This is somewhat related to bug #65291 and I am the same "Anonymous" as has been posting there.

The degrees2dm function in the mapping package from https://sourceforge.net/p/octave/mapping/ci/default/tree/inst/degrees2dm.m has some accuracy issues.  For example, degrees2dm(realmax()) returns [realmax(), NaN] instead of [realmax(), 0], and degrees2dm (2e14 + 0.25) returns [2e14, 16] instead of [2e14, 15].

Attached is a version of degrees2dm.m with the following changes:

• Documentation:
  • Specify that the minutes component will always have magnitude less than 60.
  • Adjust the first example to make everything exact and to demonstrate fractional minutes.
  • Remove the second example which was incorrect and is now redundant.
  • Correct a variable name mismatch in the last example.
  • Remove the negative sign (which does not seem to be displayed by default) from a zero in the result in the last example.
• Implementation:
  • Reject non-real input.
  • Add special handling for char and logical input to improve performance and clarity.
  • Change the computation of the minutes to improve accuracy.  It should now always return the correctly rounded result (assuming fix(), subtraction, and multiplication are correctly rounded, which I expect is true).
    • Overflow for large inputs is avoided.
    • Minutes now depend only on the fractional part of the input.
    • Possible issues are avoided by not using the rem function.  Documentation for rem claims that "values within a few eps of an integer will be rounded to that integer before computation for compatibility with MATLAB", but I have failed to verify this.
  • Update the sign-flipping logic to account for the change to the computation of the minutes, and hopefully improve clarity.
    • Signs (including of zeros) should match MATLAB R2023b.  See https://savannah.gnu.org/bugs/?65291#comment13 for source of MATLAB behavior.
  • Reject input types not explicitly handled.
    • This might be unreachable currently, but is intended to prevent applying the function to types where it hasn't been validated.  Not sure this is a good idea.
• Tests:
  • Add tests which fail with the existing implementation.
  • Add tests which do not fail with the existing implementation, but do help demonstrate correctness.
• Other:
  • Add `## Copyright (C) 2024 The Octave Project Developers` because I am offering this contribution anonymously.