[matthias-kleiner]

Follow-up to #15986. TrackParametrization, TrackParametrizationWithError and TrackUtils call the float-only gpu::CAMath functions (Sqrt, ASin, ATan2, ...), so TrackParD / PropagatorD is effectively float. Compared with a std:: double reference, propagateParamTo(x, b[3]) from x = 85 to 250 cm in 100 steps is off by 0.4 to 74 µm, depending on pt and the field (toy fields with a transverse component, no material), and finite-difference derivatives through it are noisy. This affects the barrel alignment (Detectors/Align) and the ITS3 alignment; no reconstruction workflow uses the double types.

Call math_utils::detail::{sqrt, asin, ...}<value_t> instead, as Propagator.cxx already does: for double these dispatch to the double functions, for float to the same functions as before. Add GPUCommonMath::Expd and math_utils::detail::exp for the remaining Exp calls. This restores the math_utils::detail calls of cd9835a (switched back to CAMath in bf65d3c) and extends them to TrackParametrizationWithError and TrackUtils.

Float results are bit-identical; TrackParD now agrees exactly with the double reference.

[shahor02]

Thanks for spotting and fixing!

[davidrohr]

ok for GPUCommonMath changes

[alibuild]

Error while checking build/O2/fullCI_slc9 for 98bcd15 at 2026-10-21 12:37:

## sw/BUILD/O2-full-system-test-latest/log
command /sw/slc9_x86-64/O2/slc9_x86-64-slc9_x86-64-local11/prodtests/full-system-test/dpl-workflow.sh had nonzero exit code 1
[5586:internal-dpl-ccdb-backend]: [12:37:15][ERROR] CCDBDownloader CURL transfer error - Timeout was reached
[5586:internal-dpl-ccdb-backend]: [12:37:15][ERROR] CcdbDownloader finished transfer http://alice-ccdb.cern.ch/TRD/Calib/CalGain for 1550600800023 (agent_id: o2-itsmft-stf-d/o2-itsmft-stf-decoder-workflow@5586 target/Linux_x86_64 init/1792578817806 id/mesosci@alissandra02 session/IPvB49pK) with http code: 0
[5586:internal-dpl-ccdb-backend]: [12:37:15][ERROR] File TRD/Calib/CalGain could not be retrieved. No more hosts to try.
[5586:internal-dpl-ccdb-backend]: [12:37:15][FATAL] Unable to find CCDB object TRD/Calib/CalGain/1550600800023
[5586:internal-dpl-ccdb-backend]: [12:37:16][ERROR] Exception while running: Fatal error. Rethrowing.
[5586:internal-dpl-ccdb-backend]: [12:37:16][FATAL] Unhandled o2::framework::runtime_error reached the top of main of o2-itsmft-stf-decoder-workflow, device shutting down. Reason: Fatal error
[ERROR] Workflow crashed - PID 5586 (internal-dpl-ccdb-backend) did not exit correctly however it's not clear why. Exit code forced to 128.
[ERROR]  - Device internal-dpl-ccdb-backend: pid 5586 (exit 128)
[INFO]    - First error: [12:37:15][FATAL] Unable to find CCDB object TRD/Calib/CalGain/1550600800023
[ERROR] SEVERE: Device internal-dpl-ccdb-backend (5586) had at least one message above severity 7: Unable to find CCDB object TRD/Calib/CalGain/1550600800023


## sw/BUILD/o2checkcode-latest/log
--
========== List of errors found ==========
++ GRERR=0
++ grep -a -v clang-diagnostic-error error-log.txt
++ grep -a ' error:'
++ GRERR=1
++ [[ 1 == 0 ]]
++ mkdir -p /sw/INSTALLROOT/11de5df8da57992a091a6434770fd0656d5ad36f/slc9_x86-64/o2checkcode/1.0-local17/etc/modulefiles
++ alibuild-generate-module
+ HAS_BIN=
+ HAS_LIB=
+ HAS_CMAKE=
+ HAS_ROOT=
+ '[' 0 '!=' 0 ']'
+ cat
+ printf 'if ![ is-loaded '\''BASE/1.0'\'' ] {\n module load BASE/1.0\n}'
+ echo 'BUILD_REQUIRES=CMake alibuild-recipe-tools defaults-release'
BUILD_REQUIRES=CMake alibuild-recipe-tools defaults-release
+ FULL_BUILD_REQUIRES='FairCMakeModules pytorch_cpuinfo double-conversion ninja-fortran alibuild-recipe-tools googlebenchmark json-c O2-customization MPFR Alice-GRID-Utils CMake defaults-release safe_int Python-modules-list date bz2 ninja UUID'
+ echo 'FULL_BUILD_REQUIRES=FairCMakeModules pytorch_cpuinfo double-conversion ninja-fortran alibuild-recipe-tools googlebenchmark json-c O2-customization MPFR Alice-GRID-Utils CMake defaults-release safe_int Python-modules-list date bz2 ninja UUID'
FULL_BUILD_REQUIRES=FairCMakeModules pytorch_cpuinfo double-conversion ninja-fortran alibuild-recipe-tools googlebenchmark json-c O2-customization MPFR Alice-GRID-Utils CMake defaults-release safe_int Python-modules-list date bz2 ninja UUID
++ env
++ cut -f1 -d=
++ grep -v '^DEFAULT_'
++ grep -v PKGREVISION
++ grep -v ALIBUILD_RECIPE_TOOLS
++ grep REVISION
++ sed -e s/_REVISION//
+ for x in $(env | cut -f1 -d= | grep -v "^DEFAULT_" | grep -v PKGREVISION | grep -v ALIBUILD_RECIPE_TOOLS | grep REVISION | sed -e 's/_REVISION//')
++ eval 'echo $LIBFFI_REVISION'
+++ echo 14
+ REVISION_VALUE=14
++ eval 'echo $LIBFFI_VERSION'
+++ echo v3.2.1-alice1
[0 more errors; see full log]

Full log here.