This is a bug.

The problem is triggered by your naming. You use x, y throughout your functions. It seems that actual parameters names interference with dummy parameters names. Here it's evident: arguments-bug.sm (3kb) downloaded 38 time(s).

To workaround, please change names of parameters in your functions, namely in atan2. E.g., you may make it atan2(yy;xx):= ....

Created SS-2327.

Jean, you keep amusing me. Being a bright person, and making valuable contributions, you too often post either irrelevant or plain wrong comments, this one being both. It's wise to try to get some literacy in the topic before posting.

The coding of jofegibo is done letter-to-letter by definition given in Wikipedia (just above the "2.1 Derivation of atan2(y, x)" section), and is quite correct. It is somewhat redundant, as it's not necessary to check that y = 0 in subsequent conditions (it is already true since those conditions are in "else" clause of "if y!=0" ), but this doesn't do any harm.

Anyway, your comment is not only incorrect, but also irrelevant (as in other topics, too): the origial poster didn't ask advise on the coding, but made a well-defined question that highlights existing problem.

Please, try to refrain of irrelevant comments in every topic you happen to notice, just because it distracts those who have something to say on essence of the matter, and make it harder to search the forum for a relevant info.

"atan2(x,y) => returns the angle in radian from the 'x' axis to a line
containing the ORIGIN [0,0] and the point [x,y]. The value returned is
always between -π and π including π. Both x,y must be real".

That definition is correct and universal. What's confusing is Smath built-in "mwatan2(,,)
That's why I posted an example for edu/observe. Otherwise Smath angle is even more simple:

x:=64.644 ,,,,, y:=135.355
arg(x+y*i)=64.471393°

'z' in the front end comes out of the blue. If it's further needed, and produces red ?
Maybe some info are missing about what is doing what for what.

Cheers, Jean.

Your atan2(y,x) is right with your Smath version.
But there is a bug in your version wrt to "atan2(,,)
the universal implementation and bug wrt Smath 5346
which version respects the maths adopted convention.

Your own screenshot shows that there's NO error in mwatan(#,#). Maybe you were confused by the names of arguments?

By definition, atan2(y,x)≡arg(x+i*y)

Please notice that atan2 has y and x in "reversed" order.

What is "UNIVERSAL IMPLEMENTATION" of atan2? Link please.

Oh really?

Let's ask IBM, the Fortran inventor:
http://www.ibm.com/suppo...e_ref/atan2.html?lang=en

Your version of Mathcad uses non-standard definition, but that doesn't make it standard.

Jean,
you are ignorant troll. End of it. I only ask you: please, don't ever bother to answer to my posts.

atan2.sm (19kb) downloaded 29 time(s).Hi,jofegibo.

If you take the code from Wikipedia, the error will not
https://en.wikipedia.org...finition_and_computation

... all that said: "Atan(y, x) = Arg(x + yi)"

Happy reconciliation.

Oh! You scared me!

Actually, you should look what is actually assigned to a. To do so, just put caret at the beginning of the expression, and use right arrow to travel to the right. Keep attention to the underscore.
You'll see that it's only first part (sin(dlat/2))^2 that is actually assigned. Everything else is just added to the result of assignment:

(a:(sin(dlat/2))^2)+cos({lat1*π}/180)*cos({lat2*π}/180)*(sin(dlong/2))^2=0.0151