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