Module:Sandbox/九江月/qr
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模块文档--- The qrcode library is licensed under the 3-clause BSD license (aka "new BSD") --- To get in contact with the author, mail to <[email protected]>. --- --- 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 -- To calculate xor we need to do that bitwise. This helper table speeds up the num-to-bit -- part a bit (no pun intended) local cclxvi = {[0] = {0,0,0,0,0,0,0,0}, {1,0,0,0,0,0,0,0}, {0,1,0,0,0,0,0,0}, {1,1,0,0,0,0,0,0}, {0,0,1,0,0,0,0,0}, {1,0,1,0,0,0,0,0}, {0,1,1,0,0,0,0,0}, {1,1,1,0,0,0,0,0}, {0,0,0,1,0,0,0,0}, {1,0,0,1,0,0,0,0}, {0,1,0,1,0,0,0,0}, {1,1,0,1,0,0,0,0}, {0,0,1,1,0,0,0,0}, {1,0,1,1,0,0,0,0}, {0,1,1,1,0,0,0,0}, {1,1,1,1,0,0,0,0}, {0,0,0,0,1,0,0,0}, {1,0,0,0,1,0,0,0}, {0,1,0,0,1,0,0,0}, {1,1,0,0,1,0,0,0}, {0,0,1,0,1,0,0,0}, {1,0,1,0,1,0,0,0}, {0,1,1,0,1,0,0,0}, {1,1,1,0,1,0,0,0}, {0,0,0,1,1,0,0,0}, {1,0,0,1,1,0,0,0}, {0,1,0,1,1,0,0,0}, {1,1,0,1,1,0,0,0}, {0,0,1,1,1,0,0,0}, {1,0,1,1,1,0,0,0}, {0,1,1,1,1,0,0,0}, {1,1,1,1,1,0,0,0}, {0,0,0,0,0,1,0,0}, {1,0,0,0,0,1,0,0}, {0,1,0,0,0,1,0,0}, {1,1,0,0,0,1,0,0}, {0,0,1,0,0,1,0,0}, {1,0,1,0,0,1,0,0}, {0,1,1,0,0,1,0,0}, {1,1,1,0,0,1,0,0}, {0,0,0,1,0,1,0,0}, {1,0,0,1,0,1,0,0}, {0,1,0,1,0,1,0,0}, {1,1,0,1,0,1,0,0}, {0,0,1,1,0,1,0,0}, {1,0,1,1,0,1,0,0}, {0,1,1,1,0,1,0,0}, {1,1,1,1,0,1,0,0}, {0,0,0,0,1,1,0,0}, {1,0,0,0,1,1,0,0}, {0,1,0,0,1,1,0,0}, {1,1,0,0,1,1,0,0}, {0,0,1,0,1,1,0,0}, {1,0,1,0,1,1,0,0}, {0,1,1,0,1,1,0,0}, {1,1,1,0,1,1,0,0}, {0,0,0,1,1,1,0,0}, {1,0,0,1,1,1,0,0}, {0,1,0,1,1,1,0,0}, {1,1,0,1,1,1,0,0}, {0,0,1,1,1,1,0,0}, {1,0,1,1,1,1,0,0}, {0,1,1,1,1,1,0,0}, {1,1,1,1,1,1,0,0}, {0,0,0,0,0,0,1,0}, {1,0,0,0,0,0,1,0}, {0,1,0,0,0,0,1,0}, {1,1,0,0,0,0,1,0}, {0,0,1,0,0,0,1,0}, {1,0,1,0,0,0,1,0}, {0,1,1,0,0,0,1,0}, {1,1,1,0,0,0,1,0}, {0,0,0,1,0,0,1,0}, {1,0,0,1,0,0,1,0}, {0,1,0,1,0,0,1,0}, {1,1,0,1,0,0,1,0}, {0,0,1,1,0,0,1,0}, {1,0,1,1,0,0,1,0}, {0,1,1,1,0,0,1,0}, {1,1,1,1,0,0,1,0}, {0,0,0,0,1,0,1,0}, {1,0,0,0,1,0,1,0}, {0,1,0,0,1,0,1,0}, {1,1,0,0,1,0,1,0}, {0,0,1,0,1,0,1,0}, {1,0,1,0,1,0,1,0}, {0,1,1,0,1,0,1,0}, {1,1,1,0,1,0,1,0}, {0,0,0,1,1,0,1,0}, {1,0,0,1,1,0,1,0}, {0,1,0,1,1,0,1,0}, {1,1,0,1,1,0,1,0}, {0,0,1,1,1,0,1,0}, {1,0,1,1,1,0,1,0}, {0,1,1,1,1,0,1,0}, {1,1,1,1,1,0,1,0}, {0,0,0,0,0,1,1,0}, {1,0,0,0,0,1,1,0}, {0,1,0,0,0,1,1,0}, {1,1,0,0,0,1,1,0}, {0,0,1,0,0,1,1,0}, {1,0,1,0,0,1,1,0}, {0,1,1,0,0,1,1,0}, {1,1,1,0,0,1,1,0}, {0,0,0,1,0,1,1,0}, {1,0,0,1,0,1,1,0}, {0,1,0,1,0,1,1,0}, {1,1,0,1,0,1,1,0}, {0,0,1,1,0,1,1,0}, {1,0,1,1,0,1,1,0}, {0,1,1,1,0,1,1,0}, {1,1,1,1,0,1,1,0}, {0,0,0,0,1,1,1,0}, {1,0,0,0,1,1,1,0}, {0,1,0,0,1,1,1,0}, {1,1,0,0,1,1,1,0}, {0,0,1,0,1,1,1,0}, {1,0,1,0,1,1,1,0}, {0,1,1,0,1,1,1,0}, {1,1,1,0,1,1,1,0}, {0,0,0,1,1,1,1,0}, {1,0,0,1,1,1,1,0}, {0,1,0,1,1,1,1,0}, {1,1,0,1,1,1,1,0}, {0,0,1,1,1,1,1,0}, {1,0,1,1,1,1,1,0}, {0,1,1,1,1,1,1,0}, {1,1,1,1,1,1,1,0}, {0,0,0,0,0,0,0,1}, {1,0,0,0,0,0,0,1}, {0,1,0,0,0,0,0,1}, {1,1,0,0,0,0,0,1}, {0,0,1,0,0,0,0,1}, {1,0,1,0,0,0,0,1}, {0,1,1,0,0,0,0,1}, {1,1,1,0,0,0,0,1}, {0,0,0,1,0,0,0,1}, {1,0,0,1,0,0,0,1}, {0,1,0,1,0,0,0,1}, {1,1,0,1,0,0,0,1}, {0,0,1,1,0,0,0,1}, {1,0,1,1,0,0,0,1}, {0,1,1,1,0,0,0,1}, {1,1,1,1,0,0,0,1}, {0,0,0,0,1,0,0,1}, {1,0,0,0,1,0,0,1}, {0,1,0,0,1,0,0,1}, {1,1,0,0,1,0,0,1}, {0,0,1,0,1,0,0,1}, {1,0,1,0,1,0,0,1}, {0,1,1,0,1,0,0,1}, {1,1,1,0,1,0,0,1}, {0,0,0,1,1,0,0,1}, {1,0,0,1,1,0,0,1}, {0,1,0,1,1,0,0,1}, {1,1,0,1,1,0,0,1}, {0,0,1,1,1,0,0,1}, {1,0,1,1,1,0,0,1}, {0,1,1,1,1,0,0,1}, {1,1,1,1,1,0,0,1}, {0,0,0,0,0,1,0,1}, {1,0,0,0,0,1,0,1}, {0,1,0,0,0,1,0,1}, {1,1,0,0,0,1,0,1}, {0,0,1,0,0,1,0,1}, {1,0,1,0,0,1,0,1}, {0,1,1,0,0,1,0,1}, {1,1,1,0,0,1,0,1}, {0,0,0,1,0,1,0,1}, {1,0,0,1,0,1,0,1}, {0,1,0,1,0,1,0,1}, {1,1,0,1,0,1,0,1}, {0,0,1,1,0,1,0,1}, {1,0,1,1,0,1,0,1}, {0,1,1,1,0,1,0,1}, {1,1,1,1,0,1,0,1}, {0,0,0,0,1,1,0,1}, {1,0,0,0,1,1,0,1}, {0,1,0,0,1,1,0,1}, {1,1,0,0,1,1,0,1}, {0,0,1,0,1,1,0,1}, {1,0,1,0,1,1,0,1}, {0,1,1,0,1,1,0,1}, {1,1,1,0,1,1,0,1}, {0,0,0,1,1,1,0,1}, {1,0,0,1,1,1,0,1}, {0,1,0,1,1,1,0,1}, {1,1,0,1,1,1,0,1}, {0,0,1,1,1,1,0,1}, {1,0,1,1,1,1,0,1}, {0,1,1,1,1,1,0,1}, {1,1,1,1,1,1,0,1}, {0,0,0,0,0,0,1,1}, {1,0,0,0,0,0,1,1}, {0,1,0,0,0,0,1,1}, {1,1,0,0,0,0,1,1}, {0,0,1,0,0,0,1,1}, {1,0,1,0,0,0,1,1}, {0,1,1,0,0,0,1,1}, {1,1,1,0,0,0,1,1}, {0,0,0,1,0,0,1,1}, {1,0,0,1,0,0,1,1}, {0,1,0,1,0,0,1,1}, {1,1,0,1,0,0,1,1}, {0,0,1,1,0,0,1,1}, {1,0,1,1,0,0,1,1}, {0,1,1,1,0,0,1,1}, {1,1,1,1,0,0,1,1}, {0,0,0,0,1,0,1,1}, {1,0,0,0,1,0,1,1}, {0,1,0,0,1,0,1,1}, {1,1,0,0,1,0,1,1}, {0,0,1,0,1,0,1,1}, {1,0,1,0,1,0,1,1}, {0,1,1,0,1,0,1,1}, {1,1,1,0,1,0,1,1}, {0,0,0,1,1,0,1,1}, {1,0,0,1,1,0,1,1}, {0,1,0,1,1,0,1,1}, {1,1,0,1,1,0,1,1}, {0,0,1,1,1,0,1,1}, {1,0,1,1,1,0,1,1}, {0,1,1,1,1,0,1,1}, {1,1,1,1,1,0,1,1}, {0,0,0,0,0,1,1,1}, {1,0,0,0,0,1,1,1}, {0,1,0,0,0,1,1,1}, {1,1,0,0,0,1,1,1}, {0,0,1,0,0,1,1,1}, {1,0,1,0,0,1,1,1}, {0,1,1,0,0,1,1,1}, {1,1,1,0,0,1,1,1}, {0,0,0,1,0,1,1,1}, {1,0,0,1,0,1,1,1}, {0,1,0,1,0,1,1,1}, {1,1,0,1,0,1,1,1}, {0,0,1,1,0,1,1,1}, {1,0,1,1,0,1,1,1}, {0,1,1,1,0,1,1,1}, {1,1,1,1,0,1,1,1}, {0,0,0,0,1,1,1,1}, {1,0,0,0,1,1,1,1}, {0,1,0,0,1,1,1,1}, {1,1,0,0,1,1,1,1}, {0,0,1,0,1,1,1,1}, {1,0,1,0,1,1,1,1}, {0,1,1,0,1,1,1,1}, {1,1,1,0,1,1,1,1}, {0,0,0,1,1,1,1,1}, {1,0,0,1,1,1,1,1}, {0,1,0,1,1,1,1,1}, {1,1,0,1,1,1,1,1}, {0,0,1,1,1,1,1,1}, {1,0,1,1,1,1,1,1}, {0,1,1,1,1,1,1,1}, {1,1,1,1,1,1,1,1}} -- Return a number that is the result of interpreting the table tbl (msb first) local function tbl_to_number(tbl) local n = #tbl local rslt = 0 local power = 1 for i = 1, n do rslt = rslt + tbl[i]*power power = power*2 end return rslt end -- Calculate bitwise xor of bytes m and n. 0 <= m,n <= 256. local function bit_xor(m, n) local tbl_m = cclxvi[m] local tbl_n = cclxvi[n] local tbl = {} for i = 1, 8 do if(tbl_m[i] ~= tbl_n[i]) then tbl[i] = 1 else tbl[i] = 0 end end return tbl_to_number(tbl) end -- 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 = requested_ec_level or 1 local min,max = 1, 4 if requested_ec_level and requested_ec_level >= 1 and requested_ec_level <= 4 then min = requested_ec_level max = requested_ec_level end for ec_level=min,max do 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 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 local 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 -- The reversed strings from h t t p s://www.thonky.com/qr-code-tutorial/format-version-tables local version_information = {"001010010011111000", "001111011010000100", "100110010101100100", "110010110010010100", "011011111101110100", "010001101110001100", "111000100001101100", "101100000110011100", "000101001001111100", "000111101101000010", "101110100010100010", "111010000101010010", "010011001010110010", "011001011001001010", "110000010110101010", "100100110001011010", "001101111110111010", "001000110111000110", "100001111000100110", "110101011111010110", "011100010000110110", "010110000011001110", "111111001100101110", "101011101011011110", "000010100100111110", "101010111001000001", "000011110110100001", "010111010001010001", "111110011110110001", "110100001101001001", "011101000010101001", "001001100101011001", "100000101010111001", "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. local 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) local function qrcode( str, ec_level, mode ) local arranged_data, version, data_raw, mode, len_bitstring version, ec_level, data_raw, mode, len_bitstring = get_version_eclevel_mode_bistringlength(str,ec_level) 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 tab --return true,tab end --h t t p s : //github.com/kevin1018/luaqrcode_bmp/blob/master/bmp.lua local function format_data(array, width) local left_and_top_spacing = 0 local right_bottom_spacing = 0 local quotient = math.modf( width / #array ) local remainder = width % #array left_and_top_spacing = math.ceil(remainder / 2 - 0.5) right_bottom_spacing = remainder - left_and_top_spacing local result = {} for row = 1, width, 1 do local row_data = {} if (row <= left_and_top_spacing) or (row > width - right_bottom_spacing) then for col = 1, width, 1 do table.insert(row_data, 0) end else for col = 1, width, 1 do if (col <= left_and_top_spacing) or (col > width - right_bottom_spacing) then table.insert(row_data, 0) else table.insert(row_data, array[math.modf((row - left_and_top_spacing - 1) / quotient) + 1][math.modf((col - left_and_top_spacing - 1) / quotient) + 1]) end end end table.insert(result, row_data) end return result end local function header(array) local file_size = 62 + (math.modf((#array + 31) / 32)) * 4 * #array local result = "BM" .. string.pack("i4i2i2i4", file_size, 0, 0, 54 + 8) return result end local function dib(array) local data_size = math.modf(((#array + 31) / 32)) * 4 * #array local result = string.pack("i4i4i4i2i2i4i4i4i4i4i4", 40, #array, #array, 1, 1, 0, data_size, 0, 0, 2, 0) return result end local function color_map() return "\xff\xff\xff\xff\x00\x00\x00\x00" end local function data(array) local result = "" for col = #array, 1, -1 do local row_data = "" local index = 0 local current_data = 0 for row = 1, #array, 1 do if array[row][col] > 0 then --current_data = current_data | 1 << (31 - index) current_data = (current_data % 2 ^ (32 - index) >= 2 ^ (31-index)) and current_data or current_data + 2 ^ (31-index) end index = index + 1 if index == 32 then row_data = row_data .. string.pack(">I4", current_data) current_data = 0 index = 0 end end if index > 0 then row_data = row_data .. string.pack(">I4", current_data) end result = result .. row_data end return result end local function bmp(array, width) if not width then width = #array * 10 end array = format_data(array, width) return header(array) .. dib(array) .. color_map() .. data(array) end local p={} p.qrcode = function(frame) local str=frame.args[1] local ec_level=frame.args[2] local mode = frame.args[3] return qrcode(str, ec_level, mode ) end p.ddcode = function(frame) local str=frame.args[1] local ec_level=frame.args[2] local mode = frame.args[3] local data = qrcode(str, ec_level, mode ) local rows = "" for i, row in ipairs(data) do local cells = "" for j , cell in ipairs(row) do cells = cells..cell end rows = rows..cells..'\n' end return rows end p.getbmp = function(frame) return bmp(p.qrcode(frame)) end return p