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//============================================================================
// Author : Svenson Han Gothel and Sven Gothel
// Version : 0.1
// Copyright : MIT
// Description : C++ Lesson 0.2a Applied arithmetic using C++
//============================================================================
#include <cstdio>
#include <iostream>
#include <cmath>
#include <limits>
/**
* Lesson 0.2
*
* Implementing simple arithmetic functionality
*/
struct DivisionResult {
int factor;
int remainder;
};
DivisionResult divide(const int z, const int n) {
int r=0;
int c=z;
while ( c >= n ) {
c -= n; // c = c - n;
++r; // r = r + 1;
}
return DivisionResult { .factor=r, .remainder=c };
}
int mult(const int a, const int b) {
int r=0;
for (int i=0; i<a; ++i) {
r += b; // r=r+b;
}
return r;
}
int summe_iter(const int a, const int b) {
int r=0;
for (int i=a; i<=b; ++i) {
r += i; // r=r+i;
}
return r;
}
int summe(const int a, const int b) {
// ( a + b ) * ( n / 2 )
const int n = b - a + 1;
return ( ( a + b ) * n ) / 2;
}
// function declaration
int my_pow(const int x, const int y);
// function definition
int my_pow(const int x, const int y) {
int r=1;
for (int i=0; i<y; ++i){
r=mult(r, x); // r = r * x
}
return r;
}
int factorial(int v) {
// factorial(5) = 1*2*3*4*5
int r = v;
while( v > 1 ) {
// v = v - 1;
// r = r * v;
r *= --v;
}
return r;
}
float machineEpsilon() {
const float one(1);
const float two(2);
float x = 1;
float res;
// float t;
int i=0;
do {
res = x;
x = x / two;
// t = one + x;
// fprintf(stderr, "%3d: %.48f -> %.48f, %.48f\n", i, res, x, t);
// std::cerr << i << ": " << res << " -> " << x << std::endl;
++i;
} while ( one + x > one );
(void)i;
return res;
}
void test_limits() {
unsigned int i = std::numeric_limits<unsigned int>::max() - 10;
do {
fprintf(stderr, "%u, bytes %zu\n", i, sizeof(i));
if( i == std::numeric_limits<unsigned int>::max() ) {
break; // end outter loop
}
++i;
} while( true );
}
int main(int argc, const char* argv[]) {
{
// loop through all program invocation arguments and print them
for(int i=0; i<argc; ++i) {
printf("cmd_arg[%d]: %s\n", i, argv[i]);
}
}
{
float e = machineEpsilon();
fprintf(stderr, "machineEpsilon: %.48f\n", e);
}
{
test_limits();
}
int error_counter = 0;
{
for(int numerator = 0; numerator < 100; ++numerator) {
for(int denominator=1; denominator<=10; ++denominator) {
const int expected = numerator / denominator;
const int expected_r = numerator % denominator;
const DivisionResult has = divide(numerator, denominator);
if( expected != has.factor || expected_r != has.remainder ) {
printf("Error-1: %d / %d != %d + %d / %d, error result %d + %d / %d\n",
numerator, denominator,
expected, expected_r, denominator,
has.factor, has.remainder, denominator);
++error_counter;
}
const int test_numerator = denominator*has.factor+has.remainder;
if( test_numerator != numerator ) {
printf("Error-2: %d * %d + %d != %d, error result %d + %d / %d\n",
denominator, has.factor, has.remainder,
numerator,
has.factor, has.remainder, denominator);
++error_counter;
}
}
}
}
{
for(int a = 0; a <= 10; ++a) {
for(int b = 0; b <= 10; ++b) {
const int expected = a*b;
const int has = mult(a, b);
if( expected != has ) {
printf("Error: %d * %d != %d, error result %d\n",
a, b, expected, has);
++error_counter;
}
}
}
}
if( true ) {
for(int a = 0; a <= 10; ++a) {
for(int b = a; b <= a + 10; ++b) {
const int expected = summe_iter(a, b);
const int has = summe(a, b);
if( expected != has ) {
printf("Error: Sum[%d .. %d] != %d, error result %d\n",
a, b, expected, has);
++error_counter;
}
}
}
}
{
for(int a = 0; a <= 10; ++a) {
for(int b=0; b <= 5; ++b) {
const int expected = (int)std::pow(a, b);
const int has = my_pow(a, b);
if( expected != has ) {
printf("Error: %d ** %d != %d, error result %d ? ",
a, b, expected, has);
++error_counter;
}
}
}
}
{
int last_exp = 1;
for(int a = 0; a <= 10; ++a) {
const int expected = last_exp * a;
if( 0 < expected) {
last_exp = expected;
}
const int has = factorial(a);
if( expected != has ) {
printf("Error: factorial(%d) != %d, error result %d ? ",
a, expected, has);
++error_counter;
} else {
printf("factorial(%d) = %d\n", a, has);
}
}
}
if( 0 == error_counter ) {
std::cout << "No error" << std::endl;
return 0;
} else {
std::cout << error_counter << " error(s)" << std::endl;
return 1;
}
}
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