Testing for “double” equality in javascript

Question

I have translated the experimental C# "float" version of Clipper library to javascript. In the newest sandbox version there is a function IsAlmostEqual which seems to be hard to translate. Double equality cannot be compared using == operator due to numerical stability issues, so this function is needed to handle those issues.

-9223372036854775808 - aInt and -9223372036854775808 - bInt are easy to calculate using e.g. BigInteger library, but BitConverter.DoubleToInt64Bits is harder.

Any idea how to translate IsAlmostEqual function to javascript? Or specifically how to implement BitConverter.DoubleToInt64Bits to javascript?

private static bool IsAlmostEqual(double A, double B)
{
  //http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

  Int64 aInt = BitConverter.DoubleToInt64Bits(A);
  if (aInt < 0) aInt = unchecked(-9223372036854775808 - aInt);
  Int64 bInt = BitConverter.DoubleToInt64Bits(B);
  if (bInt < 0) bInt = unchecked(-9223372036854775808 - bInt);
  return (Math.Abs(aInt - bInt) <= 10000000000);
}

Numerical stability and robustness:
http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
http://www.mpi-inf.mpg.de/~kettner/pub/nonrobust_cgta_06.pdf
http://cpc.cs.qub.ac.uk/MRSN/higham.pdf
http://www.2ality.com/2012/04/number-encoding.html

Answer 1

I ended up using completely different function to test double equality from here. The original function uses signed int64 representation of double which is not possible in Javascript without using slow and complex bitwise operations or using some BigDecimal library. It uses a combination of relative and absolute error.

var IsAlmostEqual = function(a, b)
{
  if (a == b) return true;
  var diff = Math.abs(a - b);
  if (diff < 4.94065645841247E-320) return true;
  a = Math.abs(a);
  b = Math.abs(b);
  var smallest = (b < a) ? b : a;
  return diff < smallest * 1e-12;
}

According to my tests it seems reliable. Please test in jsbin.

EDIT: I updated the code above. Now it produces the same result as with ULP technique in all 83 test cases (using maxUpls 10,000). ULP technique is 8x-20x slower than above EPSILON technique due to Javascript lack of 64 bit integers.