almostEqualNumbersBetween function

bool almostEqualNumbersBetween (double a, double b, int maxNumbersBetween)

Compares two doubles and determines if they are equal to within the tolerance or not. Equality comparison is based on the binary representation.

Determines the 'number' of floating point numbers between two values (i.e. the number of discrete steps between the two numbers) and then checks if that is within the specified tolerance. So if a tolerance of 1 is passed then the result will be true only if the two numbers have the same binary representation OR if they are two adjacent numbers that only differ by one step.

The comparison method used is explained in http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm .

Throws ArgumentError if maxNumbersBetween is smaller than one.

Implementation

bool almostEqualNumbersBetween(double a, double b, int maxNumbersBetween) {
  // Make sure maxNumbersBetween is non-negative and small enough that the
  // default NAN won't compare as equal to anything.
  if (maxNumbersBetween < 1) {
    throw ArgumentError.value(
        maxNumbersBetween, 'maxNumbersBetween', messages.argumentPositive);
  }

  // If A or B are infinity (positive or negative) then
  // only return true if they are exactly equal to each other -
  // that is, if they are both infinities of the same sign.
  if (a.isInfinite || b.isInfinite) {
    return a == b;
  }

  // If A or B are a NAN, return false. NANs are equal to nothing,
  // not even themselves.
  if (a.isNaN || b.isNaN) {
    return false;
  }

  // Get the first double and convert it to an integer value (by using the binary representation)
  int first = asDirectionalInt64(a);

  // Get the second double and convert it to an integer value (by using the binary representation)
  int second = asDirectionalInt64(b);

  // Now compare the values.
  // Note that this comparison can overflow so we'll approach this differently
  // Do note that we could overflow this way too. We should probably check that we don't.
  return (a > b)
      ? (second + maxNumbersBetween >= first)
      : (first + maxNumbersBetween >= second);
}