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

int main(){

  float minVal = pow(2,-149); // set to smallest float possible
  
  float nextCheck = ((float)((minVal/2.0f))); // divide by two
  bool isZero = (static_cast<float>(minVal/2.0f) == 0.0f); // this thing evaluates to false when it really shouldn't...!?
  bool isZero2 = (nextCheck == 0.0f); // this evaluates to true

  cout << nextCheck << " " << isZero << " " << isZero2 << endl;
  // this outputs 0 0 1
  
  return 0;

}

float minVal = pow(2,-149); // equal to or close to the smallest denormal float possible
              // it has a magnitude smaller that the smallest normal floating point number 

#include <iostream>
#include <cmath>
#include <limits>
#include <iomanip>

int main(){

  const float pow_2_149 = std::pow(2,-149); // denormal number see: http://en.wikipedia.org/wiki/Denormal_number
  const float min = std::numeric_limits<float>::min() ; // smallest normal value (FLT_MIN) 
  const float lowest = std::numeric_limits<float>::lowest() ; // lowest normal value (-FLT_MAX)
  const float denorm_min = std::numeric_limits<float>::denorm_min() ; // smallest denormal value
  
  
  const float pow_2_149_by_2 = pow_2_149 / 2 ;  
  const float min_by_2 = min / 2 ; // smaller than smallest normal value, therefore denormal
  const float lowest_by_2 = lowest / 2 ; // lower than lowest normal value, therefore denormal
  const float denorm_min_by_2 = denorm_min / 2 ; // smaller than smallest denormal value, therefore zero
  
  std::cout << std::scientific << std::setprecision( std::numeric_limits<float>::digits10 + 1 ) << std::boolalpha
            << pow_2_149 << ' '  << min << ' ' << lowest << ' ' << denorm_min << '\n' 
            << pow_2_149_by_2 << ' ' << min_by_2 << ' ' << lowest_by_2 << ' ' << denorm_min_by_2 << '\n' 
            << ( pow_2_149_by_2 == 0 ) << ' ' <<  ( min_by_2 == 0 ) << ' ' << ( lowest_by_2 == 0 ) << ' ' << ( denorm_min_by_2 == 0 ) << '\n' ;
}

float a = 0.1; // a = 0.0999997 maybe

if (a == 0.1){} // almost certainly false

if (10.0 * a == 1.0){}  // almost certainly false

const float PRECISION 1e-6;
const float MyNum = 10 * a;

if (std::abs (1.0 - MyNum) <  PRECISION ){} // should be true MyNum == 1.0 to 6dp