gfpoly.go raw

   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  // GetCoefficient returns the coefficient of x ^ degree
  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