long int表示的数多大时候被取模表示，又什么时候显示为零？
一直在自学C++，一直原地踏步。
最近重新看书，把递归求阶乘的程序改写成了非递归版。求证时，发现n很大的时候，结果有时候是负数，更大的时候一直为0.后来我想，奇怪啊，负数的话应该是取模表示了吧？取0是什么回事？溢出？
以我的理解，不管n为何数，表示的结果即使是超出long int的表示范围，应该会取模表示吧？为什么会变0？什么时候会变0？
[解决办法]
为负的原因不是取模，而是数据溢出到了符号位，导致程序误以为结论为负。
为零的原因是因为计算的数据太大。当计算到34!时，结果的低34位将全为0，再被截短到 long int 的32位，当然就是0了。然后，后面所有的阶乘值都被这个0乘，全都是0了。
[解决办法]
#include <iostream>#include <string>#include <algorithm>using namespace std;int COMPARE(string number1, string number2) { int i,j; int length1 = number1.size(); int length2 = number2.size(); if(number1.size() == 0) number1 = "0"; if(number2.size() == 0) number2 = "0"; j = 0; for(i = 0; i < length1; ++i) { if(number1[i] == '0') ++j; else break; } number1 = number1.substr(j); j = 0; for(i = 0; i < length2; ++i) { if(number2[i] == '0') ++j; else break; } number2 = number2.substr(j); length1 = number1.size(); length2 = number2.size(); if(length1 > length2) { return 1; } else if(length1 == length2) { if(number1.compare(number2) > 0) { return 1; } else if(number1.compare(number2) == 0) { return 0; } else { return -1; } } else { return -1; } return 0;}string PLUS(string number1,string number2) { int i; int length1 = number1.size(); int length2 = number2.size(); string result=""; reverse(number1.begin(), number1.end()); reverse(number2.begin(), number2.end()); for(i = 0; i < length1 && i < length2; i++) { char c = (char)(number1[i] + number2[i] - 48); result = result + c; } while(i < length1) { result = result + number1[i]; ++i; } while(i < length2) { result = result + number2[i]; ++i; } int carry = 0; for(i = 0; i < (int)result.size(); ++i) { int value = result[i] - 48 + carry; result[i] = (char)(value % 10 + 48); carry = value / 10; } if(carry !=0 ) { result = result + (char)(carry + 48); } for(i = result.size() - 1; i >= 0; i--) { if(result[i] != '0') break; } result = result.substr(0, i + 1); reverse(result.begin(), result.end()); if(result.length() == 0) result = "0"; return result;}string MINUS(string number1,string number2) { int i; string result = ""; int length1 = number1.size(); int length2 = number2.size(); if(COMPARE(number2,number1) > 0) { return "-" + MINUS(number2, number1); } reverse(number1.begin(),number1.end()); reverse(number2.begin(),number2.end()); for(i = 0; i < length1 && i < length2; i++) { char c = number1[i] - number2[i] + 48; result = result + c; } if(i < length1) { for(; i < length1; i++) { result = result + number1[i]; } } int carry = 0; for(i = 0; i < (int)result.length(); i++) { int value = result[i] - 48 + carry; if(value < 0) { value = value + 10; carry = -1; } else carry = 0; result[i]=(char)(value + 48); } for(i = result.size() - 1; i >= 0; i--) { if(result[i] != '0')break; } result = result.substr(0, i+1); reverse(result.begin(), result.end()); if(result.length()==0) result = "0"; return result;}string MULTIPLY(string number1, string number2) { int i, j; int *iresult; int length1 = number1.size(); int length2 = number2.size(); string result = ""; reverse(number1.begin(), number1.end()); reverse(number2.begin(), number2.end()); iresult = (int*)malloc(sizeof(int) * (length1 + length2 + 1)); memset(iresult, 0, sizeof(int) * (length1 + length2 + 1)); for(i = 0; i < length1; i++) { for(j = 0; j < length2; j++) { iresult[i+j] += ((number1[i] - 48) * (number2[j] - 48)); } } int carry = 0; for(i = 0; i < length1 + length2; i++) { int value = iresult[i] + carry; iresult[i] = value % 10; carry = value / 10; } for(i = length1 + length2 - 1; i >= 0; i--) { if(iresult[i] != 0)break; } for(; i >= 0; i--) { result = result + (char)(iresult[i]+48); } free(iresult); if(result == "") result = "0"; return result;}string factorial(string n) { string temp = "1"; string i; for(i = "1"; COMPARE(i, n) <= 0; i = PLUS(i, "1")) { temp = MULTIPLY(temp, i); } return temp;}int main(void) { cout << factorial("1000") << endl; return 0;}
[解决办法]