bitwise AND in Javascript with a 64 bit integer

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Javascript represents all numbers as 64-bit double precision IEEE 754 floating point numbers (see the ECMAscript spec, section 8.5.) All positive integers up to 2^53 can be encoded precisely. Larger integers get their least significant bits clipped. This leaves the question of how can you even represent a 64-bit integer in Javascript — the native number data type clearly can’t precisely represent a 64-bit int.

The following illustrates this. Although javascript appears to be able to parse hexadecimal numbers representing 64-bit numbers, the underlying numeric representation does not hold 64 bits. Try the following in your browser:

<html>
  <head>
    <script language="javascript">
      function showPrecisionLimits() {
        document.getElementById("r50").innerHTML = 0x0004000000000001 - 0x0004000000000000;
        document.getElementById("r51").innerHTML = 0x0008000000000001 - 0x0008000000000000;
        document.getElementById("r52").innerHTML = 0x0010000000000001 - 0x0010000000000000;
        document.getElementById("r53").innerHTML = 0x0020000000000001 - 0x0020000000000000;
        document.getElementById("r54").innerHTML = 0x0040000000000001 - 0x0040000000000000;
      }
    </script>
  </head>
  <body onload="showPrecisionLimits()">
    <p>(2^50+1) - (2^50) = <span id="r50"></span></p>
    <p>(2^51+1) - (2^51) = <span id="r51"></span></p>
    <p>(2^52+1) - (2^52) = <span id="r52"></span></p>
    <p>(2^53+1) - (2^53) = <span id="r53"></span></p>
    <p>(2^54+1) - (2^54) = <span id="r54"></span></p>
  </body>
</html>

In Firefox, Chrome and IE I’m getting the following. If numbers were stored in their full 64-bit glory, the result should have been 1 for all the substractions. Instead, you can see how the difference between 2^53+1 and 2^53 is lost.

(2^50+1) - (2^50) = 1
(2^51+1) - (2^51) = 1
(2^52+1) - (2^52) = 1
(2^53+1) - (2^53) = 0
(2^54+1) - (2^54) = 0

So what can you do?

If you choose to represent a 64-bit integer as two 32-bit numbers, then applying a bitwise AND is as simple as applying 2 bitwise AND’s, to the low and high 32-bit ‘words’.

For example:

var a = [ 0x0000ffff, 0xffff0000 ];
var b = [ 0x00ffff00, 0x00ffff00 ];
var c = [ a[0] & b[0], a[1] & b[1] ];

document.body.innerHTML = c[0].toString(16) + ":" + c[1].toString(16);

gets you:

ff00:ff0000

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