104 lines
2.8 KiB
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}
|
||
|
|
}
|