Compile and run my code; compare the result if you are using integers or floats with fractional values. Why is there a difference?
Here is my code:
#include <iostream>
using namespace std;
template<class T>
T find(T array[], T len, T num){
for (int i = 0; i < len; ++i){
if (array[i] == num)
return i;
}
return -1;
}
int main () {
int array1[5] = { 4, 7, 3, 5, 6 }, num1;
float array2[5] ={121.2, 111.5, 300.1, 500.1, 600.1 }, num2;
cout << "Enter an int:" << " " ;
cin >> num1;
cout << "Enter a float:" << " " ;
cin >> num2;
int x = find<int>(array1,5,num1);
float y= find<float>(array2,5,num2);
cout << "The index for the int is:" << " " << x << endl;
cout << "The index for the float is:" << " " << y << endl;
return 0;
}
I couldn't find the difference between the two results when using ints and when using floats.
The issue is that you must not compare floats with == due to the internal representation of floating point numbers. If you are using the result from an expression, it can mathematically be correct to find the number in the array, but due to the limitations in the floating point representation the == would not find it.
Consider the following code:
template<class T>
int find(T array[], size_t len, T num){
for (size_t i = 0; i < len; ++i){
cerr << std::setprecision(7) << "Compare: " << array[i] << ", " << num;
if (array[i] == num) {
cerr << " => equal" << endl;
return i;
} else {
cerr << " =>not equal" << endl;
}
}
return -1;
}
int main () {
float array2[2] ={500.1, 1.0 }, num2;
float a = 500.1 / 2;
int i = find<float>(array2, 2, 2*a);
a = 1.0 / 0.3333;
i = find<float>(array2, 2, a * 0.3333);
return 0;
}
Output:
Compare: 500.1, 500.1 => equal
Compare: 500.1, 0.9999999 =>not equal
Compare: 1, 0.9999999 =>not equal
So, even though 1.0 / 0.3333 * 0.3333 is 1.0 mathematically, it is not when using floating point arithmetics - it is 0.99999 instead. Therefore == does not treat the numbers as equal in the last comparison.
To solve this, compare the difference of the two numbers to a small epsilon value. float.h explicitly defines the constant FLT_EPSILON for this:
if (fabs(array[i] - num) < FLT_EPSILON) { ...
Related
I finished this code homework assignment tonight. I thought I was done, but I just realized that my "Average" value is coming out wrong with certain values. For example: When my professor entered the values 22, 66, 45.1, and 88 he got an "Average" of 55.27. However, when I enter those values in my program, I get an "Average" of 55.25. I have no idea what I am doing wrong. I was pretty confident in my program until I noticed that flaw. My program is due at midnight, so I am clueless on how to fix it. Any tips will be greatly appreciated!
Code Prompt: "Write a program that dynamically allocates an array large enough to hold a user-defined number of test scores. Once all the scores are entered, the array should be passed to a function that sorts them in ascending order. Another function should be called that calculates the average score. The program should display the sorted list of scores and averages with appropriate headings. Use pointer notation rather than array notation whenever possible."
Professor Notes: The book only states, "Input Validation: Do not accept negative numbers for test scores." We also need to have input validation for the number of scores. If it is negative, including 0, the program halts, we should consider this situation for 'counter' not to be negative while we have a loop to enter numbers. So negative numbers should be rejected for the number of scores and the values of scores.
Here is my code:
#include <iostream>
#include <iomanip>
using namespace std;
void showArray(double* array, int size);
double averageArray(double* array, int size);
void orderArray(double* array, int size);
int main()
{
double* scores = nullptr;
int counter;
double numberOfScores;
cout << "\nHow many test scores will you enter? ";
cin >> numberOfScores;
if (numberOfScores < 0) {
cout << "The number cannot be negative.\n"
<< "Enter another number: ";
cin >> numberOfScores;
}
if (numberOfScores == 0) {
cout << "You must enter a number greater than zero.\n"
<< "Enter another number: ";
cin >> numberOfScores;
}
scores = new double[numberOfScores];
for (counter = 0; counter < numberOfScores; counter++) {
cout << "Enter test score " << (counter + 1) << ": ";
cin >> *(scores + counter);
if (*(scores + counter) < 0) {
cout << "Negative scores are not allowed. " << endl
<< "Enter another score for this test : ";
cin >> *(scores + counter);
}
}
orderArray(scores, counter);
cout << "\nThe test scores in ascending order, and their average, are: " << endl
<< endl;
cout << " Score" << endl;
cout << " -----" << endl
<< endl;
showArray(scores, counter);
cout << "\nAverage Score: "
<< " " << averageArray(scores, counter) << endl
<< endl;
cout << "Press any key to continue...";
delete[] scores;
scores = nullptr;
system("pause>0");
}
void orderArray(double* array, int size)
{
int counterx;
int minIndex;
int minValue;
for (counterx = 0; counterx < (size - 1); counterx++) {
minIndex = counterx;
minValue = *(array + counterx);
for (int index = counterx + 1; index < size; index++) {
if (*(array + index) < minValue) {
minValue = *(array + index);
minIndex = index;
}
}
*(array + minIndex) = *(array + counterx);
*(array + counterx) = minValue;
}
}
double averageArray(double* array, int size)
{
int x;
double total{};
for (x = 0; x < size; x++) {
total += *(array + x);
}
double average = total / size;
return average;
}
void showArray(double* array, int size)
{
for (int i = 0; i < size; i++) {
cout << " " << *(array + i) << endl;
}
}
I try to start my answers with a brief code review:
#include <iostream>
#include <iomanip>
using namespace std; // Bad practice; avoid
void showArray(double* array, int size);
double averageArray(double* array, int size);
void orderArray(double* array, int size);
int main()
{
double* scores = nullptr;
int counter;
double numberOfScores;
cout << "\nHow many test scores will you enter? ";
cin >> numberOfScores;
// This is not input validation, I can enter two consecutive bad values,
// and the second one will be accepted.
if (numberOfScores < 0) {
// Weird formatting, this blank line
cout << "The number cannot be negative.\n"
<< "Enter another number: ";
cin >> numberOfScores;
}
// The homework, as presented, doesn't say you have to treat 0 differently.
if (numberOfScores == 0) {
cout << "You must enter a number greater than zero.\n"
<< "Enter another number: ";
cin >> numberOfScores;
}
scores = new double[numberOfScores];
// Declare your loop counter in the loop
for (counter = 0; counter < numberOfScores; counter++) {
cout << "Enter test score " << (counter + 1) << ": ";
cin >> *(scores + counter);
if (*(scores + counter) < 0) {
cout << "Negative scores are not allowed. " << endl
<< "Enter another score for this test : ";
cin >> *(scores + counter);
}
}
orderArray(scores, counter); // Why not use numberOfScores?
cout << "\nThe test scores in ascending order, and their average, are: " << endl
<< endl;
cout << " Score" << endl;
cout << " -----" << endl
<< endl;
showArray(scores, counter); // Same as above.
cout << "\nAverage Score: "
<< " " << averageArray(scores, counter) << endl
<< endl;
cout << "Press any key to continue...";
delete[] scores;
scores = nullptr;
system("pause>0"); // Meh, I suppose if you're on VS
}
void orderArray(double* array, int size)
{
int counterx;
int minIndex;
int minValue; // Unnecessary, and also the culprit
// This looks like selection sort
for (counterx = 0; counterx < (size - 1); counterx++) {
minIndex = counterx;
minValue = *(array + counterx);
for (int index = counterx + 1; index < size; index++) {
if (*(array + index) < minValue) {
minValue = *(array + index);
minIndex = index;
}
}
*(array + minIndex) = *(array + counterx);
*(array + counterx) = minValue;
}
}
double averageArray(double* array, int size)
{
int x;
double total{};
for (x = 0; x < size; x++) {
total += *(array + x);
}
double average = total / size;
return average;
}
void showArray(double* array, int size)
{
for (int i = 0; i < size; i++) {
cout << " " << *(array + i) << endl;
}
}
When you are sorting your array, you keep track of the minValue as an int and not a double. That's why your average of the sample input is incorrect. 45.1 is truncated to 45 for your calculations. You don't need to keep track of the minValue at all. Knowing where the minimum is, and where it needs to go is sufficient.
But as I pointed out, there are some other serious problems with your code, namely, your [lack of] input validation. Currently, if I enter two consecutive bad numbers, the second one will be accepted no matter what. You need a loop that will not exit until a good value is entered. It appears that you are allowed to assume that it's always a number at least, and not frisbee or any other non-numeric value.
Below is an example of what your program could look like if your professor decides to teach you C++. It requires that you compile to the C++17 standard. I don't know what compiler you're using, but it appears to be Visual Studio Community. I'm not very familiar with that IDE, but I imagine it's easy enough to set in the project settings.
#include <algorithm>
#include <iomanip>
#include <iostream>
#include <numeric>
#include <string>
#include <vector>
// Assumes a number is always entered
double positive_value_prompt(const std::string& prompt) {
double num;
std::cout << prompt;
do {
std::cin >> num;
if (num <= 0) {
std::cerr << "Value must be positive.\n";
}
} while (num <= 0);
return num;
}
int main() {
// Declare variables when you need them.
double numberOfScores =
positive_value_prompt("How many test scores will you enter? ");
std::vector<double> scores;
for (int counter = 0; counter < numberOfScores; counter++) {
scores.push_back(positive_value_prompt("Enter test score: "));
}
std::sort(scores.begin(), scores.end());
for (const auto& i : scores) {
std::cout << i << ' ';
}
std::cout << '\n';
std::cout << "\nAverage Score: "
<< std::reduce(
scores.begin(), scores.end(), 0.0,
[size = scores.size()](auto mean, const auto& val) mutable {
return mean += val / size;
})
<< '\n';
}
And here's an example of selection sort where you don't have to worry about the minimum value. It requires that you compile to C++20. You can see the code running here.
#include <iostream>
#include <random>
#include <vector>
void selection_sort(std::vector<int>& vec) {
for (int i = 0; i < std::ssize(vec); ++i) {
int minIdx = i;
for (int j = i + 1; j < std::ssize(vec); ++j) {
if (vec[j] < vec[minIdx]) {
minIdx = j;
}
}
int tmp = vec[i];
vec[i] = vec[minIdx];
vec[minIdx] = tmp;
}
}
void print(const std::vector<int>& v) {
for (const auto& i : v) {
std::cout << i << ' ';
}
std::cout << '\n';
}
int main() {
std::mt19937 prng(std::random_device{}());
std::uniform_int_distribution<int> dist(1, 1000);
std::vector<int> v;
for (int i = 0; i < 10; ++i) {
v.push_back(dist(prng));
}
print(v);
selection_sort(v);
print(v);
}
I opted not to give your code the 'light touch' treatment because than I would have done your homework for you, and that's just not something I do. However, the logic shown should still be able to guide you toward a working solution.
I wrote a code to manage a coffee machine,
I have a function findC that finds the cheapest capsule in the capsule array
a different function of mine findVP that is supposed to use the findC function's output as variables. however, when I pass the variables mp, ind = findC(prices_copy, quantities_copy, SIZE);
and print them it passes them as 0;
but the 2nd cout : cout << findC(prices_copy, quantities_copy, SIZE); prints the correct output.
why is this ? and how can I pass the output of the function to another
/******************************************************************************
Online C++ Compiler.
Code, Compile, Run and Debug C++ program online.
Write your code in this editor and press "Run" button to compile and execute it.
*******************************************************************************/
// Example program
#include <iostream>
#include <string>
#include <bits/stdc++.h>
using namespace std;
#define SLEEVE 10
#define SIZE 10
#define N 5
#define BUDGET 70
//int CapsuleKind[10] = {"JOE","MAC","NES","jamaica","brazil","columbia","MOJO","CLUB","JHON","COF"};
float findMostExpensiveCapsule( float prices[], int size ) // 1
{
float max = prices[0];
int count = 0;
for(int i = 1; i < size; i++)
{
if (prices[i] > max)
{
max = prices[i];
}
}
cout << "The maximum price " << max << " is found on indexes: " ;
for (int i = 0; i < size; i++)
{
if (prices[i] == max)
{
cout << i << " ";
count++;
}
}
cout << endl;
cout << "The maximum number appears " << count << " times." << endl;
return max;
}
int findStrongestCapsuleInStock( int quantities[], int size, int sleeve ) // 2
{
return 0;
}
void SellCapsules( int quantities[], int Qty, int index) // 10
{
quantities[index] = quantities[index] - Qty;
cout << "SOLD " << Qty << " capsules to the Customer, the total now is: " << quantities[index] << endl;
}
float findC( float prices[],int quantities[], int size ) // 9
{
float min = 99999;
int count = 0;
float index=0;
//sort(prices, arr + n);
for(int i = 0; i < size; i++)
{
if (quantities[i] >= SLEEVE)
{
if(prices[i] < min){
min = prices[i];
index= i;
}
else continue;
}
}
cout <<"the minimum price is : " << min << " ---- the index is : " << index << endl;
return min, index;
}
void findCheapestSleeve( float prices[],int quantities[], int size )
{
float min = prices[0];
int count = 0;
int index=0;
for(int i = 0; i < size; i++)
{
if (prices[i] < min)
{
if(quantities[i] > SLEEVE){
min = prices[i];
index= i;
}
else continue;
}
}
cout <<"the minimum price is : " << min << " ---- the index is : " << index << endl;
}
void showAllCapsulesInStock( int quantities[], float prices[], int size, int sleeve) // 3
{
for (int i = 0; i < size; i++)
{
cout << "capsule kind: " << i << " ---- sleeves available : " << (quantities[i]/sleeve) << " ---- price(for 1 sleeve): " << (prices[i]*sleeve)<< endl;
}
}
float findVP( float prices[], int quantities[], int size, float nis, int sleeve ) //4
{
float mp=0;
float ind =0;
float prices_copy[size];
int quantities_copy[size];
for(int i=0; i<size; i++){
prices_copy[i] = prices[i];
quantities_copy[i] = quantities[i];
}
mp, ind = findC(prices_copy, quantities_copy, SIZE);
cout << "The lowest price sleeve is: " << mp * 10 << " --- the capsule kind is: " << ind <<endl;
cout << findC(prices_copy, quantities_copy, SIZE);
}
void findValueForMoneyPackage( float prices[], int quantities[], int size, float nis, int sleeve )
{
int sleeve_num[size];
float sleeve_price[size];
float min=0;
int index = 0;
int counter=0;
float quant = 0;
for (int i=0; i < size; i++)
{
sleeve_num[i] = (quantities[i]/sleeve);
sleeve_price[i] = (prices[i] * sleeve);
}
//min, quant = findCheapestSleeve(sleeve_price, quantities, 10);
cout << "the cheapest sleeve costs : " << min << " and its of kind :" << quant << endl;
}
void addMoreCapsules( int quantities[], int size ) // 5
{
char answer;
int plus;
for (int i = 0; i < size; i++)
{
cout << "do you want to add capsules to capsule kind " << i << "? (Y/N) " << endl;
cin >> answer;
if (answer == 'Y')
{
cout << "How many capsules do you want to add (inter a number) " << endl;
cin >> plus;
if (plus > 0)
{
quantities[i] = quantities[i] + plus;
cout << "Added " << plus << " capsules to the inventory, the total now is: " << quantities[i] << endl;
}
}
else
{
continue;
}
}
}
// Driver Code
int main()
{
bool flag = false;
int option;
float prices[] = { 1.2, 2.2, 2.5, 1.7, 2.2, 3, 2.8, 2.5, 2.9, 3.7 };
int quantities[] = { 14, 22, 25, 13, 22, 33, 50, 60, 33, 25 };
while (flag != true)
{
cout << "Please choose an option , has to be a number 1-6" << endl;
cin >> option;
if (option == 1)
{
findMostExpensiveCapsule(prices,SIZE);
}
else if ( option == 3)
{
showAllCapsulesInStock(quantities, prices, SIZE, 10);
}
else if (option == 4){
findVP(prices, quantities, SIZE, BUDGET, SLEEVE);
}
else if(option == 5){
addMoreCapsules(quantities,SIZE);
}
else if(option == 9){
findC(prices, quantities, SIZE);
}
else
{
flag = true;
}
}
cout << "GoodBye!" << endl;
return 0;
}
This
return min, index;
doesn't do what you think it does. You obviously think it's going to return two values. But actually it just returns index.
This
mp, ind = findC(prices_copy, quantities_copy, SIZE);
doesn't do what you think it does. You obviously think it's going to assign the two returned values from findC to the variables mp and ind. But actually it's going to return the single value returned by findC to the variable ind and ignore mp.
If you want to know precisely what these constructs do then look up the comma operator, but I guess the moral of the story is that just because you can get some plausible looking code to compile it doesn't mean that it's going to do what you expected it to do.
So the real question is how to return two values from a function in C++. There are actually several possible approaches. Here's a question that reviews some of them, Returning multiple values from a C++ function.
I created a program to display an average from an array of numbers the user have decided to input. The program asks the user the amount of numbers he / she will input, then they input all positive numbers. The output for the average is always a decimal, how can I only display the whole number without any decimal points. Ex. 12.34 = 12 / 8.98 = 8
#include <iostream>
#include <iomanip>
using namespace std;
void sortingTheScores(double *, int);
void showsTheScoresNumber(double *, int);
double averageForAllScores(double, int);
int main()
{
double *scores;
double total = 0.0;
double average;
int numberOfTestScores;
cout << "How many test scores do you have? ";
cin >> numberOfTestScores;
scores = new double[numberOfTestScores];
if (scores == NULL)
return 0;
for (int count = 0; count < numberOfTestScores; )
{
cout << "Test Score #" << (count + 1) << ": ";
cin >> scores[count];
while (scores[count] <= 0)
{
cout << "Value must be one or greater: " ;
cin >> scores[count];
}
count = count +1;
}
for (int count = 0; count < numberOfTestScores; count++)
{
total += scores[count];
}
sortingTheScores(scores, numberOfTestScores);
cout << "The numbers in set are: \n";
showsTheScoresNumber(scores, numberOfTestScores);
averageForAllScores(total, numberOfTestScores);
cout << fixed << showpoint << setprecision(2);
cout << "Average Score: " << averageForAllScores(total,numberOfTestScores);
return 0;
}
void sortingTheScores (double *array, int size)
{
int sorting;
int theIndex;
double theNumbers;
for (sorting = 0; sorting < (size - 1); sorting++)
{
theIndex = sorting;
theNumbers = array[sorting];
for (int index = sorting + 1; index < size; index++)
{
if (array[index] < theNumbers)
{
theNumbers = array[index];
theIndex = index;
}
}
array[theIndex] = array[sorting];
array[sorting] = theNumbers;
}
}
void showsTheScoresNumber (double *array, int size)
{
for (int count = 0; count < size; count++)
cout << array[count] << " ";
cout << endl;
}
double averageForAllScores(double total, int numberOfTestScores)
{ double average;
average = total / numberOfTestScores;
return average;
}
You can use I/O manipulators here:
#include <iostream>
#include <iomanip>
int main()
{
std::cout << std::setprecision(0) << 1.231321 << '\n';
}
Output:
1
You can do it without using iomanip library:
std::cout.precision(0);
std::cout << 1.231321 << std::endl;
Then you'll simply get:
1
Just you need to use std::cout.precision() which is equivalent to std::setprecision() from iomanip library.
Edit:
The aforementioned solution is okay for smaller floating point values, but if you try something like 1334.231321, the std::cout will result displaying some scientific notation, something like:
1e+03
which is actually odd to read and understand. To solve it, you need std::fixed flag, you may write something like:
std::cout.precision(0), std::cout << std::fixed;
std::cout << 1334.231321 << std::endl;
Then it'll show:
1334
For numbers in a +/-2^31 range you can do:
cout << int(12.34) << " " << int(8.98) << endl;
which produces output
12 8
You may also want to consider rounding to the nearest integers. To do so
add a line
#include <cmath>
then do
cout << int(rint(12.34)) << " " << int(rint(8.98)) << endl;
this gives
12 9
I'm working through Stroustrups's "Programming Principles and Practice using C++" and got stuck in one exercise.
Here are the indications :
1) Write a program that consists of a while-loop that (each time around the loop) reads in two ints and then prints them. Exit the program when a terminating '|' is entered.
2)Change the program to write out the smaller value is: followed by the smaller of the numbers and the larger value is: followed by the larger value.
3)Augment the program so that it writes the line the numbers are equal (only) if they are equal.
4)Change the program so that it uses doubles instead of ints.
5)Change the program so that it writes out the numbers are almost equal after writing out which is the larger and the smaller if the two numbers differ by less than 1.0/100.
6) Now change the body of the loop so that it reads just one double each time around. Define two variables to keep track of which is the smallest and which is the largest value you have seen so far. Each time through the loop write out the value entered. If it’s the smallest so far, write the smallest so far after the number. If it is the largest so far, write the largest so far after the number.
This is the code I have so far:
int main(){
double number1 = 0;
double number2 = 0;
double maximum = 0;
double minimum = 0;
cout << " Keep entering numbers. If you want to exit the program press alt + z" << endl;
while (cin >> number1 && cin >> number2) {
if (number1 == '#' || number2 == '#') {
break;
}
else if (number1 < number2){
cout << "The smaller value is " << number1 << '.' << endl;
cout << "The larger value is " << number2 << '.' << endl;
maximum = number2;
minimum = number1;
if (number2 - number1 < 0.01) {
cout << "The numbers are almost equal";
}
}
else if ( number1 > number2) {
cout << "The smaller value is " << number2 << '.' << endl;
cout << "The larger value is " << number1 << '.' << endl;
maximum = number1;
minimum = number2;
if (number1 - number2 < 0.01) {
cout << "The numbers are almost equal";
}
}
else {
cout << "Both numbers are the same." << endl;
}
}
Can somebody help me modify this to find the largest, smallest number?
I've read about it and found a sorted vector solution but I can't seem to apply it to my problem.
Much appreciated :)
If you want to keep a running count of the maximum and minimum and not make structural changes to your existing program,
You'll need to '#include < algorithm >' unless you want to roll your own min and max functions.
Instead of:
maximum = number1;
minimum = number2;
Use this:
maximum = (maximum < max(number1, number2)) ? max(number1, number2) : maximum;
minimum = (minimum > min(number1, number2)) ? min(number1, number2) : minimum;
For Exercise 6, you don’t have to use std::vector. You can keep track the largest and smallest values in single variables called minn and maxn as shown in the following code snippet:
int
main()
{
std::string quit("|");
int i = 0;
std::string s;
double n;
std::vector < double >v = { 0.0, 0.0 };
double maxn = std::numeric_limits < double >::lowest();
double minn = std::numeric_limits < double >::max();
std::vector < double >in_meters;
while (std::cin >> s) {
if (quit.compare(s) == 0)
break;
if (reject(s))
continue;
n = str2meters(s);
std::cout << n << " ";
in_meters.push_back(n);
if (maxn < n) {
std::cout << "the largest so far" << std::endl;
maxn = n;
}
if (minn > n) {
std::cout << "the smallest so far" << std::endl;
minn = n;
}
v[i] = n;
if (i == 1) {
std::sort(v.begin(), v.end());
prn(v);
}
i = (i + 1) % 2;
}
prng(in_meters);
return 0;
}
I have used std::vector for Exercises 2 and 5:
void
prn(std::vector < double > &v)
{
const double one_percent = 1.0 / 100.0;
std::cout << "the smaller value is: " << v[0] << std::endl;
std::cout << "the larger value is: " << v[1] << std::endl;
if ((v[1] - v[0]) < one_percent)
std::cout << "are almost equal" << std::endl;
}
and Exercises 9-11, too:
void
prng(std::vector < double > v)
{
std::sort(v.begin(), v.end());
for (auto k : v)
std::cout << k << " " ;
std::cout << std::endl;
double sum = std::accumulate(v.begin(), v.end(), 0.0);
std::cout << "number of values " << v.size() << std::endl;
std::cout << "sum of values " << sum << std::endl;
}
You're making it complicated, start with this using 'std_lib_facilities'
#include "..\..\std_lib_facilities.h"
int main() {
cout << "type in two integers or a '|' to terminate the program:\n";
int x1 = 0;
int x2 = 0;
while (cin >> x1 >> x2)
{
cout << x1 << ", " << x2 << "\n";
}
keep_window_open("x");
}
#include <iostream>
using namespace std;
// on input n returns the value a_n as a double
double term(int n) {
double val = 1.0 / (n+1.0) / (n+1.0);
if (n%2 != 0) val = -val;
return val;
}
/* computes the sum for i from k to k+n-1 of term(i) by the
* direct upwards method */
double direct_up(int k,int n) {
double sum = 0.0;
for (int i=0; i<n; i++) {
sum += term(k+i);
}
return sum;
}
int main() {
cout.precision(16);
int nterms = 0;
int ft = 0;
cout << "Enter first term, number of terms" << endl;
cin >> ft >> nterms;
cout << "The sum of the " << nterms << " terms starting at " << ft << endl;
cout << "direct_up: " << direct_up(ft, nterms) << endl;
return 0;
}
I have created a program which takes a formula and adds term by term starting from the kth term to the (n-1)th term. However I am unable to work out how to calculate the roundoff error after each term?
Would you be able help me with this please?