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lib/qr_code/galois_field.ex
defmodule QRCode.GaloisField do
@moduledoc """
Galios Field GF(256) functions.
"""
@type value() :: 1..255
@type alpha() :: 0..254
# {index, aplha}
@gf_table [
{1, 0},
{2, 1},
{3, 25},
{4, 2},
{5, 50},
{6, 26},
{7, 198},
{8, 3},
{9, 223},
{10, 51},
{11, 238},
{12, 27},
{13, 104},
{14, 199},
{15, 75},
{16, 4},
{17, 100},
{18, 224},
{19, 14},
{20, 52},
{21, 141},
{22, 239},
{23, 129},
{24, 28},
{25, 193},
{26, 105},
{27, 248},
{28, 200},
{29, 8},
{30, 76},
{31, 113},
{32, 5},
{33, 138},
{34, 101},
{35, 47},
{36, 225},
{37, 36},
{38, 15},
{39, 33},
{40, 53},
{41, 147},
{42, 142},
{43, 218},
{44, 240},
{45, 18},
{46, 130},
{47, 69},
{48, 29},
{49, 181},
{50, 194},
{51, 125},
{52, 106},
{53, 39},
{54, 249},
{55, 185},
{56, 201},
{57, 154},
{58, 9},
{59, 120},
{60, 77},
{61, 228},
{62, 114},
{63, 166},
{64, 6},
{65, 191},
{66, 139},
{67, 98},
{68, 102},
{69, 221},
{70, 48},
{71, 253},
{72, 226},
{73, 152},
{74, 37},
{75, 179},
{76, 16},
{77, 145},
{78, 34},
{79, 136},
{80, 54},
{81, 208},
{82, 148},
{83, 206},
{84, 143},
{85, 150},
{86, 219},
{87, 189},
{88, 241},
{89, 210},
{90, 19},
{91, 92},
{92, 131},
{93, 56},
{94, 70},
{95, 64},
{96, 30},
{97, 66},
{98, 182},
{99, 163},
{100, 195},
{101, 72},
{102, 126},
{103, 110},
{104, 107},
{105, 58},
{106, 40},
{107, 84},
{108, 250},
{109, 133},
{110, 186},
{111, 61},
{112, 202},
{113, 94},
{114, 155},
{115, 159},
{116, 10},
{117, 21},
{118, 121},
{119, 43},
{120, 78},
{121, 212},
{122, 229},
{123, 172},
{124, 115},
{125, 243},
{126, 167},
{127, 87},
{128, 7},
{129, 112},
{130, 192},
{131, 247},
{132, 140},
{133, 128},
{134, 99},
{135, 13},
{136, 103},
{137, 74},
{138, 222},
{139, 237},
{140, 49},
{141, 197},
{142, 254},
{143, 24},
{144, 227},
{145, 165},
{146, 153},
{147, 119},
{148, 38},
{149, 184},
{150, 180},
{151, 124},
{152, 17},
{153, 68},
{154, 146},
{155, 217},
{156, 35},
{157, 32},
{158, 137},
{159, 46},
{160, 55},
{161, 63},
{162, 209},
{163, 91},
{164, 149},
{165, 188},
{166, 207},
{167, 205},
{168, 144},
{169, 135},
{170, 151},
{171, 178},
{172, 220},
{173, 252},
{174, 190},
{175, 97},
{176, 242},
{177, 86},
{178, 211},
{179, 171},
{180, 20},
{181, 42},
{182, 93},
{183, 158},
{184, 132},
{185, 60},
{186, 57},
{187, 83},
{188, 71},
{189, 109},
{190, 65},
{191, 162},
{192, 31},
{193, 45},
{194, 67},
{195, 216},
{196, 183},
{197, 123},
{198, 164},
{199, 118},
{200, 196},
{201, 23},
{202, 73},
{203, 236},
{204, 127},
{205, 12},
{206, 111},
{207, 246},
{208, 108},
{209, 161},
{210, 59},
{211, 82},
{212, 41},
{213, 157},
{214, 85},
{215, 170},
{216, 251},
{217, 96},
{218, 134},
{219, 177},
{220, 187},
{221, 204},
{222, 62},
{223, 90},
{224, 203},
{225, 89},
{226, 95},
{227, 176},
{228, 156},
{229, 169},
{230, 160},
{231, 81},
{232, 11},
{233, 245},
{234, 22},
{235, 235},
{236, 122},
{237, 117},
{238, 44},
{239, 215},
{240, 79},
{241, 174},
{242, 213},
{243, 233},
{244, 230},
{245, 231},
{246, 173},
{247, 232},
{248, 116},
{249, 214},
{250, 244},
{251, 234},
{252, 168},
{253, 80},
{254, 88},
{255, 175}
]
@doc """
Given alpha exponent returns integer.
Example:
iex> QRCode.GaloisField.to_i(1)
2
"""
@spec to_i(alpha()) :: value()
def to_i(alpha) when alpha in 0..254 do
@gf_table
|> Enum.find(fn {_i, a} -> alpha == a end)
|> first()
end
@doc """
Given integer returns alpha exponent.
Example:
iex> QRCode.GaloisField.to_a(2)
1
"""
@spec to_a(value()) :: alpha()
def to_a(integer) when integer in 1..255 do
@gf_table
|> Enum.find(fn {i, _a} -> integer == i end)
|> second()
end
@doc """
Add two alpha values in GF(256).
## Example
iex> QRCode.GaloisField.add(10, 251)
6
iex> QRCode.GaloisField.add(10, 13)
23
"""
@spec add(alpha(), alpha()) :: alpha()
def add(a1, a2) do
rem(a1 + a2, 255)
end
defp first({val, _}) do
val
end
defp second({_, val}) do
val
end
end