#include #include #include using namespace std; /* Shouldn't 100! fit in a double? https://www.sololearn.com/Discuss/348499/?ref=app This codes shows: Far less fits. 9007199254740991 : MAX_SAFE_INTEGER (16 digits) 100! Full calculation / doesn't fit in a double: https://code.sololearn.com/cmNS1d2qi84I/?ref=app Javascript double (float64) explorer https://code.sololearn.com/WYCTOysAGnLv/?ref=app * long: precision loss detected between 12! and 13! * double: detected 22-23 (21-22 has a problem) * long double: same but negative overflow, -0. * Double precision is 15.8 digits. * double - true values. Compare output. * 21! = 51090942171709440000 * 22! = 1124000727777607680000 (output failure) * 23! = 25852016738884976640000 (modulus error) * */ int main() { double oneMoreBack; // two calculations ago double lastResult = 1; // last calculation double thisResult = 1; double checker = 10; // stop casting everywhere int lastModulus = 1; int thisModulus; int checkModulus; for(int i=1; i<100; i++) { lastModulus = fmod(lastResult, checker); thisResult = lastResult*(double)i; thisModulus = fmod(thisResult, checker); checkModulus = fmod(lastModulus*i, checker); if(thisModulus != checkModulus) { cout << "Precision loss DETECTED between " << i-1 << "! and " << i << "! (occurred 18!-19!. Zeroes hide it from this test; that's intentional)" << endl; cout.precision(0); cout << " " << fixed << oneMoreBack << " mod: " << fmod(oneMoreBack, checker) << " (" << i-2 << "!)" << endl; cout << " " << fixed << lastResult << " mod: " << lastModulus << " (" << i-1 << "!)" << endl; cout << fixed << thisResult << " mod: " << thisModulus << " (" << i << "!)" << endl; cout << "Modulus should be: " << checkModulus << endl; break; } oneMoreBack = lastResult; lastResult = thisResult; } return 0; }

100! precision-loss weak detector