[tatsuy]

Summary

Fix loss of precision in the latitude/longitude sent to Topotek gimbals and published on the DDS /ap/goal_lla topic.
Same issue as the Xacti fix in #34925.

Classification & Testing (check all that apply and add your own)

• Checked by a human programmer
• Non-functional change
• No-binary change
• Infrastructure change (e.g. unit tests, helper scripts)
• Automated test(s) verify changes (e.g. unit test, autotest)
• Tested manually, description below (e.g. SITL)
• Tested on hardware
• Logs attached
• Logs available on request

Not tested on hardware. Build-tested only:

• Topotek: built for CubeOrange and confirmed in the disassembly that latitude/longitude are now computed in double precision (vdiv.f64).
• DDS: built SITL with --enable-DDS and confirmed in the disassembly that latitude/longitude are now computed in double precision (cvtsi2sd + divsd).

Description

Both places store the result in a double, but calculate it as loc.lat * 1e-7. With -fsingle-precision-constant, 1e-7 is a float, so the value is computed in single precision. This rounds the longitude to steps of about 1.5e-5° (~1.4 m).

• AP_Mount_Topotek: the position is sent as ddmm.mmmm (resolution ~1.9e-6°), so the float rounding is coarser than the output format.
• AP_DDS_Client: geographic_msgs/GeoPoint defines latitude/longitude as float64.

This PR casts to double before dividing, so the full precision of the int32 location is kept.

This contribution was AI-assisted.

[tatsuy]

AP_NMEA_Output.cpp uses a similar loc.lat * 1.0e-7f pattern, but I left it out of this PR because the problem is different:

• The minutes part (min_dec) is already calculated in double, so normal output does not lose precision.
• Only the integer-degree part is calculated in float. When the position is just below an integer degree (within ~1.6e-6° for latitude, ~6.4e-6° for longitude, i.e. less than 1 m), it rounds up and the minutes become negative, producing a malformed sentence, e.g. 35.9999990 → 36-0.00006.
• Fixing it needs the degree/minute split to be reworked, not just a cast, so it seemed better handled separately.

I'm happy to add the fix to this PR or open a separate one, whichever the reviewers prefer.

[github-actions]

Global Size Summary (Total Flash delta in bytes)

Built from 4ff58a8 rebased onto 6743a33

Board	Periph	tracker	blimp	bootloader	copter	heli	iofw	plane	rover	sub
DrotekP3Pro	_	_	_	*	_	_	_	_	_	_
Durandal	_	*	*	_	-4	-4	_	-4	-4	-4
Hitec-Airspeed	*	_	_	_	_	_	_	_	_	_
KakuteF7	_	*	*	_	*	*	_	*	*	*
MambaH743v4	_	*	*	_	+4	+4	_	+4	+4	+4
MatekF405-CAN	_	_	_	*	_	_	_	_	_	_
MatekF405	_	*	*	_	*	*	_	*	*	*
MatekH743-bdshot	_	*	*	_	-4	-4	_	-4	-4	-4
Pixhawk1-1M	_	*	*	_	*	*	_	*	*	*
disco	_	*	*	_	-40	-40	_	-40	-40	-40
f103-GPS	*	_	_	_	_	_	_	_	_	_