Reason for the do...while loop in toLatLon(), utm.js

[Ant1882]

More of a query than an issue. Does the do...while loop here serve much purpose?

geodesy/utm.js

Lines 135 to 142 in 761587c

	do {
	const σi = Math.sinh(e*Math.atanh(e*τi/Math.sqrt(1+τi*τi)));
	const τiʹ = τi * Math.sqrt(1+σi*σi) - σi * Math.sqrt(1+τi*τi);
	δτi = (τʹ - τiʹ)/Math.sqrt(1+τiʹ*τiʹ)
	* (1 + (1-e*e)*τi*τi) / ((1-e*e)*Math.sqrt(1+τi*τi));
	τi += δτi;
	} while (Math.abs(δτi) > 1e-12); // using IEEE 754 δτi -> 0 after 2-3 iterations
	// note relatively large convergence test as δτi toggles on ±1.12e-16 for eg 31 N 400000 5000000

The reason I ask is that I converted the code (UTM <--> Lat/Lon) to embedded C, which works fine apart from this loop. If I take out the loop then I get the correct answer anyways, it appears as though my loop condition is incorrect, and I don't understand enough about what it is doing to change it, I wrote as:

} while(fabs(delTaui) > 1e-12); // using IEEE 754 δτi -> 0 after 2-3 iterations

Where "delTaui" is of type double.

Would it be possible to explain to me the need for this loop? I'm not very mathematically minded but I appreciate things are done for a reason and me just running the loop once and getting the correct answer doesn't mean I always will... I guess it depends on the location?

Many thanks,

Ant