Function returning the ULP of a double number - the value of its least signfiicant bit position.

ulp.dart

import "dart:typed_data";

final _ulpBuffer = ByteData(8);
/// The unit of least precision for a [double] number.
///
/// A double number has 53 bits of precision. The unit of least precision (ULP) 
/// is the value of the least of those bits. 
/// The returned ULP is always positive.
double ulp(double d) {
  var buffer = _ulpBuffer;
  buffer.setFloat64(0, d, Endian.little);
  // 11 bits of mantissa stored at bits 52..62.
  int mantissa = (buffer.getUint16(6, Endian.little) >> 4) & 0x7FF;
  
  if (mantissa == 0x3ff) return d.abs(); // NaN or Infinity
  if (mantissa == 0) {
    // Input is denormal, ULP is minimal double value.
    return double.minPositive;
  }
  // Otherwise, the lowest bit is 52 bits below the highest bit.
  buffer.setFloat64(0, 0.0, Endian.host); // Clear buffer.
  if (mantissa <= 52) {
    // Result is denormal. 
    int bit = mantissa - 1;
    buffer.setUint8(bit >> 3, 1 << (bit & 7));
  } else {
    buffer.setUint16(6, (mantissa - 52) << 4, Endian.little);
  }
  return buffer.getFloat64(0, Endian.little);
}

// Sanity check
main() {
  print(ulp(0.0));
  for (double d = double.minPositive; d < double.infinity; d *= 2) {
    var u = ulp(d);
    print("$d: $u");
    if (d + u == d) print("NOT RIGHT");
    if (d + (u / 2) != d && d + (u/2) != d+ u) {
      print("NOT WAT?");
    }
  }
  print(ulp(double.infinity));
}