format_timedelta Function

    pure function format_timedelta(td, compact) result(str)
        !! version: experimental
        !!
        !! Format a timedelta_type as a readable string.
        !! When days == 0 and compact is present and .true., sub-second/sub-minute durations are
        !! formatted compactly (e.g. "5ms", "1.500s", "05:30[.mmm]"); the "0 days, " prefix is omitted.
        !! When compact is absent or .false., or when days /= 0, the original verbose format is preserved.
        type(timedelta_type), intent(in) :: td
        logical, intent(in), optional :: compact
        character(:), allocatable :: str
        integer :: h, m, s, ms
        logical :: show_compact

        h  = td%seconds / 3600
        m  = mod(td%seconds, 3600) / 60
        s  = mod(td%seconds, 60)
        ms = td%milliseconds
        show_compact = .false. ! .false. by default
        if (present(compact)) show_compact = compact

        if (td%days == 0 .and. show_compact) then
            ! Compact formatting for zero-day durations
            if (h == 0 .and. m == 0 .and. s == 0) then
                if (ms == 0) then
                    str = "0s"
                else
                    str = to_string(ms, '(I0)') // "ms"
                end if
                return
            end if

            if (h == 0 .and. m == 0) then
                if (ms == 0) then
                    str = to_string(s, '(I0)') // "s"
                else
                    str = to_string(s, '(I0)') // "." // to_string(ms, '(I3.3)') // "s"
                end if
                return
            end if

            if (h > 0) then
                str = to_string(h, '(I2.2)') // ":" // &
                      to_string(m, '(I2.2)') // ":" // &
                      to_string(s, '(I2.2)')
            else
                str = to_string(m, '(I2.2)') // ":" // &
                      to_string(s, '(I2.2)')
            end if

            if (ms /= 0) str = str // "." // to_string(ms, '(I3.3)')
        else
            ! Original format for durations with days
            str = to_string(td%days, '(I0)') // ' days, ' // &
                  to_string(h, '(I2.2)') // ':' // &
                  to_string(m, '(I2.2)') // ':' // &
                  to_string(s, '(I2.2)')

            if (ms /= 0) then
                str = str // '.' // to_string(ms, '(I3.3)')
            end if
        end if
    end function format_timedelta