QR-Code-generator/typescript-javascript/qrcodegen.ts

/* 
 * QR Code generator library (TypeScript)
 * 
 * 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.
 */

"use strict";


namespace qrcodegen {
	
	type bit  = number;
	type byte = number;
	type int  = number;
	
	
	/*---- QR Code symbol class ----*/
	
	/* 
	 * A QR Code symbol, which is a type of two-dimension barcode.
	 * Invented by Denso Wave and described in the ISO/IEC 18004 standard.
	 * Instances of this class represent an immutable square grid of dark and light cells.
	 * The class provides static factory functions to create a QR Code from text or binary data.
	 * The class covers the QR Code Model 2 specification, supporting all versions (sizes)
	 * from 1 to 40, all 4 error correction levels, and 4 character encoding modes.
	 * 
	 * Ways to create a QR Code object:
	 * - High level: Take the payload data and call QrCode.encodeText() or QrCode.encodeBinary().
	 * - Mid level: Custom-make the list of segments and call QrCode.encodeSegments().
	 * - Low level: Custom-make the array of data codeword bytes (including
	 *   segment headers and final padding, excluding error correction codewords),
	 *   supply the appropriate version number, and call the QrCode() constructor.
	 * (Note that all ways require supplying the desired error correction level.)
	 */
	export class QrCode {
		
		/*-- Static factory functions (high level) --*/
		
		// Returns a QR Code 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) if the low error correction level is used. The smallest possible
		// QR Code version is automatically chosen for the output. The ECC level of the result may be higher than the
		// ecl argument if it can be done without increasing the version.
		public static encodeText(text: string, ecl: QrCode.Ecc): QrCode {
			const segs: Array<QrSegment> = qrcodegen.QrSegment.makeSegments(text);
			return QrCode.encodeSegments(segs, ecl);
		}
		
		
		// Returns a QR Code representing the given binary data 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.
		// The ECC level of the result may be higher than the ecl argument if it can be done without increasing the version.
		public static encodeBinary(data: Array<byte>, ecl: QrCode.Ecc): QrCode {
			const seg: QrSegment = qrcodegen.QrSegment.makeBytes(data);
			return QrCode.encodeSegments([seg], ecl);
		}
		
		
		/*-- Static factory functions (mid level) --*/
		
		// Returns a QR Code representing the given segments with the given encoding parameters.
		// The smallest possible QR Code version within the given range is automatically
		// chosen for the output. Iff boostEcl is true, then the ECC level of the result
		// may be higher than the ecl argument if it can be done without increasing the
		// version. The mask number is either between 0 to 7 (inclusive) to force that
		// mask, or -1 to automatically choose an appropriate mask (which may be slow).
		// This function allows the user to create a custom sequence of segments that switches
		// between modes (such as alphanumeric and byte) to encode text in less space.
		// This is a mid-level API; the high-level API is encodeText() and encodeBinary().
		public static encodeSegments(segs: Array<QrSegment>, ecl: QrCode.Ecc,
				minVersion: int = 1, maxVersion: int = 40,
				mask: int = -1, boostEcl: boolean = true): QrCode {
			
			if (!(QrCode.MIN_VERSION <= minVersion && minVersion <= maxVersion && maxVersion <= QrCode.MAX_VERSION)
					|| mask < -1 || mask > 7)
				throw "Invalid value";
			
			// Find the minimal version number to use
			let version: int;
			let dataUsedBits: int;
			for (version = minVersion; ; version++) {
				const dataCapacityBits: int = QrCode.getNumDataCodewords(version, ecl) * 8;  // Number of data bits available
				const usedBits: number = QrSegment.getTotalBits(segs, version);
				if (usedBits <= dataCapacityBits) {
					dataUsedBits = usedBits;
					break;  // This version number is found to be suitable
				}
				if (version >= maxVersion)  // All versions in the range could not fit the given data
					throw "Data too long";
			}
			
			// Increase the error correction level while the data still fits in the current version number
			for (const newEcl of [QrCode.Ecc.MEDIUM, QrCode.Ecc.QUARTILE, QrCode.Ecc.HIGH]) {  // From low to high
				if (boostEcl && dataUsedBits <= QrCode.getNumDataCodewords(version, newEcl) * 8)
					ecl = newEcl;
			}
			
			// Concatenate all segments to create the data bit string
			let bb: Array<bit> = []
			for (const seg of segs) {
				appendBits(seg.mode.modeBits, 4, bb);
				appendBits(seg.numChars, seg.mode.numCharCountBits(version), bb);
				for (const b of seg.getData())
					bb.push(b);
			}
			if (bb.length != dataUsedBits)
				throw "Assertion error";
			
			// Add terminator and pad up to a byte if applicable
			const dataCapacityBits: int = QrCode.getNumDataCodewords(version, ecl) * 8;
			if (bb.length > dataCapacityBits)
				throw "Assertion error";
			appendBits(0, Math.min(4, dataCapacityBits - bb.length), bb);
			appendBits(0, (8 - bb.length % 8) % 8, bb);
			if (bb.length % 8 != 0)
				throw "Assertion error";
			
			// Pad with alternating bytes until data capacity is reached
			for (let padByte = 0xEC; bb.length < dataCapacityBits; padByte ^= 0xEC ^ 0x11)
				appendBits(padByte, 8, bb);
			
			// Pack bits into bytes in big endian
			let dataCodewords: Array<byte> = [];
			while (dataCodewords.length * 8 < bb.length)
				dataCodewords.push(0);
			bb.forEach((b: bit, i: int) =>
				dataCodewords[i >>> 3] |= b << (7 - (i & 7)));
			
			// Create the QR Code object
			return new QrCode(version, ecl, dataCodewords, mask);
		}
		
		
		/*-- Fields --*/
		
		// The width and height of this QR Code, measured in modules, between
		// 21 and 177 (inclusive). This is equal to version * 4 + 17.
		public readonly size: int;
		
		// The modules of this QR Code (false = light, true = dark).
		// Immutable after constructor finishes. Accessed through getModule().
		private readonly modules   : Array<Array<boolean>> = [];
		
		// Indicates function modules that are not subjected to masking. Discarded when constructor finishes.
		private readonly isFunction: Array<Array<boolean>> = [];
		
		
		/*-- Constructor (low level) and fields --*/
		
		// Creates a new QR Code with the given version number,
		// error correction level, data codeword bytes, and mask number.
		// This is a low-level API that most users should not use directly.
		// A mid-level API is the encodeSegments() function.
		public constructor(
				// The version number of this QR Code, which is between 1 and 40 (inclusive).
				// This determines the size of this barcode.
				public readonly version: int,
				
				// The error correction level used in this QR Code.
				public readonly errorCorrectionLevel: QrCode.Ecc,
				
				dataCodewords: Array<byte>,
				
				// The index of the mask pattern used in this QR Code, which is between 0 and 7 (inclusive).
				// Even if a QR Code is created with automatic masking requested (mask = -1),
				// the resulting object still has a mask value between 0 and 7.
				public readonly mask: int) {
			
			// Check scalar arguments
			if (version < QrCode.MIN_VERSION || version > QrCode.MAX_VERSION)
				throw "Version value out of range";
			if (mask < -1 || mask > 7)
				throw "Mask value out of range";
			this.size = version * 4 + 17;
			
			// Initialize both grids to be size*size arrays of Boolean false
			let row: Array<boolean> = [];
			for (let i = 0; i < this.size; i++)
				row.push(false);
			for (let i = 0; i < this.size; i++) {
				this.modules   .push(row.slice());  // Initially all light
				this.isFunction.push(row.slice());
			}
			
			// Compute ECC, draw modules
			this.drawFunctionPatterns();
			const allCodewords: Array<byte> = this.addEccAndInterleave(dataCodewords);
			this.drawCodewords(allCodewords);
			
			// Do masking
			if (mask == -1) {  // Automatically choose best mask
				let minPenalty: int = 1000000000;
				for (let i = 0; i < 8; i++) {
					this.applyMask(i);
					this.drawFormatBits(i);
					const penalty: int = this.getPenaltyScore();
					if (penalty < minPenalty) {
						mask = i;
						minPenalty = penalty;
					}
					this.applyMask(i);  // Undoes the mask due to XOR
				}
			}
			if (mask < 0 || mask > 7)
				throw "Assertion error";
			this.mask = mask;
			this.applyMask(mask);  // Apply the final choice of mask
			this.drawFormatBits(mask);  // Overwrite old format bits
			
			this.isFunction = [];
		}
		
		
		/*-- Accessor methods --*/
		
		// Returns the color of the module (pixel) at the given coordinates, which is false
		// for light or true for dark. The top left corner has the coordinates (x=0, y=0).
		// If the given coordinates are out of bounds, then false (light) is returned.
		public getModule(x: int, y: int): boolean {
			return 0 <= x && x < this.size && 0 <= y && y < this.size && this.modules[y][x];
		}
		
		
		/*-- Private helper methods for constructor: Drawing function modules --*/
		
		// Reads this object's version field, and draws and marks all function modules.
		private drawFunctionPatterns(): void {
			// Draw horizontal and vertical timing patterns
			for (let i = 0; i < this.size; i++) {
				this.setFunctionModule(6, i, i % 2 == 0);
				this.setFunctionModule(i, 6, i % 2 == 0);
			}
			
			// Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules)
			this.drawFinderPattern(3, 3);
			this.drawFinderPattern(this.size - 4, 3);
			this.drawFinderPattern(3, this.size - 4);
			
			// Draw numerous alignment patterns
			const alignPatPos: Array<int> = this.getAlignmentPatternPositions();
			const numAlign: int = alignPatPos.length;
			for (let i = 0; i < numAlign; i++) {
				for (let 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))
						this.drawAlignmentPattern(alignPatPos[i], alignPatPos[j]);
				}
			}
			
			// Draw configuration data
			this.drawFormatBits(0);  // Dummy mask value; overwritten later in the constructor
			this.drawVersion();
		}
		
		
		// Draws two copies of the format bits (with its own error correction code)
		// based on the given mask and this object's error correction level field.
		private drawFormatBits(mask: int): void {
			// Calculate error correction code and pack bits
			const data: int = this.errorCorrectionLevel.formatBits << 3 | mask;  // errCorrLvl is uint2, mask is uint3
			let rem: int = data;
			for (let i = 0; i < 10; i++)
				rem = (rem << 1) ^ ((rem >>> 9) * 0x537);
			const bits = (data << 10 | rem) ^ 0x5412;  // uint15
			if (bits >>> 15 != 0)
				throw "Assertion error";
			
			// Draw first copy
			for (let i = 0; i <= 5; i++)
				this.setFunctionModule(8, i, getBit(bits, i));
			this.setFunctionModule(8, 7, getBit(bits, 6));
			this.setFunctionModule(8, 8, getBit(bits, 7));
			this.setFunctionModule(7, 8, getBit(bits, 8));
			for (let i = 9; i < 15; i++)
				this.setFunctionModule(14 - i, 8, getBit(bits, i));
			
			// Draw second copy
			for (let i = 0; i < 8; i++)
				this.setFunctionModule(this.size - 1 - i, 8, getBit(bits, i));
			for (let i = 8; i < 15; i++)
				this.setFunctionModule(8, this.size - 15 + i, getBit(bits, i));
			this.setFunctionModule(8, this.size - 8, true);  // Always dark
		}
		
		
		// Draws two copies of the version bits (with its own error correction code),
		// based on this object's version field, iff 7 <= version <= 40.
		private drawVersion(): void {
			if (this.version < 7)
				return;
			
			// Calculate error correction code and pack bits
			let rem: int = this.version;  // version is uint6, in the range [7, 40]
			for (let i = 0; i < 12; i++)
				rem = (rem << 1) ^ ((rem >>> 11) * 0x1F25);
			const bits: int = this.version << 12 | rem;  // uint18
			if (bits >>> 18 != 0)
				throw "Assertion error";
			
			// Draw two copies
			for (let i = 0; i < 18; i++) {
				const color: boolean = getBit(bits, i);
				const a: int = this.size - 11 + i % 3;
				const b: int = Math.floor(i / 3);
				this.setFunctionModule(a, b, color);
				this.setFunctionModule(b, a, color);
			}
		}
		
		
		// Draws a 9*9 finder pattern including the border separator,
		// with the center module at (x, y). Modules can be out of bounds.
		private drawFinderPattern(x: int, y: int): void {
			for (let dy = -4; dy <= 4; dy++) {
				for (let dx = -4; dx <= 4; dx++) {
					const dist: int = Math.max(Math.abs(dx), Math.abs(dy));  // Chebyshev/infinity norm
					const xx: int = x + dx;
					const yy: int = y + dy;
					if (0 <= xx && xx < this.size && 0 <= yy && yy < this.size)
						this.setFunctionModule(xx, yy, dist != 2 && dist != 4);
				}
			}
		}
		
		
		// Draws a 5*5 alignment pattern, with the center module
		// at (x, y). All modules must be in bounds.
		private drawAlignmentPattern(x: int, y: int): void {
			for (let dy = -2; dy <= 2; dy++) {
				for (let dx = -2; dx <= 2; dx++)
					this.setFunctionModule(x + dx, y + dy, Math.max(Math.abs(dx), Math.abs(dy)) != 1);
			}
		}
		
		
		// Sets the color of a module and marks it as a function module.
		// Only used by the constructor. Coordinates must be in bounds.
		private setFunctionModule(x: int, y: int, isDark: boolean): void {
			this.modules[y][x] = isDark;
			this.isFunction[y][x] = true;
		}
		
		
		/*-- Private helper methods for constructor: Codewords and masking --*/
		
		// Returns a new byte string representing the given data with the appropriate error correction
		// codewords appended to it, based on this object's version and error correction level.
		private addEccAndInterleave(data: Array<byte>): Array<byte> {
			const ver: int = this.version;
			const ecl: QrCode.Ecc = this.errorCorrectionLevel;
			if (data.length != QrCode.getNumDataCodewords(ver, ecl))
				throw "Invalid argument";
			
			// Calculate parameter numbers
			const numBlocks: int = QrCode.NUM_ERROR_CORRECTION_BLOCKS[ecl.ordinal][ver];
			const blockEccLen: int = QrCode.ECC_CODEWORDS_PER_BLOCK  [ecl.ordinal][ver];
			const rawCodewords: int = Math.floor(QrCode.getNumRawDataModules(ver) / 8);
			const numShortBlocks: int = numBlocks - rawCodewords % numBlocks;
			const shortBlockLen: int = Math.floor(rawCodewords / numBlocks);
			
			// Split data into blocks and append ECC to each block
			let blocks: Array<Array<byte>> = [];
			const rsDiv: Array<byte> = QrCode.reedSolomonComputeDivisor(blockEccLen);
			for (let i = 0, k = 0; i < numBlocks; i++) {
				let dat: Array<byte> = data.slice(k, k + shortBlockLen - blockEccLen + (i < numShortBlocks ? 0 : 1));
				k += dat.length;
				const ecc: Array<byte> = QrCode.reedSolomonComputeRemainder(dat, rsDiv);
				if (i < numShortBlocks)
					dat.push(0);
				blocks.push(dat.concat(ecc));
			}
			
			// Interleave (not concatenate) the bytes from every block into a single sequence
			let result: Array<byte> = [];
			for (let i = 0; i < blocks[0].length; i++) {
				blocks.forEach((block, j) => {
					// Skip the padding byte in short blocks
					if (i != shortBlockLen - blockEccLen || j >= numShortBlocks)
						result.push(block[i]);
				});
			}
			if (result.length != rawCodewords)
				throw "Assertion error";
			return result;
		}
		
		
		// Draws the given sequence of 8-bit codewords (data and error correction) onto the entire
		// data area of this QR Code. Function modules need to be marked off before this is called.
		private drawCodewords(data: Array<byte>): void {
			if (data.length != Math.floor(QrCode.getNumRawDataModules(this.version) / 8))
				throw "Invalid argument";
			let i: int = 0;  // Bit index into the data
			// Do the funny zigzag scan
			for (let right = this.size - 1; right >= 1; right -= 2) {  // Index of right column in each column pair
				if (right == 6)
					right = 5;
				for (let vert = 0; vert < this.size; vert++) {  // Vertical counter
					for (let j = 0; j < 2; j++) {
						const x: int = right - j;  // Actual x coordinate
						const upward: boolean = ((right + 1) & 2) == 0;
						const y: int = upward ? this.size - 1 - vert : vert;  // Actual y coordinate
						if (!this.isFunction[y][x] && i < data.length * 8) {
							this.modules[y][x] = getBit(data[i >>> 3], 7 - (i & 7));
							i++;
						}
						// If this QR Code has any remainder bits (0 to 7), they were assigned as
						// 0/false/light by the constructor and are left unchanged by this method
					}
				}
			}
			if (i != data.length * 8)
				throw "Assertion error";
		}
		
		
		// XORs the codeword modules in this QR Code with the given mask pattern.
		// The function modules must be marked and the codeword bits must be drawn
		// before masking. Due to the arithmetic of XOR, calling applyMask() with
		// the same mask value a second time will undo the mask. A final well-formed
		// QR Code needs exactly one (not zero, two, etc.) mask applied.
		private applyMask(mask: int): void {
			if (mask < 0 || mask > 7)
				throw "Mask value out of range";
			for (let y = 0; y < this.size; y++) {
				for (let x = 0; x < this.size; x++) {
					let invert: boolean;
					switch (mask) {
						case 0:  invert = (x + y) % 2 == 0;                                  break;
						case 1:  invert = y % 2 == 0;                                        break;
						case 2:  invert = x % 3 == 0;                                        break;
						case 3:  invert = (x + y) % 3 == 0;                                  break;
						case 4:  invert = (Math.floor(x / 3) + Math.floor(y / 2)) % 2 == 0;  break;
						case 5:  invert = x * y % 2 + x * y % 3 == 0;                        break;
						case 6:  invert = (x * y % 2 + x * y % 3) % 2 == 0;                  break;
						case 7:  invert = ((x + y) % 2 + x * y % 3) % 2 == 0;                break;
						default:  throw "Assertion error";
					}
					if (!this.isFunction[y][x] && invert)
						this.modules[y][x] = !this.modules[y][x];
				}
			}
		}
		
		
		// Calculates and returns the penalty score based on state of this QR Code's current modules.
		// This is used by the automatic mask choice algorithm to find the mask pattern that yields the lowest score.
		private getPenaltyScore(): int {
			let result: int = 0;
			
			// Adjacent modules in row having same color, and finder-like patterns
			for (let y = 0; y < this.size; y++) {
				let runColor = false;
				let runX = 0;
				let runHistory = [0,0,0,0,0,0,0];
				for (let x = 0; x < this.size; x++) {
					if (this.modules[y][x] == runColor) {
						runX++;
						if (runX == 5)
							result += QrCode.PENALTY_N1;
						else if (runX > 5)
							result++;
					} else {
						this.finderPenaltyAddHistory(runX, runHistory);
						if (!runColor)
							result += this.finderPenaltyCountPatterns(runHistory) * QrCode.PENALTY_N3;
						runColor = this.modules[y][x];
						runX = 1;
					}
				}
				result += this.finderPenaltyTerminateAndCount(runColor, runX, runHistory) * QrCode.PENALTY_N3;
			}
			// Adjacent modules in column having same color, and finder-like patterns
			for (let x = 0; x < this.size; x++) {
				let runColor = false;
				let runY = 0;
				let runHistory = [0,0,0,0,0,0,0];
				for (let y = 0; y < this.size; y++) {
					if (this.modules[y][x] == runColor) {
						runY++;
						if (runY == 5)
							result += QrCode.PENALTY_N1;
						else if (runY > 5)
							result++;
					} else {
						this.finderPenaltyAddHistory(runY, runHistory);
						if (!runColor)
							result += this.finderPenaltyCountPatterns(runHistory) * QrCode.PENALTY_N3;
						runColor = this.modules[y][x];
						runY = 1;
					}
				}
				result += this.finderPenaltyTerminateAndCount(runColor, runY, runHistory) * QrCode.PENALTY_N3;
			}
			
			// 2*2 blocks of modules having same color
			for (let y = 0; y < this.size - 1; y++) {
				for (let x = 0; x < this.size - 1; x++) {
					const color: boolean = this.modules[y][x];
					if (  color == this.modules[y][x + 1] &&
					      color == this.modules[y + 1][x] &&
					      color == this.modules[y + 1][x + 1])
						result += QrCode.PENALTY_N2;
				}
			}
			
			// Balance of dark and light modules
			let dark: int = 0;
			for (const row of this.modules)
				dark = row.reduce((sum, color) => sum + (color ? 1 : 0), dark);
			const total: int = this.size * this.size;  // Note that size is odd, so dark/total != 1/2
			// Compute the smallest integer k >= 0 such that (45-5k)% <= dark/total <= (55+5k)%
			const k: int = Math.ceil(Math.abs(dark * 20 - total * 10) / total) - 1;
			result += k * QrCode.PENALTY_N4;
			return result;
		}
		
		
		/*-- Private helper functions --*/
		
		// Returns an ascending list of positions of alignment patterns for this version number.
		// Each position is in the range [0,177), and are used on both the x and y axes.
		// This could be implemented as lookup table of 40 variable-length lists of integers.
		private getAlignmentPatternPositions(): Array<int> {
			if (this.version == 1)
				return [];
			else {
				const numAlign: int = Math.floor(this.version / 7) + 2;
				const step: int = (this.version == 32) ? 26 :
					Math.ceil((this.size - 13) / (numAlign * 2 - 2)) * 2;
				let result: Array<int> = [6];
				for (let pos = this.size - 7; result.length < numAlign; pos -= step)
					result.splice(1, 0, pos);
				return result;
			}
		}
		
		
		// Returns the number of data bits that can be stored in a QR Code of the given version number, after
		// all function modules are excluded. This includes remainder bits, so it might not be a multiple of 8.
		// The result is in the range [208, 29648]. This could be implemented as a 40-entry lookup table.
		private static getNumRawDataModules(ver: int): int {
			if (ver < QrCode.MIN_VERSION || ver > QrCode.MAX_VERSION)
				throw "Version number out of range";
			let result: int = (16 * ver + 128) * ver + 64;
			if (ver >= 2) {
				const numAlign: int = Math.floor(ver / 7) + 2;
				result -= (25 * numAlign - 10) * numAlign - 55;
				if (ver >= 7)
					result -= 36;
			}
			if (!(208 <= result && result <= 29648))
				throw "Assertion error";
			return result;
		}
		
		
		// Returns the number of 8-bit data (i.e. not error correction) codewords contained in any
		// QR Code of the given version number and error correction level, with remainder bits discarded.
		// This stateless pure function could be implemented as a (40*4)-cell lookup table.
		private static getNumDataCodewords(ver: int, ecl: QrCode.Ecc): int {
			return Math.floor(QrCode.getNumRawDataModules(ver) / 8) -
				QrCode.ECC_CODEWORDS_PER_BLOCK    [ecl.ordinal][ver] *
				QrCode.NUM_ERROR_CORRECTION_BLOCKS[ecl.ordinal][ver];
		}
		
		
		// Returns a Reed-Solomon ECC generator polynomial for the given degree. This could be
		// implemented as a lookup table over all possible parameter values, instead of as an algorithm.
		private static reedSolomonComputeDivisor(degree: int): Array<byte> {
			if (degree < 1 || degree > 255)
				throw "Degree out of range";
			// Polynomial coefficients are stored from highest to lowest power, excluding the leading term which is always 1.
			// For example the polynomial x^3 + 255x^2 + 8x + 93 is stored as the uint8 array [255, 8, 93].
			let result: Array<byte> = [];
			for (let i = 0; i < degree - 1; i++)
				result.push(0);
			result.push(1);  // Start off with the monomial x^0
			
			// Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}),
			// and drop the highest monomial term which is always 1x^degree.
			// Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D).
			let root = 1;
			for (let i = 0; i < degree; i++) {
				// Multiply the current product by (x - r^i)
				for (let j = 0; j < result.length; j++) {
					result[j] = QrCode.reedSolomonMultiply(result[j], root);
					if (j + 1 < result.length)
						result[j] ^= result[j + 1];
				}
				root = QrCode.reedSolomonMultiply(root, 0x02);
			}
			return result;
		}
		
		
		// Returns the Reed-Solomon error correction codeword for the given data and divisor polynomials.
		private static reedSolomonComputeRemainder(data: Array<byte>, divisor: Array<byte>): Array<byte> {
			let result: Array<byte> = divisor.map(_ => 0);
			for (const b of data) {  // Polynomial division
				const factor: byte = b ^ (result.shift() as byte);
				result.push(0);
				divisor.forEach((coef, i) =>
					result[i] ^= QrCode.reedSolomonMultiply(coef, factor));
			}
			return result;
		}
		
		
		// Returns the product of the two given field elements modulo GF(2^8/0x11D). The arguments and result
		// are unsigned 8-bit integers. This could be implemented as a lookup table of 256*256 entries of uint8.
		private static reedSolomonMultiply(x: byte, y: byte): byte {
			if (x >>> 8 != 0 || y >>> 8 != 0)
				throw "Byte out of range";
			// Russian peasant multiplication
			let z: int = 0;
			for (let i = 7; i >= 0; i--) {
				z = (z << 1) ^ ((z >>> 7) * 0x11D);
				z ^= ((y >>> i) & 1) * x;
			}
			if (z >>> 8 != 0)
				throw "Assertion error";
			return z as byte;
		}
		
		
		// Can only be called immediately after a light run is added, and
		// returns either 0, 1, or 2. A helper function for getPenaltyScore().
		private finderPenaltyCountPatterns(runHistory: Array<int>): int {
			const n: int = runHistory[1];
			if (n > this.size * 3)
				throw "Assertion error";
			const core: boolean = n > 0 && runHistory[2] == n && runHistory[3] == n * 3 && runHistory[4] == n && runHistory[5] == n;
			return (core && runHistory[0] >= n * 4 && runHistory[6] >= n ? 1 : 0)
			     + (core && runHistory[6] >= n * 4 && runHistory[0] >= n ? 1 : 0);
		}
		
		
		// Must be called at the end of a line (row or column) of modules. A helper function for getPenaltyScore().
		private finderPenaltyTerminateAndCount(currentRunColor: boolean, currentRunLength: int, runHistory: Array<int>): int {
			if (currentRunColor) {  // Terminate dark run
				this.finderPenaltyAddHistory(currentRunLength, runHistory);
				currentRunLength = 0;
			}
			currentRunLength += this.size;  // Add light border to final run
			this.finderPenaltyAddHistory(currentRunLength, runHistory);
			return this.finderPenaltyCountPatterns(runHistory);
		}
		
		
		// Pushes the given value to the front and drops the last value. A helper function for getPenaltyScore().
		private finderPenaltyAddHistory(currentRunLength: int, runHistory: Array<int>): void {
			if (runHistory[0] == 0)
				currentRunLength += this.size;  // Add light border to initial run
			runHistory.pop();
			runHistory.unshift(currentRunLength);
		}
		
		
		/*-- Constants and tables --*/
		
		// The minimum version number supported in the QR Code Model 2 standard.
		public static readonly MIN_VERSION: int =  1;
		// The maximum version number supported in the QR Code Model 2 standard.
		public static readonly MAX_VERSION: int = 40;
		
		// For use in getPenaltyScore(), when evaluating which mask is best.
		private static readonly PENALTY_N1: int =  3;
		private static readonly PENALTY_N2: int =  3;
		private static readonly PENALTY_N3: int = 40;
		private static readonly PENALTY_N4: int = 10;
		
		private static readonly ECC_CODEWORDS_PER_BLOCK: Array<Array<int>> = [
			// Version: (note that index 0 is for padding, and is set to an illegal value)
			//0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40    Error correction level
			[-1,  7, 10, 15, 20, 26, 18, 20, 24, 30, 18, 20, 24, 26, 30, 22, 24, 28, 30, 28, 28, 28, 28, 30, 30, 26, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30],  // Low
			[-1, 10, 16, 26, 18, 24, 16, 18, 22, 22, 26, 30, 22, 22, 24, 24, 28, 28, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28],  // Medium
			[-1, 13, 22, 18, 26, 18, 24, 18, 22, 20, 24, 28, 26, 24, 20, 30, 24, 28, 28, 26, 30, 28, 30, 30, 30, 30, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30],  // Quartile
			[-1, 17, 28, 22, 16, 22, 28, 26, 26, 24, 28, 24, 28, 22, 24, 24, 30, 28, 28, 26, 28, 30, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30],  // High
		];
		
		private static readonly NUM_ERROR_CORRECTION_BLOCKS: Array<Array<int>> = [
			// 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
		];
		
	}
	
	
	// Appends the given number of low-order bits of the given value
	// to the given buffer. Requires 0 <= len <= 31 and 0 <= val < 2^len.
	function appendBits(val: int, len: int, bb: Array<bit>): void {
		if (len < 0 || len > 31 || val >>> len != 0)
			throw "Value out of range";
		for (let i = len - 1; i >= 0; i--)  // Append bit by bit
			bb.push((val >>> i) & 1);
	}
	
	
	// Returns true iff the i'th bit of x is set to 1.
	function getBit(x: int, i: int): boolean {
		return ((x >>> i) & 1) != 0;
	}
	
	
	
	/*---- Data segment class ----*/
	
	/* 
	 * A segment of character/binary/control data in a QR Code symbol.
	 * Instances of this class are immutable.
	 * The mid-level way to create a segment is to take the payload data
	 * and call a static factory function such as QrSegment.makeNumeric().
	 * The low-level way to create a segment is to custom-make the bit buffer
	 * and call the QrSegment() constructor with appropriate values.
	 * 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.
	 */
	export class QrSegment {
		
		/*-- Static factory functions (mid level) --*/
		
		// Returns a segment representing the given binary data encoded in
		// byte mode. All input byte arrays are acceptable. Any text string
		// can be converted to UTF-8 bytes and encoded as a byte mode segment.
		public static makeBytes(data: Array<byte>): QrSegment {
			let bb: Array<bit> = []
			for (const b of data)
				appendBits(b, 8, bb);
			return new QrSegment(QrSegment.Mode.BYTE, data.length, bb);
		}
		
		
		// Returns a segment representing the given string of decimal digits encoded in numeric mode.
		public static makeNumeric(digits: string): QrSegment {
			if (!this.NUMERIC_REGEX.test(digits))
				throw "String contains non-numeric characters";
			let bb: Array<bit> = []
			for (let i = 0; i < digits.length; ) {  // Consume up to 3 digits per iteration
				const n: int = Math.min(digits.length - i, 3);
				appendBits(parseInt(digits.substr(i, n), 10), n * 3 + 1, bb);
				i += n;
			}
			return new QrSegment(QrSegment.Mode.NUMERIC, digits.length, bb);
		}
		
		
		// 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.
		public static makeAlphanumeric(text: string): QrSegment {
			if (!this.ALPHANUMERIC_REGEX.test(text))
				throw "String contains unencodable characters in alphanumeric mode";
			let bb: Array<bit> = []
			let i: int;
			for (i = 0; i + 2 <= text.length; i += 2) {  // Process groups of 2
				let temp: int = QrSegment.ALPHANUMERIC_CHARSET.indexOf(text.charAt(i)) * 45;
				temp += QrSegment.ALPHANUMERIC_CHARSET.indexOf(text.charAt(i + 1));
				appendBits(temp, 11, bb);
			}
			if (i < text.length)  // 1 character remaining
				appendBits(QrSegment.ALPHANUMERIC_CHARSET.indexOf(text.charAt(i)), 6, bb);
			return new QrSegment(QrSegment.Mode.ALPHANUMERIC, text.length, bb);
		}
		
		
		// Returns a new mutable list of zero or more segments to represent the given Unicode text string.
		// The result may use various segment modes and switch modes to optimize the length of the bit stream.
		public static makeSegments(text: string): Array<QrSegment> {
			// Select the most efficient segment encoding automatically
			if (text == "")
				return [];
			else if (this.NUMERIC_REGEX.test(text))
				return [QrSegment.makeNumeric(text)];
			else if (this.ALPHANUMERIC_REGEX.test(text))
				return [QrSegment.makeAlphanumeric(text)];
			else
				return [QrSegment.makeBytes(QrSegment.toUtf8ByteArray(text))];
		}
		
		
		// Returns a segment representing an Extended Channel Interpretation
		// (ECI) designator with the given assignment value.
		public static makeEci(assignVal: int): QrSegment {
			let bb: Array<bit> = []
			if (assignVal < 0)
				throw "ECI assignment value out of range";
			else if (assignVal < (1 << 7))
				appendBits(assignVal, 8, bb);
			else if (assignVal < (1 << 14)) {
				appendBits(2, 2, bb);
				appendBits(assignVal, 14, bb);
			} else if (assignVal < 1000000) {
				appendBits(6, 3, bb);
				appendBits(assignVal, 21, bb);
			} else
				throw "ECI assignment value out of range";
			return new QrSegment(QrSegment.Mode.ECI, 0, bb);
		}
		
		
		/*-- Constructor (low level) and fields --*/
		
		// Creates a new QR Code segment with the given attributes and data.
		// The character count (numChars) must agree with the mode and the bit buffer length,
		// but the constraint isn't checked. The given bit buffer is cloned and stored.
		public constructor(
				// The mode indicator of this segment.
				public readonly mode: QrSegment.Mode,
				
				// The length of this segment's unencoded data. Measured in characters for
				// numeric/alphanumeric/kanji mode, bytes for byte mode, and 0 for ECI mode.
				// Always zero or positive. Not the same as the data's bit length.
				public readonly numChars: int,
				
				// The data bits of this segment. Accessed through getData().
				private readonly bitData: Array<bit>) {
			
			if (numChars < 0)
				throw "Invalid argument";
			this.bitData = bitData.slice();  // Make defensive copy
		}
		
		
		/*-- Methods --*/
		
		// Returns a new copy of the data bits of this segment.
		public getData(): Array<bit> {
			return this.bitData.slice();  // Make defensive copy
		}
		
		
		// (Package-private) Calculates and returns the number of bits needed to encode the given segments at
		// the given version. The result is infinity if a segment has too many characters to fit its length field.
		public static getTotalBits(segs: Array<QrSegment>, version: int): number {
			let result: number = 0;
			for (const seg of segs) {
				const ccbits: int = seg.mode.numCharCountBits(version);
				if (seg.numChars >= (1 << ccbits))
					return Infinity;  // The segment's length doesn't fit the field's bit width
				result += 4 + ccbits + seg.bitData.length;
			}
			return result;
		}
		
		
		// Returns a new array of bytes representing the given string encoded in UTF-8.
		private static toUtf8ByteArray(str: string): Array<byte> {
			str = encodeURI(str);
			let result: Array<byte> = [];
			for (let i = 0; i < str.length; i++) {
				if (str.charAt(i) != "%")
					result.push(str.charCodeAt(i));
				else {
					result.push(parseInt(str.substr(i + 1, 2), 16));
					i += 2;
				}
			}
			return result;
		}
		
		
		/*-- Constants --*/
		
		// Describes precisely all strings that are encodable in numeric mode. To test
		// whether a string s is encodable: let ok: boolean = NUMERIC_REGEX.test(s);
		// A string is encodable iff each character is in the range 0 to 9.
		public static readonly NUMERIC_REGEX: RegExp = /^[0-9]*$/;
		
		// Describes precisely all strings that are encodable in alphanumeric mode. To test
		// whether a string s is encodable: let ok: boolean = ALPHANUMERIC_REGEX.test(s);
		// A string is encodable iff each character is in the following set: 0 to 9, A to Z
		// (uppercase only), space, dollar, percent, asterisk, plus, hyphen, period, slash, colon.
		public static readonly ALPHANUMERIC_REGEX: RegExp = /^[A-Z0-9 $%*+.\/:-]*$/;
		
		// The set of all legal characters in alphanumeric mode,
		// where each character value maps to the index in the string.
		private static readonly ALPHANUMERIC_CHARSET: string = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:";
		
	}
	
}



/*---- Public helper enumeration ----*/

namespace qrcodegen.QrCode {
	
	type int = number;
	
	
	/* 
	 * The error correction level in a QR Code symbol. Immutable.
	 */
	export class Ecc {
		
		/*-- Constants --*/
		
		public static readonly LOW      = new Ecc(0, 1);  // The QR Code can tolerate about  7% erroneous codewords
		public static readonly MEDIUM   = new Ecc(1, 0);  // The QR Code can tolerate about 15% erroneous codewords
		public static readonly QUARTILE = new Ecc(2, 3);  // The QR Code can tolerate about 25% erroneous codewords
		public static readonly HIGH     = new Ecc(3, 2);  // The QR Code can tolerate about 30% erroneous codewords
		
		
		/*-- Constructor and fields --*/
		
		private constructor(
			// In the range 0 to 3 (unsigned 2-bit integer).
			public readonly ordinal: int,
			// (Package-private) In the range 0 to 3 (unsigned 2-bit integer).
			public readonly formatBits: int) {}
		
	}
}



/*---- Public helper enumeration ----*/

namespace qrcodegen.QrSegment {
	
	type int = number;
	
	
	/* 
	 * Describes how a segment's data bits are interpreted. Immutable.
	 */
	export class Mode {
		
		/*-- Constants --*/
		
		public static readonly NUMERIC      = new Mode(0x1, [10, 12, 14]);
		public static readonly ALPHANUMERIC = new Mode(0x2, [ 9, 11, 13]);
		public static readonly BYTE         = new Mode(0x4, [ 8, 16, 16]);
		public static readonly KANJI        = new Mode(0x8, [ 8, 10, 12]);
		public static readonly ECI          = new Mode(0x7, [ 0,  0,  0]);
		
		
		/*-- Constructor and fields --*/
		
		private constructor(
			// The mode indicator bits, which is a uint4 value (range 0 to 15).
			public readonly modeBits: int,
			// Number of character count bits for three different version ranges.
			private readonly numBitsCharCount: [int,int,int]) {}
		
		
		/*-- Method --*/
		
		// (Package-private) Returns the bit width of the character count field for a segment in
		// this mode in a QR Code at the given version number. The result is in the range [0, 16].
		public numCharCountBits(ver: int): int {
			return this.numBitsCharCount[Math.floor((ver + 7) / 17)];
		}
		
	}
}