Why does (int)55 == 54 in C++?

Question

So I'm learning C++. I've got my "C++ Programming Language" and "Effective C++" out and I'm running through Project Euler. Problem 1...dunzo. Problem 2...not so much. I'm working in VS2008 on a Win32 Console App.

Whats the Sum of all even terms of the Fibonacci Sequence under 4 million?

It wasn't working so I cut down to a test case of 100...

Here's what I wrote...

// Problem2.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
using namespace std;

int _tmain(int argc, _TCHAR* argv[])
{
    cout << "Project Euler Problem 2:\n\n";
    cout << "Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:\n\n";
    cout << "1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...\n\n";
    cout << "Find the sum of all the even-valued terms in the sequence which do not exceed four million.\n\n";
    cout << "Answer:  " << Solve();
}

double Solve() {
    int FibIndex = 0;
    double result = 0.0;
    double currentFib = GenerateNthFibonacciNumber(FibIndex);
    while (currentFib < 100.0){
        cout << currentFib << " " << (int)currentFib << " " << (int)currentFib % 2 << "\n";
        if ((int)currentFib % 2 == 0){
            result += currentFib;
            cout<<(int)currentFib;
        }
        currentFib = GenerateNthFibonacciNumber(++FibIndex);
    }
    return result;
}

double GenerateNthFibonacciNumber(const int n){
    //This generates the nth Fibonacci Number using Binet's Formula
    const double PHI = (1.0 + sqrt(5.0)) / 2.0;
    return ((pow(PHI,n)-pow(-1.0/PHI,n)) / sqrt(5.0));
}

And here's the output...

Project Euler Problem 2:

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

0 0 0
1 1 1
1 1 1
2 2 0
3 3 1
5 5 1
8 8 0
13 13 1
21 21 1
34 34 0
55 54 0
89 89 1
Answer: 99

So I have three columns of debug code...the number returned from the generate function, (int)generatedNumber, and (int)generatedNumber % 2

So on the 11th term we have

55,54,0

Why does (int)55 = 54?

Answer 1

Casting to int truncates the number - same as if you'd called floor(currentFib). So even if currentFib is 54.999999... (a number so close to 55 that it will be rounded up when printed), (int)currentFib will produce 54.

Answer 2

Due to floating point rounding, that 55 row is computing something like 54.99999. Casting double to int truncates the .99999 right off.

On my machine, printing a column displaying (currentFib-(int)currentFib) shows errors on the order of 1.42109e-14. So it's more like 0.999999999999986.