Written from the ISO 18004 tables. The helpers are exported so a test can read a symbol back: format bits, unmasked data, de-interleaved blocks, Reed-Solomon syndromes, and the bytes themselves.
- commit
- ec612cc73beffb48dc8536273606e11570204255
- parent
- 16544feaf216f52102148ad5b5ef8537d3641092
- author
- Dami <dami.etoile@gmail.com>
| A | src/ | 361 | ++++++++++++++++++++++++++++++ |
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1+// A QR code encoder: byte mode, error correction level M, versions 1 to 202+// (up to 666 bytes), no dependencies. Used for the group naddr on the relay3+// card and for the remote signer link. Written from the ISO 18004 tables;4+// the helpers are exported so the test can read a symbol back and check the5+// Reed-Solomon syndromes rather than trust a picture.6+7+// Error correction blocks for level M: [ec codewords per block, group 18+// block count, group 1 data codewords, group 2 block count, group 2 data9+// codewords], indexed by version. Version 0 is a placeholder.10+export const EC_M: [number, number, number, number, number][] = [11+ [0, 0, 0, 0, 0],12+ [10, 1, 16, 0, 0], [16, 1, 28, 0, 0], [26, 1, 44, 0, 0], [18, 2, 32, 0, 0], [24, 2, 43, 0, 0],13+ [16, 4, 27, 0, 0], [18, 4, 31, 0, 0], [22, 2, 38, 2, 39], [22, 3, 36, 2, 37], [26, 4, 43, 1, 44],14+ [30, 1, 50, 4, 51], [22, 6, 36, 2, 37], [22, 8, 37, 1, 38], [24, 4, 40, 5, 41], [24, 5, 41, 5, 42],15+ [28, 7, 45, 3, 46], [28, 10, 46, 1, 47], [26, 9, 43, 4, 44], [26, 3, 44, 11, 45], [26, 3, 41, 13, 42],16+];17+const ALIGN: number[][] = [18+ [], [], [6, 18], [6, 22], [6, 26], [6, 30], [6, 34], [6, 22, 38], [6, 24, 42], [6, 26, 46], [6, 28, 52],19+ [6, 30, 54], [6, 32, 58], [6, 34, 62], [6, 26, 46, 66], [6, 26, 48, 70], [6, 26, 50, 74], [6, 30, 54, 78], [6, 30, 56, 82], [6, 30, 58, 86], [6, 34, 62, 90],20+];21+export const MAX_VERSION = 20;22+23+export function dataCodewords(version: number): number {24+ const [, g1, d1, g2, d2] = EC_M[version];25+ return g1 * d1 + g2 * d2;26+}27+// capacity is how many bytes a version holds in byte mode at level M.28+export function capacity(version: number): number {29+ return Math.floor((dataCodewords(version) * 8 - 4 - (version < 10 ? 8 : 16)) / 8);30+}31+32+// ---- GF(256) and Reed-Solomon ----33+34+const EXP = new Uint8Array(512);35+const LOG = new Uint8Array(256);36+(() => {37+ let x = 1;38+ for (let i = 0; i < 255; i++) {39+ EXP[i] = x;40+ LOG[x] = i;41+ x <<= 1;42+ if (x & 0x100) x ^= 0x11d;43+ }44+ for (let i = 255; i < 512; i++) EXP[i] = EXP[i - 255];45+})();46+export function gfMul(a: number, b: number): number {47+ return a === 0 || b === 0 ? 0 : EXP[LOG[a] + LOG[b]];48+}49+export function gfPow(base: number, e: number): number {50+ return EXP[(LOG[base] * e) % 255];51+}52+function generator(ec: number): number[] {53+ let g = [1];54+ for (let i = 0; i < ec; i++) {55+ const next = new Array<number>(g.length + 1).fill(0);56+ for (let j = 0; j < g.length; j++) {57+ next[j] ^= g[j];58+ next[j + 1] ^= gfMul(g[j], EXP[i]);59+ }60+ g = next;61+ }62+ return g;63+}64+export function rsEncode(data: number[], ec: number): number[] {65+ const g = generator(ec);66+ const rem = new Array<number>(ec).fill(0);67+ for (const d of data) {68+ const f = d ^ rem[0];69+ rem.shift();70+ rem.push(0);71+ if (f === 0) continue;72+ for (let j = 0; j < ec; j++) rem[j] ^= gfMul(g[j + 1], f);73+ }74+ return rem;75+}76+77+// ---- layout ----78+79+export interface Layout {80+ size: number;81+ isFunction: Uint8Array; // 1 where a module is fixed or reserved82+}83+84+export function layout(version: number): Layout {85+ const size = version * 4 + 17;86+ const f = new Uint8Array(size * size);87+ const mark = (x: number, y: number) => {88+ if (x >= 0 && y >= 0 && x < size && y < size) f[y * size + x] = 1;89+ };90+ // Finders with separators, and the format areas next to them.91+ for (const [cx, cy] of [[0, 0], [size - 7, 0], [0, size - 7]]) {92+ for (let y = -1; y < 8; y++) for (let x = -1; x < 8; x++) mark(cx + x, cy + y);93+ }94+ for (let i = 0; i < 9; i++) {95+ mark(i, 8);96+ mark(8, i);97+ }98+ for (let i = 0; i < 8; i++) {99+ mark(size - 1 - i, 8);100+ mark(8, size - 1 - i);101+ }102+ // Timing.103+ for (let i = 8; i < size - 8; i++) {104+ mark(i, 6);105+ mark(6, i);106+ }107+ // Alignment.108+ const a = ALIGN[version];109+ for (const cy of a) {110+ for (const cx of a) {111+ if ((cx === 6 && cy === 6) || (cx === 6 && cy === size - 7) || (cx === size - 7 && cy === 6)) continue;112+ for (let y = -2; y <= 2; y++) for (let x = -2; x <= 2; x++) mark(cx + x, cy + y);113+ }114+ }115+ // Version information.116+ if (version >= 7) {117+ for (let i = 0; i < 18; i++) {118+ mark(Math.floor(i / 3), size - 11 + (i % 3));119+ mark(size - 11 + (i % 3), Math.floor(i / 3));120+ }121+ }122+ return { size, isFunction: f };123+}124+125+// dataOrder lists the non-function modules in the zigzag order data bits are placed.126+export function dataOrder(l: Layout): [number, number][] {127+ const out: [number, number][] = [];128+ const { size, isFunction } = l;129+ let up = true;130+ for (let col = size - 1; col > 0; col -= 2) {131+ if (col === 6) col = 5;132+ for (let i = 0; i < size; i++) {133+ const y = up ? size - 1 - i : i;134+ for (const dx of [0, 1]) {135+ const x = col - dx;136+ if (!isFunction[y * size + x]) out.push([x, y]);137+ }138+ }139+ up = !up;140+ }141+ return out;142+}143+144+export const MASKS: ((x: number, y: number) => boolean)[] = [145+ (x, y) => (x + y) % 2 === 0,146+ (_x, y) => y % 2 === 0,147+ (x) => x % 3 === 0,148+ (x, y) => (x + y) % 3 === 0,149+ (x, y) => (Math.floor(y / 2) + Math.floor(x / 3)) % 2 === 0,150+ (x, y) => ((x * y) % 2) + ((x * y) % 3) === 0,151+ (x, y) => (((x * y) % 2) + ((x * y) % 3)) % 2 === 0,152+ (x, y) => (((x + y) % 2) + ((x * y) % 3)) % 2 === 0,153+];154+155+// formatBits is the 15-bit BCH-coded format information for level M and a mask.156+export function formatBits(mask: number): number {157+ const data = (0 << 3) | mask; // level M is 00158+ let bch = data << 10;159+ for (let i = 14; i >= 10; i--) if (bch & (1 << i)) bch ^= 0x537 << (i - 10);160+ return ((data << 10) | bch) ^ 0x5412;161+}162+export function versionBits(version: number): number {163+ let rem = version << 12;164+ for (let i = 17; i >= 12; i--) if (rem & (1 << i)) rem ^= 0x1f25 << (i - 12);165+ return (version << 12) | rem;166+}167+168+// ---- encoding ----169+170+export interface Symbol {171+ version: number;172+ size: number;173+ mask: number;174+ modules: Uint8Array; // 1 is dark175+}176+177+// codewords builds the interleaved data and error correction stream.178+export function codewords(bytes: Uint8Array, version: number): number[] {179+ const bits: number[] = [];180+ const push = (v: number, n: number) => {181+ for (let i = n - 1; i >= 0; i--) bits.push((v >> i) & 1);182+ };183+ push(0b0100, 4);184+ push(bytes.length, version < 10 ? 8 : 16);185+ for (const b of bytes) push(b, 8);186+ const total = dataCodewords(version) * 8;187+ push(0, Math.min(4, total - bits.length));188+ while (bits.length % 8) bits.push(0);189+ const data: number[] = [];190+ for (let i = 0; i < bits.length; i += 8) data.push(parseInt(bits.slice(i, i + 8).join(""), 2));191+ for (let pad = 0xec; data.length < dataCodewords(version); pad ^= 0xec ^ 0x11) data.push(pad);192+ // Split into blocks, compute EC, interleave.193+ const [ec, g1, d1, g2, d2] = EC_M[version];194+ const blocks: number[][] = [];195+ let off = 0;196+ for (let i = 0; i < g1 + g2; i++) {197+ const len = i < g1 ? d1 : d2;198+ blocks.push(data.slice(off, off + len));199+ off += len;200+ }201+ const ecs = blocks.map((b) => rsEncode(b, ec));202+ const out: number[] = [];203+ const longest = Math.max(d1, d2);204+ for (let i = 0; i < longest; i++) for (const b of blocks) if (i < b.length) out.push(b[i]);205+ for (let i = 0; i < ec; i++) for (const e of ecs) out.push(e[i]);206+ return out;207+}208+209+function penalty(m: Uint8Array, size: number): number {210+ let score = 0;211+ const at = (x: number, y: number) => m[y * size + x];212+ // Runs of five or more in a row or column.213+ for (let y = 0; y < size; y++) {214+ let run = 1;215+ for (let x = 1; x < size; x++) {216+ if (at(x, y) === at(x - 1, y)) run++;217+ else {218+ if (run >= 5) score += run - 2;219+ run = 1;220+ }221+ }222+ if (run >= 5) score += run - 2;223+ }224+ for (let x = 0; x < size; x++) {225+ let run = 1;226+ for (let y = 1; y < size; y++) {227+ if (at(x, y) === at(x, y - 1)) run++;228+ else {229+ if (run >= 5) score += run - 2;230+ run = 1;231+ }232+ }233+ if (run >= 5) score += run - 2;234+ }235+ // Two by two blocks.236+ for (let y = 0; y < size - 1; y++) {237+ for (let x = 0; x < size - 1; x++) {238+ const v = at(x, y);239+ if (v === at(x + 1, y) && v === at(x, y + 1) && v === at(x + 1, y + 1)) score += 3;240+ }241+ }242+ // Finder-like patterns with four light modules on a side.243+ const pat = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0];244+ const check = (get: (i: number) => number, len: number) => {245+ for (let i = 0; i + 11 <= len; i++) {246+ let fwd = true;247+ let back = true;248+ for (let j = 0; j < 11; j++) {249+ const v = get(i + j);250+ if (v !== pat[j]) fwd = false;251+ if (v !== pat[10 - j]) back = false;252+ }253+ if (fwd || back) score += 40;254+ }255+ };256+ for (let y = 0; y < size; y++) check((i) => at(i, y), size);257+ for (let x = 0; x < size; x++) check((i) => at(x, i), size);258+ // Dark proportion.259+ let dark = 0;260+ for (const v of m) dark += v;261+ const pct = (dark * 100) / (size * size);262+ score += Math.floor(Math.abs(pct - 50) / 5) * 10;263+ return score;264+}265+266+// encode picks the smallest version that fits, tries every mask and keeps267+// the one with the lowest penalty.268+export function encode(text: string | Uint8Array): Symbol {269+ const bytes = typeof text === "string" ? new TextEncoder().encode(text) : text;270+ let version = 1;271+ while (version <= MAX_VERSION && capacity(version) < bytes.length) version++;272+ if (version > MAX_VERSION) throw new Error(`too long for a QR code: ${bytes.length} bytes, at most ${capacity(MAX_VERSION)}`);273+ const l = layout(version);274+ const { size } = l;275+ const cw = codewords(bytes, version);276+ const order = dataOrder(l);277+ const base = new Uint8Array(size * size);278+ const set = (x: number, y: number, v: number) => {279+ base[y * size + x] = v;280+ };281+ // Finders.282+ for (const [cx, cy] of [[0, 0], [size - 7, 0], [0, size - 7]]) {283+ for (let y = 0; y < 7; y++) {284+ for (let x = 0; x < 7; x++) {285+ const edge = x === 0 || y === 0 || x === 6 || y === 6;286+ const core = x >= 2 && x <= 4 && y >= 2 && y <= 4;287+ set(cx + x, cy + y, edge || core ? 1 : 0);288+ }289+ }290+ }291+ // Timing.292+ for (let i = 8; i < size - 8; i++) {293+ set(i, 6, i % 2 === 0 ? 1 : 0);294+ set(6, i, i % 2 === 0 ? 1 : 0);295+ }296+ // Alignment.297+ const a = ALIGN[version];298+ for (const cy of a) {299+ for (const cx of a) {300+ if ((cx === 6 && cy === 6) || (cx === 6 && cy === size - 7) || (cx === size - 7 && cy === 6)) continue;301+ for (let y = -2; y <= 2; y++) for (let x = -2; x <= 2; x++) set(cx + x, cy + y, Math.max(Math.abs(x), Math.abs(y)) !== 1 ? 1 : 0);302+ }303+ }304+ // Dark module.305+ set(8, size - 8, 1);306+ // Version information.307+ if (version >= 7) {308+ const vb = versionBits(version);309+ for (let i = 0; i < 18; i++) {310+ const bit = (vb >> i) & 1;311+ set(Math.floor(i / 3), size - 11 + (i % 3), bit);312+ set(size - 11 + (i % 3), Math.floor(i / 3), bit);313+ }314+ }315+ // Data bits, zeros where the stream runs out (the remainder bits).316+ const bitAt = (i: number) => (i < cw.length * 8 ? (cw[i >> 3] >> (7 - (i & 7))) & 1 : 0);317+ order.forEach(([x, y], i) => set(x, y, bitAt(i)));318+319+ let best: Uint8Array | null = null;320+ let bestMask = 0;321+ let bestScore = Infinity;322+ for (let mask = 0; mask < 8; mask++) {323+ const m = base.slice();324+ for (const [x, y] of order) if (MASKS[mask](x, y)) m[y * size + x] ^= 1;325+ const fb = formatBits(mask);326+ const bit = (i: number) => (fb >> i) & 1;327+ // Around the top-left finder.328+ for (let i = 0; i < 6; i++) m[8 * size + i] = bit(i);329+ m[8 * size + 7] = bit(6);330+ m[8 * size + 8] = bit(7);331+ m[7 * size + 8] = bit(8);332+ for (let i = 9; i < 15; i++) m[(14 - i) * size + 8] = bit(i);333+ // Split between the other two finders.334+ for (let i = 0; i < 8; i++) m[(size - 1 - i) * size + 8] = bit(i);335+ for (let i = 8; i < 15; i++) m[8 * size + (size - 15 + i)] = bit(i);336+ const s = penalty(m, size);337+ if (s < bestScore) {338+ bestScore = s;339+ best = m;340+ bestMask = mask;341+ }342+ }343+ return { version, size, mask: bestMask, modules: best as Uint8Array };344+}345+346+// svg renders a symbol with a quiet zone, dark on transparent so it sits on347+// any background; pass a fill and a background to change that.348+export function svg(text: string | Uint8Array, opts: { margin?: number; fill?: string; background?: string; title?: string } = {}): string {349+ const q = encode(text);350+ const margin = opts.margin ?? 2;351+ const n = q.size + margin * 2;352+ let d = "";353+ for (let y = 0; y < q.size; y++) {354+ for (let x = 0; x < q.size; x++) {355+ if (q.modules[y * q.size + x]) d += `M${x + margin} ${y + margin}h1v1h-1z`;356+ }357+ }358+ const bg = opts.background ? `<rect width="${n}" height="${n}" fill="${opts.background}"/>` : "";359+ const title = opts.title ? `<title>${opts.title.replace(/[<&>]/g, (c) => ({ "<": "<", "&": "&", ">": ">" })[c] as string)}</title>` : "";360+ return `<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 ${n} ${n}" shape-rendering="crispEdges">${title}${bg}<path d="${d}" fill="${opts.fill ?? "#1c1b18"}"/></svg>`;361+}