git.sr.ht/~pingoo/stdx@v0.0.0-20240218134121-094174641f6e/barcode/utils/gfpoly.go (about)

     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  }