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Tulir Asokan
387
vendor/github.com/skip2/go-qrcode/reedsolomon/gf2_8.go
generated
vendored
Normal file
387
vendor/github.com/skip2/go-qrcode/reedsolomon/gf2_8.go
generated
vendored
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@ -0,0 +1,387 @@
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// go-qrcode
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// Copyright 2014 Tom Harwood
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package reedsolomon
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// Addition, subtraction, multiplication, and division in GF(2^8).
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// Operations are performed modulo x^8 + x^4 + x^3 + x^2 + 1.
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// http://en.wikipedia.org/wiki/Finite_field_arithmetic
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import "log"
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const (
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gfZero = gfElement(0)
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gfOne = gfElement(1)
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)
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var (
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gfExpTable = [256]gfElement{
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/* 0 - 9 */ 1, 2, 4, 8, 16, 32, 64, 128, 29, 58,
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/* 10 - 19 */ 116, 232, 205, 135, 19, 38, 76, 152, 45, 90,
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/* 20 - 29 */ 180, 117, 234, 201, 143, 3, 6, 12, 24, 48,
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/* 30 - 39 */ 96, 192, 157, 39, 78, 156, 37, 74, 148, 53,
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/* 40 - 49 */ 106, 212, 181, 119, 238, 193, 159, 35, 70, 140,
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/* 50 - 59 */ 5, 10, 20, 40, 80, 160, 93, 186, 105, 210,
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/* 60 - 69 */ 185, 111, 222, 161, 95, 190, 97, 194, 153, 47,
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/* 70 - 79 */ 94, 188, 101, 202, 137, 15, 30, 60, 120, 240,
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/* 80 - 89 */ 253, 231, 211, 187, 107, 214, 177, 127, 254, 225,
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/* 90 - 99 */ 223, 163, 91, 182, 113, 226, 217, 175, 67, 134,
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/* 100 - 109 */ 17, 34, 68, 136, 13, 26, 52, 104, 208, 189,
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/* 110 - 119 */ 103, 206, 129, 31, 62, 124, 248, 237, 199, 147,
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/* 120 - 129 */ 59, 118, 236, 197, 151, 51, 102, 204, 133, 23,
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/* 130 - 139 */ 46, 92, 184, 109, 218, 169, 79, 158, 33, 66,
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/* 140 - 149 */ 132, 21, 42, 84, 168, 77, 154, 41, 82, 164,
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/* 150 - 159 */ 85, 170, 73, 146, 57, 114, 228, 213, 183, 115,
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/* 160 - 169 */ 230, 209, 191, 99, 198, 145, 63, 126, 252, 229,
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/* 170 - 179 */ 215, 179, 123, 246, 241, 255, 227, 219, 171, 75,
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/* 180 - 189 */ 150, 49, 98, 196, 149, 55, 110, 220, 165, 87,
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/* 190 - 199 */ 174, 65, 130, 25, 50, 100, 200, 141, 7, 14,
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/* 200 - 209 */ 28, 56, 112, 224, 221, 167, 83, 166, 81, 162,
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/* 210 - 219 */ 89, 178, 121, 242, 249, 239, 195, 155, 43, 86,
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/* 220 - 229 */ 172, 69, 138, 9, 18, 36, 72, 144, 61, 122,
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/* 230 - 239 */ 244, 245, 247, 243, 251, 235, 203, 139, 11, 22,
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/* 240 - 249 */ 44, 88, 176, 125, 250, 233, 207, 131, 27, 54,
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/* 250 - 255 */ 108, 216, 173, 71, 142, 1}
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gfLogTable = [256]int{
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/* 0 - 9 */ -1, 0, 1, 25, 2, 50, 26, 198, 3, 223,
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/* 10 - 19 */ 51, 238, 27, 104, 199, 75, 4, 100, 224, 14,
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/* 20 - 29 */ 52, 141, 239, 129, 28, 193, 105, 248, 200, 8,
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/* 30 - 39 */ 76, 113, 5, 138, 101, 47, 225, 36, 15, 33,
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/* 40 - 49 */ 53, 147, 142, 218, 240, 18, 130, 69, 29, 181,
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/* 50 - 59 */ 194, 125, 106, 39, 249, 185, 201, 154, 9, 120,
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/* 60 - 69 */ 77, 228, 114, 166, 6, 191, 139, 98, 102, 221,
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/* 70 - 79 */ 48, 253, 226, 152, 37, 179, 16, 145, 34, 136,
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/* 80 - 89 */ 54, 208, 148, 206, 143, 150, 219, 189, 241, 210,
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/* 90 - 99 */ 19, 92, 131, 56, 70, 64, 30, 66, 182, 163,
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/* 100 - 109 */ 195, 72, 126, 110, 107, 58, 40, 84, 250, 133,
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/* 110 - 119 */ 186, 61, 202, 94, 155, 159, 10, 21, 121, 43,
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/* 120 - 129 */ 78, 212, 229, 172, 115, 243, 167, 87, 7, 112,
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/* 130 - 139 */ 192, 247, 140, 128, 99, 13, 103, 74, 222, 237,
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/* 140 - 149 */ 49, 197, 254, 24, 227, 165, 153, 119, 38, 184,
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/* 150 - 159 */ 180, 124, 17, 68, 146, 217, 35, 32, 137, 46,
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/* 160 - 169 */ 55, 63, 209, 91, 149, 188, 207, 205, 144, 135,
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/* 170 - 179 */ 151, 178, 220, 252, 190, 97, 242, 86, 211, 171,
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/* 180 - 189 */ 20, 42, 93, 158, 132, 60, 57, 83, 71, 109,
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/* 190 - 199 */ 65, 162, 31, 45, 67, 216, 183, 123, 164, 118,
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/* 200 - 209 */ 196, 23, 73, 236, 127, 12, 111, 246, 108, 161,
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/* 210 - 219 */ 59, 82, 41, 157, 85, 170, 251, 96, 134, 177,
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/* 220 - 229 */ 187, 204, 62, 90, 203, 89, 95, 176, 156, 169,
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/* 230 - 239 */ 160, 81, 11, 245, 22, 235, 122, 117, 44, 215,
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/* 240 - 249 */ 79, 174, 213, 233, 230, 231, 173, 232, 116, 214,
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/* 250 - 255 */ 244, 234, 168, 80, 88, 175}
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)
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// gfElement is an element in GF(2^8).
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type gfElement uint8
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// newGFElement creates and returns a new gfElement.
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func newGFElement(data byte) gfElement {
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return gfElement(data)
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}
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// gfAdd returns a + b.
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func gfAdd(a, b gfElement) gfElement {
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return a ^ b
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}
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// gfSub returns a - b.
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//
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// Note addition is equivalent to subtraction in GF(2).
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func gfSub(a, b gfElement) gfElement {
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return a ^ b
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}
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// gfMultiply returns a * b.
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func gfMultiply(a, b gfElement) gfElement {
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if a == gfZero || b == gfZero {
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return gfZero
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}
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return gfExpTable[(gfLogTable[a]+gfLogTable[b])%255]
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}
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// gfDivide returns a / b.
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//
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// Divide by zero results in a panic.
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func gfDivide(a, b gfElement) gfElement {
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if a == gfZero {
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return gfZero
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} else if b == gfZero {
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log.Panicln("Divide by zero")
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}
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return gfMultiply(a, gfInverse(b))
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}
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// gfInverse returns the multiplicative inverse of a, a^-1.
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//
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// a * a^-1 = 1
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func gfInverse(a gfElement) gfElement {
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if a == gfZero {
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log.Panicln("No multiplicative inverse of 0")
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}
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return gfExpTable[255-gfLogTable[a]]
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}
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// a^i | bits | polynomial | decimal
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// --------------------------------------------------------------------------
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// 0 | 000000000 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 0
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// a^0 | 000000001 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 1
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// a^1 | 000000010 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 2
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// a^2 | 000000100 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 4
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// a^3 | 000001000 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 8
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// a^4 | 000010000 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 16
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// a^5 | 000100000 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 32
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// a^6 | 001000000 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 64
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// a^7 | 010000000 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 128
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// a^8 | 000011101 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 29
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// a^9 | 000111010 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 58
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// a^10 | 001110100 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 116
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// a^11 | 011101000 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 232
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// a^12 | 011001101 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 205
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// a^13 | 010000111 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 135
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// a^14 | 000010011 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 19
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// a^15 | 000100110 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 38
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// a^16 | 001001100 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 76
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// a^17 | 010011000 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 152
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// a^18 | 000101101 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 45
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// a^19 | 001011010 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 90
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// a^20 | 010110100 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 180
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// a^21 | 001110101 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 117
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// a^22 | 011101010 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 234
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// a^23 | 011001001 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 201
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// a^24 | 010001111 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 143
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// a^25 | 000000011 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 3
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// a^26 | 000000110 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 6
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// a^27 | 000001100 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 12
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// a^28 | 000011000 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 24
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// a^29 | 000110000 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 48
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// a^30 | 001100000 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 96
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// a^31 | 011000000 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 192
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// a^32 | 010011101 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 157
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// a^33 | 000100111 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 39
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// a^34 | 001001110 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 78
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// a^35 | 010011100 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 156
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// a^36 | 000100101 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 37
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// a^37 | 001001010 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 74
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// a^38 | 010010100 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 148
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// a^39 | 000110101 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 53
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// a^40 | 001101010 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 106
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// a^41 | 011010100 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 212
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// a^42 | 010110101 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 181
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// a^43 | 001110111 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 119
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// a^44 | 011101110 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 238
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// a^45 | 011000001 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 193
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// a^46 | 010011111 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 159
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// a^47 | 000100011 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 35
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// a^48 | 001000110 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 70
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// a^49 | 010001100 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 140
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// a^50 | 000000101 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 5
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// a^51 | 000001010 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 10
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// a^52 | 000010100 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 20
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// a^53 | 000101000 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 40
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// a^54 | 001010000 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 80
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// a^55 | 010100000 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 160
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// a^56 | 001011101 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 93
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// a^57 | 010111010 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 186
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// a^58 | 001101001 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 105
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// a^59 | 011010010 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 210
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// a^60 | 010111001 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 185
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// a^61 | 001101111 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 111
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// a^62 | 011011110 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 222
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// a^63 | 010100001 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 161
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// a^64 | 001011111 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 95
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// a^65 | 010111110 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 190
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// a^66 | 001100001 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 97
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// a^67 | 011000010 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 194
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// a^68 | 010011001 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 153
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// a^69 | 000101111 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 47
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// a^70 | 001011110 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 94
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// a^71 | 010111100 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 188
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// a^72 | 001100101 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 101
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// a^73 | 011001010 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 202
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// a^74 | 010001001 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 137
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// a^75 | 000001111 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 15
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// a^76 | 000011110 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 30
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// a^77 | 000111100 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 60
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// a^78 | 001111000 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 120
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// a^79 | 011110000 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 240
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// a^80 | 011111101 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 253
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// a^81 | 011100111 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 231
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// a^82 | 011010011 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 211
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// a^83 | 010111011 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 187
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// a^84 | 001101011 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 107
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// a^85 | 011010110 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 214
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// a^86 | 010110001 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 177
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// a^87 | 001111111 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 127
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// a^88 | 011111110 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 254
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// a^89 | 011100001 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 225
|
||||
// a^90 | 011011111 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 223
|
||||
// a^91 | 010100011 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 163
|
||||
// a^92 | 001011011 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 91
|
||||
// a^93 | 010110110 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 182
|
||||
// a^94 | 001110001 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 113
|
||||
// a^95 | 011100010 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 226
|
||||
// a^96 | 011011001 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 217
|
||||
// a^97 | 010101111 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 175
|
||||
// a^98 | 001000011 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 67
|
||||
// a^99 | 010000110 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 134
|
||||
// a^100 | 000010001 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 17
|
||||
// a^101 | 000100010 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 34
|
||||
// a^102 | 001000100 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 68
|
||||
// a^103 | 010001000 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 136
|
||||
// a^104 | 000001101 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 13
|
||||
// a^105 | 000011010 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 26
|
||||
// a^106 | 000110100 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 52
|
||||
// a^107 | 001101000 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 104
|
||||
// a^108 | 011010000 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 208
|
||||
// a^109 | 010111101 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 189
|
||||
// a^110 | 001100111 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 103
|
||||
// a^111 | 011001110 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 206
|
||||
// a^112 | 010000001 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 129
|
||||
// a^113 | 000011111 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 31
|
||||
// a^114 | 000111110 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 62
|
||||
// a^115 | 001111100 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 124
|
||||
// a^116 | 011111000 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 248
|
||||
// a^117 | 011101101 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 237
|
||||
// a^118 | 011000111 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 199
|
||||
// a^119 | 010010011 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 147
|
||||
// a^120 | 000111011 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 59
|
||||
// a^121 | 001110110 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 118
|
||||
// a^122 | 011101100 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 236
|
||||
// a^123 | 011000101 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 197
|
||||
// a^124 | 010010111 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 151
|
||||
// a^125 | 000110011 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 51
|
||||
// a^126 | 001100110 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 102
|
||||
// a^127 | 011001100 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 204
|
||||
// a^128 | 010000101 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 133
|
||||
// a^129 | 000010111 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 23
|
||||
// a^130 | 000101110 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 46
|
||||
// a^131 | 001011100 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 92
|
||||
// a^132 | 010111000 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 184
|
||||
// a^133 | 001101101 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 109
|
||||
// a^134 | 011011010 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 218
|
||||
// a^135 | 010101001 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 169
|
||||
// a^136 | 001001111 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 79
|
||||
// a^137 | 010011110 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 158
|
||||
// a^138 | 000100001 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 33
|
||||
// a^139 | 001000010 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 66
|
||||
// a^140 | 010000100 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 132
|
||||
// a^141 | 000010101 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 21
|
||||
// a^142 | 000101010 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 42
|
||||
// a^143 | 001010100 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 84
|
||||
// a^144 | 010101000 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 168
|
||||
// a^145 | 001001101 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 77
|
||||
// a^146 | 010011010 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 154
|
||||
// a^147 | 000101001 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 41
|
||||
// a^148 | 001010010 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 82
|
||||
// a^149 | 010100100 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 164
|
||||
// a^150 | 001010101 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 85
|
||||
// a^151 | 010101010 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 170
|
||||
// a^152 | 001001001 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 73
|
||||
// a^153 | 010010010 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 146
|
||||
// a^154 | 000111001 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 57
|
||||
// a^155 | 001110010 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 114
|
||||
// a^156 | 011100100 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 228
|
||||
// a^157 | 011010101 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 213
|
||||
// a^158 | 010110111 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 183
|
||||
// a^159 | 001110011 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 115
|
||||
// a^160 | 011100110 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 230
|
||||
// a^161 | 011010001 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 209
|
||||
// a^162 | 010111111 | 0x^8 1x^7 0x^6 1x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 191
|
||||
// a^163 | 001100011 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 99
|
||||
// a^164 | 011000110 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 198
|
||||
// a^165 | 010010001 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 145
|
||||
// a^166 | 000111111 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 63
|
||||
// a^167 | 001111110 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 1x^2 1x^1 0x^0 | 126
|
||||
// a^168 | 011111100 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 252
|
||||
// a^169 | 011100101 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 229
|
||||
// a^170 | 011010111 | 0x^8 1x^7 1x^6 0x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 215
|
||||
// a^171 | 010110011 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 179
|
||||
// a^172 | 001111011 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 123
|
||||
// a^173 | 011110110 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 246
|
||||
// a^174 | 011110001 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 241
|
||||
// a^175 | 011111111 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 1x^2 1x^1 1x^0 | 255
|
||||
// a^176 | 011100011 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 227
|
||||
// a^177 | 011011011 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 219
|
||||
// a^178 | 010101011 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 171
|
||||
// a^179 | 001001011 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 75
|
||||
// a^180 | 010010110 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 150
|
||||
// a^181 | 000110001 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 49
|
||||
// a^182 | 001100010 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 98
|
||||
// a^183 | 011000100 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 196
|
||||
// a^184 | 010010101 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 149
|
||||
// a^185 | 000110111 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 55
|
||||
// a^186 | 001101110 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 110
|
||||
// a^187 | 011011100 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 220
|
||||
// a^188 | 010100101 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 165
|
||||
// a^189 | 001010111 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 87
|
||||
// a^190 | 010101110 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 174
|
||||
// a^191 | 001000001 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 65
|
||||
// a^192 | 010000010 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 130
|
||||
// a^193 | 000011001 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 25
|
||||
// a^194 | 000110010 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 50
|
||||
// a^195 | 001100100 | 0x^8 0x^7 1x^6 1x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 100
|
||||
// a^196 | 011001000 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 200
|
||||
// a^197 | 010001101 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 141
|
||||
// a^198 | 000000111 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 7
|
||||
// a^199 | 000001110 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 14
|
||||
// a^200 | 000011100 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 1x^2 0x^1 0x^0 | 28
|
||||
// a^201 | 000111000 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 56
|
||||
// a^202 | 001110000 | 0x^8 0x^7 1x^6 1x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 112
|
||||
// a^203 | 011100000 | 0x^8 1x^7 1x^6 1x^5 0x^4 0x^3 0x^2 0x^1 0x^0 | 224
|
||||
// a^204 | 011011101 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 221
|
||||
// a^205 | 010100111 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 167
|
||||
// a^206 | 001010011 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 83
|
||||
// a^207 | 010100110 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 1x^2 1x^1 0x^0 | 166
|
||||
// a^208 | 001010001 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 0x^2 0x^1 1x^0 | 81
|
||||
// a^209 | 010100010 | 0x^8 1x^7 0x^6 1x^5 0x^4 0x^3 0x^2 1x^1 0x^0 | 162
|
||||
// a^210 | 001011001 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 89
|
||||
// a^211 | 010110010 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 178
|
||||
// a^212 | 001111001 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 121
|
||||
// a^213 | 011110010 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 242
|
||||
// a^214 | 011111001 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 0x^2 0x^1 1x^0 | 249
|
||||
// a^215 | 011101111 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 239
|
||||
// a^216 | 011000011 | 0x^8 1x^7 1x^6 0x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 195
|
||||
// a^217 | 010011011 | 0x^8 1x^7 0x^6 0x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 155
|
||||
// a^218 | 000101011 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 43
|
||||
// a^219 | 001010110 | 0x^8 0x^7 1x^6 0x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 86
|
||||
// a^220 | 010101100 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 172
|
||||
// a^221 | 001000101 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 1x^2 0x^1 1x^0 | 69
|
||||
// a^222 | 010001010 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 0x^2 1x^1 0x^0 | 138
|
||||
// a^223 | 000001001 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 9
|
||||
// a^224 | 000010010 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 0x^2 1x^1 0x^0 | 18
|
||||
// a^225 | 000100100 | 0x^8 0x^7 0x^6 1x^5 0x^4 0x^3 1x^2 0x^1 0x^0 | 36
|
||||
// a^226 | 001001000 | 0x^8 0x^7 1x^6 0x^5 0x^4 1x^3 0x^2 0x^1 0x^0 | 72
|
||||
// a^227 | 010010000 | 0x^8 1x^7 0x^6 0x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 144
|
||||
// a^228 | 000111101 | 0x^8 0x^7 0x^6 1x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 61
|
||||
// a^229 | 001111010 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 122
|
||||
// a^230 | 011110100 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 1x^2 0x^1 0x^0 | 244
|
||||
// a^231 | 011110101 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 1x^2 0x^1 1x^0 | 245
|
||||
// a^232 | 011110111 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 1x^2 1x^1 1x^0 | 247
|
||||
// a^233 | 011110011 | 0x^8 1x^7 1x^6 1x^5 1x^4 0x^3 0x^2 1x^1 1x^0 | 243
|
||||
// a^234 | 011111011 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 251
|
||||
// a^235 | 011101011 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 235
|
||||
// a^236 | 011001011 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 203
|
||||
// a^237 | 010001011 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 139
|
||||
// a^238 | 000001011 | 0x^8 0x^7 0x^6 0x^5 0x^4 1x^3 0x^2 1x^1 1x^0 | 11
|
||||
// a^239 | 000010110 | 0x^8 0x^7 0x^6 0x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 22
|
||||
// a^240 | 000101100 | 0x^8 0x^7 0x^6 1x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 44
|
||||
// a^241 | 001011000 | 0x^8 0x^7 1x^6 0x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 88
|
||||
// a^242 | 010110000 | 0x^8 1x^7 0x^6 1x^5 1x^4 0x^3 0x^2 0x^1 0x^0 | 176
|
||||
// a^243 | 001111101 | 0x^8 0x^7 1x^6 1x^5 1x^4 1x^3 1x^2 0x^1 1x^0 | 125
|
||||
// a^244 | 011111010 | 0x^8 1x^7 1x^6 1x^5 1x^4 1x^3 0x^2 1x^1 0x^0 | 250
|
||||
// a^245 | 011101001 | 0x^8 1x^7 1x^6 1x^5 0x^4 1x^3 0x^2 0x^1 1x^0 | 233
|
||||
// a^246 | 011001111 | 0x^8 1x^7 1x^6 0x^5 0x^4 1x^3 1x^2 1x^1 1x^0 | 207
|
||||
// a^247 | 010000011 | 0x^8 1x^7 0x^6 0x^5 0x^4 0x^3 0x^2 1x^1 1x^0 | 131
|
||||
// a^248 | 000011011 | 0x^8 0x^7 0x^6 0x^5 1x^4 1x^3 0x^2 1x^1 1x^0 | 27
|
||||
// a^249 | 000110110 | 0x^8 0x^7 0x^6 1x^5 1x^4 0x^3 1x^2 1x^1 0x^0 | 54
|
||||
// a^250 | 001101100 | 0x^8 0x^7 1x^6 1x^5 0x^4 1x^3 1x^2 0x^1 0x^0 | 108
|
||||
// a^251 | 011011000 | 0x^8 1x^7 1x^6 0x^5 1x^4 1x^3 0x^2 0x^1 0x^0 | 216
|
||||
// a^252 | 010101101 | 0x^8 1x^7 0x^6 1x^5 0x^4 1x^3 1x^2 0x^1 1x^0 | 173
|
||||
// a^253 | 001000111 | 0x^8 0x^7 1x^6 0x^5 0x^4 0x^3 1x^2 1x^1 1x^0 | 71
|
||||
// a^254 | 010001110 | 0x^8 1x^7 0x^6 0x^5 0x^4 1x^3 1x^2 1x^1 0x^0 | 142
|
||||
// a^255 | 000000001 | 0x^8 0x^7 0x^6 0x^5 0x^4 0x^3 0x^2 0x^1 1x^0 | 1
|
||||
216
vendor/github.com/skip2/go-qrcode/reedsolomon/gf_poly.go
generated
vendored
Normal file
216
vendor/github.com/skip2/go-qrcode/reedsolomon/gf_poly.go
generated
vendored
Normal file
@ -0,0 +1,216 @@
|
||||
// go-qrcode
|
||||
// Copyright 2014 Tom Harwood
|
||||
|
||||
package reedsolomon
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"log"
|
||||
|
||||
bitset "github.com/skip2/go-qrcode/bitset"
|
||||
)
|
||||
|
||||
// gfPoly is a polynomial over GF(2^8).
|
||||
type gfPoly struct {
|
||||
// The ith value is the coefficient of the ith degree of x.
|
||||
// term[0]*(x^0) + term[1]*(x^1) + term[2]*(x^2) ...
|
||||
term []gfElement
|
||||
}
|
||||
|
||||
// newGFPolyFromData returns |data| as a polynomial over GF(2^8).
|
||||
//
|
||||
// Each data byte becomes the coefficient of an x term.
|
||||
//
|
||||
// For an n byte input the polynomial is:
|
||||
// data[n-1]*(x^n-1) + data[n-2]*(x^n-2) ... + data[0]*(x^0).
|
||||
func newGFPolyFromData(data *bitset.Bitset) gfPoly {
|
||||
numTotalBytes := data.Len() / 8
|
||||
if data.Len()%8 != 0 {
|
||||
numTotalBytes++
|
||||
}
|
||||
|
||||
result := gfPoly{term: make([]gfElement, numTotalBytes)}
|
||||
|
||||
i := numTotalBytes - 1
|
||||
for j := 0; j < data.Len(); j += 8 {
|
||||
result.term[i] = gfElement(data.ByteAt(j))
|
||||
i--
|
||||
}
|
||||
|
||||
return result
|
||||
}
|
||||
|
||||
// newGFPolyMonomial returns term*(x^degree).
|
||||
func newGFPolyMonomial(term gfElement, degree int) gfPoly {
|
||||
if term == gfZero {
|
||||
return gfPoly{}
|
||||
}
|
||||
|
||||
result := gfPoly{term: make([]gfElement, degree+1)}
|
||||
result.term[degree] = term
|
||||
|
||||
return result
|
||||
}
|
||||
|
||||
func (e gfPoly) data(numTerms int) []byte {
|
||||
result := make([]byte, numTerms)
|
||||
|
||||
i := numTerms - len(e.term)
|
||||
for j := len(e.term) - 1; j >= 0; j-- {
|
||||
result[i] = byte(e.term[j])
|
||||
i++
|
||||
}
|
||||
|
||||
return result
|
||||
}
|
||||
|
||||
// numTerms returns the number of
|
||||
func (e gfPoly) numTerms() int {
|
||||
return len(e.term)
|
||||
}
|
||||
|
||||
// gfPolyMultiply returns a * b.
|
||||
func gfPolyMultiply(a, b gfPoly) gfPoly {
|
||||
numATerms := a.numTerms()
|
||||
numBTerms := b.numTerms()
|
||||
|
||||
result := gfPoly{term: make([]gfElement, numATerms+numBTerms)}
|
||||
|
||||
for i := 0; i < numATerms; i++ {
|
||||
for j := 0; j < numBTerms; j++ {
|
||||
if a.term[i] != 0 && b.term[j] != 0 {
|
||||
monomial := gfPoly{term: make([]gfElement, i+j+1)}
|
||||
monomial.term[i+j] = gfMultiply(a.term[i], b.term[j])
|
||||
|
||||
result = gfPolyAdd(result, monomial)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return result.normalised()
|
||||
}
|
||||
|
||||
// gfPolyRemainder return the remainder of numerator / denominator.
|
||||
func gfPolyRemainder(numerator, denominator gfPoly) gfPoly {
|
||||
if denominator.equals(gfPoly{}) {
|
||||
log.Panicln("Remainder by zero")
|
||||
}
|
||||
|
||||
remainder := numerator
|
||||
|
||||
for remainder.numTerms() >= denominator.numTerms() {
|
||||
degree := remainder.numTerms() - denominator.numTerms()
|
||||
coefficient := gfDivide(remainder.term[remainder.numTerms()-1],
|
||||
denominator.term[denominator.numTerms()-1])
|
||||
|
||||
divisor := gfPolyMultiply(denominator,
|
||||
newGFPolyMonomial(coefficient, degree))
|
||||
|
||||
remainder = gfPolyAdd(remainder, divisor)
|
||||
}
|
||||
|
||||
return remainder.normalised()
|
||||
}
|
||||
|
||||
// gfPolyAdd returns a + b.
|
||||
func gfPolyAdd(a, b gfPoly) gfPoly {
|
||||
numATerms := a.numTerms()
|
||||
numBTerms := b.numTerms()
|
||||
|
||||
numTerms := numATerms
|
||||
if numBTerms > numTerms {
|
||||
numTerms = numBTerms
|
||||
}
|
||||
|
||||
result := gfPoly{term: make([]gfElement, numTerms)}
|
||||
|
||||
for i := 0; i < numTerms; i++ {
|
||||
switch {
|
||||
case numATerms > i && numBTerms > i:
|
||||
result.term[i] = gfAdd(a.term[i], b.term[i])
|
||||
case numATerms > i:
|
||||
result.term[i] = a.term[i]
|
||||
default:
|
||||
result.term[i] = b.term[i]
|
||||
}
|
||||
}
|
||||
|
||||
return result.normalised()
|
||||
}
|
||||
|
||||
func (e gfPoly) normalised() gfPoly {
|
||||
numTerms := e.numTerms()
|
||||
maxNonzeroTerm := numTerms - 1
|
||||
|
||||
for i := numTerms - 1; i >= 0; i-- {
|
||||
if e.term[i] != 0 {
|
||||
break
|
||||
}
|
||||
|
||||
maxNonzeroTerm = i - 1
|
||||
}
|
||||
|
||||
if maxNonzeroTerm < 0 {
|
||||
return gfPoly{}
|
||||
} else if maxNonzeroTerm < numTerms-1 {
|
||||
e.term = e.term[0 : maxNonzeroTerm+1]
|
||||
}
|
||||
|
||||
return e
|
||||
}
|
||||
|
||||
func (e gfPoly) string(useIndexForm bool) string {
|
||||
var str string
|
||||
numTerms := e.numTerms()
|
||||
|
||||
for i := numTerms - 1; i >= 0; i-- {
|
||||
if e.term[i] > 0 {
|
||||
if len(str) > 0 {
|
||||
str += " + "
|
||||
}
|
||||
|
||||
if !useIndexForm {
|
||||
str += fmt.Sprintf("%dx^%d", e.term[i], i)
|
||||
} else {
|
||||
str += fmt.Sprintf("a^%dx^%d", gfLogTable[e.term[i]], i)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if len(str) == 0 {
|
||||
str = "0"
|
||||
}
|
||||
|
||||
return str
|
||||
}
|
||||
|
||||
// equals returns true if e == other.
|
||||
func (e gfPoly) equals(other gfPoly) bool {
|
||||
var minecPoly *gfPoly
|
||||
var maxecPoly *gfPoly
|
||||
|
||||
if e.numTerms() > other.numTerms() {
|
||||
minecPoly = &other
|
||||
maxecPoly = &e
|
||||
} else {
|
||||
minecPoly = &e
|
||||
maxecPoly = &other
|
||||
}
|
||||
|
||||
numMinTerms := minecPoly.numTerms()
|
||||
numMaxTerms := maxecPoly.numTerms()
|
||||
|
||||
for i := 0; i < numMinTerms; i++ {
|
||||
if e.term[i] != other.term[i] {
|
||||
return false
|
||||
}
|
||||
}
|
||||
|
||||
for i := numMinTerms; i < numMaxTerms; i++ {
|
||||
if maxecPoly.term[i] != 0 {
|
||||
return false
|
||||
}
|
||||
}
|
||||
|
||||
return true
|
||||
}
|
||||
73
vendor/github.com/skip2/go-qrcode/reedsolomon/reed_solomon.go
generated
vendored
Normal file
73
vendor/github.com/skip2/go-qrcode/reedsolomon/reed_solomon.go
generated
vendored
Normal file
@ -0,0 +1,73 @@
|
||||
// go-qrcode
|
||||
// Copyright 2014 Tom Harwood
|
||||
|
||||
// Package reedsolomon provides error correction encoding for QR Code 2005.
|
||||
//
|
||||
// QR Code 2005 uses a Reed-Solomon error correcting code to detect and correct
|
||||
// errors encountered during decoding.
|
||||
//
|
||||
// The generated RS codes are systematic, and consist of the input data with
|
||||
// error correction bytes appended.
|
||||
package reedsolomon
|
||||
|
||||
import (
|
||||
"log"
|
||||
|
||||
bitset "github.com/skip2/go-qrcode/bitset"
|
||||
)
|
||||
|
||||
// Encode data for QR Code 2005 using the appropriate Reed-Solomon code.
|
||||
//
|
||||
// numECBytes is the number of error correction bytes to append, and is
|
||||
// determined by the target QR Code's version and error correction level.
|
||||
//
|
||||
// ISO/IEC 18004 table 9 specifies the numECBytes required. e.g. a 1-L code has
|
||||
// numECBytes=7.
|
||||
func Encode(data *bitset.Bitset, numECBytes int) *bitset.Bitset {
|
||||
// Create a polynomial representing |data|.
|
||||
//
|
||||
// The bytes are interpreted as the sequence of coefficients of a polynomial.
|
||||
// The last byte's value becomes the x^0 coefficient, the second to last
|
||||
// becomes the x^1 coefficient and so on.
|
||||
ecpoly := newGFPolyFromData(data)
|
||||
ecpoly = gfPolyMultiply(ecpoly, newGFPolyMonomial(gfOne, numECBytes))
|
||||
|
||||
// Pick the generator polynomial.
|
||||
generator := rsGeneratorPoly(numECBytes)
|
||||
|
||||
// Generate the error correction bytes.
|
||||
remainder := gfPolyRemainder(ecpoly, generator)
|
||||
|
||||
// Combine the data & error correcting bytes.
|
||||
// The mathematically correct answer is:
|
||||
//
|
||||
// result := gfPolyAdd(ecpoly, remainder).
|
||||
//
|
||||
// The encoding used by QR Code 2005 is slightly different this result: To
|
||||
// preserve the original |data| bit sequence exactly, the data and remainder
|
||||
// are combined manually below. This ensures any most significant zero bits
|
||||
// are preserved (and not optimised away).
|
||||
result := bitset.Clone(data)
|
||||
result.AppendBytes(remainder.data(numECBytes))
|
||||
|
||||
return result
|
||||
}
|
||||
|
||||
// rsGeneratorPoly returns the Reed-Solomon generator polynomial with |degree|.
|
||||
//
|
||||
// The generator polynomial is calculated as:
|
||||
// (x + a^0)(x + a^1)...(x + a^degree-1)
|
||||
func rsGeneratorPoly(degree int) gfPoly {
|
||||
if degree < 2 {
|
||||
log.Panic("degree < 2")
|
||||
}
|
||||
|
||||
generator := gfPoly{term: []gfElement{1}}
|
||||
|
||||
for i := 0; i < degree; i++ {
|
||||
nextPoly := gfPoly{term: []gfElement{gfExpTable[i], 1}}
|
||||
generator = gfPolyMultiply(generator, nextPoly)
|
||||
}
|
||||
|
||||
return generator
|
||||
}
|
||||
Reference in New Issue
Block a user