Invalid array length") + # Initialize grids of modules + self._modules = [[False] * self._size for _ in range(self._size)] # The modules of the QR symbol; start with entirely white grid + self._isfunction = [[False] * self._size for _ in range(self._size)] # Indicates function modules that are not subjected to masking + # Draw function patterns, draw all codewords + self._draw_function_patterns() + allcodewords = self._append_error_correction(datacodewords) + self._draw_codewords(allcodewords) + elif qrcode is not None: # Modify the mask of an existing QR Code + self._modules = [list(row) for row in qrcode._modules] # Deep copy + self._isfunction = qrcode._isfunction # Shallow copy because the data is read-only + self._apply_mask(qrcode._mask) # Undo existing mask + + # Handle masking + if mask == -1: # Automatically choose best mask + minpenalty = 1 << 32 + for i in range(8): + self._draw_format_bits(i) + self._apply_mask(i) + penalty = self._get_penalty_score() + if penalty < minpenalty: + mask = i + minpenalty = penalty + self._apply_mask(i) # Undoes the mask due to XOR + assert 0 <= mask <= 7 + self._draw_format_bits(mask) # Overwrite old format bits + self._apply_mask(mask) # Apply the final choice of mask + self._mask = mask + + + # ---- Accessor methods ---- + + def get_version(self): + """Returns this QR Code symbol's version number, which is always between 1 and 40 (inclusive).""" + return self._version + + def get_size(self): + """Returns the width and height of this QR Code symbol, measured in modules. + Always equal to version * 4 + 17, in the range 21 to 177.""" + return self._size + + def get_error_correction_level(self): + """Returns the error correction level used in this QR Code symbol.""" + return self._errcorlvl + + def get_mask(self): + """Returns the mask pattern used in this QR Code symbol, in the range 0 to 7 (i.e. unsigned 3-bit integer). + Note that even if a constructor was called with automatic masking requested + (mask = -1), the resulting object will still have a mask value between 0 and 7.""" + return self._mask + + def get_module(self, x, y): + """Returns the color of the module (pixel) at the given coordinates, which is either 0 for white or 1 for black. The top + left corner has the coordinates (x=0, y=0). If the given coordinates are out of bounds, then 0 (white) is returned.""" + return 1 if (0 <= x < self._size and 0 <= y < self._size and self._modules[y][x]) else 0 + + + # ---- Public instance methods ---- + + def to_svg_str(self, border): + """Based on the given number of border modules to add as padding, this returns a + string whose contents represents an SVG XML file that depicts this QR Code symbol.""" + if border < 0: + raise ValueError("Border must be non-negative") + parts = [] + for y in range(-border, self.size + border): + for x in range(-border, self.size + border): + if self.get_module(x, y) == 1: + parts.append("M{},{}h1v1h-1z".format(x + border, y + border)) + return """ + + + + +""".format(self.size + border * 2, " ".join(parts)) + + + # ---- Private helper methods for constructor: Drawing function modules ---- + + def _draw_function_patterns(self): + # Draw the horizontal and vertical timing patterns + for i in range(self._size): + self._set_function_module(6, i, i % 2 == 0) + self._set_function_module(i, 6, i % 2 == 0) + + # Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules) + self._draw_finder_pattern(3, 3) + self._draw_finder_pattern(self._size - 4, 3) + self._draw_finder_pattern(3, self._size - 4) + + # Draw the numerous alignment patterns + alignpatpos = QrCode._get_alignment_pattern_positions(self._version) + numalign = len(alignpatpos) + skips = ((0, 0), (0, numalign - 1), (numalign - 1, 0)) # Skip the three finder corners + for i in range(numalign): + for j in range(numalign): + if (i, j) not in skips: + self._draw_alignment_pattern(alignpatpos[i], alignpatpos[j]) + + # Draw configuration data + self._draw_format_bits(0) # Dummy mask value; overwritten later in the constructor + self._draw_version() + + + def _draw_format_bits(self, mask): + """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.""" + # Calculate error correction code and pack bits + data = self._errcorlvl.formatbits << 3 | mask # errCorrLvl is uint2, mask is uint3 + rem = data + for _ in range(10): + rem = (rem << 1) ^ ((rem >> 9) * 0x537) + data = data << 10 | rem + data ^= 0x5412 # uint15 + assert data & ((1 << 15) - 1) == data + + # Draw first copy + for i in range(0, 6): + self._set_function_module(8, i, ((data >> i) & 1) != 0) + self._set_function_module(8, 7, ((data >> 6) & 1) != 0) + self._set_function_module(8, 8, ((data >> 7) & 1) != 0) + self._set_function_module(7, 8, ((data >> 8) & 1) != 0) + for i in range(9, 15): + self._set_function_module(14 - i, 8, ((data >> i) & 1) != 0) + + # Draw second copy + for i in range(0, 8): + self._set_function_module(self._size - 1 - i, 8, ((data >> i) & 1) != 0) + for i in range(8, 15): + self._set_function_module(8, self._size - 15 + i, ((data >> i) & 1) != 0) + self._set_function_module(8, self._size - 8, True) + + + def _draw_version(self): + """Draws two copies of the version bits (with its own error correction code), + based on this object's version field (which only has an effect for 7 <= version <= 40).""" + if self._version < 7: + return + + # Calculate error correction code and pack bits + rem = self._version # version is uint6, in the range [7, 40] + for _ in range(12): + rem = (rem << 1) ^ ((rem >> 11) * 0x1F25) + data = self._version << 12 | rem # uint18 + assert data & ((1 << 18) - 1) == data + + # Draw two copies + for i in range(18): + bit = ((data >> i) & 1) != 0 + a, b = self._size - 11 + i % 3, i // 3 + self._set_function_module(a, b, bit) + self._set_function_module(b, a, bit) + + + def _draw_finder_pattern(self, x, y): + """Draws a 9*9 finder pattern including the border separator, with the center module at (x, y).""" + for i in range(-4, 5): + for j in range(-4, 5): + dist = max(abs(i), abs(j)) # Chebyshev/infinity norm + xx, yy = x + j, y + i + if 0 <= xx < self._size and 0 <= yy < self._size: + self._set_function_module(xx, yy, dist not in (2, 4)) + + + def _draw_alignment_pattern(self, x, y): + """Draws a 5*5 alignment pattern, with the center module at (x, y).""" + for i in range(-2, 3): + for j in range(-2, 3): + self._set_function_module(x + j, y + i, max(abs(i), abs(j)) != 1) + + + def _set_function_module(self, x, y, isblack): + """Sets the color of a module and marks it as a function module. + Only used by the constructor. Coordinates must be in range.""" + assert type(isblack) is bool + self._modules[y][x] = isblack + self._isfunction[y][x] = True + + + # ---- Private helper methods for constructor: Codewords and masking ---- + + def _append_error_correction(self, data): + """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.""" + version = self._version + assert len(data) == QrCode._get_num_data_codewords(version, self._errcorlvl) + numblocks = QrCode._NUM_ERROR_CORRECTION_BLOCKS[self._errcorlvl.ordinal][version] + numecc = QrCode._NUM_ERROR_CORRECTION_CODEWORDS[self._errcorlvl.ordinal][version] + assert numecc % numblocks == 0 + ecclen = numecc // numblocks + numshortblocks = numblocks - QrCode._get_num_raw_data_modules(version) // 8 % numblocks + shortblocklen = self._get_num_raw_data_modules(version) // 8 // numblocks + + blocks = [] + rs = _ReedSolomonGenerator(ecclen) + k = 0 + for i in range(numblocks): + dat = data[k : k + shortblocklen - ecclen + (0 if i < numshortblocks else 1)] + k += len(dat) + ecc = rs.get_remainder(dat) + if i < numshortblocks: + dat.append(0) + dat.extend(ecc) + blocks.append(dat) + assert k == len(data) + + result = [] + for i in range(len(blocks[0])): + for (j, blk) in enumerate(blocks): + if i != shortblocklen - ecclen or j >= numshortblocks: + result.append(blk[i]) + assert len(result) == QrCode._get_num_raw_data_modules(version) // 8 + return result + + + def _draw_codewords(self, data): + """Draws the given sequence of 8-bit codewords (data and error correction) onto the entire + data area of this QR Code symbol. Function modules need to be marked off before this is called.""" + assert len(data) == QrCode._get_num_raw_data_modules(self._version) // 8 + + i = 0 # Bit index into the data + # Do the funny zigzag scan + for right in range(self._size - 1, 0, -2): # Index of right column in each column pair + if right <= 6: + right -= 1 + for vert in range(self._size): # Vertical counter + for j in range(2): + x = right - j # Actual x coordinate + upwards = ((right & 2) == 0) ^ (x < 6) + y = (self._size - 1 - vert) if upwards else vert # Actual y coordinate + if not self._isfunction[y][x] and i < len(data) * 8: + self._modules[y][x] = ((data[i >> 3] >> (7 - (i & 7))) & 1) != 0 + i += 1 + assert i == len(data) * 8 + + + def _apply_mask(self, mask): + """XORs the data modules in this QR Code with the given mask pattern. Due to XOR's mathematical + properties, calling applyMask(m) twice with the same value is equivalent to no change at all. + This means it is possible to apply a mask, undo it, and try another mask. Note that a final + well-formed QR Code symbol needs exactly one mask applied (not zero, not two, etc.).""" + if not 0 <= mask <= 7: + raise ValueError("Mask value out of range") + masker = QrCode._MASK_PATTERNS[mask] + for y in range(self._size): + for x in range(self._size): + self._modules[y][x] ^= (masker(x, y) == 0) and (not self._isfunction[y][x]) + + + def _get_penalty_score(self): + """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.""" + result = 0 + size = self._size + modules = self._modules + + # Adjacent modules in row having same color + for y in range(size): + colorx = modules[y][0] + runx = 1 + for x in range(1, size): + if modules[y][x] != colorx: + colorx = modules[y][x] + runx = 1 + else: + runx += 1 + if runx == 5: + result += QrCode._PENALTY_N1 + elif runx > 5: + result += 1 + # Adjacent modules in column having same color + for x in range(size): + colory = modules[0][x] + runy = 1 + for y in range(1, size): + if modules[y][x] != colory: + colory = modules[y][x] + runy = 1 + else: + runy += 1 + if runy == 5: + result += QrCode._PENALTY_N1 + elif runy > 5: + result += 1 + + # 2*2 blocks of modules having same color + for y in range(size - 1): + for x in range(size - 1): + color = modules[y][x] + if color == modules[y][x + 1] == modules[y + 1][x] == modules[y + 1][x + 1]: + result += QrCode._PENALTY_N2 + + # Finder-like pattern in rows + for y in range(size): + bits = 0 + for x in range(size): + bits = ((bits << 1) & 0x7FF) | (1 if modules[y][x] else 0) + if x >= 10 and bits in (0x05D, 0x5D0): # Needs 11 bits accumulated + result += QrCode._PENALTY_N3 + # Finder-like pattern in columns + for x in range(size): + bits = 0 + for y in range(size): + bits = ((bits << 1) & 0x7FF) | (1 if modules[y][x] else 0) + if y >= 10 and bits in (0x05D, 0x5D0): # Needs 11 bits accumulated + result += QrCode._PENALTY_N3 + + # Balance of black and white modules + black = 0 + for row in modules: + for color in row: + if color: + black += 1 + total = size**2 + # Find smallest k such that (45-5k)% <= dark/total <= (55+5k)% + for k in itertools.count(): + if (9-k)*total <= black*20 <= (11+k)*total: + break + result += QrCode._PENALTY_N4 + return result + + + # ---- Private static helper functions ---- + + @staticmethod + def _get_alignment_pattern_positions(ver): + """Returns a sequence of positions of the alignment patterns in ascending order. These positions are + used on both the x and y axes. Each value in the resulting sequence is in the range [0, 177). + This stateless pure function could be implemented as table of 40 variable-length lists of integers.""" + if not 1 <= ver <= 40: + raise ValueError("Version number out of range") + elif ver == 1: + return [] + else: + numalign = ver // 7 + 2 + if ver != 32: + step = (ver * 4 + numalign * 2 + 1) // (2 * numalign - 2) * 2 # ceil((size - 13) / (2*numalign - 2)) * 2 + else: # C-C-C-Combo breaker! + step = 26 + result = [6] + [None] * (numalign - 1) + pos = ver * 4 + 10 + for i in reversed(range(1, numalign)): + result[i] = pos + pos -= step + return result + + + @staticmethod + def _get_num_raw_data_modules(ver): + """Returns the number of raw data modules (bits) available at the given version number. + These data modules are used for both user data codewords and error correction codewords. + This stateless pure function could be implemented as a 40-entry lookup table.""" + if not 1 <= ver <= 40: + raise ValueError("Version number out of range") + result = (16 * ver + 128) * ver + 64 + if ver >= 2: + numalign = ver // 7 + 2 + result -= (25 * numalign - 10) * numalign - 55 + if ver >= 7: + result -= 18 * 2 # Subtract version information + return result + + + @staticmethod + def _get_num_data_codewords(ver, ecl): + """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.""" + return QrCode._get_num_raw_data_modules(ver) // 8 - QrCode._NUM_ERROR_CORRECTION_CODEWORDS[ecl.ordinal][ver] + + + # ---- Tables of constants ---- + + # For use in getPenaltyScore(), when evaluating which mask is best. + _PENALTY_N1 = 3 + _PENALTY_N2 = 3 + _PENALTY_N3 = 40 + _PENALTY_N4 = 10 + + _NUM_ERROR_CORRECTION_CODEWORDS = ( + # 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 + (None, 7, 10, 15, 20, 26, 36, 40, 48, 60, 72, 80, 96, 104, 120, 132, 144, 168, 180, 196, 224, 224, 252, 270, 300, 312, 336, 360, 390, 420, 450, 480, 510, 540, 570, 570, 600, 630, 660, 720, 750), # Low + (None, 10, 16, 26, 36, 48, 64, 72, 88, 110, 130, 150, 176, 198, 216, 240, 280, 308, 338, 364, 416, 442, 476, 504, 560, 588, 644, 700, 728, 784, 812, 868, 924, 980, 1036, 1064, 1120, 1204, 1260, 1316, 1372), # Medium + (None, 13, 22, 36, 52, 72, 96, 108, 132, 160, 192, 224, 260, 288, 320, 360, 408, 448, 504, 546, 600, 644, 690, 750, 810, 870, 952, 1020, 1050, 1140, 1200, 1290, 1350, 1440, 1530, 1590, 1680, 1770, 1860, 1950, 2040), # Quartile + (None, 17, 28, 44, 64, 88, 112, 130, 156, 192, 224, 264, 308, 352, 384, 432, 480, 532, 588, 650, 700, 750, 816, 900, 960, 1050, 1110, 1200, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2100, 2220, 2310, 2430)) # High + + _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 + (None, 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 + (None, 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 + (None, 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 + (None, 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 + + _MASK_PATTERNS = ( + (lambda x, y: (x + y) % 2 ), + (lambda x, y: y % 2 ), + (lambda x, y: x % 3 ), + (lambda x, y: (x + y) % 3 ), + (lambda x, y: (x // 3 + y // 2) % 2 ), + (lambda x, y: x * y % 2 + x * y % 3 ), + (lambda x, y: (x * y % 2 + x * y % 3) % 2 ), + (lambda x, y: ((x + y) % 2 + x * y % 3) % 2), + ) + + + # ---- Public helper enumeration ---- + + class Ecc(object): + """Represents the error correction level used in a QR Code symbol.""" + # Private constructor + def __init__(self, i, fb): + self.ordinal = i # In the range 0 to 3 (unsigned 2-bit integer) + self.formatbits = fb # In the range 0 to 3 (unsigned 2-bit integer) + + # Create the class constants outside the class + Ecc.LOW = Ecc(0, 1) + Ecc.MEDIUM = Ecc(1, 0) + Ecc.QUARTILE = Ecc(2, 3) + Ecc.HIGH = Ecc(3, 2) + + + +# ---- Data segment class ---- + +class QrSegment(object): + """Represents a character string to be encoded in a QR Code symbol. Each segment has + a mode, and a sequence of characters that is already encoded as a sequence of bits. + Instances of this class are immutable. + This segment class imposes no length restrictions, but QR Codes have restrictions. + Even in the most favorable conditions, a QR Code can only hold 7089 characters of data. + Any segment longer than this is meaningless for the purpose of generating QR Codes.""" + + # -- Public static factory functions -- + + @staticmethod + def make_bytes(data): + """Returns a segment representing the given binary data encoded in byte mode.""" + bb = _BitBuffer() + for b in data: + if sys.version_info[0] < 3: + b = ord(b) + bb.append_bits(b, 8) + return QrSegment(QrSegment.Mode.BYTE, len(data), bb.get_bits()) + + + @staticmethod + def make_numeric(digits): + """Returns a segment representing the given string of decimal digits encoded in numeric mode.""" + if QrSegment.NUMERIC_REGEX.match(digits) is None: + raise ValueError("String contains non-numeric characters") + bb = _BitBuffer() + for i in range(0, len(digits) - 2, 3): # Process groups of 3 + bb.append_bits(int(digits[i : i + 3]), 10) + rem = len(digits) % 3 + if rem > 0: # 1 or 2 digits remaining + bb.append_bits(int(digits[-rem : ]), rem * 3 + 1) + return QrSegment(QrSegment.Mode.NUMERIC, len(digits), bb.get_bits()) + + + @staticmethod + def make_alphanumeric(text): + """Returns a segment representing the given text string encoded in alphanumeric mode. The characters allowed are: + 0 to 9, A to Z (uppercase only), space, dollar, percent, asterisk, plus, hyphen, period, slash, colon.""" + if QrSegment.ALPHANUMERIC_REGEX.match(text) is None: + raise ValueError("String contains unencodable characters in alphanumeric mode") + bb = _BitBuffer() + for i in range(0, len(text) - 1, 2): # Process groups of 2 + temp = QrSegment.ALPHANUMERIC_ENCODING_TABLE[text[i]] * 45 + temp += QrSegment.ALPHANUMERIC_ENCODING_TABLE[text[i + 1]] + bb.append_bits(temp, 11) + if len(text) % 2 > 0: # 1 character remaining + bb.append_bits(QrSegment.ALPHANUMERIC_ENCODING_TABLE[text[-1]], 6) + return QrSegment(QrSegment.Mode.ALPHANUMERIC, len(text), bb.get_bits()) + + + # -- Constructor -- + + def __init__(self, mode, numch, bitdata): + if numch < 0 or not isinstance(mode, QrSegment.Mode): + raise ValueError() + self._mode = mode + self._numchars = numch + self._bitdata = list(bitdata) # Defensive copy + + + # -- Accessor methods -- + + def get_mode(self): + return self._mode + + def get_num_chars(self): + return self._numchars + + def get_bits(self): + return list(self._bitdata) # Defensive copy + + + # -- Constants -- + + # Can test whether a string is encodable in numeric mode (such as by using make_numeric()) + NUMERIC_REGEX = re.compile("[0-9]*$") + + # Can test whether a string is encodable in alphanumeric mode (such as by using make_alphanumeric()) + ALPHANUMERIC_REGEX = re.compile("[A-Z0-9 $%*+./:-]*$") + + # Dictionary of "0"->0, "A"->10, "$"->37, etc. + ALPHANUMERIC_ENCODING_TABLE = {ch: i for (i, ch) in enumerate("0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:")} + + + # -- Helper enumeration -- + + class Mode(object): + """The mode field of a segment. Immutable. Provides methods to retrieve closely related values.""" + # Private constructor + def __init__(self, modebits, charcounts): + self._modebits = modebits + self._charcounts = charcounts + + def get_mode_bits(self): + return self._modebits + + def num_char_count_bits(self, ver): + """Returns the bit width of the segment character count field for this mode object at the given version number.""" + if 1 <= ver <= 9: return self._charcounts[0] + elif 10 <= ver <= 26: return self._charcounts[1] + elif 27 <= ver <= 40: return self._charcounts[2] + else: raise ValueError("Version number out of range") + + # Create the class constants outside the class + Mode.NUMERIC = Mode(0x1, (10, 12, 14)) + Mode.ALPHANUMERIC = Mode(0x2, ( 9, 11, 13)) + Mode.BYTE = Mode(0x4, ( 8, 16, 16)) + Mode.KANJI = Mode(0x8, ( 8, 10, 12)) + + + +# ---- Private helper classes ---- + +class _ReedSolomonGenerator(object): + """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 the divisor polynomial does not need to be recalculated for every input.""" + + def __init__(self, degree): + """Creates a Reed-Solomon ECC generator for the given degree. This could be implemented + as a lookup table over all possible parameter values, instead of as an algorithm.""" + if degree < 1 or degree > 255: + raise ValueError("Degree out of range") + + # Start with the monomial x^0 + self.coefficients = [0] * (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). + root = 1 + for i in range(degree): + # Multiply the current product by (x - r^i) + for j in range(degree): + self.coefficients[j] = _ReedSolomonGenerator.multiply(self.coefficients[j], root) + if j + 1 < degree: + self.coefficients[j] ^= self.coefficients[j + 1] + root = (root << 1) ^ ((root >> 7) * 0x11D) # Multiply by 0x02 mod GF(2^8/0x11D) + + + def get_remainder(self, data): + """Computes and returns the Reed-Solomon error correction codewords for the given sequence of data codewords. + The returned object is always a new byte list. This method does not alter this object's state (because it is immutable).""" + # Compute the remainder by performing polynomial division + result = [0] * len(self.coefficients) + for b in data: + factor = (b ^ result[0]) + del result[0] + result.append(0) + for j in range(len(result)): + result[j] ^= _ReedSolomonGenerator.multiply(self.coefficients[j], factor) + return result + + + @staticmethod + def multiply(x, y): + """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.""" + if x & 0xFF != x or y & 0xFF != y: + raise ValueError("Byte out of range") + # Russian peasant multiplication + z = 0 + for i in reversed(range(8)): + z = (z << 1) ^ ((z >> 7) * 0x11D) + z ^= ((y >> i) & 1) * x + assert z & 0xFF == z + return z + + + +class _BitBuffer(object): + """An appendable sequence of bits. Bits are packed in big endian within a byte.""" + + def __init__(self): + """Creates an empty bit buffer (length 0).""" + self.data = [] + + def bit_length(self): + """Returns the number of bits in the buffer, which is a non-negative value.""" + return len(self.data) + + def get_bits(self): + """Returns a copy of all bits.""" + return list(self.data) + + def get_bytes(self): + """Returns a copy of all bytes, padding up to the nearest byte.""" + result = [0] * ((len(self.data) + 7) // 8) + for (i, bit) in enumerate(self.data): + result[i >> 3] |= bit << (7 - (i & 7)) + return result + + def append_bits(self, val, n): + """Appends the given number of bits of the given value to this sequence. This requires 0 <= val < 2^n.""" + if n < 0 or not 0 <= val < (1 << n): + raise ValueError("Value out of range") + for i in reversed(range(n)): # Append bit by bit + self.data.append((val >> i) & 1) + + def append_all(self, seg): + """Appends the data of the given segment to this bit buffer.""" + if not isinstance(seg, QrSegment): + raise TypeError("QrSegment expected") + self.data.extend(seg.get_bits())