Demonstrating how doubles are approximating Real numbers and how direct comparison must be avoided.

cpsc120_double_comparison.cc

// Gist https://gist.github.com/mshafae/77d3cda92a90746210f3224c1cf83555
// Filename cpsc120_double_comparison.cc
// CompileCommand clang++ -std=c++17 cpsc120_double_comparison.cc
// Demonstrating how doubles are approximating Real numbers and how direct
// comparison must be avoided.

#include <iomanip>
#include <iostream>

// lhs stands for "left hand side"
// rhs stands for "right hand side"
// For example:
//    some_var == some_other_var
// some_var is lhs and some_other_var is rhs

bool DoubleSameAs(double lhs, double rhs, double epsilon) {
  // If they're the same, we got lucky.
  // Otherwise, check to see that lhs is + or - epsilon away from rhs.
  return (lhs == rhs) || ((lhs - epsilon) < rhs && (lhs + epsilon) > rhs);
}

bool DoubleNotSameAs(double lhs, double rhs, double epsilon) {
  return (lhs != rhs) && ((lhs - epsilon) > rhs || (lhs + epsilon) < rhs);
}

int main(int argc, char const *argv[]) {
  std::cout << std::fixed;
  std::cout << std::setprecision(20);
  
  std::cout << "Floating point math works differently than what we expect.\n";
  if ((0.1 + 0.1 + 0.1) == 0.3) {
    std::cout << "(0.1 + 0.1 + 0.1) is the same as 0.3\n";
  } else {
    std::cout << "(0.1 + 0.1 + 0.1) is not the same as 0.3\n";
  }
  
  // We want our doubles to be within 0.0000001 of each other to be considered
  // the same.
  double epsilon{1e-7};
  double a{123.456};
  double b{123.45600001};
  std::cout << "Safely comparing.\n";
  if (DoubleSameAs(a, b, epsilon)) {
    std::cout << a << " is effectively the same as " << b << "\n";
  } else {
    std::cout << a << " is not the same as " << b << "\n";
  }
  std::cout << "Directly comparing.\n";
  if (a == b) {
    std::cout << a << " is effectively the same as " << b << "\n";
  } else {
    std::cout << a << " is not the same as " << b << "\n";
  }

  a = 3.6;
  b = (3.6 / 2.12) * 2.12;
  std::cout << "Safely comparing.\n";
  if (DoubleSameAs(a, b, epsilon)) {
    std::cout << a << " is effectively the same as " << b << "\n";
  } else {
    std::cout << a << " is not the same as " << b << "\n";
  }
  std::cout << "Directly comparing.\n";
  if (a == b) {
    std::cout << a << " is effectively the same as " << b << "\n";
  } else {
    std::cout << a << " is not the same as " << b << "\n";
  }

  a = 1.01;
  b = 0.99;
  a = a - b;
  b = 0.02;
  std::cout << "Safely comparing.";
  if (DoubleSameAs(a, b, epsilon)) {
    std::cout << a << " is effectively the same as " << b << "\n";
  } else {
    std::cout << a << " is not the same as " << b << "\n";
  }
  std::cout << "Directly comparing.\n";
  if (a == b) {
    std::cout << a << " is effectively the same as " << b << "\n";
  } else {
    std::cout << a << " is not the same as " << b << "\n";
  }

  return 0;
}