高精度类的实现 加减乘除幂余
from my csdn blog
信息安全原理 hw2-1
- HW2. Large number arithmetic
- Write a +-*/ algorithm for large integers. (10 point)
- Implement the DH algorithm. (5 point)
// name: bigint.h
// author: amrzs
// date: 2014/03/18
#ifndef BIGINT_H
#define BIGINT_H
#include <string>
using namespace std;
class Bigint{
private:
static const int MAX_SIZE = 500;
int size;
int arr[MAX_SIZE];
public:
Bigint();
Bigint(string &s); //initialize with a string num
~Bigint();
int getSize();
Bigint operator+(Bigint &);
Bigint operator-(Bigint &);
Bigint operator*(Bigint &);
Bigint operator/(Bigint &);
Bigint operator%(Bigint &);
Bigint operator/(int x);
Bigint getPow(int n, Bigint &); //return this^n % x
Bigint getPow(Bigint &, Bigint &);
Bigint getPow10(int n); //return this*(10^n)
bool operator>=(Bigint &);
bool isOdd();
bool equalOne();
void clear();
void printNum();
};
#endif // BIGINT_H
// name: bigint.cpp
// author: amrzs
// date: 2014/03/18
#include <cstring>
#include <iostream>
#include "bigint.h"
using namespace std;
Bigint::Bigint(){
//make sure to be zero(0)
clear();
}
Bigint::Bigint(string &s){
clear();
size = s.length();
if (size > MAX_SIZE){
//something wrong
cout << "too many numbers" << endl;
}
for (int i = size-1; i >= 0; i--)
arr[i] = s[size-i-1] - '0';
}
Bigint::~Bigint(){
//to do sth
}
int Bigint::getSize(){
return size;
}
Bigint Bigint::operator+(Bigint &x){
Bigint result;
result.size = max(size, x.size);
for (int i = 0; i < result.size; i++)
result.arr[i] = arr[i] + x.arr[i];
for (int i = 0; i < result.size; i++)
if (result.arr[i] > 9){
result.arr[i+1] += result.arr[i] / 10;
result.arr[i] %= 10;
}
if(result.size > MAX_SIZE){
cout << "Out of range in operator+" << endl;
}
return result;
}
Bigint Bigint::operator-(Bigint &x){
Bigint result = *this;
for (int i = 0; i < x.size; i++)
result.arr[i] = arr[i] - x.arr[i];
for (int i = 0; i < result.size; i++)
if (result.arr[i] < 0){
result.arr[i] += 10;
result.arr[i+1]--;
}
while(result.size > 1 && 0 == result.arr[result.size-1])
result.size--;
return result;
}
Bigint Bigint::operator*(Bigint &x){
Bigint result;
result.size = size + x.size - 1;
if(result.size > MAX_SIZE){
cout << "Out of range in operator*" << endl;
}
for (int i = 0; i < size; i++)
for (int j = 0; j < x.size; j++){
result.arr[i+j] += arr[i] * x.arr[j];
if (result.arr[i+j] > 9){
result.arr[i+j+1] += result.arr[i+j] / 10;
result.arr[i+j] %= 10;
}
}
if (result.arr[result.size] > 0)
result.size++;
return result;
}
Bigint Bigint::operator/(Bigint &x){
Bigint result;
if(size < x.size)
return result;
Bigint y = *this, z;
int pow = y.size - x.size;
while(y >= x){
z = x.getPow10(pow);
while(y >= z){
y = y - z;
result.arr[pow]++;
}
pow--;
}
result.size = size - x.size + 1;
while(result.size > 1 && 0 == result.arr[result.size-1])
result.size--;
return result;
}
Bigint Bigint::operator/(int x){
Bigint result;
int tmp = 0;
for(int i = size-1; i >= 0; i--){
tmp = tmp * 10 + arr[i];
result.arr[i] = tmp / x;
tmp %= x;
}
result.size = size;
while(result.size > 1 && 0 == result.arr[result.size-1])
result.size--;
return result;
}
Bigint Bigint::operator%(Bigint &x){
Bigint t = *this / x * x;
return *this - t;
}
Bigint Bigint::getPow(int n, Bigint &x){
if(n < 1){
cout << "Parameter out of range in operator^" << endl;
}
if(1 == n){
return *this % x;
}
Bigint t = getPow(n/2, x);
Bigint result = t * t % x;
if(1 == n%2){
result = *this * result % x;
}
return result;
}
Bigint Bigint::getPow(Bigint &n, Bigint &x){
if(n.equalOne()){
return *this % x;
}
Bigint nDiv2 = n / 2;
Bigint t = getPow(nDiv2, x);
Bigint result = t * t % x;
if(n.isOdd()){
result = *this * result % x;
}
return result;
}
Bigint Bigint::getPow10(int n){
if(size+n >= MAX_SIZE || n < 0)
cout << "Out of range" << endl;
Bigint x;
for(int i = 0; i < size; i++)
x.arr[i+n] = arr[i];
x.size = size + n;
return x;
}
bool Bigint::operator>=(Bigint &x){
if(size < x.size)
return false;
if(size == x.size){
for(int i = size-1; i >= 0; i--)
if(arr[i] > x.arr[i])
return true; //greater
else if(arr[i] < x.arr[i])
return false;
return true; //equal
}
return true; //greater
}
bool Bigint::isOdd(){
return (arr[0] & 1);
}
bool Bigint::equalOne(){
return (1==size && 1==arr[0]);
}
void Bigint::clear(){
size = 1;
memset(arr, 0, sizeof(*arr) * MAX_SIZE);
}
void Bigint::printNum(){
for (int i = size-1; i >= 0; i--)
cout << arr[i];
cout << endl;
}
// name: main.cpp
// author: amrzs
// date: 2014/03/18
#include <string>
#include <iostream>
#include "bigint.h"
using namespace std;
Bigint calc(Bigint a, Bigint b, char c){
Bigint result;
switch(c){
case '+':
result = a + b;
break;
case '-':
result = a - b;
break;
case '*':
result = a * b;
break;
case '/':
result = a / b;
break;
case '%':
result = a % b;
break;
default:
cout << "You input a wrong operator" << endl;
break;
}
return result;
}
int main(){
cout <<"Please input a expression like 123456789 * 987654321"
<<"if DH then like 123456789 ^ 987654321 % 123456789" << endl;
string s1, s2, s3;
char ch1, ch2;
while(true){ // don't like for(;;)
cin >> s1 >> ch1 >> s2;
if("quit" == s1){
break;
}
Bigint a(s1), b(s2), result;
if('^' == ch1){ //for DH
cin >> ch2 >> s3;
Bigint c(s3);
result = a.getPow(b, c);
}else{ //normal expression
result = calc(a, b, ch1);
}
result.printNum();
}
return 0;
}
Makefile:
CPP = g++
OFLAG = -o
TARGET = a.out
OBJS = main.o bigint.o
$(TARGET): $(OBJS)
$(CPP) $(OFLAG) $(TARGET) $(OBJS)
main.o: main.cpp bigint.o
bigint.o: bigint.cpp
.PHONY: clean
clean:
-rm $(TARGET) $(OBJS)
不足
以前写高精度，总是函数方式，当然这样不妥当，我都是将最低位放在arr[1]中，而这次是放在arr[0]中，这样造成了一些细微的差别使得程序写的时候发生了一些小问题
要考虑到类的数组中没有清0这件事情，我总觉得清0不好，因为效率么，当然这就带来了编程的复杂性，总是被数组里的垃圾数据干扰，出现很多错误，使得11号写的程序13号才总算完成，以后的话，我宁愿降低一些效率，使程序逻辑简单一些
学了一下gdb，发现听不错的，clang++和g++在调试的时候有些区别，最好还是用g++来调试程序，当然，生成可执行文件g++和clang++都不错，主要clang++的错误提示信息很友好
