Converting a JavaScript binary string and back again is not equal

Question

I have a 64 element JavaScript array that I'm using as a bitmask. Unfortunately, I've run into a problem when converting from a string to binary, and back. This has worked for some other arrays, but what is going on here?

var a = [1, 1, 1, 1, 1, 1, 1, 1,
         1, 1, 1, 1, 1, 1, 1, 1,
         1, 1, 0, 0, 1, 1, 1, 1,
         1, 1, 0, 0, 1, 1, 1, 1,
         1, 1, 0, 0, 0, 0, 1, 1,
         1, 1, 0, 0, 0, 0, 1, 1,
         1, 1, 1, 1, 1, 1, 1, 1,
         1, 1, 1, 1, 1, 1, 1, 1];

var str1 = a.join('');
  //-> '1111111111111111110011111100111111000011110000111111111111111111'

var str2 = parseInt(str1, 2).toString(2);
  //-> '1111111111111111110011111100111111000011110001000000000000000000'

str1 === str2  //-> false

I would expect str2 to be the same as str1, which is not the case.

You're loosing precision. See stackoverflow.com/questions/307179/…. — ziesemer
– ziesemer, Commented Jan 9, 2012 at 0:36
If you use a more flexible language (like python) you can see that those two binary strings are only 1 value off. 18446691089982423040 and 18446691089982423039 respectively. (As @zie was saying about precision) — Brigand
– Brigand, Commented Jan 9, 2012 at 0:41
May I just say that using parseInt on a string-representation of a bitmask sound .... rather stupid? If you must have it as a string representation, how about just doing someting like function matchMask(str, pos) { return str.charAt(pos) != '0'; }. — Alxandr
– Alxandr, Commented Jan 9, 2012 at 0:41
If you don't care about politeness, you can say whatever you like. But calling matchMask for each element sounds a tad inefficient. — Marcus Booster
– Marcus Booster, Commented Jan 9, 2012 at 0:51

T.J. Crowder · Accepted Answer · 2012-01-09 01:07:34Z

6

In JavaScript, the Number type is a 64-bit double-precision value (more, and more). You've specified 64 bits there, which is beyond the realm that a 64-bit double-precision value can specify accurately (as it's a floating point type, and so must devote some bits to precision). JavaScript doesn't have an integer type (much less a 64-bit version of one), which is what a perfect-fidelity conversion would require.

I'm not all that up on floating point bit representations, but IIRC a 64-bit double-precision number can accurately represent integer values on the order of 53 significant bits, see the links for details.

edited Jan 9, 2012 at 1:07

answered Jan 9, 2012 at 0:36

T.J. Crowder

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2 Comments

Brigand Over a year ago

According to this, it's only accurate to 53 bits.

T.J. Crowder Over a year ago

@FakeRainBrigand: Thanks, I've added a link to Section 8.5. (I'd already added a mention of the 53-bit thing, but I couldn't remember a source for it; I read it somewhere other than the spec, thanks.)

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