--- The qrcode library is licensed under the 3-clause BSD license (aka "new BSD")
--- To get in contact with the author, mail to <gundlach@speedata.de>.
---
--- Please report bugs on the [github project page](http://speedata.github.com/luaqrcode/).
-- Copyright (c) 2012, Patrick Gundlach
-- All rights reserved.
--
-- Redistribution and use in source and binary forms, with or without
-- modification, are permitted provided that the following conditions are met:
--	 * Redistributions of source code must retain the above copyright
--	   notice, this list of conditions and the following disclaimer.
--	 * Redistributions in binary form must reproduce the above copyright
--	   notice, this list of conditions and the following disclaimer in the
--	   documentation and/or other materials provided with the distribution.
--	 * Neither the name of the <organization> nor the
--	   names of its contributors may be used to endorse or promote products
--	   derived from this software without specific prior written permission.
--
-- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
-- ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
-- WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
-- DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
-- DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
-- (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
-- LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
-- ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-- (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
-- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.


--- Overall workflow
--- ================
--- The steps to generate the qrcode, assuming we already have the codeword:
---
--- 1. Determine version, ec level and mode (=encoding) for codeword
--- 1. Encode data
--- 1. Arrange data and calculate error correction code
--- 1. Generate 8 matrices with different masks and calculate the penalty
--- 1. Return qrcode with least penalty
---
--- Each step is of course more or less complex and needs further description

--- Helper functions
--- ================
---
--- We start with some helper functions

local bit_xor = bit.bxor

-- Return the binary representation of the number x with the width of `digits`.
local function binary(x,digits)
  local s=string.format("%o",x)
  local a={["0"]="000",["1"]="001", ["2"]="010",["3"]="011",
		   ["4"]="100",["5"]="101", ["6"]="110",["7"]="111"}
  s=string.gsub(s,"(.)",function (d) return a[d] end)
  -- remove leading 0s
  s = string.gsub(s,"^0*(.*)$","%1")
  local fmtstring = string.format("%%%ds",digits)
  local ret = string.format(fmtstring,s)
  return string.gsub(ret," ","0")
end

-- A small helper function for add_typeinfo_to_matrix() and add_version_information()
-- Add a 2 (black by default) / -2 (blank by default) to the matrix at position x,y
-- depending on the bitstring (size 1!) where "0"=blank and "1"=black.
local function fill_matrix_position(matrix,bitstring,x,y)
	if bitstring == "1" then
		matrix[x][y] = 2
	else
		matrix[x][y] = -2
	end
end


--- Step 1: Determine version, ec level and mode for codeword
--- ========================================================
---
--- First we need to find out the version (= size) of the QR code. This depends on
--- the input data (the mode to be used), the requested error correction level
--- (normally we use the maximum level that fits into the minimal size).

-- Return the mode for the given string `str`.
-- See table 2 of the spec. We only support mode 1, 2 and 4.
-- That is: numeric, alaphnumeric and binary.
local function get_mode( str )
	local mode
	if string.match(str,"^[0-9]+$") then
		return 1
	elseif string.match(str,"^[0-9A-Z $%%*./:+-]+$") then
		return 2
	else
		return 4
	end
	assert(false,"never reached")
	return nil
end



--- Capacity of QR codes
--- --------------------
--- The capacity is calculated as follow: \\(\text{Number of data bits} = \text{number of codewords} * 8\\).
--- The number of data bits is now reduced by 4 (the mode indicator) and the length string,
--- that varies between 8 and 16, depending on the version and the mode (see method `get_length()`). The
--- remaining capacity is multiplied by the amount of data per bit string (numeric: 3, alphanumeric: 2, other: 1)
--- and divided by the length of the bit string (numeric: 10, alphanumeric: 11, binary: 8, kanji: 13).
--- Then the floor function is applied to the result:
--- $$\Big\lfloor \frac{( \text{#data bits} - 4 - \text{length string}) * \text{data per bit string}}{\text{length of the bit string}} \Big\rfloor$$
---
--- There is one problem remaining. The length string depends on the version,
--- and the version depends on the length string. But we take this into account when calculating the
--- the capacity, so this is not really a problem here.

-- The capacity (number of codewords) of each version (1-40) for error correction levels 1-4 (LMQH).
-- The higher the ec level, the lower the capacity of the version. Taken from spec, tables 7-11.
local capacity = {
  {  19,   16,   13,	9},{  34,   28,   22,   16},{  55,   44,   34,   26},{  80,   64,   48,   36},
  { 108,   86,   62,   46},{ 136,  108,   76,   60},{ 156,  124,   88,   66},{ 194,  154,  110,   86},
  { 232,  182,  132,  100},{ 274,  216,  154,  122},{ 324,  254,  180,  140},{ 370,  290,  206,  158},
  { 428,  334,  244,  180},{ 461,  365,  261,  197},{ 523,  415,  295,  223},{ 589,  453,  325,  253},
  { 647,  507,  367,  283},{ 721,  563,  397,  313},{ 795,  627,  445,  341},{ 861,  669,  485,  385},
  { 932,  714,  512,  406},{1006,  782,  568,  442},{1094,  860,  614,  464},{1174,  914,  664,  514},
  {1276, 1000,  718,  538},{1370, 1062,  754,  596},{1468, 1128,  808,  628},{1531, 1193,  871,  661},
  {1631, 1267,  911,  701},{1735, 1373,  985,  745},{1843, 1455, 1033,  793},{1955, 1541, 1115,  845},
  {2071, 1631, 1171,  901},{2191, 1725, 1231,  961},{2306, 1812, 1286,  986},{2434, 1914, 1354, 1054},
  {2566, 1992, 1426, 1096},{2702, 2102, 1502, 1142},{2812, 2216, 1582, 1222},{2956, 2334, 1666, 1276}}


--- Return the smallest version for this codeword. If `requested_ec_level` is supplied,
--- then the ec level (LMQH - 1,2,3,4) must be at least the requested level.
-- mode = 1,2,4,8
local function get_version_eclevel(len,mode,requested_ec_level)
	local local_mode = mode
	if mode == 4 then
		local_mode = 3
	elseif mode == 8 then
		local_mode = 4
	end
	assert( local_mode <= 4 )

	local bytes, bits, digits, modebits, c
	local tab = { {10,9,8,8},{12,11,16,10},{14,13,16,12} }
	local minversion = 40
	local maxec_level = 1
	for ec_level=1,4 do
		if requested_ec_level == nil or ec_level >= requested_ec_level then
			for version=1,#capacity do
				bits = capacity[version][ec_level] * 8
				bits = bits - 4 -- the mode indicator
				if version < 10 then
					digits = tab[1][local_mode]
				elseif version < 27 then
					digits = tab[2][local_mode]
				elseif version <= 40 then
					digits = tab[3][local_mode]
				end
				modebits = bits - digits
				if local_mode == 1 then -- numeric
					c = math.floor(modebits * 3 / 10)
				elseif local_mode == 2 then -- alphanumeric
					c = math.floor(modebits * 2 / 11)
				elseif local_mode == 3 then -- binary
					c = math.floor(modebits * 1 / 8)
				else
					c = math.floor(modebits * 1 / 13)
				end
				if c >= len then
					if version <= minversion then
						minversion = version
						maxec_level = ec_level
					end
					break
				end
			end
		end
	end
	return minversion, maxec_level
end

-- Return a bit string of 0s and 1s that includes the length of the code string.
-- The modes are numeric = 1, alphanumeric = 2, binary = 4, and japanese = 8
local function get_length(str,version,mode)
	local i = mode
	if mode == 4 then
		i = 3
	elseif mode == 8 then
		i = 4
	end
	assert( i <= 4 )
	local tab = { {10,9,8,8},{12,11,16,10},{14,13,16,12} }
	local digits
	if version < 10 then
		digits = tab[1][i]
	elseif version < 27 then
		digits = tab[2][i]
	elseif version <= 40 then
		digits = tab[3][i]
	else
		assert(false, "get_length, version > 40 not supported")
	end
	local len = binary(#str,digits)
	return len
end

--- If the `requested_ec_level` or the `mode` are provided, this will be used if possible.
--- The mode depends on the characters used in the string `str`. It seems to be
--- possible to split the QR code to handle multiple modes, but we don't do that.
local function get_version_eclevel_mode_bistringlength(str,requested_ec_level,mode)
	local local_mode
	if mode then
		assert(false,"not implemented")
		-- check if the mode is OK for the string
		local_mode = mode
	else
		local_mode = get_mode(str)
	end
	local version, ec_level
	version, ec_level = get_version_eclevel(#str,local_mode,requested_ec_level)
	local length_string = get_length(str,version,local_mode)
	return version,ec_level,binary(local_mode,4),local_mode,length_string
end

--- Step 2: Encode data
--- ===================

--- There are several ways to encode the data. We currently support only numeric, alphanumeric and binary.
--- We already chose the encoding (a.k.a. mode) in the first step, so we need to apply the mode to the
--- codeword.
---
--- **Numeric**: take three digits and encode them in 10 bits
--- **Alphanumeric**: take two characters and encode them in 11 bits
--- **Binary**: take one octet and encode it in 8 bits

local asciitbl = {
	    -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,  -- 0x01-0x0f
	-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,  -- 0x10-0x1f
	36, -1, -1, -1, 37, 38, -1, -1, -1, -1, 39, 40, -1, 41, 42, 43,  -- 0x20-0x2f
	 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 44, -1, -1, -1, -1, -1,  -- 0x30-0x3f
	-1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,  -- 0x40-0x4f
	25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, -1, -1, -1, -1, -1,  -- 0x50-0x5f
  }

-- Return a binary representation of the numeric string `str`. This must contain only digits 0-9.
local function encode_string_numeric(str)
	local bitstring = ""
	local int
	string.gsub(str,"..?.?",function(a)
		int = tonumber(a)
		if #a == 3 then
			bitstring = bitstring .. binary(int,10)
		elseif #a == 2 then
			bitstring = bitstring .. binary(int,7)
		else
			bitstring = bitstring .. binary(int,4)
		end
	end)
	return bitstring
end

-- Return a binary representation of the alphanumeric string `str`. This must contain only
-- digits 0-9, uppercase letters A-Z, space and the following chars: $%*./:+-.
local function encode_string_ascii(str)
	local bitstring = ""
	local int
	local b1, b2
	string.gsub(str,"..?",function(a)
		if #a == 2 then
			b1 = asciitbl[string.byte(string.sub(a,1,1))]
			b2 = asciitbl[string.byte(string.sub(a,2,2))]
			int = b1 * 45 + b2
			bitstring = bitstring .. binary(int,11)
		else
			int = asciitbl[string.byte(a)]
			bitstring = bitstring .. binary(int,6)
		end
	  end)
	return bitstring
end

-- Return a bitstring representing string str in binary mode.
-- We don't handle UTF-8 in any special way because we assume the
-- scanner recognizes UTF-8 and displays it correctly.
local function encode_string_binary(str)
	local ret = {}
	string.gsub(str,".",function(x)
		ret[#ret + 1] = binary(string.byte(x),8)
	end)
	return table.concat(ret)
end

-- Return a bitstring representing string str in the given mode.
local function encode_data(str,mode)
	if mode == 1 then
		return encode_string_numeric(str)
	elseif mode == 2 then
		return encode_string_ascii(str)
	elseif mode == 4 then
		return encode_string_binary(str)
	else
		assert(false,"not implemented yet")
	end
end

-- Encoding the codeword is not enough. We need to make sure that
-- the length of the binary string is equal to the number of codewords of the version.
local function add_pad_data(version,ec_level,data)
	local count_to_pad, missing_digits
	local cpty = capacity[version][ec_level] * 8
	count_to_pad = math.min(4,cpty - #data)
	if count_to_pad > 0 then
		data = data .. string.rep("0",count_to_pad)
	end
	if math.fmod(#data,8) ~= 0 then
		missing_digits = 8 - math.fmod(#data,8)
		data = data .. string.rep("0",missing_digits)
	end
	assert(math.fmod(#data,8) == 0)
	-- add "11101100" and "00010001" until enough data
	while #data < cpty do
		data = data .. "11101100"
		if #data < cpty then
			data = data .. "00010001"
		end
	end
	return data
end



--- Step 3: Organize data and calculate error correction code
--- =======================================================
--- The data in the qrcode is not encoded linearly. For example code 5-H has four blocks, the first two blocks
--- contain 11 codewords and 22 error correction codes each, the second block contain 12 codewords and 22 ec codes each.
--- We just take the table from the spec and don't calculate the blocks ourself. The table `ecblocks` contains this info.
---
--- During the phase of splitting the data into codewords, we do the calculation for error correction codes. This step involves
--- polynomial division. Find a math book from school and follow the code here :)

--- ### Reed Solomon error correction
--- Now this is the slightly ugly part of the error correction. We start with log/antilog tables
local alpha_int = {
	[0] = 0,
	  2,   4,   8,  16,  32,  64, 128,  29,  58, 116, 232, 205, 135,  19,  38,  76,
	152,  45,  90, 180, 117, 234, 201, 143,   3,   6,  12,  24,  48,  96, 192, 157,
	 39,  78, 156,  37,  74, 148,  53, 106, 212, 181, 119, 238, 193, 159,  35,  70,
	140,   5,  10,  20,  40,  80, 160,  93, 186, 105, 210, 185, 111, 222, 161,  95,
	190,  97, 194, 153,  47,  94, 188, 101, 202, 137,  15,  30,  60, 120, 240, 253,
	231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163,  91, 182, 113, 226, 217,
	175,  67, 134,  17,  34,  68, 136,  13,  26,  52, 104, 208, 189, 103, 206, 129,
	 31,  62, 124, 248, 237, 199, 147,  59, 118, 236, 197, 151,  51, 102, 204, 133,
	 23,  46,  92, 184, 109, 218, 169,  79, 158,  33,  66, 132,  21,  42,  84, 168,
	 77, 154,  41,  82, 164,  85, 170,  73, 146,  57, 114, 228, 213, 183, 115, 230,
	209, 191,  99, 198, 145,  63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227,
	219, 171,  75, 150,  49,  98, 196, 149,  55, 110, 220, 165,  87, 174,  65, 130,
	 25,  50, 100, 200, 141,   7,  14,  28,  56, 112, 224, 221, 167,  83, 166,  81,
	162,  89, 178, 121, 242, 249, 239, 195, 155,  43,  86, 172,  69, 138,   9,  18,
	 36,  72, 144,  61, 122, 244, 245, 247, 243, 251, 235, 203, 139,  11,  22,  44,
	 88, 176, 125, 250, 233, 207, 131,  27,  54, 108, 216, 173,  71, 142,   1
}

local int_alpha = {
	[0] = 0,
	255,   1,  25,   2,  50,  26, 198,   3, 223,  51, 238,  27, 104, 199,  75,   4,
	100, 224,  14,  52, 141, 239, 129,  28, 193, 105, 248, 200,   8,  76, 113,   5,
	138, 101,  47, 225,  36,  15,  33,  53, 147, 142, 218, 240,  18, 130,  69,  29,
	181, 194, 125, 106,  39, 249, 185, 201, 154,   9, 120,  77, 228, 114, 166,   6,
	191, 139,  98, 102, 221,  48, 253, 226, 152,  37, 179,  16, 145,  34, 136,  54,
	208, 148, 206, 143, 150, 219, 189, 241, 210,  19,  92, 131,  56,  70,  64,  30,
	 66, 182, 163, 195,  72, 126, 110, 107,  58,  40,  84, 250, 133, 186,  61, 202,
	 94, 155, 159,  10,  21, 121,  43,  78, 212, 229, 172, 115, 243, 167,  87,   7,
	112, 192, 247, 140, 128,  99,  13, 103,  74, 222, 237,  49, 197, 254,  24, 227,
	165, 153, 119,  38, 184, 180, 124,  17,  68, 146, 217,  35,  32, 137,  46,  55,
	 63, 209,  91, 149, 188, 207, 205, 144, 135, 151, 178, 220, 252, 190,  97, 242,
	 86, 211, 171,  20,  42,  93, 158, 132,  60,  57,  83,  71, 109,  65, 162,  31,
	 45,  67, 216, 183, 123, 164, 118, 196,  23,  73, 236, 127,  12, 111, 246, 108,
	161,  59,  82,  41, 157,  85, 170, 251,  96, 134, 177, 187, 204,  62,  90, 203,
	 89,  95, 176, 156, 169, 160,  81,  11, 245,  22, 235, 122, 117,  44, 215,  79,
	174, 213, 233, 230, 231, 173, 232, 116, 214, 244, 234, 168,  80,  88, 175
}

-- We only need the polynomial generators for block sizes 7, 10, 13, 15, 16, 17, 18, 20, 22, 24, 26, 28, and 30. Version
-- 2 of the qr codes don't need larger ones (as opposed to version 1). The table has the format x^1*ɑ^21 + x^2*a^102 ...
local generator_polynomial = {
	 [7] = { 21, 102, 238, 149, 146, 229,  87,   0},
	[10] = { 45,  32,  94,  64,  70, 118,  61,  46,  67, 251,   0 },
	[13] = { 78, 140, 206, 218, 130, 104, 106, 100,  86, 100, 176, 152,  74,   0 },
	[15] = {105,  99,   5, 124, 140, 237,  58,  58,  51,  37, 202,  91,  61, 183,   8,   0},
	[16] = {120, 225, 194, 182, 169, 147, 191,  91,   3,  76, 161, 102, 109, 107, 104, 120,   0},
	[17] = {136, 163, 243,  39, 150,  99,  24, 147, 214, 206, 123, 239,  43,  78, 206, 139,  43,   0},
	[18] = {153,  96,  98,   5, 179, 252, 148, 152, 187,  79, 170, 118,  97, 184,  94, 158, 234, 215,   0},
	[20] = {190, 188, 212, 212, 164, 156, 239,  83, 225, 221, 180, 202, 187,  26, 163,  61,  50,  79,  60,  17,   0},
	[22] = {231, 165, 105, 160, 134, 219,  80,  98, 172,   8,  74, 200,  53, 221, 109,  14, 230,  93, 242, 247, 171, 210,   0},
	[24] = { 21, 227,  96,  87, 232, 117,   0, 111, 218, 228, 226, 192, 152, 169, 180, 159, 126, 251, 117, 211,  48, 135, 121, 229,   0},
	[26] = { 70, 218, 145, 153, 227,  48, 102,  13, 142, 245,  21, 161,  53, 165,  28, 111, 201, 145,  17, 118, 182, 103,   2, 158, 125, 173,   0},
	[28] = {123,   9,  37, 242, 119, 212, 195,  42,  87, 245,  43,  21, 201, 232,  27, 205, 147, 195, 190, 110, 180, 108, 234, 224, 104, 200, 223, 168,   0},
	[30] = {180, 192,  40, 238, 216, 251,  37, 156, 130, 224, 193, 226, 173,  42, 125, 222,  96, 239,  86, 110,  48,  50, 182, 179,  31, 216, 152, 145, 173, 41, 0}}


-- Turn a binary string of length 8*x into a table size x of numbers.
local function convert_bitstring_to_bytes(data)
	local msg = {}
	local tab = string.gsub(data,"(........)",function(x)
		msg[#msg+1] = tonumber(x,2)
		end)
	return msg
end

-- Return a table that has 0's in the first entries and then the alpha
-- representation of the generator polynominal
function get_generator_polynominal_adjusted(num_ec_codewords,highest_exponent)
	local gp_alpha = {[0]=0}
	for i=0,highest_exponent - num_ec_codewords - 1 do
		gp_alpha[i] = 0
	end
	local gp = generator_polynomial[num_ec_codewords]
	for i=1,num_ec_codewords + 1 do
		gp_alpha[highest_exponent - num_ec_codewords + i - 1] = gp[i]
	end
	return gp_alpha
end

--- These converter functions use the log/antilog table above.
--- We could have created the table programatically, but I like fixed tables.
-- Convert polynominal in int notation to alpha notation.
local function convert_to_alpha( tab )
	local new_tab = {}
	for i=0,#tab do
		new_tab[i] = int_alpha[tab[i]]
	end
	return new_tab
end

-- Convert polynominal in alpha notation to int notation.
local function convert_to_int(tab,len_message)
	local new_tab = {}
	for i=0,#tab do
		new_tab[i] = alpha_int[tab[i]]
	end
	return new_tab
end

-- That's the heart of the error correction calculation.
local function calculate_error_correction(data,num_ec_codewords)
	local mp
	if type(data)=="string" then
		mp = convert_bitstring_to_bytes(data)
	elseif type(data)=="table" then
		mp = data
	else
		assert(false,"Unknown type for data: %s",type(data))
	end
	local len_message = #mp

	local highest_exponent = len_message + num_ec_codewords - 1
	local gp_alpha,tmp
	local he
	local gp_int = {}
	local mp_int,mp_alpha = {},{}
	-- create message shifted to left (highest exponent)
	for i=1,len_message do
		mp_int[highest_exponent - i + 1] = mp[i]
	end
	for i=1,highest_exponent - len_message do
		mp_int[i] = 0
	end
	mp_int[0] = 0

	mp_alpha = convert_to_alpha(mp_int)

	while highest_exponent >= num_ec_codewords do
		gp_alpha = get_generator_polynominal_adjusted(num_ec_codewords,highest_exponent)

		-- Multiply generator polynomial by first coefficient of the above polynomial

		-- take the highest exponent from the message polynom (alpha) and add
		-- it to the generator polynom
		local exp = mp_alpha[highest_exponent]
		for i=highest_exponent,highest_exponent - num_ec_codewords,-1 do
			if gp_alpha[i] + exp > 255 then
				gp_alpha[i] = math.fmod(gp_alpha[i] + exp,255)
			else
				gp_alpha[i] = gp_alpha[i] + exp
			end
		end
		for i=highest_exponent - num_ec_codewords - 1,0,-1 do
			gp_alpha[i] = 0
		end

		gp_int = convert_to_int(gp_alpha)
		mp_int = convert_to_int(mp_alpha)


		tmp = {}
		for i=highest_exponent,0,-1 do
			tmp[i] = bit_xor(gp_int[i],mp_int[i])
		end
		-- remove leading 0's
		he = highest_exponent
		for i=he,0,-1 do
			-- We need to stop if the length of the codeword is matched
			if i < num_ec_codewords then break end
			if tmp[i] == 0 then
				tmp[i] = nil
				highest_exponent = highest_exponent - 1
			else
				break
			end
		end
		mp_int = tmp
		mp_alpha = convert_to_alpha(mp_int)
	end
	local ret = {}

	-- reverse data
	for i=#mp_int,0,-1 do
		ret[#ret + 1] = mp_int[i]
	end
	return ret
end

--- #### Arranging the data
--- Now we arrange the data into smaller chunks. This table is taken from the spec.
-- ecblocks has 40 entries, one for each version. Each version entry has 4 entries, for each LMQH
-- ec level. Each entry has two or four fields, the odd files are the number of repetitions for the
-- folowing block info. The first entry of the block is the total number of codewords in the block,
-- the second entry is the number of data codewords. The third is not important.
local ecblocks = {
  {{  1,{ 26, 19, 2}                 },   {  1,{26,16, 4}},                  {  1,{26,13, 6}},                  {  1, {26, 9, 8}               }},
  {{  1,{ 44, 34, 4}                 },   {  1,{44,28, 8}},                  {  1,{44,22,11}},                  {  1, {44,16,14}               }},
  {{  1,{ 70, 55, 7}                 },   {  1,{70,44,13}},                  {  2,{35,17, 9}},                  {  2, {35,13,11}               }},
  {{  1,{100, 80,10}                 },   {  2,{50,32, 9}},                  {  2,{50,24,13}},                  {  4, {25, 9, 8}               }},
  {{  1,{134,108,13}                 },   {  2,{67,43,12}},                  {  2,{33,15, 9},  2,{34,16, 9}},   {  2, {33,11,11},  2,{34,12,11}}},
  {{  2,{ 86, 68, 9}                 },   {  4,{43,27, 8}},                  {  4,{43,19,12}},                  {  4, {43,15,14}               }},
  {{  2,{ 98, 78,10}                 },   {  4,{49,31, 9}},                  {  2,{32,14, 9},  4,{33,15, 9}},   {  4, {39,13,13},  1,{40,14,13}}},
  {{  2,{121, 97,12}                 },   {  2,{60,38,11},  2,{61,39,11}},   {  4,{40,18,11},  2,{41,19,11}},   {  4, {40,14,13},  2,{41,15,13}}},
  {{  2,{146,116,15}                 },   {  3,{58,36,11},  2,{59,37,11}},   {  4,{36,16,10},  4,{37,17,10}},   {  4, {36,12,12},  4,{37,13,12}}},
  {{  2,{ 86, 68, 9},  2,{ 87, 69, 9}},   {  4,{69,43,13},  1,{70,44,13}},   {  6,{43,19,12},  2,{44,20,12}},   {  6, {43,15,14},  2,{44,16,14}}},
  {{  4,{101, 81,10}                 },   {  1,{80,50,15},  4,{81,51,15}},   {  4,{50,22,14},  4,{51,23,14}},   {  3, {36,12,12},  8,{37,13,12}}},
  {{  2,{116, 92,12},  2,{117, 93,12}},   {  6,{58,36,11},  2,{59,37,11}},   {  4,{46,20,13},  6,{47,21,13}},   {  7, {42,14,14},  4,{43,15,14}}},
  {{  4,{133,107,13}                 },   {  8,{59,37,11},  1,{60,38,11}},   {  8,{44,20,12},  4,{45,21,12}},   { 12, {33,11,11},  4,{34,12,11}}},
  {{  3,{145,115,15},  1,{146,116,15}},   {  4,{64,40,12},  5,{65,41,12}},   { 11,{36,16,10},  5,{37,17,10}},   { 11, {36,12,12},  5,{37,13,12}}},
  {{  5,{109, 87,11},  1,{110, 88,11}},   {  5,{65,41,12},  5,{66,42,12}},   {  5,{54,24,15},  7,{55,25,15}},   { 11, {36,12,12},  7,{37,13,12}}},
  {{  5,{122, 98,12},  1,{123, 99,12}},   {  7,{73,45,14},  3,{74,46,14}},   { 15,{43,19,12},  2,{44,20,12}},   {  3, {45,15,15}, 13,{46,16,15}}},
  {{  1,{135,107,14},  5,{136,108,14}},   { 10,{74,46,14},  1,{75,47,14}},   {  1,{50,22,14}, 15,{51,23,14}},   {  2, {42,14,14}, 17,{43,15,14}}},
  {{  5,{150,120,15},  1,{151,121,15}},   {  9,{69,43,13},  4,{70,44,13}},   { 17,{50,22,14},  1,{51,23,14}},   {  2, {42,14,14}, 19,{43,15,14}}},
  {{  3,{141,113,14},  4,{142,114,14}},   {  3,{70,44,13}, 11,{71,45,13}},   { 17,{47,21,13},  4,{48,22,13}},   {  9, {39,13,13}, 16,{40,14,13}}},
  {{  3,{135,107,14},  5,{136,108,14}},   {  3,{67,41,13}, 13,{68,42,13}},   { 15,{54,24,15},  5,{55,25,15}},   { 15, {43,15,14}, 10,{44,16,14}}},
  {{  4,{144,116,14},  4,{145,117,14}},   { 17,{68,42,13}},                  { 17,{50,22,14},  6,{51,23,14}},   { 19, {46,16,15},  6,{47,17,15}}},
  {{  2,{139,111,14},  7,{140,112,14}},   { 17,{74,46,14}},                  {  7,{54,24,15}, 16,{55,25,15}},   { 34, {37,13,12}               }},
  {{  4,{151,121,15},  5,{152,122,15}},   {  4,{75,47,14}, 14,{76,48,14}},   { 11,{54,24,15}, 14,{55,25,15}},   { 16, {45,15,15}, 14,{46,16,15}}},
  {{  6,{147,117,15},  4,{148,118,15}},   {  6,{73,45,14}, 14,{74,46,14}},   { 11,{54,24,15}, 16,{55,25,15}},   { 30, {46,16,15},  2,{47,17,15}}},
  {{  8,{132,106,13},  4,{133,107,13}},   {  8,{75,47,14}, 13,{76,48,14}},   {  7,{54,24,15}, 22,{55,25,15}},   { 22, {45,15,15}, 13,{46,16,15}}},
  {{ 10,{142,114,14},  2,{143,115,14}},   { 19,{74,46,14},  4,{75,47,14}},   { 28,{50,22,14},  6,{51,23,14}},   { 33, {46,16,15},  4,{47,17,15}}},
  {{  8,{152,122,15},  4,{153,123,15}},   { 22,{73,45,14},  3,{74,46,14}},   {  8,{53,23,15}, 26,{54,24,15}},   { 12, {45,15,15}, 28,{46,16,15}}},
  {{  3,{147,117,15}, 10,{148,118,15}},   {  3,{73,45,14}, 23,{74,46,14}},   {  4,{54,24,15}, 31,{55,25,15}},   { 11, {45,15,15}, 31,{46,16,15}}},
  {{  7,{146,116,15},  7,{147,117,15}},   { 21,{73,45,14},  7,{74,46,14}},   {  1,{53,23,15}, 37,{54,24,15}},   { 19, {45,15,15}, 26,{46,16,15}}},
  {{  5,{145,115,15}, 10,{146,116,15}},   { 19,{75,47,14}, 10,{76,48,14}},   { 15,{54,24,15}, 25,{55,25,15}},   { 23, {45,15,15}, 25,{46,16,15}}},
  {{ 13,{145,115,15},  3,{146,116,15}},   {  2,{74,46,14}, 29,{75,47,14}},   { 42,{54,24,15},  1,{55,25,15}},   { 23, {45,15,15}, 28,{46,16,15}}},
  {{ 17,{145,115,15}            	 },   { 10,{74,46,14}, 23,{75,47,14}},   { 10,{54,24,15}, 35,{55,25,15}},   { 19, {45,15,15}, 35,{46,16,15}}},
  {{ 17,{145,115,15},  1,{146,116,15}},   { 14,{74,46,14}, 21,{75,47,14}},   { 29,{54,24,15}, 19,{55,25,15}},   { 11, {45,15,15}, 46,{46,16,15}}},
  {{ 13,{145,115,15},  6,{146,116,15}},   { 14,{74,46,14}, 23,{75,47,14}},   { 44,{54,24,15},  7,{55,25,15}},   { 59, {46,16,15},  1,{47,17,15}}},
  {{ 12,{151,121,15},  7,{152,122,15}},   { 12,{75,47,14}, 26,{76,48,14}},   { 39,{54,24,15}, 14,{55,25,15}},   { 22, {45,15,15}, 41,{46,16,15}}},
  {{  6,{151,121,15}, 14,{152,122,15}},   {  6,{75,47,14}, 34,{76,48,14}},   { 46,{54,24,15}, 10,{55,25,15}},   {  2, {45,15,15}, 64,{46,16,15}}},
  {{ 17,{152,122,15},  4,{153,123,15}},   { 29,{74,46,14}, 14,{75,47,14}},   { 49,{54,24,15}, 10,{55,25,15}},   { 24, {45,15,15}, 46,{46,16,15}}},
  {{  4,{152,122,15}, 18,{153,123,15}},   { 13,{74,46,14}, 32,{75,47,14}},   { 48,{54,24,15}, 14,{55,25,15}},   { 42, {45,15,15}, 32,{46,16,15}}},
  {{ 20,{147,117,15},  4,{148,118,15}},   { 40,{75,47,14},  7,{76,48,14}},   { 43,{54,24,15}, 22,{55,25,15}},   { 10, {45,15,15}, 67,{46,16,15}}},
  {{ 19,{148,118,15},  6,{149,119,15}},   { 18,{75,47,14}, 31,{76,48,14}},   { 34,{54,24,15}, 34,{55,25,15}},   { 20, {45,15,15}, 61,{46,16,15}}}
}

-- The bits that must be 0 if the version does fill the complete matrix.
-- Example: for version 1, no bits need to be added after arranging the data, for version 2 we need to add 7 bits at the end.
local remainder = {0, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0}

-- This is the formula for table 1 in the spec:
-- function get_capacity_remainder( version )
-- 	local len = version * 4 + 17
-- 	local size = len^2
-- 	local function_pattern_modules = 192 + 2 * len - 32 -- Position Adjustment pattern + timing pattern
-- 	local count_alignemnt_pattern = #alignment_pattern[version]
-- 	if count_alignemnt_pattern > 0 then
-- 		-- add 25 for each aligment pattern
-- 		function_pattern_modules = function_pattern_modules + 25 * ( count_alignemnt_pattern^2 - 3 )
-- 		-- but substract the timing pattern occupied by the aligment pattern on the top and left
-- 		function_pattern_modules = function_pattern_modules - ( count_alignemnt_pattern - 2) * 10
-- 	end
-- 	size = size - function_pattern_modules
-- 	if version > 6 then
-- 		size = size - 67
-- 	else
-- 		size = size - 31
-- 	end
-- 	return math.floor(size/8),math.fmod(size,8)
-- end


--- Example: Version 5-H has four data and four error correction blocks. The table above lists
--- `2, {33,11,11},  2,{34,12,11}` for entry [5][4]. This means we take two blocks with 11 codewords
--- and two blocks with 12 codewords, and two blocks with 33 - 11 = 22 ec codes and another
--- two blocks with 34 - 12 = 22 ec codes.
---	     Block 1: D1  D2  D3  ... D11
---	     Block 2: D12 D13 D14 ... D22
---	     Block 3: D23 D24 D25 ... D33 D34
---	     Block 4: D35 D36 D37 ... D45 D46
--- Then we place the data like this in the matrix: D1, D12, D23, D35, D2, D13, D24, D36 ... D45, D34, D46.  The same goes
--- with error correction codes.

-- The given data can be a string of 0's and 1' (with #string mod 8 == 0).
-- Alternatively the data can be a table of codewords. The number of codewords
-- must match the capacity of the qr code.
local function arrange_codewords_and_calculate_ec( version,ec_level,data )
	if type(data)=="table" then
		local tmp = ""
		for i=1,#data do
			tmp = tmp .. binary(data[i],8)
		end
		data = tmp
	end
	-- If the size of the data is not enough for the codeword, we add 0's and two special bytes until finished.
	local blocks = ecblocks[version][ec_level]
	local size_datablock_bytes, size_ecblock_bytes
	local datablocks = {}
	local ecblocks = {}
	local count = 1
	local pos = 0
	local cpty_ec_bits = 0
	for i=1,#blocks/2 do
		for j=1,blocks[2*i - 1] do
			size_datablock_bytes = blocks[2*i][2]
			size_ecblock_bytes   = blocks[2*i][1] - blocks[2*i][2]
			cpty_ec_bits = cpty_ec_bits + size_ecblock_bytes * 8
			datablocks[#datablocks + 1] = string.sub(data, pos * 8 + 1,( pos + size_datablock_bytes)*8)
			tmp_tab = calculate_error_correction(datablocks[#datablocks],size_ecblock_bytes)
			tmp_str = ""
			for x=1,#tmp_tab do
				tmp_str = tmp_str .. binary(tmp_tab[x],8)
			end
			ecblocks[#ecblocks + 1] = tmp_str
			pos = pos + size_datablock_bytes
			count = count + 1
		end
	end
	local arranged_data = ""
	pos = 1
	repeat
		for i=1,#datablocks do
			if pos < #datablocks[i] then
				arranged_data = arranged_data .. string.sub(datablocks[i],pos, pos + 7)
			end
		end
		pos = pos + 8
	until #arranged_data == #data
	-- ec
	local arranged_ec = ""
	pos = 1
	repeat
		for i=1,#ecblocks do
			if pos < #ecblocks[i] then
				arranged_ec = arranged_ec .. string.sub(ecblocks[i],pos, pos + 7)
			end
		end
		pos = pos + 8
	until #arranged_ec == cpty_ec_bits
	return arranged_data .. arranged_ec
end

--- Step 4: Generate 8 matrices with different masks and calculate the penalty
--- ==========================================================================
---
--- Prepare matrix
--- --------------
--- The first step is to prepare an _empty_ matrix for a given size/mask. The matrix has a
--- few predefined areas that must be black or blank. We encode the matrix with a two
--- dimensional field where the numbers determine which pixel is blank or not.
---
--- The following code is used for our matrix:
---	     0 = not in use yet,
---	    -2 = blank by mandatory pattern,
---	     2 = black by mandatory pattern,
---	    -1 = blank by data,
---	     1 = black by data
---
---
--- To prepare the _empty_, we add positioning, alingment and timing patters.

--- ### Positioning patterns ###
local function add_position_detection_patterns(tab_x)
	local size = #tab_x
	-- allocate quite zone in the matrix area
	for i=1,8 do
		for j=1,8 do
			tab_x[i][j] = -2
			tab_x[size - 8 + i][j] = -2
			tab_x[i][size - 8 + j] = -2
		end
	end
	-- draw the detection pattern (outer)
	for i=1,7 do
		-- top left
		tab_x[1][i]=2
		tab_x[7][i]=2
		tab_x[i][1]=2
		tab_x[i][7]=2

		-- top right
		tab_x[size][i]=2
		tab_x[size - 6][i]=2
		tab_x[size - i + 1][1]=2
		tab_x[size - i + 1][7]=2

		-- bottom left
		tab_x[1][size - i + 1]=2
		tab_x[7][size - i + 1]=2
		tab_x[i][size - 6]=2
		tab_x[i][size]=2
	end
	-- draw the detection pattern (inner)
	for i=1,3 do
		for j=1,3 do
			-- top left
			tab_x[2+j][i+2]=2
			-- top right
			tab_x[size - j - 1][i+2]=2
			-- bottom left
			tab_x[2 + j][size - i - 1]=2
		end
	end
end

--- ### Timing patterns ###
-- The timing patterns (two) are the dashed lines between two adjacent positioning patterns on row/column 7.
local function add_timing_pattern(tab_x)
	local line,col
	line = 7
	col = 9
	for i=col,#tab_x - 8 do
		if math.fmod(i,2) == 1 then
			tab_x[i][line] = 2
		else
			tab_x[i][line] = -2
		end
	end
	for i=col,#tab_x - 8 do
		if math.fmod(i,2) == 1 then
			tab_x[line][i] = 2
		else
			tab_x[line][i] = -2
		end
	end
end


--- ### Alignment patterns ###
--- The alignment patterns must be added to the matrix for versions > 1. The amount and positions depend on the versions and are
--- given by the spec. Beware: the patterns must not be placed where we have the positioning patterns
--- (that is: top left, top right and bottom left.)

-- For each version, where should we place the alignment patterns? See table E.1 of the spec
local alignment_pattern = {
  {},{6,18},{6,22},{6,26},{6,30},{6,34}, -- 1-6
  {6,22,38},{6,24,42},{6,26,46},{6,28,50},{6,30,54},{6,32,58},{6,34,62}, -- 7-13
  {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}, -- 14-20
  {6,28,50,72,94},{6,26,50,74,98},{6,30,54,78,102},{6,28,54,80,106},{6,32,58,84,110},{6,30,58,86,114},{6,34,62,90,118}, -- 21-27
  {6,26,50,74,98 ,122},{6,30,54,78,102,126},{6,26,52,78,104,130},{6,30,56,82,108,134},{6,34,60,86,112,138},{6,30,58,86,114,142},{6,34,62,90,118,146}, -- 28-34
  {6,30,54,78,102,126,150}, {6,24,50,76,102,128,154},{6,28,54,80,106,132,158},{6,32,58,84,110,136,162},{6,26,54,82,110,138,166},{6,30,58,86,114,142,170} -- 35 - 40
}

--- The alignment pattern has size 5x5 and looks like this:
---     XXXXX
---     X   X
---     X X X
---     X   X
---     XXXXX
local function add_alignment_pattern( tab_x )
	local version = (#tab_x - 17) / 4
	local ap = alignment_pattern[version]
	local pos_x, pos_y
	for x=1,#ap do
		for y=1,#ap do
			-- we must not put an alignment pattern on top of the positioning pattern
			if not (x == 1 and y == 1 or x == #ap and y == 1 or x == 1 and y == #ap ) then
				pos_x = ap[x] + 1
				pos_y = ap[y] + 1
				tab_x[pos_x][pos_y] = 2
				tab_x[pos_x+1][pos_y] = -2
				tab_x[pos_x-1][pos_y] = -2
				tab_x[pos_x+2][pos_y] =  2
				tab_x[pos_x-2][pos_y] =  2
				tab_x[pos_x  ][pos_y - 2] = 2
				tab_x[pos_x+1][pos_y - 2] = 2
				tab_x[pos_x-1][pos_y - 2] = 2
				tab_x[pos_x+2][pos_y - 2] = 2
				tab_x[pos_x-2][pos_y - 2] = 2
				tab_x[pos_x  ][pos_y + 2] = 2
				tab_x[pos_x+1][pos_y + 2] = 2
				tab_x[pos_x-1][pos_y + 2] = 2
				tab_x[pos_x+2][pos_y + 2] = 2
				tab_x[pos_x-2][pos_y + 2] = 2

				tab_x[pos_x  ][pos_y - 1] = -2
				tab_x[pos_x+1][pos_y - 1] = -2
				tab_x[pos_x-1][pos_y - 1] = -2
				tab_x[pos_x+2][pos_y - 1] =  2
				tab_x[pos_x-2][pos_y - 1] =  2
				tab_x[pos_x  ][pos_y + 1] = -2
				tab_x[pos_x+1][pos_y + 1] = -2
				tab_x[pos_x-1][pos_y + 1] = -2
				tab_x[pos_x+2][pos_y + 1] =  2
				tab_x[pos_x-2][pos_y + 1] =  2
			end
		end
	end
end

--- ### Type information ###
--- Let's not forget the type information that is in column 9 next to the left positioning patterns and on row 9 below
--- the top positioning patterns. This type information is not fixed, it depends on the mask and the error correction.

-- The first index is ec level (LMQH,1-4), the second is the mask (0-7). This bitstring of length 15 is to be used
-- as mandatory pattern in the qrcode. Mask -1 is for debugging purpose only and is the 'noop' mask.
local typeinfo = {
	{ [-1]= "111111111111111", [0] = "111011111000100", "111001011110011", "111110110101010", "111100010011101", "110011000101111", "110001100011000", "110110001000001", "110100101110110" },
	{ [-1]= "111111111111111", [0] = "101010000010010", "101000100100101", "101111001111100", "101101101001011", "100010111111001", "100000011001110", "100111110010111", "100101010100000" },
	{ [-1]= "111111111111111", [0] = "011010101011111", "011000001101000", "011111100110001", "011101000000110", "010010010110100", "010000110000011", "010111011011010", "010101111101101" },
	{ [-1]= "111111111111111", [0] = "001011010001001", "001001110111110", "001110011100111", "001100111010000", "000011101100010", "000001001010101", "000110100001100", "000100000111011" }
}

-- The typeinfo is a mixture of mask and ec level information and is
-- added twice to the qr code, one horizontal, one vertical.
local function add_typeinfo_to_matrix( matrix,ec_level,mask )
	local ec_mask_type = typeinfo[ec_level][mask]

	local bit
	-- vertical from bottom to top
	for i=1,7 do
		bit = string.sub(ec_mask_type,i,i)
		fill_matrix_position(matrix, bit, 9, #matrix - i + 1)
	end
	for i=8,9 do
		bit = string.sub(ec_mask_type,i,i)
		fill_matrix_position(matrix,bit,9,17-i)
	end
	for i=10,15 do
		bit = string.sub(ec_mask_type,i,i)
		fill_matrix_position(matrix,bit,9,16 - i)
	end
	-- horizontal, left to right
	for i=1,6 do
		bit = string.sub(ec_mask_type,i,i)
		fill_matrix_position(matrix,bit,i,9)
	end
	bit = string.sub(ec_mask_type,7,7)
	fill_matrix_position(matrix,bit,8,9)
	for i=8,15 do
		bit = string.sub(ec_mask_type,i,i)
		fill_matrix_position(matrix,bit,#matrix - 15 + i,9)
	end
end

-- Bits for version information 7-40
local version_information = {"001010010011111000", "000111101101000100", "100110010101100100","011001011001010100",
  "011011111101110100", "001000110111001100", "111000100001101100", "010110000011011100", "000101001001111100",
  "000111101101000010", "010111010001100010", "111010000101010010", "001001100101110010", "011001011001001010",
  "011000001011101010", "100100110001011010", "000110111111111010", "001000110111000110", "000100001111100110",
  "110101011111010110", "000001110001110110", "010110000011001110", "001111110011101110", "101011101011011110",
  "000000101001111110", "101010111001000001", "000001111011100001", "010111010001010001", "011111001111110001",
  "110100001101001001", "001110100001101001", "001001100101011001", "010000010101111001", "100101100011000101" }

-- Versions 7 and above need two bitfields with version information added to the code
local function add_version_information(matrix,version)
	if version < 7 then return end
	local size = #matrix
	local bitstring = version_information[version - 6]
	local x,y, bit
	local start_x, start_y
	-- first top right
	start_x = #matrix - 10
	start_y = 1
	for i=1,#bitstring do
		bit = string.sub(bitstring,i,i)
		x = start_x + math.fmod(i - 1,3)
		y = start_y + math.floor( (i - 1) / 3 )
		fill_matrix_position(matrix,bit,x,y)
	end

	-- now bottom left
	start_x = 1
	start_y = #matrix - 10
	for i=1,#bitstring do
		bit = string.sub(bitstring,i,i)
		x = start_x + math.floor( (i - 1) / 3 )
		y = start_y + math.fmod(i - 1,3)
		fill_matrix_position(matrix,bit,x,y)
	end
end

--- Now it's time to use the methods above to create a prefilled matrix for the given mask
local function prepare_matrix_with_mask( version,ec_level, mask )
	local size
	local tab_x = {}

	size = version * 4 + 17
	for i=1,size do
		tab_x[i]={}
		for j=1,size do
			tab_x[i][j] = 0
		end
	end
	add_position_detection_patterns(tab_x)
	add_timing_pattern(tab_x)
	add_version_information(tab_x,version)

	-- black pixel above lower left position detection pattern
	tab_x[9][size - 7] = 2
	add_alignment_pattern(tab_x)
	add_typeinfo_to_matrix(tab_x,ec_level, mask)
	return tab_x
end

--- Finally we come to the place where we need to put the calculated data (remember step 3?) into the qr code.
--- We do this for each mask. BTW speaking of mask, this is what we find in the spec:
---	     Mask Pattern Reference   Condition
---	     000                      (y + x) mod 2 = 0
---	     001                      y mod 2 = 0
---	     010                      x mod 3 = 0
---	     011                      (y + x) mod 3 = 0
---	     100                      ((y div 2) + (x div 3)) mod 2 = 0
---	     101                      (y x) mod 2 + (y x) mod 3 = 0
---	     110                      ((y x) mod 2 + (y x) mod 3) mod 2 = 0
---	     111                      ((y x) mod 3 + (y+x) mod 2) mod 2 = 0

-- Return 1 (black) or -1 (blank) depending on the mask, value and position.
-- Parameter mask is 0-7 (-1 for 'no mask'). x and y are 1-based coordinates,
-- 1,1 = upper left. tonumber(value) must be 0 or 1.
local function get_pixel_with_mask( mask, x,y,value )
	x = x - 1
	y = y - 1
	local invert = false
	-- test purpose only:
	if mask == -1 then
		-- ignore, no masking applied
	elseif mask == 0 then
		if math.fmod(x + y,2) == 0 then invert = true end
	elseif mask == 1 then
		if math.fmod(y,2) == 0 then invert = true end
	elseif mask == 2 then
		if math.fmod(x,3) == 0 then invert = true end
	elseif mask == 3 then
		if math.fmod(x + y,3) == 0 then invert = true end
	elseif mask == 4 then
		if math.fmod(math.floor(y / 2) + math.floor(x / 3),2) == 0 then invert = true end
	elseif mask == 5 then
		if math.fmod(x * y,2) + math.fmod(x * y,3) == 0 then invert = true end
	elseif mask == 6 then
		if math.fmod(math.fmod(x * y,2) + math.fmod(x * y,3),2) == 0 then invert = true end
	elseif mask == 7 then
		if math.fmod(math.fmod(x * y,3) + math.fmod(x + y,2),2) == 0 then invert = true end
	else
		assert(false,"This can't happen (mask must be <= 7)")
	end
	if invert then
		-- value = 1? -> -1, value = 0? -> 1
		return 1 - 2 * tonumber(value)
	else
		-- value = 1? -> 1, value = 0? -> -1
		return -1 + 2*tonumber(value)
	end
end


-- We need up to 8 positions in the matrix. Only the last few bits may be less then 8.
-- The function returns a table of (up to) 8 entries with subtables where
-- the x coordinate is the first and the y coordinate is the second entry.
function get_next_free_positions(matrix,x,y,dir,byte)
	local ret = {}
	local count = 1
	local mode = "right"
	while count <= #byte do
		if mode == "right" and matrix[x][y] == 0 then
			ret[#ret + 1] = {x,y}
			mode = "left"
			count = count + 1
		elseif mode == "left" and matrix[x-1][y] == 0 then
			ret[#ret + 1] = {x-1,y}
			mode = "right"
			count = count + 1
			if dir == "up" then
				y = y - 1
			else
				y = y + 1
			end
		elseif mode == "right" and matrix[x-1][y] == 0 then
			ret[#ret + 1] = {x-1,y}
			count = count + 1
			if dir == "up" then
				y = y - 1
			else
				y = y + 1
			end
		else
			if dir == "up" then
				y = y - 1
			else
				y = y + 1
			end
		end
		if y < 1 or y > #matrix then
			x = x - 2
			-- don't overwrite the timing pattern
			if x == 7 then x = 6 end
			if dir == "up" then
				dir = "down"
				y = 1
			else
				dir = "up"
				y = #matrix
			end
		end
	end
	return ret,x,y,dir
end

-- Add the data string (0's and 1's) to the matrix for the given mask.
local function add_data_to_matrix(matrix,data,mask)
	size = #matrix
	local x,y,positions
	local _x,_y,m
	local dir = "up"
	local byte_number = 0
	x,y = size,size
	string.gsub(data,".?.?.?.?.?.?.?.?",function ( byte )
		byte_number = byte_number + 1
		positions,x,y,dir = get_next_free_positions(matrix,x,y,dir,byte,mask)
		for i=1,#byte do
			_x = positions[i][1]
			_y = positions[i][2]
			m = get_pixel_with_mask(mask,_x,_y,string.sub(byte,i,i))
			if debugging then
				matrix[_x][_y] = m * (i + 10)
			else
				matrix[_x][_y] = m
			end
		end
	end)
end


--- The total penalty of the matrix is the sum of four steps. The following steps are taken into account:
---
--- 1. Adjacent modules in row/column in same color
--- 1. Block of modules in same color
--- 1. 1:1:3:1:1 ratio (dark:light:dark:light:dark) pattern in row/column
--- 1. Proportion of dark modules in entire symbol
---
--- This all is done to avoid bad patterns in the code that prevent the scanner from
--- reading the code.
-- Return the penalty for the given matrix
local function calculate_penalty(matrix)
	local penalty1, penalty2, penalty3, penalty4 = 0,0,0,0
	local size = #matrix
	-- this is for penalty 4
	local number_of_dark_cells = 0

	-- 1: Adjacent modules in row/column in same color
	-- --------------------------------------------
	-- No. of modules = (5+i)  -> 3 + i
	local last_bit_blank -- < 0:  blank, > 0: black
	local is_blank
	local number_of_consecutive_bits
	-- first: vertical
	for x=1,size do
		number_of_consecutive_bits = 0
		last_bit_blank = nil
		for y = 1,size do
			if matrix[x][y] > 0 then
				-- small optimization: this is for penalty 4
				number_of_dark_cells = number_of_dark_cells + 1
				is_blank = false
			else
				is_blank = true
			end
			is_blank = matrix[x][y] < 0
			if last_bit_blank == is_blank then
				number_of_consecutive_bits = number_of_consecutive_bits + 1
			else
				if number_of_consecutive_bits >= 5 then
					penalty1 = penalty1 + number_of_consecutive_bits - 2
				end
				number_of_consecutive_bits = 1
			end
			last_bit_blank = is_blank
		end
		if number_of_consecutive_bits >= 5 then
			penalty1 = penalty1 + number_of_consecutive_bits - 2
		end
	end
	-- now horizontal
	for y=1,size do
		number_of_consecutive_bits = 0
		last_bit_blank = nil
		for x = 1,size do
			is_blank = matrix[x][y] < 0
			if last_bit_blank == is_blank then
				number_of_consecutive_bits = number_of_consecutive_bits + 1
			else
				if number_of_consecutive_bits >= 5 then
					penalty1 = penalty1 + number_of_consecutive_bits - 2
				end
				number_of_consecutive_bits = 1
			end
			last_bit_blank = is_blank
		end
		if number_of_consecutive_bits >= 5 then
			penalty1 = penalty1 + number_of_consecutive_bits - 2
		end
	end
	for x=1,size do
		for y=1,size do
			-- 2: Block of modules in same color
			-- -----------------------------------
			-- Blocksize = m × n  -> 3 × (m-1) × (n-1)
			if (y < size - 1) and ( x < size - 1) and ( (matrix[x][y] < 0 and matrix[x+1][y] < 0 and matrix[x][y+1] < 0 and matrix[x+1][y+1] < 0) or (matrix[x][y] > 0 and matrix[x+1][y] > 0 and matrix[x][y+1] > 0 and matrix[x+1][y+1] > 0) ) then
				penalty2 = penalty2 + 3
			end

			-- 3: 1:1:3:1:1 ratio (dark:light:dark:light:dark) pattern in row/column
			-- ------------------------------------------------------------------
			-- Gives 40 points each
			--
			-- I have no idea why we need the extra 0000 on left or right side. The spec doesn't mention it,
			-- other sources do mention it. This is heavily inspired by zxing.
			if (y + 6 < size and
				matrix[x][y] > 0 and
				matrix[x][y +  1] < 0 and
				matrix[x][y +  2] > 0 and
				matrix[x][y +  3] > 0 and
				matrix[x][y +  4] > 0 and
				matrix[x][y +  5] < 0 and
				matrix[x][y +  6] > 0 and
				((y + 10 < size and
					matrix[x][y +  7] < 0 and
					matrix[x][y +  8] < 0 and
					matrix[x][y +  9] < 0 and
					matrix[x][y + 10] < 0) or
				 (y - 4 >= 1 and
					matrix[x][y -  1] < 0 and
					matrix[x][y -  2] < 0 and
					matrix[x][y -  3] < 0 and
					matrix[x][y -  4] < 0))) then penalty3 = penalty3 + 40 end
			if (x + 6 <= size and
				matrix[x][y] > 0 and
				matrix[x +  1][y] < 0 and
				matrix[x +  2][y] > 0 and
				matrix[x +  3][y] > 0 and
				matrix[x +  4][y] > 0 and
				matrix[x +  5][y] < 0 and
				matrix[x +  6][y] > 0 and
				((x + 10 <= size and
					matrix[x +  7][y] < 0 and
					matrix[x +  8][y] < 0 and
					matrix[x +  9][y] < 0 and
					matrix[x + 10][y] < 0) or
				 (x - 4 >= 1 and
					matrix[x -  1][y] < 0 and
					matrix[x -  2][y] < 0 and
					matrix[x -  3][y] < 0 and
					matrix[x -  4][y] < 0))) then penalty3 = penalty3 + 40 end
		end
	end
	-- 4: Proportion of dark modules in entire symbol
	-- ----------------------------------------------
	-- 50 ± (5 × k)% to 50 ± (5 × (k + 1))% -> 10 × k
	local dark_ratio = number_of_dark_cells / ( size * size )
	penalty4 = math.floor(math.abs(dark_ratio * 100 - 50)) * 2
	return penalty1 + penalty2 + penalty3 + penalty4
end

-- Create a matrix for the given parameters and calculate the penalty score.
-- Return both (matrix and penalty)
local function get_matrix_and_penalty(version,ec_level,data,mask)
	local tab = prepare_matrix_with_mask(version,ec_level,mask)
	add_data_to_matrix(tab,data,mask)
	local penalty = calculate_penalty(tab)
	return tab, penalty
end

-- Return the matrix with the smallest penalty. To to this
-- we try out the matrix for all 8 masks and determine the
-- penalty (score) each.
local function get_matrix_with_lowest_penalty(version,ec_level,data)
	local tab, penalty
	local tab_min_penalty, min_penalty

	-- try masks 0-7
	tab_min_penalty, min_penalty = get_matrix_and_penalty(version,ec_level,data,0)
	for i=1,7 do
		tab, penalty = get_matrix_and_penalty(version,ec_level,data,i)
		if penalty < min_penalty then
			tab_min_penalty = tab
			min_penalty = penalty
		end
	end
	return tab_min_penalty
end

--- The main function. We connect everything together. Remember from above:
---
--- 1. Determine version, ec level and mode (=encoding) for codeword
--- 1. Encode data
--- 1. Arrange data and calculate error correction code
--- 1. Generate 8 matrices with different masks and calculate the penalty
--- 1. Return qrcode with least penalty
-- If ec_level or mode is given, use the ones for generating the qrcode. (mode is not implemented yet)
function qrcode( str, ec_level, mode )
	local arranged_data, version, ec_level, data_raw, mode, len_bitstring
	version, ec_level, data_raw, mode, len_bitstring = get_version_eclevel_mode_bistringlength(str)
	data_raw = data_raw .. len_bitstring
	data_raw = data_raw .. encode_data(str,mode)
	data_raw = add_pad_data(version,ec_level,data_raw)
	arranged_data = arrange_codewords_and_calculate_ec(version,ec_level,data_raw)
	if math.fmod(#arranged_data,8) ~= 0 then
		return false, string.format("Arranged data %% 8 != 0: data length = %d, mod 8 = %d",#arranged_data, math.fmod(#arranged_data,8))
	end
	arranged_data = arranged_data .. string.rep("0",remainder[version])
	local tab = get_matrix_with_lowest_penalty(version,ec_level,arranged_data)
	return true, tab
end
