/*
* QR Code generator library (C)
*
* 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.
*/
#include <assert.h>
#include <limits.h>
#include <stdlib.h>
#include <string.h>
#include "qrcodegen.h"
#ifndef QRCODEGEN_TEST
#define testable static // Keep functions private
#else
#define testable // Expose private functions
#endif
/*---- Forward declarations for private functions ----*/
// Regarding all public and private functions defined in this source file:
// - They require all pointer/array arguments to be not null unless the array length is zero.
// - They only read input scalar/array arguments, write to output pointer/array
// arguments, and return scalar values; they are "pure" functions.
// - They don't read mutable global variables or write to any global variables.
// - They don't perform I/O, read the clock, print to console, etc.
// - They allocate a small and constant amount of stack memory.
// - They don't allocate or free any memory on the heap.
// - They don't recurse or mutually recurse. All the code
// could be inlined into the top-level public functions.
// - They run in at most quadratic time with respect to input arguments.
// Most functions run in linear time, and some in constant time.
// There are no unbounded loops or non-obvious termination conditions.
// - They are completely thread-safe if the caller does not give the
// same writable buffer to concurrent calls to these functions.
testable void appendBitsToBuffer(unsigned int val, int numBits, uint8_t buffer[], int *bitLen);
testable void addEccAndInterleave(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]);
testable int getNumDataCodewords(int version, enum qrcodegen_Ecc ecl);
testable int getNumRawDataModules(int ver);
testable void calcReedSolomonGenerator(int degree, uint8_t result[]);
testable void calcReedSolomonRemainder(const uint8_t data[], int dataLen,
const uint8_t generator[], int degree, uint8_t result[]);
testable uint8_t finiteFieldMultiply(uint8_t x, uint8_t y);
testable void initializeFunctionModules(int version, uint8_t qrcode[]);
static void drawWhiteFunctionModules(uint8_t qrcode[], int version);
static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[]);
testable int getAlignmentPatternPositions(int version, uint8_t result[7]);
static void fillRectangle(int left, int top, int width, int height, uint8_t qrcode[]);
static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[]);
static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], enum qrcodegen_Mask mask);
static long getPenaltyScore(const uint8_t qrcode[]);
static void addRunToHistory(unsigned char run, unsigned char history[7]);
static bool hasFinderLikePattern(unsigned char runHistory[7]);
testable bool getModule(const uint8_t qrcode[], int x, int y);
testable void setModule(uint8_t qrcode[], int x, int y, bool isBlack);
testable void setModuleBounded(uint8_t qrcode[], int x, int y, bool isBlack);
static bool getBit(int x, int i);
testable int calcSegmentBitLength(enum qrcodegen_Mode mode, size_t numChars);
testable int getTotalBits(const struct qrcodegen_Segment segs[], size_t len, int version);
static int numCharCountBits(enum qrcodegen_Mode mode, int version);
/*---- Private tables of constants ----*/
// The set of all legal characters in alphanumeric mode, where each character
// value maps to the index in the string. For checking text and encoding segments.
static const char *ALPHANUMERIC_CHARSET = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:";
// For generating error correction codes.
testable const int8_t ECC_CODEWORDS_PER_BLOCK[4][41] = {
// 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
};
#define qrcodegen_REED_SOLOMON_DEGREE_MAX 30 // Based on the table above
// For generating error correction codes.
testable const int8_t NUM_ERROR_CORRECTION_BLOCKS[4][41] = {
// 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
};
// For automatic mask pattern selection.
static const int PENALTY_N1 = 3;
static const int PENALTY_N2 = 3;
static const int PENALTY_N3 = 40;
static const int PENALTY_N4 = 10;
/*---- High-level QR Code encoding functions ----*/
// Public function - see documentation comment in header file.
bool qrcodegen_encodeText(const char *text, uint8_t tempBuffer[], uint8_t qrcode[],
enum qrcodegen_Ecc ecl, int minVersion, int maxVersion, enum qrcodegen_Mask mask, bool boostEcl) {
size_t textLen = strlen(text);
if (textLen == 0)
return qrcodegen_encodeSegmentsAdvanced(NULL, 0, ecl, minVersion, maxVersion, mask, boostEcl, tempBuffer, qrcode);
size_t bufLen = qrcodegen_BUFFER_LEN_FOR_VERSION(maxVersion);
struct qrcodegen_Segment seg;
if (qrcodegen_isNumeric(text)) {
if (qrcodegen_calcSegmentBufferSize(qrcodegen_Mode_NUMERIC, textLen) > bufLen)
goto fail;
seg = qrcodegen_makeNumeric(text, tempBuffer);
} else if (qrcodegen_isAlphanumeric(text)) {
if (qrcodegen_calcSegmentBufferSize(qrcodegen_Mode_ALPHANUMERIC, textLen) > bufLen)
goto fail;
seg = qrcodegen_makeAlphanumeric(text, tempBuffer);
} else {
if (textLen > bufLen)
goto fail;
for (size_t i = 0; i < textLen; i++)
tempBuffer[i] = (uint8_t)text[i];
seg.mode = qrcodegen_Mode_BYTE;
seg.bitLength = calcSegmentBitLength(seg.mode, textLen);
if (seg.bitLength == -1)
goto fail;
seg.numChars = (int)textLen;
seg.data = tempBuffer;
}
return qrcodegen_encodeSegmentsAdvanced(&seg, 1, ecl, minVersion, maxVersion, mask, boostEcl, tempBuffer, qrcode);
fail:
qrcode[0] = 0; // Set size to invalid value for safety
return false;
}
// Public function - see documentation comment in header file.
bool qrcodegen_encodeBinary(uint8_t dataAndTemp[], size_t dataLen, uint8_t qrcode[],
enum qrcodegen_Ecc ecl, int minVersion, int maxVersion, enum qrcodegen_Mask mask, bool boostEcl) {
struct qrcodegen_Segment seg;
seg.mode = qrcodegen_Mode_BYTE;
seg.bitLength = calcSegmentBitLength(seg.mode, dataLen);
if (seg.bitLength == -1) {
qrcode[0] = 0; // Set size to invalid value for safety
return false;
}
seg.numChars = (int)dataLen;
seg.data = dataAndTemp;
return qrcodegen_encodeSegmentsAdvanced(&seg, 1, ecl, minVersion, maxVersion, mask, boostEcl, dataAndTemp, qrcode);
}
// Appends the given number of low-order bits of the given value to the given byte-based
// bit buffer, increasing the bit length. Requires 0 <= numBits <= 16 and val < 2^numBits.
testable void appendBitsToBuffer(unsigned int val, int numBits, uint8_t buffer[], int *bitLen) {
assert(0 <= numBits && numBits <= 16 && (unsigned long)val >> numBits == 0);
for (int i = numBits - 1; i >= 0; i--, (*bitLen)++)
buffer[*bitLen >> 3] |= ((val >> i) & 1) << (7 - (*bitLen & 7));
}
/*---- Low-level QR Code encoding functions ----*/
// Public function - see documentation comment in header file.
bool qrcodegen_encodeSegments(const struct qrcodegen_Segment segs[], size_t len,
enum qrcodegen_Ecc ecl, uint8_t tempBuffer[], uint8_t qrcode[]) {
return qrcodegen_encodeSegmentsAdvanced(segs, len, ecl,
qrcodegen_VERSION_MIN, qrcodegen_VERSION_MAX, -1, true, tempBuffer, qrcode);
}
// Public function - see documentation comment in header file.
bool qrcodegen_encodeSegmentsAdvanced(const struct qrcodegen_Segment segs[], size_t len, enum qrcodegen_Ecc ecl,
int minVersion, int maxVersion, int mask, bool boostEcl, uint8_t tempBuffer[], uint8_t qrcode[]) {
assert(segs != NULL || len == 0);
assert(qrcodegen_VERSION_MIN <= minVersion && minVersion <= maxVersion && maxVersion <= qrcodegen_VERSION_MAX);
assert(0 <= (int)ecl && (int)ecl <= 3 && -1 <= (int)mask && (int)mask <= 7);
// 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 = getTotalBits(segs, len, 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
qrcode[0] = 0; // Set size to invalid value for safety
return false;
}
}
assert(dataUsedBits != -1);
// Increase the error correction level while the data still fits in the current version number
for (int i = (int)qrcodegen_Ecc_MEDIUM; i <= (int)qrcodegen_Ecc_HIGH; i++) { // From low to high
if (boostEcl && dataUsedBits <= getNumDataCodewords(version, (enum qrcodegen_Ecc)i) * 8)
ecl = (enum qrcodegen_Ecc)i;
}
// Concatenate all segments to create the data bit string
memset(qrcode, 0, qrcodegen_BUFFER_LEN_FOR_VERSION(version) * sizeof(qrcode[0]));
int bitLen = 0;
for (size_t i = 0; i < len; i++) {
const struct qrcodegen_Segment *seg = &segs[i];
appendBitsToBuffer((int)seg->mode, 4, qrcode, &bitLen);
appendBitsToBuffer(seg->numChars, numCharCountBits(seg->mode, version), qrcode, &bitLen);
for (int j = 0; j < seg->bitLength; j++)
appendBitsToBuffer((seg->data[j >> 3] >> (7 - (j & 7))) & 1, 1, qrcode, &bitLen);
}
assert(bitLen == dataUsedBits);
// Add terminator and pad up to a byte if applicable
int dataCapacityBits = getNumDataCodewords(version, ecl) * 8;
assert(bitLen <= dataCapacityBits);
int terminatorBits = dataCapacityBits - bitLen;
if (terminatorBits > 4)
terminatorBits = 4;
appendBitsToBuffer(0, terminatorBits, qrcode, &bitLen);
appendBitsToBuffer(0, (8 - bitLen % 8) % 8, qrcode, &bitLen);
assert(bitLen % 8 == 0);
// Pad with alternating bytes until data capacity is reached
for (uint8_t padByte = 0xEC; bitLen < dataCapacityBits; padByte ^= 0xEC ^ 0x11)
appendBitsToBuffer(padByte, 8, qrcode, &bitLen);
// Draw function and data codeword modules
addEccAndInterleave(qrcode, version, ecl, tempBuffer);
initializeFunctionModules(version, qrcode);
drawCodewords(tempBuffer, getNumRawDataModules(version) / 8, qrcode);
drawWhiteFunctionModules(qrcode, version);
initializeFunctionModules(version, tempBuffer);
// Handle masking
if (mask == qrcodegen_Mask_AUTO) { // Automatically choose best mask
long minPenalty = LONG_MAX;
for (int i = 0; i < 8; i++) {
enum qrcodegen_Mask msk = (enum qrcodegen_Mask)i;
drawFormatBits(ecl, msk, qrcode);
applyMask(tempBuffer, qrcode, msk);
long penalty = getPenaltyScore(qrcode);
if (penalty < minPenalty) {
mask = msk;
minPenalty = penalty;
}
applyMask(tempBuffer, qrcode, msk); // Undoes the mask due to XOR
}
}
assert(0 <= (int)mask && (int)mask <= 7);
drawFormatBits(ecl, mask, qrcode);
applyMask(tempBuffer, qrcode, mask);
return true;
}
/*---- Error correction code generation functions ----*/
// Appends error correction bytes to each block of the given data array, then interleaves
// bytes from the blocks and stores them in the result array. data[0 : dataLen] contains
// the input data. data[dataLen : rawCodewords] is used as a temporary work area and will
// be clobbered by this function. The final answer is stored in result[0 : rawCodewords].
testable void addEccAndInterleave(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]) {
// Calculate parameter numbers
assert(0 <= (int)ecl && (int)ecl < 4 && qrcodegen_VERSION_MIN <= version && version <= qrcodegen_VERSION_MAX);
int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[(int)ecl][version];
int blockEccLen = ECC_CODEWORDS_PER_BLOCK [(int)ecl][version];
int rawCodewords = getNumRawDataModules(version) / 8;
int dataLen = getNumDataCodewords(version, ecl);
int numShortBlocks = numBlocks - rawCodewords % numBlocks;
int shortBlockDataLen = rawCodewords / numBlocks - blockEccLen;
// Split data into blocks, calculate ECC, and interleave
// (not concatenate) the bytes into a single sequence
uint8_t generator[qrcodegen_REED_SOLOMON_DEGREE_MAX];
calcReedSolomonGenerator(blockEccLen, generator);
const uint8_t *dat = data;
for (int i = 0; i < numBlocks; i++) {
int datLen = shortBlockDataLen + (i < numShortBlocks ? 0 : 1);
uint8_t *ecc = &data[dataLen]; // Temporary storage
calcReedSolomonRemainder(dat, datLen, generator, blockEccLen, ecc);
for (int j = 0, k = i; j < datLen; j++, k += numBlocks) { // Copy data
if (j == shortBlockDataLen)
k -= numShortBlocks;
result[k] = dat[j];
}
for (int j = 0, k = dataLen + i; j < blockEccLen; j++, k += numBlocks) // Copy ECC
result[k] = ecc[j];
dat += datLen;
}
}
// Returns the number of 8-bit codewords that can be used for storing data (not ECC),
// for the given version number and error correction level. The result is in the range [9, 2956].
testable int getNumDataCodewords(int version, enum qrcodegen_Ecc ecl) {
int v = version, e = (int)ecl;
assert(0 <= e && e < 4);
return getNumRawDataModules(v) / 8
- ECC_CODEWORDS_PER_BLOCK [e][v]
* NUM_ERROR_CORRECTION_BLOCKS[e][v];
}
// 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.
testable int getNumRawDataModules(int ver) {
assert(qrcodegen_VERSION_MIN <= ver && ver <= qrcodegen_VERSION_MAX);
int result = (16 * ver + 128) * ver + 64;
if (ver >= 2) {
int numAlign = ver / 7 + 2;
result -= (25 * numAlign - 10) * numAlign - 55;
if (ver >= 7)
result -= 36;
}
return result;
}
/*---- Reed-Solomon ECC generator functions ----*/
// Calculates the Reed-Solomon generator polynomial of the given degree, storing in result[0 : degree].
testable void calcReedSolomonGenerator(int degree, uint8_t result[]) {
// Start with the monomial x^0
assert(1 <= degree && degree <= qrcodegen_REED_SOLOMON_DEGREE_MAX);
memset(result, 0, degree * sizeof(result[0]));
result[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).
uint8_t root = 1;
for (int i = 0; i < degree; i++) {
// Multiply the current product by (x - r^i)
for (int j = 0; j < degree; j++) {
result[j] = finiteFieldMultiply(result[j], root);
if (j + 1 < degree)
result[j] ^= result[j + 1];
}
root = finiteFieldMultiply(root, 0x02);
}
}
// Calculates the remainder of the polynomial data[0 : dataLen] when divided by the generator[0 : degree], where all
// polynomials are in big endian and the generator has an implicit leading 1 term, storing the result in result[0 : degree].
testable void calcReedSolomonRemainder(const uint8_t data[], int dataLen,
const uint8_t generator[], int degree, uint8_t result[]) {
// Perform polynomial division
assert(1 <= degree && degree <= qrcodegen_REED_SOLOMON_DEGREE_MAX);
memset(result, 0, degree * sizeof(result[0]));
for (int i = 0; i < dataLen; i++) {
uint8_t factor = data[i] ^ result[0];
memmove(&result[0], &result[1], (degree - 1) * sizeof(result[0]));
result[degree - 1] = 0;
for (int j = 0; j < degree; j++)
result[j] ^= finiteFieldMultiply(generator[j], factor);
}
}
#undef qrcodegen_REED_SOLOMON_DEGREE_MAX
// Returns the product of the two given field elements modulo GF(2^8/0x11D).
// All inputs are valid. This could be implemented as a 256*256 lookup table.
testable uint8_t finiteFieldMultiply(uint8_t x, uint8_t y) {
// Russian peasant multiplication
uint8_t z = 0;
for (int i = 7; i >= 0; i--) {
z = (z << 1) ^ ((z >> 7) * 0x11D);
z ^= ((y >> i) & 1) * x;
}
return z;
}
/*---- Drawing function modules ----*/
// Clears the given QR Code grid with white modules for the given
// version's size, then marks every function module as black.
testable void initializeFunctionModules(int version, uint8_t qrcode[]) {
// Initialize QR Code
int qrsize = version * 4 + 17;
memset(qrcode, 0, ((qrsize * qrsize + 7) / 8 + 1) * sizeof(qrcode[0]));
qrcode[0] = (uint8_t)qrsize;
// Fill horizontal and vertical timing patterns
fillRectangle(6, 0, 1, qrsize, qrcode);
fillRectangle(0, 6, qrsize, 1, qrcode);
// Fill 3 finder patterns (all corners except bottom right) and format bits
fillRectangle(0, 0, 9, 9, qrcode);
fillRectangle(qrsize - 8, 0, 8, 9, qrcode);
fillRectangle(0, qrsize - 8, 9, 8, qrcode);
// Fill numerous alignment patterns
uint8_t alignPatPos[7];
int numAlign = getAlignmentPatternPositions(version, alignPatPos);
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)))
fillRectangle(alignPatPos[i] - 2, alignPatPos[j] - 2, 5, 5, qrcode);
}
}
// Fill version blocks
if (version >= 7) {
fillRectangle(qrsize - 11, 0, 3, 6, qrcode);
fillRectangle(0, qrsize - 11, 6, 3, qrcode);
}
}
// Draws white function modules and possibly some black modules onto the given QR Code, without changing
// non-function modules. This does not draw the format bits. This requires all function modules to be previously
// marked black (namely by initializeFunctionModules()), because this may skip redrawing black function modules.
static void drawWhiteFunctionModules(uint8_t qrcode[], int version) {
// Draw horizontal and vertical timing patterns
int qrsize = qrcodegen_getSize(qrcode);
for (int i = 7; i < qrsize - 7; i += 2) {
setModule(qrcode, 6, i, false);
setModule(qrcode, i, 6, false);
}
// Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules)
for (int dy = -4; dy <= 4; dy++) {
for (int dx = -4; dx <= 4; dx++) {
int dist = abs(dx);
if (abs(dy) > dist)
dist = abs(dy);
if (dist == 2 || dist == 4) {
setModuleBounded(qrcode, 3 + dx, 3 + dy, false);
setModuleBounded(qrcode, qrsize - 4 + dx, 3 + dy, false);
setModuleBounded(qrcode, 3 + dx, qrsize - 4 + dy, false);
}
}
}
// Draw numerous alignment patterns
uint8_t alignPatPos[7];
int numAlign = getAlignmentPatternPositions(version, alignPatPos);
for (int i = 0; i < numAlign; i++) {
for (int j = 0; j < numAlign; j++) {
if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0))
continue; // Don't draw on the three finder corners
for (int dy = -1; dy <= 1; dy++) {
for (int dx = -1; dx <= 1; dx++)
setModule(qrcode, alignPatPos[i] + dx, alignPatPos[j] + dy, dx == 0 && dy == 0);
}
}
}
// Draw version blocks
if (version >= 7) {
// 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);
long bits = (long)version << 12 | rem; // uint18
assert(bits >> 18 == 0);
// Draw two copies
for (int i = 0; i < 6; i++) {
for (int j = 0; j < 3; j++) {
int k = qrsize - 11 + j;
setModule(qrcode, k, i, (bits & 1) != 0);
setModule(qrcode, i, k, (bits & 1) != 0);
bits >>= 1;
}
}
}
}
// Draws two copies of the format bits (with its own error correction code) based
// on the given mask and error correction level. This always draws all modules of
// the format bits, unlike drawWhiteFunctionModules() which might skip black modules.
static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[]) {
// Calculate error correction code and pack bits
assert(0 <= (int)mask && (int)mask <= 7);
static const int table[] = {1, 0, 3, 2};
int data = table[(int)ecl] << 3 | (int)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++)
setModule(qrcode, 8, i, getBit(bits, i));
setModule(qrcode, 8, 7, getBit(bits, 6));
setModule(qrcode, 8, 8, getBit(bits, 7));
setModule(qrcode, 7, 8, getBit(bits, 8));
for (int i = 9; i < 15; i++)
setModule(qrcode, 14 - i, 8, getBit(bits, i));
// Draw second copy
int qrsize = qrcodegen_getSize(qrcode);
for (int i = 0; i < 8; i++)
setModule(qrcode, qrsize - 1 - i, 8, getBit(bits, i));
for (int i = 8; i < 15; i++)
setModule(qrcode, 8, qrsize - 15 + i, getBit(bits, i));
setModule(qrcode, 8, qrsize - 8, true); // Always black
}
// Calculates and stores an ascending list of positions of alignment patterns
// for this version number, returning the length of the list (in the range [0,7]).
// 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.
testable int getAlignmentPatternPositions(int version, uint8_t result[7]) {
if (version == 1)
return 0;
int numAlign = version / 7 + 2;
int step = (version == 32) ? 26 :
(version*4 + numAlign*2 + 1) / (numAlign*2 - 2) * 2;
for (int i = numAlign - 1, pos = version * 4 + 10; i >= 1; i--, pos -= step)
result[i] = pos;
result[0] = 6;
return numAlign;
}
// Sets every pixel in the range [left : left + width] * [top : top + height] to black.
static void fillRectangle(int left, int top, int width, int height, uint8_t qrcode[]) {
for (int dy = 0; dy < height; dy++) {
for (int dx = 0; dx < width; dx++)
setModule(qrcode, left + dx, top + dy, true);
}
}
/*---- Drawing data modules and masking ----*/
// Draws the raw codewords (including data and ECC) onto the given QR Code. This requires the initial state of
// the QR Code to be black at function modules and white at codeword modules (including unused remainder bits).
static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[]) {
int qrsize = qrcodegen_getSize(qrcode);
int i = 0; // Bit index into the data
// Do the funny zigzag scan
for (int right = qrsize - 1; right >= 1; right -= 2) { // Index of right column in each column pair
if (right == 6)
right = 5;
for (int vert = 0; vert < qrsize; vert++) { // Vertical counter
for (int j = 0; j < 2; j++) {
int x = right - j; // Actual x coordinate
bool upward = ((right + 1) & 2) == 0;
int y = upward ? qrsize - 1 - vert : vert; // Actual y coordinate
if (!getModule(qrcode, x, y) && i < dataLen * 8) {
bool black = getBit(data[i >> 3], 7 - (i & 7));
setModule(qrcode, x, y, black);
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 == dataLen * 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.
static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], enum qrcodegen_Mask mask) {
assert(0 <= (int)mask && (int)mask <= 7); // Disallows qrcodegen_Mask_AUTO
int qrsize = qrcodegen_getSize(qrcode);
for (int y = 0; y < qrsize; y++) {
for (int x = 0; x < qrsize; x++) {
if (getModule(functionModules, x, y))
continue;
bool invert;
switch ((int)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: assert(false); return;
}
bool val = getModule(qrcode, x, y);
setModule(qrcode, x, y, val ^ invert);
}
}
}
// Calculates and returns the penalty score based on state of the given QR Code's current modules.
// This is used by the automatic mask choice algorithm to find the mask pattern that yields the lowest score.
static long getPenaltyScore(const uint8_t qrcode[]) {
int qrsize = qrcodegen_getSize(qrcode);
long result = 0;
// Adjacent modules in row having same color, and finder-like patterns
for (int y = 0; y < qrsize; y++) {
unsigned char runHistory[7] = {0};
bool color = false;
unsigned char runX = 0;
for (int x = 0; x < qrsize; x++) {
if (getModule(qrcode, x, y) == color) {
runX++;
if (runX == 5)
result += PENALTY_N1;
else if (runX > 5)
result++;
} else {
addRunToHistory(runX, runHistory);
if (!color && hasFinderLikePattern(runHistory))
result += PENALTY_N3;
color = getModule(qrcode, x, y);
runX = 1;
}
}
addRunToHistory(runX, runHistory);
if (color)
addRunToHistory(0, runHistory); // Dummy run of white
if (hasFinderLikePattern(runHistory))
result += PENALTY_N3;
}
// Adjacent modules in column having same color, and finder-like patterns
for (int x = 0; x < qrsize; x++) {
unsigned char runHistory[7] = {0};
bool color = false;
unsigned char runY = 0;
for (int y = 0; y < qrsize; y++) {
if (getModule(qrcode, x, y) == color) {
runY++;
if (runY == 5)
result += PENALTY_N1;
else if (runY > 5)
result++;
} else {
addRunToHistory(runY, runHistory);
if (!color && hasFinderLikePattern(runHistory))
result += PENALTY_N3;
color = getModule(qrcode, x, y);
runY = 1;
}
}
addRunToHistory(runY, runHistory);
if (color)
addRunToHistory(0, runHistory); // Dummy run of white
if (hasFinderLikePattern(runHistory))
result += PENALTY_N3;
}
// 2*2 blocks of modules having same color
for (int y = 0; y < qrsize - 1; y++) {
for (int x = 0; x < qrsize - 1; x++) {
bool color = getModule(qrcode, x, y);
if ( color == getModule(qrcode, x + 1, y) &&
color == getModule(qrcode, x, y + 1) &&
color == getModule(qrcode, x + 1, y + 1))
result += PENALTY_N2;
}
}
// Balance of black and white modules
int black = 0;
for (int y = 0; y < qrsize; y++) {
for (int x = 0; x < qrsize; x++) {
if (getModule(qrcode, x, y))
black++;
}
}
int total = qrsize * qrsize; // 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 = (int)((labs(black * 20L - total * 10L) + total - 1) / total) - 1;
result += k * PENALTY_N4;
return result;
}
// Inserts the given value to the front of the given array, which shifts over the
// existing values and deletes the last value. A helper function for getPenaltyScore().
static void addRunToHistory(unsigned char run, unsigned char history[7]) {
memmove(&history[1], &history[0], 6 * sizeof(history[0]));
history[0] = run;
}
// Tests whether the given run history has the pattern of ratio 1:1:3:1:1 in the middle, and
// surrounded by at least 4 on either or both ends. A helper function for getPenaltyScore().
// Must only be called immediately after a run of white modules has ended.
static bool hasFinderLikePattern(unsigned char runHistory[7]) {
unsigned char n = runHistory[1];
// The maximum QR Code size is 177, hence the run length n <= 177.
// Arithmetic is promoted to int, so n*4 will not overflow.
return n > 0 && runHistory[2] == n && runHistory[4] == n && runHistory[5] == n
&& runHistory[3] == n * 3 && (runHistory[0] >= n * 4 || runHistory[6] >= n * 4);
}
/*---- Basic QR Code information ----*/
// Public function - see documentation comment in header file.
int qrcodegen_getSize(const uint8_t qrcode[]) {
assert(qrcode != NULL);
int result = qrcode[0];
assert((qrcodegen_VERSION_MIN * 4 + 17) <= result
&& result <= (qrcodegen_VERSION_MAX * 4 + 17));
return result;
}
// Public function - see documentation comment in header file.
bool qrcodegen_getModule(const uint8_t qrcode[], int x, int y) {
assert(qrcode != NULL);
int qrsize = qrcode[0];
return (0 <= x && x < qrsize && 0 <= y && y < qrsize) && getModule(qrcode, x, y);
}
// Gets the module at the given coordinates, which must be in bounds.
testable bool getModule(const uint8_t qrcode[], int x, int y) {
int qrsize = qrcode[0];
assert(21 <= qrsize && qrsize <= 177 && 0 <= x && x < qrsize && 0 <= y && y < qrsize);
int index = y * qrsize + x;
return getBit(qrcode[(index >> 3) + 1], index & 7);
}
// Sets the module at the given coordinates, which must be in bounds.
testable void setModule(uint8_t qrcode[], int x, int y, bool isBlack) {
int qrsize = qrcode[0];
assert(21 <= qrsize && qrsize <= 177 && 0 <= x && x < qrsize && 0 <= y && y < qrsize);
int index = y * qrsize + x;
int bitIndex = index & 7;
int byteIndex = (index >> 3) + 1;
if (isBlack)
qrcode[byteIndex] |= 1 << bitIndex;
else
qrcode[byteIndex] &= (1 << bitIndex) ^ 0xFF;
}
// Sets the module at the given coordinates, doing nothing if out of bounds.
testable void setModuleBounded(uint8_t qrcode[], int x, int y, bool isBlack) {
int qrsize = qrcode[0];
if (0 <= x && x < qrsize && 0 <= y && y < qrsize)
setModule(qrcode, x, y, isBlack);
}
// Returns true iff the i'th bit of x is set to 1. Requires x >= 0 and 0 <= i <= 14.
static bool getBit(int x, int i) {
return ((x >> i) & 1) != 0;
}
/*---- Segment handling ----*/
// Public function - see documentation comment in header file.
bool qrcodegen_isAlphanumeric(const char *text) {
assert(text != NULL);
for (; *text != '\0'; text++) {
if (strchr(ALPHANUMERIC_CHARSET, *text) == NULL)
return false;
}
return true;
}
// Public function - see documentation comment in header file.
bool qrcodegen_isNumeric(const char *text) {
assert(text != NULL);
for (; *text != '\0'; text++) {
if (*text < '0' || *text > '9')
return false;
}
return true;
}
// Public function - see documentation comment in header file.
size_t qrcodegen_calcSegmentBufferSize(enum qrcodegen_Mode mode, size_t numChars) {
int temp = calcSegmentBitLength(mode, numChars);
if (temp == -1)
return SIZE_MAX;
assert(0 <= temp && temp <= INT16_MAX);
return ((size_t)temp + 7) / 8;
}
// Returns the number of data bits needed to represent a segment
// containing the given number of characters using the given mode. Notes:
// - Returns -1 on failure, i.e. numChars > INT16_MAX or
// the number of needed bits exceeds INT16_MAX (i.e. 32767).
// - Otherwise, all valid results are in the range [0, INT16_MAX].
// - For byte mode, numChars measures the number of bytes, not Unicode code points.
// - For ECI mode, numChars must be 0, and the worst-case number of bits is returned.
// An actual ECI segment can have shorter data. For non-ECI modes, the result is exact.
testable int calcSegmentBitLength(enum qrcodegen_Mode mode, size_t numChars) {
// All calculations are designed to avoid overflow on all platforms
if (numChars > (unsigned int)INT16_MAX)
return -1;
long result = (long)numChars;
if (mode == qrcodegen_Mode_NUMERIC)
result = (result * 10 + 2) / 3; // ceil(10/3 * n)
else if (mode == qrcodegen_Mode_ALPHANUMERIC)
result = (result * 11 + 1) / 2; // ceil(11/2 * n)
else if (mode == qrcodegen_Mode_BYTE)
result *= 8;
else if (mode == qrcodegen_Mode_KANJI)
result *= 13;
else if (mode == qrcodegen_Mode_ECI && numChars == 0)
result = 3 * 8;
else { // Invalid argument
assert(false);
return -1;
}
assert(result >= 0);
if (result > (unsigned int)INT16_MAX)
return -1;
return (int)result;
}
// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeBytes(const uint8_t data[], size_t len, uint8_t buf[]) {
assert(data != NULL || len == 0);
struct qrcodegen_Segment result;
result.mode = qrcodegen_Mode_BYTE;
result.bitLength = calcSegmentBitLength(result.mode, len);
assert(result.bitLength != -1);
result.numChars = (int)len;
if (len > 0)
memcpy(buf, data, len * sizeof(buf[0]));
result.data = buf;
return result;
}
// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeNumeric(const char *digits, uint8_t buf[]) {
assert(digits != NULL);
struct qrcodegen_Segment result;
size_t len = strlen(digits);
result.mode = qrcodegen_Mode_NUMERIC;
int bitLen = calcSegmentBitLength(result.mode, len);
assert(bitLen != -1);
result.numChars = (int)len;
if (bitLen > 0)
memset(buf, 0, ((size_t)bitLen + 7) / 8 * sizeof(buf[0]));
result.bitLength = 0;
unsigned int accumData = 0;
int accumCount = 0;
for (; *digits != '\0'; digits++) {
char c = *digits;
assert('0' <= c && c <= '9');
accumData = accumData * 10 + (unsigned int)(c - '0');
accumCount++;
if (accumCount == 3) {
appendBitsToBuffer(accumData, 10, buf, &result.bitLength);
accumData = 0;
accumCount = 0;
}
}
if (accumCount > 0) // 1 or 2 digits remaining
appendBitsToBuffer(accumData, accumCount * 3 + 1, buf, &result.bitLength);
assert(result.bitLength == bitLen);
result.data = buf;
return result;
}
// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeAlphanumeric(const char *text, uint8_t buf[]) {
assert(text != NULL);
struct qrcodegen_Segment result;
size_t len = strlen(text);
result.mode = qrcodegen_Mode_ALPHANUMERIC;
int bitLen = calcSegmentBitLength(result.mode, len);
assert(bitLen != -1);
result.numChars = (int)len;
if (bitLen > 0)
memset(buf, 0, ((size_t)bitLen + 7) / 8 * sizeof(buf[0]));
result.bitLength = 0;
unsigned int accumData = 0;
int accumCount = 0;
for (; *text != '\0'; text++) {
const char *temp = strchr(ALPHANUMERIC_CHARSET, *text);
assert(temp != NULL);
accumData = accumData * 45 + (unsigned int)(temp - ALPHANUMERIC_CHARSET);
accumCount++;
if (accumCount == 2) {
appendBitsToBuffer(accumData, 11, buf, &result.bitLength);
accumData = 0;
accumCount = 0;
}
}
if (accumCount > 0) // 1 character remaining
appendBitsToBuffer(accumData, 6, buf, &result.bitLength);
assert(result.bitLength == bitLen);
result.data = buf;
return result;
}
// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeEci(long assignVal, uint8_t buf[]) {
struct qrcodegen_Segment result;
result.mode = qrcodegen_Mode_ECI;
result.numChars = 0;
result.bitLength = 0;
if (assignVal < 0)
assert(false);
else if (assignVal < (1 << 7)) {
memset(buf, 0, 1 * sizeof(buf[0]));
appendBitsToBuffer(assignVal, 8, buf, &result.bitLength);
} else if (assignVal < (1 << 14)) {
memset(buf, 0, 2 * sizeof(buf[0]));
appendBitsToBuffer(2, 2, buf, &result.bitLength);
appendBitsToBuffer(assignVal, 14, buf, &result.bitLength);
} else if (assignVal < 1000000L) {
memset(buf, 0, 3 * sizeof(buf[0]));
appendBitsToBuffer(6, 3, buf, &result.bitLength);
appendBitsToBuffer(assignVal >> 10, 11, buf, &result.bitLength);
appendBitsToBuffer(assignVal & 0x3FF, 10, buf, &result.bitLength);
} else
assert(false);
result.data = buf;
return result;
}
// Calculates the number of bits needed to encode the given segments at the given version.
// Returns a non-negative number if successful. Otherwise returns -1 if a segment has too
// many characters to fit its length field, or the total bits exceeds INT16_MAX.
testable int getTotalBits(const struct qrcodegen_Segment segs[], size_t len, int version) {
assert(segs != NULL || len == 0);
long result = 0;
for (size_t i = 0; i < len; i++) {
int numChars = segs[i].numChars;
int bitLength = segs[i].bitLength;
assert(0 <= numChars && numChars <= INT16_MAX);
assert(0 <= bitLength && bitLength <= INT16_MAX);
int ccbits = numCharCountBits(segs[i].mode, version);
assert(0 <= ccbits && ccbits <= 16);
if (numChars >= (1L << ccbits))
return -1; // The segment's length doesn't fit the field's bit width
result += 4L + ccbits + bitLength;
if (result > INT16_MAX)
return -1; // The sum might overflow an int type
}
assert(0 <= result && result <= INT16_MAX);
return (int)result;
}
// Returns the bit width of the character count field for a segment in the given mode
// in a QR Code at the given version number. The result is in the range [0, 16].
static int numCharCountBits(enum qrcodegen_Mode mode, int version) {
assert(qrcodegen_VERSION_MIN <= version && version <= qrcodegen_VERSION_MAX);
int i = (version + 7) / 17;
switch (mode) {
case qrcodegen_Mode_NUMERIC : { static const int temp[] = {10, 12, 14}; return temp[i]; }
case qrcodegen_Mode_ALPHANUMERIC: { static const int temp[] = { 9, 11, 13}; return temp[i]; }
case qrcodegen_Mode_BYTE : { static const int temp[] = { 8, 16, 16}; return temp[i]; }
case qrcodegen_Mode_KANJI : { static const int temp[] = { 8, 10, 12}; return temp[i]; }
case qrcodegen_Mode_ECI : return 0;
default: assert(false); return -1; // Dummy value
}
}