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74 lines
2.3 KiB
Go
74 lines
2.3 KiB
Go
// go-qrcode
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// Copyright 2014 Tom Harwood
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// Package reedsolomon provides error correction encoding for QR Code 2005.
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//
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// QR Code 2005 uses a Reed-Solomon error correcting code to detect and correct
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// errors encountered during decoding.
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//
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// The generated RS codes are systematic, and consist of the input data with
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// error correction bytes appended.
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package reedsolomon
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import (
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"log"
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bitset "github.com/skip2/go-qrcode/bitset"
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)
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// Encode data for QR Code 2005 using the appropriate Reed-Solomon code.
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//
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// numECBytes is the number of error correction bytes to append, and is
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// determined by the target QR Code's version and error correction level.
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//
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// ISO/IEC 18004 table 9 specifies the numECBytes required. e.g. a 1-L code has
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// numECBytes=7.
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func Encode(data *bitset.Bitset, numECBytes int) *bitset.Bitset {
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// Create a polynomial representing |data|.
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//
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// The bytes are interpreted as the sequence of coefficients of a polynomial.
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// The last byte's value becomes the x^0 coefficient, the second to last
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// becomes the x^1 coefficient and so on.
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ecpoly := newGFPolyFromData(data)
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ecpoly = gfPolyMultiply(ecpoly, newGFPolyMonomial(gfOne, numECBytes))
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// Pick the generator polynomial.
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generator := rsGeneratorPoly(numECBytes)
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// Generate the error correction bytes.
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remainder := gfPolyRemainder(ecpoly, generator)
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// Combine the data & error correcting bytes.
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// The mathematically correct answer is:
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//
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// result := gfPolyAdd(ecpoly, remainder).
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//
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// The encoding used by QR Code 2005 is slightly different this result: To
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// preserve the original |data| bit sequence exactly, the data and remainder
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// are combined manually below. This ensures any most significant zero bits
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// are preserved (and not optimised away).
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result := bitset.Clone(data)
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result.AppendBytes(remainder.data(numECBytes))
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return result
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}
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// rsGeneratorPoly returns the Reed-Solomon generator polynomial with |degree|.
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//
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// The generator polynomial is calculated as:
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// (x + a^0)(x + a^1)...(x + a^degree-1)
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func rsGeneratorPoly(degree int) gfPoly {
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if degree < 2 {
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log.Panic("degree < 2")
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}
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generator := gfPoly{term: []gfElement{1}}
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for i := 0; i < degree; i++ {
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nextPoly := gfPoly{term: []gfElement{gfExpTable[i], 1}}
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generator = gfPolyMultiply(generator, nextPoly)
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}
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return generator
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}
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