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// Copyright 2011 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Package coding implements low-level QR coding details.
package coding // import "rsc.io/qr/coding"
import (
"fmt"
"strconv"
"strings"
"rsc.io/qr/gf256"
)
// Field is the field for QR error correction.
var Field = gf256.NewField(0x11d, 2)
// A Version represents a QR version.
// The version specifies the size of the QR code:
// a QR code with version v has 4v+17 pixels on a side.
// Versions number from 1 to 40: the larger the version,
// the more information the code can store.
type Version int
const MinVersion = 1
const MaxVersion = 40
func (v Version) String() string {
return strconv.Itoa(int(v))
}
func (v Version) sizeClass() int {
if v <= 9 {
return 0
}
if v <= 26 {
return 1
}
return 2
}
// DataBytes returns the number of data bytes that can be
// stored in a QR code with the given version and level.
func (v Version) DataBytes(l Level) int {
vt := &vtab[v]
lev := &vt.level[l]
return vt.bytes - lev.nblock*lev.check
}
// Encoding implements a QR data encoding scheme.
// The implementations--Numeric, Alphanumeric, and String--specify
// the character set and the mapping from UTF-8 to code bits.
// The more restrictive the mode, the fewer code bits are needed.
type Encoding interface {
Check() error
Bits(v Version) int
Encode(b *Bits, v Version)
}
type Bits struct {
b []byte
nbit int
}
func (b *Bits) Reset() {
b.b = b.b[:0]
b.nbit = 0
}
func (b *Bits) Bits() int {
return b.nbit
}
func (b *Bits) Bytes() []byte {
if b.nbit%8 != 0 {
panic("fractional byte")
}
return b.b
}
func (b *Bits) Append(p []byte) {
if b.nbit%8 != 0 {
panic("fractional byte")
}
b.b = append(b.b, p...)
b.nbit += 8 * len(p)
}
func (b *Bits) Write(v uint, nbit int) {
for nbit > 0 {
n := nbit
if n > 8 {
n = 8
}
if b.nbit%8 == 0 {
b.b = append(b.b, 0)
} else {
m := -b.nbit & 7
if n > m {
n = m
}
}
b.nbit += n
sh := uint(nbit - n)
b.b[len(b.b)-1] |= uint8(v >> sh << uint(-b.nbit&7))
v -= v >> sh << sh
nbit -= n
}
}
// Num is the encoding for numeric data.
// The only valid characters are the decimal digits 0 through 9.
type Num string
func (s Num) String() string {
return fmt.Sprintf("Num(%#q)", string(s))
}
func (s Num) Check() error {
for _, c := range s {
if c < '0' || '9' < c {
return fmt.Errorf("non-numeric string %#q", string(s))
}
}
return nil
}
var numLen = [3]int{10, 12, 14}
func (s Num) Bits(v Version) int {
return 4 + numLen[v.sizeClass()] + (10*len(s)+2)/3
}
func (s Num) Encode(b *Bits, v Version) {
b.Write(1, 4)
b.Write(uint(len(s)), numLen[v.sizeClass()])
var i int
for i = 0; i+3 <= len(s); i += 3 {
w := uint(s[i]-'0')*100 + uint(s[i+1]-'0')*10 + uint(s[i+2]-'0')
b.Write(w, 10)
}
switch len(s) - i {
case 1:
w := uint(s[i] - '0')
b.Write(w, 4)
case 2:
w := uint(s[i]-'0')*10 + uint(s[i+1]-'0')
b.Write(w, 7)
}
}
// Alpha is the encoding for alphanumeric data.
// The valid characters are 0-9A-Z$%*+-./: and space.
type Alpha string
const alphabet = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:"
func (s Alpha) String() string {
return fmt.Sprintf("Alpha(%#q)", string(s))
}
func (s Alpha) Check() error {
for _, c := range s {
if strings.IndexRune(alphabet, c) < 0 {
return fmt.Errorf("non-alphanumeric string %#q", string(s))
}
}
return nil
}
var alphaLen = [3]int{9, 11, 13}
func (s Alpha) Bits(v Version) int {
return 4 + alphaLen[v.sizeClass()] + (11*len(s)+1)/2
}
func (s Alpha) Encode(b *Bits, v Version) {
b.Write(2, 4)
b.Write(uint(len(s)), alphaLen[v.sizeClass()])
var i int
for i = 0; i+2 <= len(s); i += 2 {
w := uint(strings.IndexRune(alphabet, rune(s[i])))*45 +
uint(strings.IndexRune(alphabet, rune(s[i+1])))
b.Write(w, 11)
}
if i < len(s) {
w := uint(strings.IndexRune(alphabet, rune(s[i])))
b.Write(w, 6)
}
}
// String is the encoding for 8-bit data. All bytes are valid.
type String string
func (s String) String() string {
return fmt.Sprintf("String(%#q)", string(s))
}
func (s String) Check() error {
return nil
}
var stringLen = [3]int{8, 16, 16}
func (s String) Bits(v Version) int {
return 4 + stringLen[v.sizeClass()] + 8*len(s)
}
func (s String) Encode(b *Bits, v Version) {
b.Write(4, 4)
b.Write(uint(len(s)), stringLen[v.sizeClass()])
for i := 0; i < len(s); i++ {
b.Write(uint(s[i]), 8)
}
}
// A Pixel describes a single pixel in a QR code.
type Pixel uint32
const (
Black Pixel = 1 << iota
Invert
)
func (p Pixel) Offset() uint {
return uint(p >> 6)
}
func OffsetPixel(o uint) Pixel {
return Pixel(o << 6)
}
func (r PixelRole) Pixel() Pixel {
return Pixel(r << 2)
}
func (p Pixel) Role() PixelRole {
return PixelRole(p>>2) & 15
}
func (p Pixel) String() string {
s := p.Role().String()
if p&Black != 0 {
s += "+black"
}
if p&Invert != 0 {
s += "+invert"
}
s += "+" + strconv.FormatUint(uint64(p.Offset()), 10)
return s
}
// A PixelRole describes the role of a QR pixel.
type PixelRole uint32
const (
_ PixelRole = iota
Position // position squares (large)
Alignment // alignment squares (small)
Timing // timing strip between position squares
Format // format metadata
PVersion // version pattern
Unused // unused pixel
Data // data bit
Check // error correction check bit
Extra
)
var roles = []string{
"",
"position",
"alignment",
"timing",
"format",
"pversion",
"unused",
"data",
"check",
"extra",
}
func (r PixelRole) String() string {
if Position <= r && r <= Check {
return roles[r]
}
return strconv.Itoa(int(r))
}
// A Level represents a QR error correction level.
// From least to most tolerant of errors, they are L, M, Q, H.
type Level int
const (
L Level = iota
M
Q
H
)
func (l Level) String() string {
if L <= l && l <= H {
return "LMQH"[l : l+1]
}
return strconv.Itoa(int(l))
}
// A Code is a square pixel grid.
type Code struct {
Bitmap []byte // 1 is black, 0 is white
Size int // number of pixels on a side
Stride int // number of bytes per row
}
func (c *Code) Black(x, y int) bool {
return 0 <= x && x < c.Size && 0 <= y && y < c.Size &&
c.Bitmap[y*c.Stride+x/8]&(1<<uint(7-x&7)) != 0
}
// A Mask describes a mask that is applied to the QR
// code to avoid QR artifacts being interpreted as
// alignment and timing patterns (such as the squares
// in the corners). Valid masks are integers from 0 to 7.
type Mask int
// http://www.swetake.com/qr/qr5_en.html
var mfunc = []func(int, int) bool{
func(i, j int) bool { return (i+j)%2 == 0 },
func(i, j int) bool { return i%2 == 0 },
func(i, j int) bool { return j%3 == 0 },
func(i, j int) bool { return (i+j)%3 == 0 },
func(i, j int) bool { return (i/2+j/3)%2 == 0 },
func(i, j int) bool { return i*j%2+i*j%3 == 0 },
func(i, j int) bool { return (i*j%2+i*j%3)%2 == 0 },
func(i, j int) bool { return (i*j%3+(i+j)%2)%2 == 0 },
}
func (m Mask) Invert(y, x int) bool {
if m < 0 {
return false
}
return mfunc[m](y, x)
}
// A Plan describes how to construct a QR code
// with a specific version, level, and mask.
type Plan struct {
Version Version
Level Level
Mask Mask
DataBytes int // number of data bytes
CheckBytes int // number of error correcting (checksum) bytes
Blocks int // number of data blocks
Pixel [][]Pixel // pixel map
}
// NewPlan returns a Plan for a QR code with the given
// version, level, and mask.
func NewPlan(version Version, level Level, mask Mask) (*Plan, error) {
p, err := vplan(version)
if err != nil {
return nil, err
}
if err := fplan(level, mask, p); err != nil {
return nil, err
}
if err := lplan(version, level, p); err != nil {
return nil, err
}
if err := mplan(mask, p); err != nil {
return nil, err
}
return p, nil
}
func (b *Bits) Pad(n int) {
if n < 0 {
panic("qr: invalid pad size")
}
if n <= 4 {
b.Write(0, n)
} else {
b.Write(0, 4)
n -= 4
n -= -b.Bits() & 7
b.Write(0, -b.Bits()&7)
pad := n / 8
for i := 0; i < pad; i += 2 {
b.Write(0xec, 8)
if i+1 >= pad {
break
}
b.Write(0x11, 8)
}
}
}
func (b *Bits) AddCheckBytes(v Version, l Level) {
nd := v.DataBytes(l)
if b.nbit < nd*8 {
b.Pad(nd*8 - b.nbit)
}
if b.nbit != nd*8 {
panic("qr: too much data")
}
dat := b.Bytes()
vt := &vtab[v]
lev := &vt.level[l]
db := nd / lev.nblock
extra := nd % lev.nblock
chk := make([]byte, lev.check)
rs := gf256.NewRSEncoder(Field, lev.check)
for i := 0; i < lev.nblock; i++ {
if i == lev.nblock-extra {
db++
}
rs.ECC(dat[:db], chk)
b.Append(chk)
dat = dat[db:]
}
if len(b.Bytes()) != vt.bytes {
panic("qr: internal error")
}
}
func (p *Plan) Encode(text ...Encoding) (*Code, error) {
var b Bits
for _, t := range text {
if err := t.Check(); err != nil {
return nil, err
}
t.Encode(&b, p.Version)
}
if b.Bits() > p.DataBytes*8 {
return nil, fmt.Errorf("cannot encode %d bits into %d-bit code", b.Bits(), p.DataBytes*8)
}
b.AddCheckBytes(p.Version, p.Level)
bytes := b.Bytes()
// Now we have the checksum bytes and the data bytes.
// Construct the actual code.
c := &Code{Size: len(p.Pixel), Stride: (len(p.Pixel) + 7) &^ 7}
c.Bitmap = make([]byte, c.Stride*c.Size)
crow := c.Bitmap
for _, row := range p.Pixel {
for x, pix := range row {
switch pix.Role() {
case Data, Check:
o := pix.Offset()
if bytes[o/8]&(1<<uint(7-o&7)) != 0 {
pix ^= Black
}
}
if pix&Black != 0 {
crow[x/8] |= 1 << uint(7-x&7)
}
}
crow = crow[c.Stride:]
}
return c, nil
}
// A version describes metadata associated with a version.
type version struct {
apos int
astride int
bytes int
pattern int
level [4]level
}
type level struct {
nblock int
check int
}
var vtab = []version{
{},
{100, 100, 26, 0x0, [4]level{{1, 7}, {1, 10}, {1, 13}, {1, 17}}}, // 1
{16, 100, 44, 0x0, [4]level{{1, 10}, {1, 16}, {1, 22}, {1, 28}}}, // 2
{20, 100, 70, 0x0, [4]level{{1, 15}, {1, 26}, {2, 18}, {2, 22}}}, // 3
{24, 100, 100, 0x0, [4]level{{1, 20}, {2, 18}, {2, 26}, {4, 16}}}, // 4
{28, 100, 134, 0x0, [4]level{{1, 26}, {2, 24}, {4, 18}, {4, 22}}}, // 5
{32, 100, 172, 0x0, [4]level{{2, 18}, {4, 16}, {4, 24}, {4, 28}}}, // 6
{20, 16, 196, 0x7c94, [4]level{{2, 20}, {4, 18}, {6, 18}, {5, 26}}}, // 7
{22, 18, 242, 0x85bc, [4]level{{2, 24}, {4, 22}, {6, 22}, {6, 26}}}, // 8
{24, 20, 292, 0x9a99, [4]level{{2, 30}, {5, 22}, {8, 20}, {8, 24}}}, // 9
{26, 22, 346, 0xa4d3, [4]level{{4, 18}, {5, 26}, {8, 24}, {8, 28}}}, // 10
{28, 24, 404, 0xbbf6, [4]level{{4, 20}, {5, 30}, {8, 28}, {11, 24}}}, // 11
{30, 26, 466, 0xc762, [4]level{{4, 24}, {8, 22}, {10, 26}, {11, 28}}}, // 12
{32, 28, 532, 0xd847, [4]level{{4, 26}, {9, 22}, {12, 24}, {16, 22}}}, // 13
{24, 20, 581, 0xe60d, [4]level{{4, 30}, {9, 24}, {16, 20}, {16, 24}}}, // 14
{24, 22, 655, 0xf928, [4]level{{6, 22}, {10, 24}, {12, 30}, {18, 24}}}, // 15
{24, 24, 733, 0x10b78, [4]level{{6, 24}, {10, 28}, {17, 24}, {16, 30}}}, // 16
{28, 24, 815, 0x1145d, [4]level{{6, 28}, {11, 28}, {16, 28}, {19, 28}}}, // 17
{28, 26, 901, 0x12a17, [4]level{{6, 30}, {13, 26}, {18, 28}, {21, 28}}}, // 18
{28, 28, 991, 0x13532, [4]level{{7, 28}, {14, 26}, {21, 26}, {25, 26}}}, // 19
{32, 28, 1085, 0x149a6, [4]level{{8, 28}, {16, 26}, {20, 30}, {25, 28}}}, // 20
{26, 22, 1156, 0x15683, [4]level{{8, 28}, {17, 26}, {23, 28}, {25, 30}}}, // 21
{24, 24, 1258, 0x168c9, [4]level{{9, 28}, {17, 28}, {23, 30}, {34, 24}}}, // 22
{28, 24, 1364, 0x177ec, [4]level{{9, 30}, {18, 28}, {25, 30}, {30, 30}}}, // 23
{26, 26, 1474, 0x18ec4, [4]level{{10, 30}, {20, 28}, {27, 30}, {32, 30}}}, // 24
{30, 26, 1588, 0x191e1, [4]level{{12, 26}, {21, 28}, {29, 30}, {35, 30}}}, // 25
{28, 28, 1706, 0x1afab, [4]level{{12, 28}, {23, 28}, {34, 28}, {37, 30}}}, // 26
{32, 28, 1828, 0x1b08e, [4]level{{12, 30}, {25, 28}, {34, 30}, {40, 30}}}, // 27
{24, 24, 1921, 0x1cc1a, [4]level{{13, 30}, {26, 28}, {35, 30}, {42, 30}}}, // 28
{28, 24, 2051, 0x1d33f, [4]level{{14, 30}, {28, 28}, {38, 30}, {45, 30}}}, // 29
{24, 26, 2185, 0x1ed75, [4]level{{15, 30}, {29, 28}, {40, 30}, {48, 30}}}, // 30
{28, 26, 2323, 0x1f250, [4]level{{16, 30}, {31, 28}, {43, 30}, {51, 30}}}, // 31
{32, 26, 2465, 0x209d5, [4]level{{17, 30}, {33, 28}, {45, 30}, {54, 30}}}, // 32
{28, 28, 2611, 0x216f0, [4]level{{18, 30}, {35, 28}, {48, 30}, {57, 30}}}, // 33
{32, 28, 2761, 0x228ba, [4]level{{19, 30}, {37, 28}, {51, 30}, {60, 30}}}, // 34
{28, 24, 2876, 0x2379f, [4]level{{19, 30}, {38, 28}, {53, 30}, {63, 30}}}, // 35
{22, 26, 3034, 0x24b0b, [4]level{{20, 30}, {40, 28}, {56, 30}, {66, 30}}}, // 36
{26, 26, 3196, 0x2542e, [4]level{{21, 30}, {43, 28}, {59, 30}, {70, 30}}}, // 37
{30, 26, 3362, 0x26a64, [4]level{{22, 30}, {45, 28}, {62, 30}, {74, 30}}}, // 38
{24, 28, 3532, 0x27541, [4]level{{24, 30}, {47, 28}, {65, 30}, {77, 30}}}, // 39
{28, 28, 3706, 0x28c69, [4]level{{25, 30}, {49, 28}, {68, 30}, {81, 30}}}, // 40
}
func grid(siz int) [][]Pixel {
m := make([][]Pixel, siz)
pix := make([]Pixel, siz*siz)
for i := range m {
m[i], pix = pix[:siz], pix[siz:]
}
return m
}
// vplan creates a Plan for the given version.
func vplan(v Version) (*Plan, error) {
p := &Plan{Version: v}
if v < 1 || v > 40 {
return nil, fmt.Errorf("invalid QR version %d", int(v))
}
siz := 17 + int(v)*4
m := grid(siz)
p.Pixel = m
// Timing markers (overwritten by boxes).
const ti = 6 // timing is in row/column 6 (counting from 0)
for i := range m {
p := Timing.Pixel()
if i&1 == 0 {
p |= Black
}
m[i][ti] = p
m[ti][i] = p
}
// Position boxes.
posBox(m, 0, 0)
posBox(m, siz-7, 0)
posBox(m, 0, siz-7)
// Alignment boxes.
info := &vtab[v]
for x := 4; x+5 < siz; {
for y := 4; y+5 < siz; {
// don't overwrite timing markers
if (x < 7 && y < 7) || (x < 7 && y+5 >= siz-7) || (x+5 >= siz-7 && y < 7) {
} else {
alignBox(m, x, y)
}
if y == 4 {
y = info.apos
} else {
y += info.astride
}
}
if x == 4 {
x = info.apos
} else {
x += info.astride
}
}
// Version pattern.
pat := vtab[v].pattern
if pat != 0 {
v := pat
for x := 0; x < 6; x++ {
for y := 0; y < 3; y++ {
p := PVersion.Pixel()
if v&1 != 0 {
p |= Black
}
m[siz-11+y][x] = p
m[x][siz-11+y] = p
v >>= 1
}
}
}
// One lonely black pixel
m[siz-8][8] = Unused.Pixel() | Black
return p, nil
}
// fplan adds the format pixels
func fplan(l Level, m Mask, p *Plan) error {
// Format pixels.
fb := uint32(l^1) << 13 // level: L=01, M=00, Q=11, H=10
fb |= uint32(m) << 10 // mask
const formatPoly = 0x537
rem := fb
for i := 14; i >= 10; i-- {
if rem&(1<<uint(i)) != 0 {
rem ^= formatPoly << uint(i-10)
}
}
fb |= rem
invert := uint32(0x5412)
siz := len(p.Pixel)
for i := uint(0); i < 15; i++ {
pix := Format.Pixel() + OffsetPixel(i)
if (fb>>i)&1 == 1 {
pix |= Black
}
if (invert>>i)&1 == 1 {
pix ^= Invert | Black
}
// top left
switch {
case i < 6:
p.Pixel[i][8] = pix
case i < 8:
p.Pixel[i+1][8] = pix
case i < 9:
p.Pixel[8][7] = pix
default:
p.Pixel[8][14-i] = pix
}
// bottom right
switch {
case i < 8:
p.Pixel[8][siz-1-int(i)] = pix
default:
p.Pixel[siz-1-int(14-i)][8] = pix
}
}
return nil
}
// lplan edits a version-only Plan to add information
// about the error correction levels.
func lplan(v Version, l Level, p *Plan) error {
p.Level = l
nblock := vtab[v].level[l].nblock
ne := vtab[v].level[l].check
nde := (vtab[v].bytes - ne*nblock) / nblock
extra := (vtab[v].bytes - ne*nblock) % nblock
dataBits := (nde*nblock + extra) * 8
checkBits := ne * nblock * 8
p.DataBytes = vtab[v].bytes - ne*nblock
p.CheckBytes = ne * nblock
p.Blocks = nblock
// Make data + checksum pixels.
data := make([]Pixel, dataBits)
for i := range data {
data[i] = Data.Pixel() | OffsetPixel(uint(i))
}
check := make([]Pixel, checkBits)
for i := range check {
check[i] = Check.Pixel() | OffsetPixel(uint(i+dataBits))
}
// Split into blocks.
dataList := make([][]Pixel, nblock)
checkList := make([][]Pixel, nblock)
for i := 0; i < nblock; i++ {
// The last few blocks have an extra data byte (8 pixels).
nd := nde
if i >= nblock-extra {
nd++
}
dataList[i], data = data[0:nd*8], data[nd*8:]
checkList[i], check = check[0:ne*8], check[ne*8:]
}
if len(data) != 0 || len(check) != 0 {
panic("data/check math")
}
// Build up bit sequence, taking first byte of each block,
// then second byte, and so on. Then checksums.
bits := make([]Pixel, dataBits+checkBits)
dst := bits
for i := 0; i < nde+1; i++ {
for _, b := range dataList {
if i*8 < len(b) {
copy(dst, b[i*8:(i+1)*8])
dst = dst[8:]
}
}
}
for i := 0; i < ne; i++ {
for _, b := range checkList {
if i*8 < len(b) {
copy(dst, b[i*8:(i+1)*8])
dst = dst[8:]
}
}
}
if len(dst) != 0 {
panic("dst math")
}
// Sweep up pair of columns,
// then down, assigning to right then left pixel.
// Repeat.
// See Figure 2 of http://www.pclviewer.com/rs2/qrtopology.htm
siz := len(p.Pixel)
rem := make([]Pixel, 7)
for i := range rem {
rem[i] = Extra.Pixel()
}
src := append(bits, rem...)
for x := siz; x > 0; {
for y := siz - 1; y >= 0; y-- {
if p.Pixel[y][x-1].Role() == 0 {
p.Pixel[y][x-1], src = src[0], src[1:]
}
if p.Pixel[y][x-2].Role() == 0 {
p.Pixel[y][x-2], src = src[0], src[1:]
}
}
x -= 2
if x == 7 { // vertical timing strip
x--
}
for y := 0; y < siz; y++ {
if p.Pixel[y][x-1].Role() == 0 {
p.Pixel[y][x-1], src = src[0], src[1:]
}
if p.Pixel[y][x-2].Role() == 0 {
p.Pixel[y][x-2], src = src[0], src[1:]
}
}
x -= 2
}
return nil
}
// mplan edits a version+level-only Plan to add the mask.
func mplan(m Mask, p *Plan) error {
p.Mask = m
for y, row := range p.Pixel {
for x, pix := range row {
if r := pix.Role(); (r == Data || r == Check || r == Extra) && p.Mask.Invert(y, x) {
row[x] ^= Black | Invert
}
}
}
return nil
}
// posBox draws a position (large) box at upper left x, y.
func posBox(m [][]Pixel, x, y int) {
pos := Position.Pixel()
// box
for dy := 0; dy < 7; dy++ {
for dx := 0; dx < 7; dx++ {
p := pos
if dx == 0 || dx == 6 || dy == 0 || dy == 6 || 2 <= dx && dx <= 4 && 2 <= dy && dy <= 4 {
p |= Black
}
m[y+dy][x+dx] = p
}
}
// white border
for dy := -1; dy < 8; dy++ {
if 0 <= y+dy && y+dy < len(m) {
if x > 0 {
m[y+dy][x-1] = pos
}
if x+7 < len(m) {
m[y+dy][x+7] = pos
}
}
}
for dx := -1; dx < 8; dx++ {
if 0 <= x+dx && x+dx < len(m) {
if y > 0 {
m[y-1][x+dx] = pos
}
if y+7 < len(m) {
m[y+7][x+dx] = pos
}
}
}
}
// alignBox draw an alignment (small) box at upper left x, y.
func alignBox(m [][]Pixel, x, y int) {
// box
align := Alignment.Pixel()
for dy := 0; dy < 5; dy++ {
for dx := 0; dx < 5; dx++ {
p := align
if dx == 0 || dx == 4 || dy == 0 || dy == 4 || dx == 2 && dy == 2 {
p |= Black
}
m[y+dy][x+dx] = p
}
}
}