Floating Point, how much can I trust less than / greater than comparisons?

Question

Let\'s say I have two floating point numbers, and I want to compare them. If one is greater than the other, the program should take one fork. If the opposite is true, it should

Answer 1

What about less than check with an epsilon window ? if a is less than b then a can not be equal to b

/**
 * checks whether a <= b with epsilon window
 */
template 
bool eq(T a, T b){
    T e = std::numeric_limits::epsilon();
    return std::fabs(a-b) <= e;
}
/**
 * checks whether a < b with epsilon window
 */
template 
bool lt(T a, T b){
     if(!eq(a,b)){ // if a < b then a != b
         return a < b;
     }
     return false;
}
/**
 * checks whether a <= b with epsilon window
 */
template 
bool lte(T a, T b){
     if(eq(a,b)){
         return true;
     }
     return a < b;
}