234 lines
10 KiB
C++
234 lines
10 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2008-2023 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef _BITVECTOR_H_
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#define _BITVECTOR_H_
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#include "vec.h"
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#include "numbers.h"
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#include "laerror.h"
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#include <stdint.h>
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//TODO: if efficiency is requires, make also a monic_bitvector, which will not store the leading 1 explicitly
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//and then the field operations will be done without any resize
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//To avoid confusion this class must NOT be derived from bitvector and have only explicit constructor conversion
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namespace LA {
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//compressed storage of large bit vectors
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//let's now use 64-bit blocks exclusively for simplicity
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typedef uint64_t bitvector_block;
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#define blockbits (8*sizeof(bitvector_block))
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inline unsigned int bitvector_rounded(unsigned int n)
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{
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return ((n+blockbits-1)/blockbits)*blockbits;
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}
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class bitvector : public NRVec<bitvector_block>
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{
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private:
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unsigned int modulo;
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public:
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bitvector() : NRVec<bitvector_block>() {};
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explicit bitvector (const unsigned int n):NRVec<bitvector_block>((n+blockbits-1)/blockbits) {modulo=n%blockbits; memset(v,0,nn*sizeof(bitvector_block));};
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bitvector (const bitvector_block a, const unsigned int n):NRVec<bitvector_block>(a,(n+blockbits-1)/blockbits) {modulo=n%blockbits;};
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bitvector(const bitvector &rhs) : NRVec<bitvector_block>(rhs) {modulo=rhs.modulo;};
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explicit bitvector(const uint8_t *data, const unsigned int n): NRVec<bitvector_block>((n+blockbits-1)/blockbits)
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{
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modulo=n%blockbits;
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if(endianity()) laerror("not portable to big endian");
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else memcpy(&v[0],data,(n+7)/8);
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zero_padding();
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};
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void getdata(uint8_t *data)
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{
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if(endianity()) laerror("not portable to big endian");
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else memcpy(data,&v[0],(size()+7)/8);
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}
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//operator= seems to be correctly synthetized by the compiler
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//override dereferencing to address single bits, is however possible
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//only in the const context (otherwise we would have to define a type which, when assigned to, changes a single bit - possible but probably inefficient)
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void resize(const unsigned int n, bool preserve=false); //preserve data or clear
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unsigned int size() const {return (nn*blockbits)-blockbits+(modulo?modulo:blockbits);};
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//arguments must be unsigned to keep the resulting assembly code simple and efficient
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const bool operator[](const unsigned int i) const {return (v[i/blockbits] >>(i%blockbits))&1ULL;};
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const bool get(const unsigned int i) const {return (*this)[i];};
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bitvector_block getblock(const unsigned int i) const {return v[i];}; //integer interpretation
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void setblock(const unsigned int i, const bitvector_block b) {v[i]=b;};
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int getblocksize() const {return 8*sizeof(bitvector_block);};
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void set(const unsigned int i)
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{
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#ifdef DEBUG
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if(i>=size()) laerror("bitvector index out of range in");
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#endif
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v[i/blockbits] |= (1UL<<(i%blockbits));
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};
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void reset(const unsigned int i)
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{
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#ifdef DEBUG
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if(i>=size()) laerror("bitvector index out of range in");
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#endif
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v[i/blockbits] &= ~(1UL<<(i%blockbits));
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};
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void flip(const unsigned int i)
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{
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#ifdef DEBUG
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if(i>=size()) laerror("bitvector index out of range in");
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#endif
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v[i/blockbits] ^= (1UL<<(i%blockbits));
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};
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const bool assign(const unsigned int i, const bool r) {if(r) set(i); else reset(i); return r;};
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void clear() {copyonwrite(true); memset(v,0,nn*sizeof(bitvector_block));};
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void fill() {memset(v,0xff,nn*sizeof(bitvector_block));};
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void zero_padding() const;
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bool is_zero() const {zero_padding(); for(int i=0; i<nn; ++i) if(v[i]) return false; return true;};
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bool is_one() const {zero_padding(); if(v[0]!=1) return false; for(int i=1; i<nn; ++i) if(v[i]) return false;return true;};
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bool iszero() const {return is_zero();};
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void randomize();
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bitvector& operator++();
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bitvector& operator--();
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bool operator!=(const bitvector &rhs) const;
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bool operator==(const bitvector &rhs) const {return !(*this != rhs);};
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bool operator>(const bitvector &rhs) const;
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bool operator<(const bitvector &rhs) const;
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bool operator>=(const bitvector &rhs) const {return !(*this < rhs);};
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bool operator<=(const bitvector &rhs) const {return !(*this > rhs);};
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bitvector operator~() const;
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bitvector& operator&=(const bitvector &rhs);
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bitvector& operator|=(const bitvector &rhs);
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bitvector& operator^=(const bitvector &rhs);
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bitvector& operator&=(const bitvector_block rhs) {v[0]&=rhs; return *this;};
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bitvector& operator|=(const bitvector_block rhs) {v[0]|=rhs; return *this;};
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bitvector& operator^=(const bitvector_block rhs) {v[0]^=rhs; return *this;};
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bitvector& operator+=(const bitvector &rhs) {return (*this)^=rhs;}; //addition modulo 2
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bitvector& operator-=(const bitvector &rhs) {return (*this)^=rhs;}; //subtraction modulo 2
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bitvector operator&(const bitvector &rhs) const {return bitvector(*this) &= rhs;};
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bitvector operator|(const bitvector &rhs) const {return bitvector(*this) |= rhs;};
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bitvector operator^(const bitvector &rhs) const {return bitvector(*this) ^= rhs;};
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bitvector operator+(const bitvector &rhs) const {return *this ^ rhs;}; //addition modulo 2
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bitvector operator-(const bitvector &rhs) const {return *this ^ rhs;}; //subtraction modulo 2
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bitvector multiply(const bitvector &rhs, bool autoresize=true) const; //use autoresize=false only if you know it will not overflow!
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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!!!
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bitvector& operator*=(const bitvector &rhs) {*this = (*this)*rhs; return *this;}
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bitvector pow(unsigned int n) const;
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bitvector field_mult(const bitvector &rhs, const bitvector &irpolynom) const; //multiplication in GF(2^n)
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bitvector field_inv(const bitvector &irpolynom) const; //multiplication in GF(2^n)
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bitvector field_div(const bitvector &rhs, const bitvector &irpolynom) const {return field_mult(rhs.field_inv(irpolynom),irpolynom);};
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bitvector field_composition(const bitvector &rhs, const bitvector &irpolynom) const;
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bitvector field_pow(unsigned int n, const bitvector &irpolynom) const;
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bitvector field_sqrt(const bitvector &irpolynom) const;
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bool is_irreducible() const; //test irreducibility of polynomial over GF2
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bitvector division(const bitvector &rhs, bitvector &remainder) const;
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bitvector operator/(const bitvector &rhs) const {bitvector rem(rhs.size()); return division(rhs,rem);};
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bitvector operator%(const bitvector &rhs) const {bitvector rem(rhs.size()); division(rhs,rem); return rem;};
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bitvector gcd(const bitvector &rhs) const; //as a polynomial over GF2
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bitvector lcm(const bitvector &rhs) const {return (*this)*rhs/this->gcd(rhs);};
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bitvector composition(const bitvector &rhs) const;
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unsigned int bitdiff(const bitvector &y) const; //number of differing bits (Hamming distance)
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unsigned int population(const unsigned int before=0) const; //number of 1's (Hamming weight)
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unsigned int nlz() const; //number of leading zeroes
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unsigned int degree() const {if(iszero()) return 0; else return size()-nlz()-1;}; //interprested as a polynomial over GF(2)
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void truncate(int t=0) {int s=degree()+1; if(t>s) s=t; resize(s,true);};
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unsigned int ntz() const; //number of trailing zeroes
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//extended, truncated const i.e. not on *this but return new entity, take care of modulo's bits
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//logical shifts
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bitvector& operator>>=(unsigned int i);
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bitvector& leftshift(unsigned int i, bool autoresize=false);
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bitvector& operator<<=(unsigned int i) {return leftshift(i,true);};
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bitvector operator>>(unsigned int i) const {bitvector r(*this); return r>>=i;};
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bitvector operator<<(unsigned int i) const {bitvector r(*this); return r<<=i;};
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//logical rotations not implemented yet
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//unformatted file IO
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void read(int fd, bool dimensions=1, bool transp=0);
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void write(int fd, bool dimensions=1, bool transp=0);
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};
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extern bitvector find_irreducible(int deg, int pop= -1, int nth=1); //degree and requested Hamming weight or -1 for random trial
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//expand to separate bytes or ints
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template <typename T>
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void bitvector_expand(const bitvector &v, NRVec<T> &r)
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{
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int n=v.size();
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r.resize(n);
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r.clear();
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for(int i=0; i<n; ++i) if(v[i]) r[i]=1;
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}
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//mantissa of a floating number between 0 and 1
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template <typename T>
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bitvector mantissa(T x, int nbits, int shift=0)
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{
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while(shift >0) {x+=x; --shift;}
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while(shift <0) {x*=.5; ++shift;}
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if(x<0||x>=1) laerror("number not normalized in bitvector mantissa");
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bitvector b(nbits);
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b.clear();
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T y= x+x;
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for(int i=0; i<nbits-1; ++i)
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{
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int n= (int) y;
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if(n&1) b.set(i+1);
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y += y;
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}
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return b;
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}
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template <typename T>
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void bitvector_decimal(T &x, const bitvector &b, int shift=0)
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{
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x=0;
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for(int i=b.size()-1; i>=0; --i) if(b[i]) x += 1./(1ULL<<i);
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while(shift >0) {x+=x; --shift;}
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while(shift <0) {x*=.5; ++shift;}
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}
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template <typename T>
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void bitvector_compress(bitvector &r, const NRVec<T> &v)
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{
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int n=v.size();
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r.resize(n);
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r.clear();
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for(int i=0; i<n; ++i) if(v[i]) r.set(i);
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}
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extern std::ostream & operator<<(std::ostream &s, const bitvector &x);
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extern std::istream & operator>>(std::istream &s, bitvector &x);
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class bitvector_from1 : public bitvector
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{
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public:
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bitvector_from1() : bitvector() {};
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bitvector_from1(const bitvector &rhs) :bitvector(rhs) {};
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explicit bitvector_from1(const unsigned int n) : bitvector(n) {};
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const bool operator[](const unsigned int i) {return bitvector::operator[](i-1);};
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void set(const unsigned int i) {bitvector::set(i-1);};
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void reset(const unsigned int i) {bitvector::reset(i-1);};
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const bool get(const unsigned int i) {return bitvector::get(i-1);};
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const bool assign(const unsigned int i, const bool r) {return bitvector::assign(i-1,r);};
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unsigned int population(const unsigned int before=0) const {return bitvector::population(before?before-1:0);};
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};
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}//namespace
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#endif
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