Implementing QR Code in Elixir

1. IMPLEMENTING QR CODE
SUBSPLASH TECH TALK 2017

2. IMPLEMENTING QR CODE
WHY QR CODE?
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3. IMPLEMENTING QR CODE
OVERVIEW
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"show me the money"
|
+---------------------+
| QR Code Encoder |
+---------------------+
|
v
|
+---------------------+
| QR Code Decoder |
+---------------------+
|
v
"show me the money"

4. IMPLEMENTING QR CODE
ENCODER
▸ Encode data
▸ Draw the QR code
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5. IMPLEMENTING QR CODE
QR CODE DATA STRUCTURE
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{{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0}}

6. IMPLEMENTING QR CODE
QR CODE STRUCTURE
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7. IMPLEMENTING QR CODE
STRUCTURE: FINDER PATTERNS
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8. IMPLEMENTING QR CODE
STRUCTURE: SEPARATORS
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9. IMPLEMENTING QR CODE
STRUCTURE: ALIGNMENT PATTERNS
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10. IMPLEMENTING QR CODE
STRUCTURE: ALIGNMENT PATTERNS
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Version 1 Version 2 Version 7

11. IMPLEMENTING QR CODE
STRUCTURE: ALIGNMENT PATTERNS
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12. IMPLEMENTING QR CODE
STRUCTURE: TIMING PATTERNS
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13. IMPLEMENTING QR CODE
STRUCTURE: TIMING PATTERNS
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Version 2 Version 7

14. IMPLEMENTING QR CODE
STRUCTURE: TIMING PATTERNS
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15. IMPLEMENTING QR CODE
STRUCTURE: DARK MODULE
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16. IMPLEMENTING QR CODE
STRUCTURE: RESERVED FORMAT AREAS
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STRUCTURE: RESERVED VERSION AREAS
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18. IMPLEMENTING QR CODE
STRUCTURE: RESERVED VERSION AREAS
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Version 2 Version 7

19. IMPLEMENTING QR CODE
STRUCTURE: RESERVED VERSION AREAS
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20. IMPLEMENTING QR CODE
STRUCTURE: DATA & ECC
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21. IMPLEMENTING QR CODE
STRUCTURE: QUITE ZONE
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22. IMPLEMENTING QR CODE
STRUCTURE: QUITE ZONE
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Version 1 Version 2 Version 7

23. IMPLEMENTING QR CODE
ENCODING MODE
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Numeric 12345, 9527
Alphanumeric "HELLO WORLD 123"
Kanji "⾃自動⾞車車"
Byte "Hello, world!", "你好, 世界!”

24. IMPLEMENTING QR CODE
BYTE MODE ENCODING
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s 115 0111 0011
h 104 0110 1000
o 111 0110 1111
w 119 0111 0111
032 0010 0000
m 109 0110 1101
e 101 0110 0101
032 0010 0000
t 116 0111 0100
h 104 0110 1000
e 101 0110 0101
032 0010 0000
m 109 0110 1101
o 111 0110 1111
n 110 0110 1110
e 101 0110 0101
y 121 0111 1001
Mode Indicator 0100
Count Indicator 0001 0001
Encoded data 0111 0011 ...
Terminator 0000
Padding byte 1110 1100
0001 0001

25. IMPLEMENTING QR CODE
BYTE MODE ENCODING
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0100 0001 0001 0111 0011 0110 1000 0110 1111 0111
0111 0010 0000 0110 1101 0110 0101 0010 0000 0111
0100 0110 1000 0110 0101 0010 0000 0110 1101 0110
1111 0110 1110 0110 0101 0111 1001 0000

26. IMPLEMENTING QR CODE
ERROR CORRECTION CODING
▸ Reed-Solomon
▸ Galois Field GF(256)
▸ Polynomial long division
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message polynomial
rs_ecc = ----------------------
generator polynomial

27. IMPLEMENTING QR CODE
REED-SOLOMON
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0100 0001 0001 0111 0011 0110 1000 0110 1111 0111
0111 0010 0000 0110 1101 0110 0101 0010 0000 0111
0100 0110 1000 0110 0101 0010 0000 0110 1101 0110
1111 0110 1110 0110 0101 0111 1001 0000
[65, 23, 54, 134, 247, 114, 6, 214, 82, 7, 70, 134, 82, 6, 214, 246, 230, 87, 144]
----------------------------------------------------------------
[0, 87, 229, 146, 149, 238, 102, 21]
[87, 3, 122, 77, 183, 109, 202]
||

28. IMPLEMENTING QR CODE
FINAL ENCODED DATA + ECC
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0100 0001 0001 0111 0011 0110 1000 0110 1111 0111
0111 0010 0000 0110 1101 0110 0101 0010 0000 0111
0100 0110 1000 0110 0101 0010 0000 0110 1101 0110
1111 0110 1110 0110 0101 0111 1001 0000 0101 0111
0000 0011 0111 1010 0100 1101 1011 0111 0110 1101
1100 1010

29. IMPLEMENTING QR CODE
MATRIX SO FAR
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30. IMPLEMENTING QR CODE
FILL IN THE DATA
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31. IMPLEMENTING QR CODE
DATA MASKING
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32. IMPLEMENTING QR CODE
MASK 0
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33. IMPLEMENTING QR CODE
MASK 1
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34. IMPLEMENTING QR CODE
MASK 2
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35. IMPLEMENTING QR CODE
MASK 3
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36. IMPLEMENTING QR CODE
MASK 4
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37. IMPLEMENTING QR CODE
MASK 5
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38. IMPLEMENTING QR CODE
MASK 6
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39. IMPLEMENTING QR CODE
MASK 7
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40. IMPLEMENTING QR CODE
APPLY MASKS
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41. IMPLEMENTING QR CODE
APPLY MASKS
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42. IMPLEMENTING QR CODE
PENALTY RULES
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43. IMPLEMENTING QR CODE
RULE 1
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every consecutive 5 blocks +3
every 1 block after that +1
score: 208

44. IMPLEMENTING QR CODE
RULE 2
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every m x n rectangle 3 * (m - 1) * (n - 1)
score: 120

45. IMPLEMENTING QR CODE
RULE 3
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score: 80
every 00001011101 40
every 10111010000 40

46. IMPLEMENTING QR CODE
RULE 4
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dark module percentage
every 5% away from 45-55% 10
score: 10

47. 277
IMPLEMENTING QR CODE
AND THE WINNER IS…
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418 321 378 277
337 379 344 318

48. IMPLEMENTING QR CODE
MASK 3
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49. IMPLEMENTING QR CODE
FORMAT INFORMATION
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ecc level L 01
mask pattern 011
result 01011
ecc 111100010011
format info 01011111100010011

50. IMPLEMENTING QR CODE
FORMAT INFORMATION
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ecc level L 01
mask pattern 011
result 01011
ecc 111100010011
format info 01011111100010011

51. IMPLEMENTING QR CODE
ALMOST DONE
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52. IMPLEMENTING QR CODE
FINISHED
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53. IMPLEMENTING QR CODE
IMPLEMENTATION NOTES
▸ Pattern matching
▸ Bitstring manipulation <<>>
▸ Recursion
▸ High order functions: Stream/Enum
▸ Meta programming
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total loc 670
loc w/o comments 420

54. IMPLEMENTING QR CODE
IMMUTABLE DATA
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def encode(binary) do
data = QRCode.Encode.encode(binary)
|> QRCode.ReedSolomon.encode()
QRCode.Encode.version(binary)
|> QRCode.Matrix.new()
|> QRCode.Matrix.draw_finder_patterns()
|> QRCode.Matrix.draw_seperators()
|> QRCode.Matrix.draw_alignment_patterns()
|> QRCode.Matrix.draw_timing_patterns()
|> QRCode.Matrix.draw_dark_module()
|> QRCode.Matrix.draw_reserved_format_areas()
|> QRCode.Matrix.draw_reserved_version_areas()
|> QRCode.Matrix.draw_data_with_mask(data)
|> QRCode.Matrix.draw_format_areas()
|> QRCode.Matrix.draw_version_areas()
|> QRCode.Matrix.draw_quite_zone()
end
‣ Encode data
‣ Draw the QR code

55. IMPLEMENTING QR CODE
FUN
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@finder_pattern [
1, 1, 1, 1, 1, 1, 1,
1, 0, 0, 0, 0, 0, 1,
1, 0, 1, 1, 1, 0, 1,
1, 0, 1, 1, 1, 0, 1,
1, 0, 1, 1, 1, 0, 1,
1, 0, 0, 0, 0, 0, 1,
1, 1, 1, 1, 1, 1, 1,
]

56. IMPLEMENTING QR CODE
BITSTRING MANIPULATION
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s 115 0111 0011
h 104 0110 1000
o 111 0110 1111
w 119 0111 0111
032 0010 0000
m 109 0110 1101
e 101 0110 0101
032 0010 0000
t 116 0111 0100
h 104 0110 1000
e 101 0110 0101
iex(1)> for <<b::1 <- "show me the money">>, do: b
[0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1,
1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, ...]

57. IMPLEMENTING QR CODE
META PROGRAMMING
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0 1
1 2
2 4
3 8
4 16
5 32
6 64
7 128
8 29
9 58
. .
. .
. .
255 1
defmodule GaloisField do
Stream.iterate(1, fn e ->
n = e <<< 1
if n >= 256, do: n ^^^ 0b100011101, else: n
end)
|> Stream.take(256)
|> Stream.with_index()
|> Enum.each(fn {e, i} ->
def to_i(unquote(i)), do: unquote(e)
def to_a(unquote(e)), do: unquote(i)
end)
end

58. IMPLEMENTING QR CODE
RULE 1 RECURSION
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defp do_rule1([h | t], {_, 0}, acc), do: do_rule1(t, {h, 1}, acc)
defp do_rule1([h | t], {h, 4}, acc), do: do_rule1(t, {h, 5}, acc + 3)
defp do_rule1([h | t], {h, 5}, acc), do: do_rule1(t, {h, 5}, acc + 1)
defp do_rule1([h | t], {h, n}, acc), do: do_rule1(t, {h, n + 1}, acc)
defp do_rule1([h | t], {_, _}, acc), do: do_rule1(t, {h, 1}, acc)
defp do_rule1([], _, acc), do: acc
[1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]
every consecutive 5 blocks +3
every 1 block after that +1

59. IMPLEMENTING QR CODE
RULE 2/3 PATTERN MATCHING
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defp do_rule2([1, 1, 1, 1], acc), do: acc + 3
defp do_rule2([0, 0, 0, 0], acc), do: acc + 3
defp do_rule2([_, _, _, _], acc), do: acc
defp do_rule3([1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]), do: 40
defp do_rule3([0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]), do: 40
defp do_rule3([_, _, _, _, _, _, _, _, _, _, _]), do: 0

60. IMPLEMENTING QR CODE
SOURCE CODE
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61. IMPLEMENTING QR CODE
USE CASE
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62. IMPLEMENTING QR CODE
ADDING LOGO
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63. IMPLEMENTING QR CODE
CUSTOMIZE QR CODE
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