Please explain the purpose of the bitwise or in this javascript function

Question

I am converting a javascript function to java, and don't understand the purpose of the bitwise ors in the code below:

(Math.tan(PHId)) ^ 2) - is this ensuring the number always ends in 2?
(Et ^ 6)

The code is part of a library to convert Irish Grid References to/from Latitude and Longitude: http://www.nearby.org.uk/tests/geotools2.js

GT_Math.E_N_to_Lat = function(East, North, a, b, e0, n0, f0, PHI0, LAM0)
{
    //Un-project Transverse Mercator eastings and northings back to latitude.
    //Input: - _
    //eastings (East) and northings (North) in meters; _
    //ellipsoid axis dimensions (a & b) in meters; _
    //eastings (e0) and northings (n0) of false origin in meters; _
    //central meridian scale factor (f0) and _
    //latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.

    //'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS

    //Convert angle measures to radians
    var Pi = 3.14159265358979;
    var RadPHI0 = PHI0 * (Pi / 180);
    var RadLAM0 = LAM0 * (Pi / 180);

    //Compute af0, bf0, e squared (e2), n and Et
    var af0 = a * f0;
    var bf0 = b * f0;
    var e2 = (Math.pow(af0,2) - Math.pow(bf0,2)) / Math.pow(af0,2);
    var n = (af0 - bf0) / (af0 + bf0);
    var Et = East - e0;

    //Compute initial value for latitude (PHI) in radians
    var PHId = GT_Math.InitialLat(North, n0, af0, RadPHI0, n, bf0);
    
    //Compute nu, rho and eta2 using value for PHId
    var nu = af0 / (Math.sqrt(1 - (e2 * ( Math.pow(Math.sin(PHId),2)))));
    var rho = (nu * (1 - e2)) / (1 - (e2 * Math.pow(Math.sin(PHId),2)));
    var eta2 = (nu / rho) - 1;
    
    //Compute Latitude
    var VII = (Math.tan(PHId)) / (2 * rho * nu);
    var VIII = ((Math.tan(PHId)) / (24 * rho * Math.pow(nu,3))) * (5 + (3 * (Math.pow(Math.tan(PHId),2))) + eta2 - (9 * eta2 * (Math.pow(Math.tan(PHId),2))));
    var IX = ((Math.tan(PHId)) / (720 * rho * Math.pow(nu,5))) * (61 + (90 * ((Math.tan(PHId)) ^ 2)) + (45 * (Math.pow(Math.tan(PHId),4))));
    
    var E_N_to_Lat = (180 / Pi) * (PHId - (Math.pow(Et,2) * VII) + (Math.pow(Et,4) * VIII) - ((Et ^ 6) * IX));
    
    return (E_N_to_Lat);
}

Can you please explain a bit further what you don't understand exactly? ^ is bitwise XOR. — Etheryte
– Etheryte, Commented May 6, 2022 at 21:15
I'm not sure what the type will be of the result of (Math.tan(PHId)) in javascript? I would imagine this is some sort of arithmetic shortcut, but I can't see how that would work if the result is a double/float. Thanks, Mark. — Mark Wickens
– Mark Wickens, Commented May 6, 2022 at 21:25
OK I found this: Before a bitwise operation is performed, JavaScript converts numbers to 32 bits signed integers. After the bitwise operation is performed, the result is converted back to 64 bits JavaScript numbers. — Mark Wickens
– Mark Wickens, Commented May 6, 2022 at 21:32

Bergi · Accepted Answer · 2022-05-06 23:20:13Z

4

I recommend to ask the author of the script.

However, I am reasonably certain that this is simply a mistake, and what was meant is Math.tan(PHId) ** 2 / Math.pow(Math.tan(PHId), 2) and Et ** 6/ Math.pow(Et, 6), i.e. exponentiation instead of bitwise OR. I believe this because

bitwise OR just doesn't make sense in numeric code
this looks very much like a series expansion - the preceeding terms also use exponentiation, and the mistake likely wasn't noticed because it introduces only a small error
All the other methods in the script (E_N_to_Long, Lat_Long_to_East, Lat_Long_to_North) use Math.pow everywhere, E_N_to_Lat is the only one to use ^

I am converting a javascript function to java

Notice the comment at the top of the script:

 * Credits

 * The algorithm used by the script for WGS84-OSGB36 conversions is derived 
 * from an OSGB spreadsheet (www.gps.gov.uk) with permission. This has been
 * adapted into PHP by Ian Harris, and Irish added by Barry Hunter

I would advise to start from these primary sources, instead of translating the JavaScript translation of a PHP translation of a spreadsheet formula translation of mathematics into Java.

answered May 6, 2022 at 23:20

Bergi

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2 Comments

Mark Wickens Over a year ago

Thank you very much for the response. I have asked the author, he is going to check against the original PHP code. The error introduced by the ^2 is 2x10-8 so as you rightly concluded very small.

Mark Wickens Over a year ago

I contacted the author and it is indeed a conversion error from the original PHP code, the XOR should be raise to power. Thanks for all the help.

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