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gitea/vendor/github.com/boombuler/barcode/utils/gfpoly.go

104 lines
2.8 KiB
Go

package utils
type GFPoly struct {
gf *GaloisField
Coefficients []int
}
func (gp *GFPoly) Degree() int {
return len(gp.Coefficients) - 1
}
func (gp *GFPoly) Zero() bool {
return gp.Coefficients[0] == 0
}
// GetCoefficient returns the coefficient of x ^ degree
func (gp *GFPoly) GetCoefficient(degree int) int {
return gp.Coefficients[gp.Degree()-degree]
}
func (gp *GFPoly) AddOrSubstract(other *GFPoly) *GFPoly {
if gp.Zero() {
return other
} else if other.Zero() {
return gp
}
smallCoeff := gp.Coefficients
largeCoeff := other.Coefficients
if len(smallCoeff) > len(largeCoeff) {
largeCoeff, smallCoeff = smallCoeff, largeCoeff
}
sumDiff := make([]int, len(largeCoeff))
lenDiff := len(largeCoeff) - len(smallCoeff)
copy(sumDiff, largeCoeff[:lenDiff])
for i := lenDiff; i < len(largeCoeff); i++ {
sumDiff[i] = int(gp.gf.AddOrSub(int(smallCoeff[i-lenDiff]), int(largeCoeff[i])))
}
return NewGFPoly(gp.gf, sumDiff)
}
func (gp *GFPoly) MultByMonominal(degree int, coeff int) *GFPoly {
if coeff == 0 {
return gp.gf.Zero()
}
size := len(gp.Coefficients)
result := make([]int, size+degree)
for i := 0; i < size; i++ {
result[i] = int(gp.gf.Multiply(int(gp.Coefficients[i]), int(coeff)))
}
return NewGFPoly(gp.gf, result)
}
func (gp *GFPoly) Multiply(other *GFPoly) *GFPoly {
if gp.Zero() || other.Zero() {
return gp.gf.Zero()
}
aCoeff := gp.Coefficients
aLen := len(aCoeff)
bCoeff := other.Coefficients
bLen := len(bCoeff)
product := make([]int, aLen+bLen-1)
for i := 0; i < aLen; i++ {
ac := int(aCoeff[i])
for j := 0; j < bLen; j++ {
bc := int(bCoeff[j])
product[i+j] = int(gp.gf.AddOrSub(int(product[i+j]), gp.gf.Multiply(ac, bc)))
}
}
return NewGFPoly(gp.gf, product)
}
func (gp *GFPoly) Divide(other *GFPoly) (quotient *GFPoly, remainder *GFPoly) {
quotient = gp.gf.Zero()
remainder = gp
fld := gp.gf
denomLeadTerm := other.GetCoefficient(other.Degree())
inversDenomLeadTerm := fld.Invers(int(denomLeadTerm))
for remainder.Degree() >= other.Degree() && !remainder.Zero() {
degreeDiff := remainder.Degree() - other.Degree()
scale := int(fld.Multiply(int(remainder.GetCoefficient(remainder.Degree())), inversDenomLeadTerm))
term := other.MultByMonominal(degreeDiff, scale)
itQuot := NewMonominalPoly(fld, degreeDiff, scale)
quotient = quotient.AddOrSubstract(itQuot)
remainder = remainder.AddOrSubstract(term)
}
return
}
func NewMonominalPoly(field *GaloisField, degree int, coeff int) *GFPoly {
if coeff == 0 {
return field.Zero()
}
result := make([]int, degree+1)
result[0] = coeff
return NewGFPoly(field, result)
}
func NewGFPoly(field *GaloisField, coefficients []int) *GFPoly {
for len(coefficients) > 1 && coefficients[0] == 0 {
coefficients = coefficients[1:]
}
return &GFPoly{field, coefficients}
}