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|
// 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
}
|
