Added parentheses to expressions taking the squares of the wind stress
components in 70 lines in 7 files so that these expressions will be rotationally
invariant when fused-multiply-adds are enabled.  All answers are bitwise
identical in cases without FMAs, but answers could change with FMAs.

  Added parentheses to 9 expressions like `curv_3 = h_W(i) + h_E(i) - 2.0*h(i)`
in PPM_limit_pos, zonal_flux_layer, zonal_flux_thickness, merid_flux_layer and
merid_flux_thickness, changing them to `curv_3 = (h_W(i) + h_E(i)) - 2.0*h(i)`.
This change enforces the order of arithmetic that is required to give rotational
symmetry, but it also is the order that the Intel, GNU, and Nvidia compliers
were all already using in these expressions.  Moreover, had the order of
arithmetic ever been anything else, this would have led to failures in our
rotational consistency and redundant point consistency testing, and almost
certainly would have been detected before. However, by adding these parentheses,
there is a remote chance that the addition of these parentheses could change
answers for some compiler or compiler settings we have never tested before.
This change should not impact any FMA-enabled calculations.  All answers are
bitwise identical in the MOM6-examples regression suite as run on Gaea.

  Added parentheses to 16 expressions setting the grad_gradient arrays with
oblique_grad open boundary conditions and setting cff_new with all kinds of
oblique boundary conditions so that they will be rotationally invariant when
fused-multiply-adds are enabled.  All answers are bitwise identical in cases
without FMAs, but answers with certain types of open boundary conditions could
change with FMAs.

  Added parentheses to 150 lines in the 5 generic density integral routines
(int_density_dz_generic_pcm, int_density_dz_generic_plm,
int_density_dz_generic_ppm, int_spec_vol_dp_generic_pcm and
int_spec_vol_dp_generic_plm) in the MOM_density_integrals module so that they
will be rotationally invariant when fused-multiply-adds are enabled.  All
answers are bitwise identical in cases without FMAs, but answers could change
with FMAs.

  Added parentheses to 140 lines in 8 int_density_dz and int_spec_vol_dp
routines for the linear, Wright, Wright_full and Wright_red equations of state
so that they will be rotationally invariant when fused-multiply-adds are
enabled.  All answers are bitwise identical in cases without FMAs, but answers
could change with FMAs.

  Removed recently added parentheses around expressions like '+ (hL*hR)' in 110
lines in MOM_density_integrals and 4 equation of state module to reflect that
these parentheses are not necessary for rotational symmetry in
FMAs.  All answers are bitwise identical in cases without FMAs, but
answers could change with FMAs.

  Added parentheses to 4 lines in PressureForce_Mont_nonBouss and
PressureForce_Mont_Bouss so that they will be rotationally invariant when
fused-multiply-adds are enabled.  All answers are bitwise identical in cases
without FMAs, but answers could change with FMAs in cases that use the
Montgomery potential form of the pressure gradient accelerations.

  Added parentheses to 4 lines in calc_isoneutral_slopes so that they will be rotationally invariant when
fused-multiply-adds are enabled.  All answers are bitwise identical in cases
without FMAs, but answers could change with FMAs.

  Added parentheses to 2 lines in MOM_calc_varT so that they will be
rotationally invariant when fused-multiply-adds are enabled.  In this case, FMAs
can still be applied to the impacted lines, exploiting that the masks are always
0 or 1.  Also added parentheses to 2 other lines used to generate the stochastic
pattern for rotational symmetry with FMAs.  All answers are bitwise identical in
cases without FMAs, but answers could change with FMAs.

  Added parentheses to the calculation of the diffusive temperature changes in
tracer_hordiff so that it will be rotationally invariant when
fused-multiply-adds are enabled.  All answers are bitwise identical in cases
without FMAs, but answers could change with FMAs.

  Added parentheses to the calculation of the iceberg contribution to the
fractional area of ice shelves in iceberg_forces so that it will be rotationally
invariant when fused-multiply-adds are enabled.  All answers are bitwise
identical in cases without FMAs, but answers could change with FMAs enabled in
cases with tabular icebergs.

  Added parentheses to the calculation of the Stokes-drift Coriolis velocity
increments in CoriolisStokes so that it will be rotationally invariant when
fused-multiply-adds are enabled.  All answers are bitwise identical because
CoriolisStokes is still under development and is never called, with a fatal
error occurring if anyone tries to use it.  Also added parentheses to two
expressions calculating the magnitude of the Stokes velocity in
get_Langmuir_Number.  Answers could change for some cases that use Langmuir
turbulence parameterizations with FMAs enabled.

  Added the new element Coriolis2Bu to the ocean_grid_type and the
dyn_horgrid_type to hold the square of the Coriolis parameter, and use this
array in 10 routines (including btstep, set_dtbt, calculate_diagnostic_fields,
VarMix_init, propagate_int_tide, Calculate_kappa_shear, Calc_kappa_shear_vertex
and add_MLrad_diffusivity) that had been calculating and averaging the square of
the Coriolis parameter.  This could change some answers with FMAs enabled
because the compilers were previously free to split up some of the squares
when averaging the squared Coriolis parameter, but without FMAs all answers are
bitwise identical.  This commit does add a new element to two transparent
types.

  Added parentheses to 17 expressions in thickness_diffuse_full,
thickness_diffuse and thickness_diffuse_init to give rotationally consistent
solutions when fused-multiply-adds are enabled.  One comment was also added to
note that the calculation of PE_release_h is does not exhibit rotational
symmetry when MEKE_GM_SRC_ALT is set to true.  All answers are bitwise identical
in cases without FMAs, but answers could change when FMAs are enabled.

  Added parentheses to 2 expressions in the Zanna_Bolton code and rearranged
another line so that the u- and v-discretizations introduce terms in the same
order so that the Zanna_Bolton code will exhibit rotationally consistent
solutions when fused-multiply-adds are enabled.  All answers are bitwise
identical in cases without FMAs, but answers could change with FMAs enabled in
cases that use the Zanna-Bolton parameterization.

  Added parentheses to 19 expressions in the MOM_internal_tides propagation code
to exhibit rotationally consistent solutions when fused-multiply-adds are
enabled.  All answers are bitwise identical in cases without FMAs, but answers
could change when FMAs are enabled in models that use the ray-tracing based
internal tides code.

  Added parentheses to 10 expressions in find_uv_at_h to exhibit rotationally
consistent solutions and treat the velocities at both edges of a tracer cell
equivalently when fused-multiply-adds are enabled. All answers are bitwise
identical in cases without FMAs, but answers could change when FMAs are enabled.

  Added parentheses to 19 expressions in set_viscous_ML, set_u_at_v and
set_v_at_u to treat the velocities at both edges of a tracer cell equivalently
when fused-multiply-adds are enabled, and thereby to exhibit exhibit
rotationally consistent solutions.  Also swapped the order of the u- and
v-components in the u-point calculation of Uh2 to mirror the order of the
corresponging v-point calculation for the same purpose.  All answers are bitwise
identical in cases without FMAs, but answers could change when FMAs are enabled.

  Added mathematically equivalent rearrangements of the code in
calc_kappa_shear_vertex that interpolates velocities, temperatures and
salinities to the vertices to expose the mask variables while ensuring that the
other multiplications occur within parentheses so that they will exhibit
rotational symmetry when fused-multiply-adds are enabled.  FMAs can still occur,
but it will be multiplication by the 0-or-1 masks that are fused with an
addition.  Also added parentheses to 3 expressions calculating the squared shear
in calculate_projected_state for rotational symmetry with FMAs.  All answers are
bitwise identical in cases without FMAs, but answers could change when FMAs are
enabled.

  Added parentheses to 4 expressions in add_drag_diffusivity, set_BBL_TKE and
add_LOTW_BBL_diffusivity setting the bottom-drag contributions to TKE and
friction velocity so that they will exhibit rotationally consistent solutions
when fused-multiply-adds are enabled.  All answers are bitwise identical in
cases without FMAs, but answers could change when FMAs are enabled.

  Added parentheses to 20 expressions in CorAdCalc and one in gradKE to exhibit
rotationally consistent solutions when fused-multiply-adds are enabled.  All
answers are bitwise identical in cases without FMAs, but answers could change
when FMAs are enabled.

  Added parentheses to 18 expressions in btstep, and one more each in set_dtbt
and barotropic_init to exhibit rotationally consistent solutions when
fused-multiply-adds are enabled.  All answers are bitwise identical in cases
without FMAs, but answers could change when FMAs are enabled.

  Added parentheses to 19 expressions in 5 routines (calc_Visbeck_coeffs_old,
calc_Eady_growth_rate_2D, calc_slope_functions_using_just_e,
calc_QG_Leith_viscosity VarMix_init) in MOM_lateral_mixing_coeffs.F90 to give
rotationally consistent solutions when fused-multiply-adds are enabled.  Also
reordered terms in a sum in the calculation of beta_dx2_u to mirror that of
beta_dx2_v, also for rotational symmetry with FMAs.  All answers are bitwise
identical in cases without FMAs, but answers could change for some parameter
settings when FMAs are enabled.

  Added parentheses to 40 expressions horizontal_viscosity and another 14
expressions in in hor_visc_init and 3 more in align_aniso_tensor_to_grid to give
rotationally consistent solutions when fused-multiply-adds are enabled.   Also
swapped the order of two terms in the expression for Del2u to mirror the order
of the corresponding terms in Del2v for rotational symmetry with FMAs.  All
answers are bitwise identical in cases without FMAs, but answers could change
when FMAs are enabled.

  Added parentheses to 20 sums of squares of x- and y- distances or velocity
components used for initialization in 8 modules to give rotationally consistent
solutions when fused-multiply-adds are enabled.  All answers are bitwise
identical in cases without FMAs, but answers could change when FMAs are enabled.

  Added parentheses to 29 sums of squares of velocity or other vector components
used in parameterizations in 9 modules to give rotationally consistent solutions
when fused-multiply-adds are enabled.  All answers are bitwise identical in
cases without FMAs, but answers could change when FMAs are enabled.

  Added parentheses to 9 diagnostics of Coriolis accelerations or expressions
used in the kinetic energy budgets to give rotationally consistent solutions
when fused-multiply-adds are enabled.  All answers are bitwise identical in
cases without FMAs, but answers could change when FMAs are enabled.

  Added parentheses to 4 tracer edge value calculations used with PPM tracer
advection to give rotationally consistent solutions when fused-multiply-adds are
enabled.  Although these lines may not appear to need parentheses, some
compliers appear to be putting these expressions directly into others, where the
direction of the flow seems to determine which multiplications are incorporated
into FMAs.  All answers are bitwise identical in cases without FMAs, but answers
could change when FMAs are enabled.

  Added parentheses around the full expressions for intz and intp in 10 more
lines in 4 generic density integral routines (int_density_dz_generic_pcm,
int_density_dz_generic_ppm, int_spec_vol_dp_generic_pcm and
int_spec_vol_dp_generic_plm) in the MOM_density_integrals module so that
non-Boussinesq cases will be rotationally invariant when fused-multiply-adds are
enabled.  Although this might not seem to do anything, these parentheses do
matter if these expressions are in-lined in the sums where they are used a few
lines later.  The analogous parentheses had previously been added to
int_density_dz_generic_plm.  All answers are bitwise identical in cases without
FMAs, but answers could change with FMAs.

  Added parentheses to prevent FMAs in 4 expressions in end_value_h4 that rely
on exact vertical symmetry in order to get the cancellations that are necessary
to pass the vertical remapping unit testing.  Before this change, the MOM6
unit-testing was failing when FMAs are enabled, but with it the unit-testing is
passing even when FMAs are enabled.  All answers are bitwise identical in cases
without FMAs, but answers could change with FMAs.

initialize cpl_scalar field when created

…240531

update to main 20240729 commit (gfdl-to-main-2024-05-31)

…ymmetry_main

(*)Add parentheses for FMA rotational symmetry

…20240824

…240824

update to main 20240824

…l-scalar

initialize cpl_scalar field in nuopc cap