高精度大数运算的实现
一个简单的高精度大数运算的实现，实现了加法，乘法，乘方
#include <string> #include <sstream> #include <iostream> #include <cctype> #include <algorithm> using namespace std; #define sz(a) int((a).size()) class BigNum { public: BigNum() : integer("0"), dec_digits("0") {} BigNum(string digit) { int n = count(digit.begin(), digit.end(), '.'); if (n == 0) { get_BigNum(digit, "0"); } else if (n == 1) { if (digit[0] == '.') { get_BigNum("0", digit.substr(1, sz(digit) - 1)); } else { *find(digit.begin(), digit.end(), '.') = ' '; istringstream is(digit); string a, b; is >> a >> b; get_BigNum(a, b); } } else { integer = "0"; dec_digits = "0"; } } BigNum(string a, string b) { get_BigNum(a, b); } BigNum operator +(BigNum rhs) { int overflow = 0; string b = add_decimal(dec_digits, rhs.dec_digits, overflow); string a = add_integer(integer, rhs.integer, overflow); while ( *b.rbegin() == '0' && sz(b) != 1) { b.erase(b.end() - 1); } return BigNum(a, b); } BigNum operator *(BigNum b) { BigNum total("0"); for ( int i = 0 ; i < sz(b.integer) ; ++i ) { total = total + multi_bignum_leftshift(b.integer[i] - '0', sz(b.integer) - i - 1); } for ( int i = 0 ; i < sz(b.dec_digits) ; ++i ) { total = total + multi_bignum_rightshift(b.dec_digits[i] - '0', i + 1); } return total; } BigNum operator ^(int n) { BigNum total("1"); for ( int i = 0 ; i < n ; ++i ) { total = *this * total; } return total; } friend ostream &operator <<(ostream &os, BigNum a); private: string integer; string dec_digits; void get_BigNum(string a = "0", string b = "0") { if (sz(a) == 0) { a = "0"; } if (sz(b) == 0) { b = "0"; } integer = a; dec_digits = b; if (!valid_string(integer)) { integer = "0"; } else { while (integer[0] == '0' && sz(integer) != 1 ) { integer.erase(integer.begin()); } } if (!valid_string(dec_digits)) { dec_digits = "0"; } else { while (*dec_digits.rbegin() == '0' && sz(dec_digits) != 1 ) { dec_digits.erase(dec_digits.end() - 1); } } } bool valid_string(const string s) { for ( int i = 0 ; i < sz(s) ; ++i ) { if (!isdigit(s[i]) ) { return false; } } return true; } string add_decimal(string a, string b, int &overflow) { int m = max(sz(a), sz(b)); a += string(m - sz(a), '0'); b += string(m - sz(b), '0'); return add_string(a, b, overflow, false); } string add_integer(string a, string b, int &overflow) { int m = max(sz(a), sz(b)); a = string(m - sz(a), '0') + a; b = string(m - sz(b), '0') + b; return add_string(a, b, overflow, true); } string add_string(string a, string b, int &overflow, bool carry) { for ( int i = sz(a) - 1; i >= 0; --i) { int k = a[i] - '0' + b[i] - '0' + overflow; overflow = k / 10; k %= 10; a[i] = char(k + '0'); } if (overflow != 0 && carry) { a = char(overflow + '0') + a; } return a; } string multi_string(string a, int n, int &overflow, bool carry) { for ( int i = sz(a) - 1 ; i >= 0 ; --i ) { int k = (a[i] - '0') * n + overflow; overflow = k / 10; k %= 10; a[i] = char(k + '0'); } if (overflow != 0 && carry ) { a = char(overflow + '0') + a; } return a; } BigNum multi_bignum_leftshift(int j, int n) { //*this * j * 10^n int overflow = 0; string d = multi_string(dec_digits, j, overflow, false); string i = multi_string(integer, j, overflow, true); while (sz(d) <= n ) { d += "0"; } return BigNum(i + d.substr(0, n), d.substr(n, sz(d) -n)); } BigNum multi_bignum_rightshift(int j, int n) { //*this * j / 10^n int overflow = 0; string d = multi_string(dec_digits, j, overflow, false); string i = multi_string(integer, j, overflow, true); while (sz(i) <= n ) { i = "0" + i; } return BigNum(i.substr(0, sz(i) - n), i.substr(sz(i) - n, n) + d); } }; ostream &operator <<(ostream &os, BigNum a) { os << a.integer << "." << a.dec_digits; return os; } int main(int argc, char *argv[]) { BigNum a("111111111111111111111111111111.422"); BigNum b("1.17800000000000"); BigNum c(".456"); BigNum d(".3x5."); cout << a << endl; cout << b << endl; cout << c << endl; cout << d << endl; cout << a + b << endl; cout << a * b << endl; cout << (a ^ 5) << endl; return 0; }
E:/>make
g++ -Wall -O2 -o a.exe BigNum.cpp
111111111111111111111111111111.422
1.178
0.456
0.0
111111111111111111111111111112.6
130888888888888888888888888889.255116
16935087808430286711036596724990939728022489796609595420753582415282223238327490
728039428594047924943690833036969296690993088119224372978373892868.6374280665456
32