1 package utils
2
3 type GFPoly struct {
4 gf *GaloisField
5 Coefficients []int
6 }
7
8 func (gp *GFPoly) Degree() int {
9 return len(gp.Coefficients) - 1
10 }
11
12 func (gp *GFPoly) Zero() bool {
13 return gp.Coefficients[0] == 0
14 }
15
16
17 func (gp *GFPoly) GetCoefficient(degree int) int {
18 return gp.Coefficients[gp.Degree()-degree]
19 }
20
21 func (gp *GFPoly) AddOrSubstract(other *GFPoly) *GFPoly {
22 if gp.Zero() {
23 return other
24 } else if other.Zero() {
25 return gp
26 }
27 smallCoeff := gp.Coefficients
28 largeCoeff := other.Coefficients
29 if len(smallCoeff) > len(largeCoeff) {
30 largeCoeff, smallCoeff = smallCoeff, largeCoeff
31 }
32 sumDiff := make([]int, len(largeCoeff))
33 lenDiff := len(largeCoeff) - len(smallCoeff)
34 copy(sumDiff, largeCoeff[:lenDiff])
35 for i := lenDiff; i < len(largeCoeff); i++ {
36 sumDiff[i] = int(gp.gf.AddOrSub(int(smallCoeff[i-lenDiff]), int(largeCoeff[i])))
37 }
38 return NewGFPoly(gp.gf, sumDiff)
39 }
40
41 func (gp *GFPoly) MultByMonominal(degree int, coeff int) *GFPoly {
42 if coeff == 0 {
43 return gp.gf.Zero()
44 }
45 size := len(gp.Coefficients)
46 result := make([]int, size+degree)
47 for i := 0; i < size; i++ {
48 result[i] = int(gp.gf.Multiply(int(gp.Coefficients[i]), int(coeff)))
49 }
50 return NewGFPoly(gp.gf, result)
51 }
52
53 func (gp *GFPoly) Multiply(other *GFPoly) *GFPoly {
54 if gp.Zero() || other.Zero() {
55 return gp.gf.Zero()
56 }
57 aCoeff := gp.Coefficients
58 aLen := len(aCoeff)
59 bCoeff := other.Coefficients
60 bLen := len(bCoeff)
61 product := make([]int, aLen+bLen-1)
62 for i := 0; i < aLen; i++ {
63 ac := int(aCoeff[i])
64 for j := 0; j < bLen; j++ {
65 bc := int(bCoeff[j])
66 product[i+j] = int(gp.gf.AddOrSub(int(product[i+j]), gp.gf.Multiply(ac, bc)))
67 }
68 }
69 return NewGFPoly(gp.gf, product)
70 }
71
72 func (gp *GFPoly) Divide(other *GFPoly) (quotient *GFPoly, remainder *GFPoly) {
73 quotient = gp.gf.Zero()
74 remainder = gp
75 fld := gp.gf
76 denomLeadTerm := other.GetCoefficient(other.Degree())
77 inversDenomLeadTerm := fld.Invers(int(denomLeadTerm))
78 for remainder.Degree() >= other.Degree() && !remainder.Zero() {
79 degreeDiff := remainder.Degree() - other.Degree()
80 scale := int(fld.Multiply(int(remainder.GetCoefficient(remainder.Degree())), inversDenomLeadTerm))
81 term := other.MultByMonominal(degreeDiff, scale)
82 itQuot := NewMonominalPoly(fld, degreeDiff, scale)
83 quotient = quotient.AddOrSubstract(itQuot)
84 remainder = remainder.AddOrSubstract(term)
85 }
86 return
87 }
88
89 func NewMonominalPoly(field *GaloisField, degree int, coeff int) *GFPoly {
90 if coeff == 0 {
91 return field.Zero()
92 }
93 result := make([]int, degree+1)
94 result[0] = coeff
95 return NewGFPoly(field, result)
96 }
97
98 func NewGFPoly(field *GaloisField, coefficients []int) *GFPoly {
99 for len(coefficients) > 1 && coefficients[0] == 0 {
100 coefficients = coefficients[1:]
101 }
102 return &GFPoly{field, coefficients}
103 }
104
View as plain text