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GF(2^n) arithmetics in bitvector

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Jiri Pittner
2023-12-31 19:48:07 +01:00
parent f0325ba6f5
commit 1e00570f66
3 changed files with 80 additions and 9 deletions
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10
bitvector.h
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@@ -83,13 +83,17 @@ public:
bitvector operator^(const bitvector &rhs) const {return bitvector(*this) ^= rhs;};
bitvector operator+(const bitvector &rhs) const {return *this ^ rhs;}; //addition modulo 2
bitvector operator-(const bitvector &rhs) const {return *this ^ rhs;}; //subtraction modulo 2
bitvector operator*(const bitvector &rhs) const; //multiplication of polynomials over GF(2) NOTE: naive algorithm, does not employ CLMUL nor fft-like approach, only for short vectors!!!
bitvector multiply(const bitvector &rhs, bool autoresize=true) const; //use autoresize=false only if you know it will not overflow!
bitvector operator*(const bitvector &rhs) const {return multiply(rhs,true);} //multiplication of polynomials over GF(2) NOTE: naive algorithm, does not employ CLMUL nor fft-like approach, only for short vectors!!!
bitvector field_mult(const bitvector &rhs, const bitvector &irpolynom) const; //multiplication in GF(2^n)
bitvector field_inv(const bitvector &irpolynom) const; //multiplication in GF(2^n)
bitvector field_div(const bitvector &rhs, const bitvector &irpolynom) const {return field_mult(rhs.field_inv(irpolynom),irpolynom);};
bitvector division(const bitvector &rhs, bitvector &remainder) const;
bitvector operator/(const bitvector &rhs) const {bitvector rem(rhs.size()); return division(rhs,rem);};
bitvector operator%(const bitvector &rhs) const {bitvector rem(rhs.size()); division(rhs,rem); return rem;};
bitvector gcd(const bitvector &rhs) const;
bitvector gcd(const bitvector &rhs) const; //as a polynomial over GF2
bitvector lcm(const bitvector &rhs) const {return (*this)*rhs/this->gcd(rhs);};
unsigned int bitdiff(const bitvector &y) const; //number of differing bits
unsigned int bitdiff(const bitvector &y) const; //number of differing bits (Hamming distance)
unsigned int population(const unsigned int before=0) const; //number of 1's
unsigned int nlz() const; //number of leading zeroes
unsigned int degree() const {if(iszero()) return 0; else return size()-nlz()-1;}; //interprested as a polynomial over GF(2)