Bigfloat II: Integer, BINT

Mr. K입니다

어제 같이 올릴까 말까 했다가 그냥 어제 안올리고 오늘 올립니다

[헤더]

#ifndef BINT_H #define BINT_H #include <iostream> using std::ostream; using std::istream; #include <string> using std::string; #include "ubint.h" // bint: Big INTeger class bint : public ubint { protected: int sign; // 0 is positive, 1 is negative public: bint(); bint( bint& b ); bint operator =( bint b2 ); bint( ubint ub ); bint operator =( ubint ub2 ); bint( string number ); bint operator =( string n2 ); bint( int number ); bint operator =( int n2 ); int getsign(); void setsign( int s ); string subtract( string n2 ); // main heritage 1 bint operator -( bint b2 ); bint operator -(); // negation bint operator +( bint b2 ); bint operator *( bint b2 ); string divide( string n2 ); // main heritage 2 bint operator /( bint b2 ); bint operator %( bint b2 ); bint operator +=( bint b2 ); bint operator -=( bint b2 ); bint operator *=( bint b2 ); bint operator /=( bint b2 ); bint operator %=( bint b2 ); bint operator ++(); bint operator ++( int dummy ); bint operator --(); bint operator --( int dummy ); friend ostream& operator <<( ostream& os, bint b ); friend istream& operator >>( istream& is, bint& b ); bool operator <( bint b2 ); bool operator >( bint b2 ); bool operator !=( bint b2 ); bool operator ==( bint b2 ); bool operator <=( bint b2 ); bool operator >=( bint b2 ); // bint-?-ubint bint operator +( ubint ub2 ); bint operator +=( ubint ub2 ); bint operator -( ubint ub2 ); bint operator -=( ubint ub2 ); bint operator *( ubint ub2 ); bint operator *=( ubint ub2 ); bint operator /( ubint ub2 ); bint operator /=( ubint ub2 ); bint operator %( ubint ub2 ); bint operator %=( ubint ub2 ); bool operator <( ubint ub2 ); bool operator >( ubint ub2 ); bool operator !=( ubint ub2 ); bool operator ==( ubint ub2 ); bool operator <=( ubint ub2 ); bool operator >=( ubint ub2 ); // bint-?-string bint operator +( string n2 ); bint operator +=( string n2 ); bint operator -( string n2 ); bint operator -=( string n2 ); bint operator *( string n2 ); bint operator *=( string n2 ); bint operator /( string n2 ); bint operator /=( string n2 ); bint operator %( string n2 ); bint operator %=( string n2 ); bool operator <( string n2 ); bool operator >( string n2 ); bool operator !=( string n2 ); bool operator ==( string n2 ); bool operator <=( string n2 ); bool operator >=( string n2 ); // bint-?-int bint operator +( int n2 ); bint operator +=( int n2 ); bint operator -( int n2 ); bint operator -=( int n2 ); bint operator *( int n2 ); bint operator *=( int n2 ); bint operator /( int n2 ); bint operator /=( int n2 ); bint operator %( int n2 ); bint operator %=( int n2 ); bool operator <( int n2 ); bool operator >( int n2 ); bool operator !=( int n2 ); bool operator ==( int n2 ); bool operator <=( int n2 ); bool operator >=( int n2 ); // ubint-?-bint friend bint operator +( ubint ub1, bint b2 ); friend bint operator -( ubint ub1, bint b2 ); // Fatal Error in VC++ 6.0 friend bint operator *( ubint ub1, bint b2 ); friend bint operator /( ubint ub1, bint b2 ); friend bint operator %( ubint ub1, bint b2 ); friend bool operator <( ubint ub1, bint b2 ); friend bool operator >( ubint ub1, bint b2 ); friend bool operator !=( ubint ub1, bint b2 ); friend bool operator ==( ubint ub1, bint b2 ); friend bool operator <=( ubint ub1, bint b2 ); friend bool operator >=( ubint ub1, bint b2 ); // string-?-bint friend bint operator +( string n1, bint b2 ); friend bint operator -( string n1, bint b2 ); // Fatal Error in VC++ 6.0 friend bint operator *( string n1, bint b2 ); friend bint operator /( string n1, bint b2 ); friend bint operator %( string n1, bint b2 ); friend bool operator <( string n1, bint b2 ); friend bool operator >( string n1, bint b2 ); friend bool operator !=( string n1, bint b2 ); friend bool operator ==( string n1, bint b2 ); friend bool operator <=( string n1, bint b2 ); friend bool operator >=( string n1, bint b2 ); // int-?-ubint friend bint operator +( int n1, bint b2 ); friend bint operator -( int n1, bint b2 ); // Fatal Error in VC++ 6.0 friend bint operator *( int n1, bint b2 ); friend bint operator /( int n1, bint b2 ); friend bint operator %( int n1, bint b2 ); friend bool operator <( int n1, bint b2 ); friend bool operator >( int n1, bint b2 ); friend bool operator !=( int n1, bint b2 ); friend bool operator ==( int n1, bint b2 ); friend bool operator <=( int n1, bint b2 ); friend bool operator >=( int n1, bint b2 ); }; #endif

아랫부분을 보시면 뺄셈 연산자 오버로딩에서 fatal error가 뜬다고 주석으로 적어놓았습니다

다 만들고 컴파일하면 이상이 없는데, 실행은 되지 않는 error입니다

실행을 하기 위해서는 저 3줄을 모두 주석처리해야하지요 -_-;

Dlbo군한테 물어보니 VS 2005 이상이면 에러가 뜨지 않을거라고 합니다

[구현cpp]

#include "bint.h" // default constructor bint::bint() : ubint() { sign = 0; } // copy constructor bint::bint( bint& b ) { sign = b.sign; num = b.num; } // overloading: bint = bint bint bint::operator =( bint b2 ) { sign = b2.sign; num = b2.num; return b2; } /******************************************************************************/ // constructor: ubint bint::bint( ubint ub ) : ubint( ub ) { sign = 0; } // overloading: bint = ubint bint bint::operator =( ubint ub2 ) { bint temp(ub2); sign = temp.sign; num = temp.num; return temp; } /******************************************************************************/ // constructor: string bint::bint( string number ) { if( number[0] == '-' ) { sign = 1; num = number.substr(1, number.size()-1); } else { sign = 0; num = number; } } // overloading: bint = string bint bint::operator =( string n2 ) { bint temp(n2); sign = temp.sign; num = temp.num; return temp; } /******************************************************************************/ // constructor: int bint::bint( int number ) : ubint( number ) { if( number < 0 ) sign = 1; else sign = 0; } // overloading: bint = int bint bint::operator =( int n2 ) { bint temp(n2); sign = temp.sign; num = temp.num; return temp; } /******************************************************************************/ // additional operation for bratio int bint::getsign() { return sign; } // additional operation for bratio void bint::setsign( int s ) { sign = s; } /******************************************************************************/ // subtraction of two strings; main heritage 1 string bint::subtract( string n2 ) { string t1, t2; int s1, s2; t1 = num; t2 = n2; s1 = t1.size(); s2 = t2.size(); if( s1 > s2 ) t2 = string(s1-s2, '0') + n2; else if( s1 < s2 ) t1 = string(s2-s1, '0') + num; int i, s = t1.size(), carry = 0; string res = string(s, '0'); for( i = s-1; i >= 0; i-- ) { res[i] = t1[i] - t2[i] + '0' + carry; if( res[i] < '0' ) { carry = -1; res[i] += 10; } else carry = 0; } for( i = 0; i < s; i++ ) if( res[i] != '0' ) break; if( i < s ) res = res.substr(i, s-i); else res = '0'; return res; } // overloading: bint - bint bint bint::operator -( bint b2 ) { bint res; if( sign != b2.sign ) { res.num = this->add(b2.num); res.sign = sign; } else { ubint ub1(num), ub2(b2.num); if( ub1 >= ub2 ) { res.num = this->subtract(b2.num); res.sign = sign; } else { res.num = b2.subtract(this->num); res.sign = !sign; } } return res; } /******************************************************************************/ // overloading: - bint bint bint::operator -() { bint res; res.sign = !sign; res.num = num; return res; } // overloading: bint + bint bint bint::operator +( bint b2 ) { bint res; res = *this - -b2; return res; } // overloading: bint * bint bint bint::operator *( bint b2 ) { bint res; ubint ub1(num), ub2(b2.num), temp; res.num = ub1.multiply(ub2.getnum()); temp.setnum(res.num); if( temp == 0 ) res.sign = 0; else res.sign = sign ^ b2.sign; return res; } /******************************************************************************/ // division of two strings; main heritage 2 string bint::divide( string n2 ) { ubint low, up("1"); ubint numer(num), divisor(n2); while( numer >= divisor * up ) { low = up; up *= 10; } ubint key(low); up = low + key; while(1) { while( numer >= divisor * up ) { low += key; up += key; } string temp = key.getnum(); if( key > 1 ) key.setnum(temp.substr(0, temp.size()-1)); else break; up = low + key; } return low.getnum(); } // overloading: bint / bint bint bint::operator /( bint b2 ) { bint res; res.sign = sign ^ b2.sign; res.num = this->divide(b2.num); return res; } // overloading: bint % bint bint bint::operator %( bint b2 ) { bint res, quotient; quotient = *this / b2; res = *this - quotient * b2; return res; } /******************************************************************************/ // overloading: bint += bint bint bint::operator +=( bint b2 ) { *this = *this + b2; return *this; } // overloading: bint -= bint bint bint::operator -=( bint b2 ) { *this = *this - b2; return *this; } // overloading: bint *= bint bint bint::operator *=( bint b2 ) { *this = *this * b2; return *this; } // overloading: bint /= bint bint bint::operator /=( bint b2 ) { *this = *this / b2; return *this; } // overloading: bint %= bint bint bint::operator %=( bint b2 ) { *this = *this % b2; return *this; } /******************************************************************************/ // overloading: ++bint bint bint::operator ++() { bint temp("1"); *this += temp; return *this; } // overloading: bint++ bint bint::operator ++( int dummy ) { bint temp("1"); bint old = *this; *this += temp; return old; } // overloading: --bint bint bint::operator --() { bint temp("1"); *this -= temp; return *this; } // overloading: bint-- bint bint::operator --( int dummy ) { bint temp("1"); bint old = *this; *this -= temp; return old; } /******************************************************************************/ // overloading: ostream ostream& operator <<( ostream& os, bint b ) { os << ((b.sign == 1)? "-": "") << b.num; return os; } // overloading: istream istream& operator >>( istream& is, bint& b ) { string numstr; is >> numstr; bint temp(numstr); b = temp; return is; } /******************************************************************************/ // overloading: bint < bint bool bint::operator <( bint b2 ) { // reference: 0 is positive, 1 is negative if( sign != b2.sign ) { return (sign > b2.sign); } else { ubint ub1(num), ub2(b2.num); bool res = ub1 < ub2; if( !sign ) return res; else return !res; } } // overloading: bint > bint bool bint::operator >( bint b2 ) { // reference: 0 is positive, 1 is negative if( sign != b2.sign ) { return (sign < b2.sign); } else { ubint ub1(num), ub2(b2.num); bool res = ub1 > ub2; if( !sign ) return res; else return !res; } } // overloading: bint != bint bool bint::operator !=( bint b2 ) { return (*this < b2) || (*this > b2); } // overloading: bint == bint bool bint::operator ==( bint b2 ) { return !(*this != b2); } // overloading: bint <= bint bool bint::operator <=( bint b2 ) { return !(*this > b2); } // overloading: bint >= bint bool bint::operator >=( bint b2 ) { return !(*this < b2); } /******************************************************************************/ // overloading: bint + ubint bint bint::operator +( ubint ub2 ) { bint temp(ub2); return (*this + temp); } // overloading: bint += ubint bint bint::operator +=( ubint ub2 ) { bint temp(ub2); return (*this += temp); } // overloading: bint - ubint bint bint::operator -( ubint ub2 ) { bint temp(ub2); return (*this - temp); } // overloading: bint -= ubint bint bint::operator -=( ubint ub2 ) { bint temp(ub2); return (*this -= temp); } // overloading: bint * ubint bint bint::operator *( ubint ub2 ) { bint temp(ub2); return (*this * temp); } // overloading: bint *= ubint bint bint::operator *=( ubint ub2 ) { bint temp(ub2); return (*this *= temp); } // overloading: bint / ubint bint bint::operator /( ubint ub2 ) { bint temp(ub2); return (*this / temp); } // overloading: bint /= ubint bint bint::operator /=( ubint ub2 ) { bint temp(ub2); return (*this /= temp); } // overloading: bint % ubint bint bint::operator %( ubint ub2 ) { bint temp(ub2); return (*this % temp); } // overloading: bint %= ubint bint bint::operator %=( ubint ub2 ) { bint temp(ub2); return (*this %= temp); } // overloading: bint < ubint bool bint::operator <( ubint ub2 ) { bint temp(ub2); return (*this < temp); } // overloading: bint > ubint bool bint::operator >( ubint ub2 ) { bint temp(ub2); return (*this > temp); } // overloading: bint != ubint bool bint::operator !=( ubint ub2 ) { bint temp(ub2); return (*this != temp); } // overloading: bint == ubint bool bint::operator ==( ubint ub2 ) { bint temp(ub2); return (*this == temp); } // overloading: bint <= ubint bool bint::operator <=( ubint ub2 ) { bint temp(ub2); return (*this <= temp); } // overloading: bint >= ubint bool bint::operator >=( ubint ub2 ) { bint temp(ub2); return (*this >= temp); } /******************************************************************************/ // overloading: bint + string bint bint::operator +( string n2 ) { bint temp(n2); return (*this + temp); } // overloading: bint += string bint bint::operator +=( string n2 ) { bint temp(n2); return (*this += temp); } // overloading: bint - string bint bint::operator -( string n2 ) { bint temp(n2); return (*this - temp); } // overloading: bint -= string bint bint::operator -=( string n2 ) { bint temp(n2); return (*this -= temp); } // overloading: bint * string bint bint::operator *( string n2 ) { bint temp(n2); return (*this * temp); } // overloading: bint *= string bint bint::operator *=( string n2 ) { bint temp(n2); return (*this *= temp); } // overloading: bint / string bint bint::operator /( string n2 ) { bint temp(n2); return (*this / temp); } // overloading: bint /= string bint bint::operator /=( string n2 ) { bint temp(n2); return (*this /= temp); } // overloading: bint % string bint bint::operator %( string n2 ) { bint temp(n2); return (*this % temp); } // overloading: bint %= string bint bint::operator %=( string n2 ) { bint temp(n2); return (*this %= temp); } // overloading: bint < string bool bint::operator <( string n2 ) { bint temp(n2); return (*this < temp); } // overloading: bint > string bool bint::operator >( string n2 ) { bint temp(n2); return (*this > temp); } // overloading: bint != string bool bint::operator !=( string n2 ) { bint temp(n2); return (*this != temp); } // overloading: bint == string bool bint::operator ==( string n2 ) { bint temp(n2); return (*this == temp); } // overloading: bint <= string bool bint::operator <=( string n2 ) { bint temp(n2); return (*this <= temp); } // overloading: bint >= string bool bint::operator >=( string n2 ) { bint temp(n2); return (*this >= temp); } /******************************************************************************/ // overloading: bint + int bint bint::operator +( int n2 ) { bint temp(n2); return (*this + temp); } // overloading: bint += int bint bint::operator +=( int n2 ) { bint temp(n2); return (*this += temp); } // overloading: bint - int bint bint::operator -( int n2 ) { bint temp(n2); return (*this - temp); } // overloading: bint -= int bint bint::operator -=( int n2 ) { bint temp(n2); return (*this -= temp); } // overloading: bint * int bint bint::operator *( int n2 ) { bint temp(n2); return (*this * temp); } // overloading: bint *= int bint bint::operator *=( int n2 ) { bint temp(n2); return (*this *= temp); } // overloading: bint / int bint bint::operator /( int n2 ) { bint temp(n2); return (*this / temp); } // overloading: bint /= int bint bint::operator /=( int n2 ) { bint temp(n2); return (*this /= temp); } // overloading: bint % int bint bint::operator %( int n2 ) { bint temp(n2); return (*this % temp); } // overloading: bint %= int bint bint::operator %=( int n2 ) { bint temp(n2); return (*this %= temp); } // overloading: bint < int bool bint::operator <( int n2 ) { bint temp(n2); return (*this < temp); } // overloading: bint > int bool bint::operator >( int n2 ) { bint temp(n2); return (*this > temp); } // overloading: bint != int bool bint::operator !=( int n2 ) { bint temp(n2); return (*this != temp); } // overloading: bint == int bool bint::operator ==( int n2 ) { bint temp(n2); return (*this == temp); } // overloading: bint <= int bool bint::operator <=( int n2 ) { bint temp(n2); return (*this <= temp); } // overloading: bint >= int bool bint::operator >=( int n2 ) { bint temp(n2); return (*this >= temp); } /******************************************************************************/ // overloading with friend: ubint + bint bint operator +( ubint ub1, bint b2 ) { return (b2 + ub1); } bint operator -( ubint ub1, bint b2 ) { return (b2 - ub1); } bint operator *( ubint ub1, bint b2 ) { return (b2 * ub1); } bint operator /( ubint ub1, bint b2 ) { return (b2 / ub1); } bint operator %( ubint ub1, bint b2 ) { return (b2 % ub1); } bool operator <( ubint ub1, bint b2 ) { return (b2 > ub1); } bool operator >( ubint ub1, bint b2 ) { return (b2 < ub1); } bool operator !=( ubint ub1, bint b2 ) { return (b2 != ub1); } bool operator ==( ubint ub1, bint b2 ) { return (b2 == ub1); } bool operator <=( ubint ub1, bint b2 ) { return (b2 >= ub1); } bool operator >=( ubint ub1, bint b2 ) { return (b2 <= ub1); } /******************************************************************************/ // overloading with friend: string + bint bint operator +( string n1, bint b2 ) { return (b2 + n1); } bint operator -( string n1, bint b2 ) { return (b2 - n1); } bint operator *( string n1, bint b2 ) { return (b2 * n1); } bint operator /( string n1, bint b2 ) { return (b2 / n1); } bint operator %( string n1, bint b2 ) { return (b2 % n1); } bool operator <( string n1, bint b2 ) { return (b2 > n1); } bool operator >( string n1, bint b2 ) { return (b2 < n1); } bool operator !=( string n1, bint b2 ) { return (b2 != n1); } bool operator ==( string n1, bint b2 ) { return (b2 == n1); } bool operator <=( string n1, bint b2 ) { return (b2 >= n1); } bool operator >=( string n1, bint b2 ) { return (b2 <= n1); } /******************************************************************************/ // overloading with friend: int + bint bint operator +( int n1, bint b2 ) { return (b2 + n1); } bint operator -( int n1, bint b2 ) { return (b2 - n1); } bint operator *( int n1, bint b2 ) { return (b2 * n1); } bint operator /( int n1, bint b2 ) { return (b2 / n1); } bint operator %( int n1, bint b2 ) { return (b2 % n1); } bool operator <( int n1, bint b2 ) { return (b2 > n1); } bool operator >( int n1, bint b2 ) { return (b2 < n1); } bool operator !=( int n1, bint b2 ) { return (b2 != n1); } bool operator ==( int n1, bint b2 ) { return (b2 == n1); } bool operator <=( int n1, bint b2 ) { return (b2 >= n1); } bool operator >=( int n1, bint b2 ) { return (b2 <= n1); }

bint의 핵심은 뺄셈연산과 나눗셈 연산입니다

덧셈과 곱셈은 이미 ubint에서 구현해놓았으니 상속으로 해결하였습니다

그리고,

ubint가 input이 되는 몇몇 함수에서

우변에 놓이는 ubint의 멤버변수를 참조했더니 private이라 안된다고 해서 get함수와 set함수를 ubint에 추가했습니다

subtract함수는 항상 this가 가지고 있는 string이 input으로 들어온 string을 빼도록 해놓았습니다

실제로 subtract함수를 호출할 때는 함수를 호출하는 곳에서 크기에 따라 적당한 조치를 취하지요

그러고나서 뺄셈연산을 오버로딩하고, 덧셈연산을 오버로딩하였습니다

덧셈연산은 ubint에 add가 있기 때문에 그것을 이용해서 해도 상관없지만, 뺄셈을 오버로딩했기 때문에 뺄셈을 통해 구현했습니다

곱셈연산은 ubint에 multiply가 있어서 그것을 그대로 사용하였습니다

부호에 대한 문제는 XOR로 처리했습니다, 그게 제일 간단하거든요 :D

divide함수의 알고리즘은 예전에 혼자 만들던 클래스로는 감히 구현하기 힘든 것이었는데,

숫자열을 char형 배열 또는 short형 배열 대신 string으로 사용함으로써 가능해졌습니다

( 정확히 얘기하면 동적 배열이 필요했는데, string이 딱 그것에 맞게 설계되어있지요 ㄷㄷ )

divide함수를 완성함에 따라 나눗셈연산과 나머지연산을 오버로딩했습니다

그리고나서

덧셈, 뺄셈, 곱셈, 나눗셈, 나머지연산에 대한 축약연산을 오버로딩하고

전위++, 후위++, 전위--, 후위--를 오버로딩하고

출력스트림과 입력스트림을 오버로딩하고

마지막으로 관계연산자를 오버로딩했습니다

그 밑으로는 죄다

bint와 다른 자료형간의 연산자 오버로딩입니다 :D