Wrong answer on bisection method program (C++)

Question

I am solving the typical bisection method task but with fixed tolerance (1e-20), fixed interval (0, 10) and given function: x^5 - a*x - 84422%100, where user inputs a as a parameter.

For the example with a = 5 I should get the answer 2.3227751229355622988 with precision 20 digits after floating point but I get 2.50000000000000000000. Where am I wrong here is my code:

#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;

const double e = 1e-20;
const int fn = 84422;

double f(int a, int x)
{
     double y = x * x * x * x * x - a * x - fn % 100;
     return (double)y;
}

int main()
{
    double lv, rv, midv, mid, root, tol;

    int left = 0;
    int right = 10;
    int a;
    cin >> a;

    do
    {
        mid = (left + right) / 2.0;
        rv = f(a, right);
        lv = f(a, left);
        midv = f(a, mid);

        if(midv == 0)
        {
             root = mid;
             break;
        }

        if(midv * lv < 0)
        {
            right = mid;
        }
        else
            left = mid;
     } while ((right - left) > e);

     root = (left + right) / 2.0;
     cout << " The Root is approximately: ";
     cout << fixed << setprecision(20) << root << endl;

     cin.get();
     cin.get();
     return 0;
  }

you wont get 20 significant digits with doubles (see e.g. [here](http://stackoverflow.com/questions/13542944/how-many-significant-digits-have-floats-and-doubles-in-java)) — 463035818_is_not_an_ai, Jan 03 '17 at 12:03
@tambre 64 bits doubles dont have more significant digits, just because it is c++ not java — 463035818_is_not_an_ai, Jan 03 '17 at 12:04

score 1 · Answer 1 · answered Jan 03 '17 at 12:04

1

Your left and right are integers.

When you assign mid to them, you lose significant digits (all of them virtually).

Change them to be doubles.

answered Jan 03 '17 at 12:04

StoryTeller - Unslander Monica

165,132
21
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i fixed them with doubles and still is not working and i get the same result – Kristian Kamenov Jan 03 '17 at 12:06
2

@KristianKamenov - Your `f` accepts `int`s as well. Every integer in your algorithm truncates the calculation you actually want to preform. – StoryTeller - Unslander Monica Jan 03 '17 at 12:07
fixed everything to doubles and now i got answer 2.0000000000000000000 – Kristian Kamenov Jan 03 '17 at 12:09
2

@KristianKamenov even with everything as double you wont get 20 significant digits – 463035818_is_not_an_ai Jan 03 '17 at 12:10
@KristianKamenov - Have you taken a look at the [graph of the function you calculate](https://www.google.co.il/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=x%5E5+-+5x+-+22)? The root is at 2.0 – StoryTeller - Unslander Monica Jan 03 '17 at 12:25

Wrong answer on bisection method program (C++)

1 Answers1