Remove midpoint integration, superseded by free-body gyroscopic derivatives.

The gyroscopic (bias) derivatives applied to standalone free bodies by the
implicitfast integrator provide comparable stability for spinning bodies,
with none of midpoint's restrictions: they apply under contacts, fluid
forces and constraints, and preserve the linear force-velocity relation
required by discrete-time inverse dynamics. The invdiscrete flag reverts to
its original single meaning and no longer affects forward dynamics.

Restore implicitfast coverage in the DiscreteInverseMatch test, removed
when midpoint made discrete inverse dynamics untestable.

Add implicit gyroscopic (bias) derivatives for free bodies in implicitfast.

The implicitfast integrator drops the RNE (bias) derivative to stay on the
symmetric Cholesky path, so fast-spinning free bodies integrate gyroscopic
forces explicitly and can gain energy. Symmetrizing the gyroscopic Jacobian
is not an option: its stabilizing content is the antisymmetric part, and
adding only the symmetric part is destabilizing.

Instead, exploit the fact that for a standalone free body the 6x6 block of
M - h*D is decoupled from the rest of the system (qDeriv sparsity is
tree-local): after the global solve, rebuild the block with the exact bias
derivative in closed form (mjd_freeBias_vel) and re-solve it with dense
unsymmetric LU, overwriting the block's rows of qacc. For lone spinning
bodies this makes implicitfast match implicit to rounding, at ~150ns per
eligible body: cheaper than the midpoint machinery it will replace.
Eligibility is structural only; contacts, fluid and constraints need no
gating. The same block is mirrored in discrete inverse dynamics
(mj_discreteAcc), making invdiscrete exact for spinning free bodies.

PiperOrigin-RevId: 948472495
Change-Id: I813ef3d98c7b399881bc8603b9f9208cfb02eb58

doc/changelog.rst

@@ -7,6 +7,14 @@ Upcoming version (not yet released)
 
 General
 ^^^^^^^
+- Replaced midpoint integration of free bodies with :ref:`gyroscopic derivatives<geFreeBody>` in the ``implicitfast``
+  :ref:`integrator<geIntegrators>`: the bias-force derivative of every standalone free body is applied via a local
+  unsymmetric solve of its decoupled block, making ``implicitfast`` identical to ``implicit`` for such bodies.
+  Unlike midpoint integration, which required vacuum and no constraints, this applies in all environments (contacts,
+  fluid, constraints), and is compatible with discrete-time inverse dynamics. Spinning free bodies no
+  longer gain energy, but tumbling motion is now mildly damped; models requiring long-horizon energy conservation of
+  tumbling bodies in vacuum should use ``RK4``. The :ref:`invdiscrete<option-flag-invdiscrete>` flag no longer has any
+  effect on forward dynamics.
 - Added Nesterov momentum extrapolation with adaptive gradient restart (O'Donoghue-Candès) to the PGS solver,
   significantly improving convergence. Overall PGS now requires ~2x fewer iterations.
 - Added the Newton decrement -- the quadratic model's predicted cost improvement of the next iteration -- as a third
@@ -233,7 +241,7 @@ General
    improving performance by ~20%.
 3. :commit:`b9c1877e` Added support for :ref:`elastic2d<flex-elasticity-elastic2d>` for trilinear and quadratic flex
    :ref:`dofs<body-flexcomp-dof>`.
-4. :commit:`910b3336` :ref:`Midpoint integration<geMidpoint>` is now restricted to the ``implicitfast``
+4. :commit:`910b3336` Midpoint integration is now restricted to the ``implicitfast``
    :ref:`integrator<geIntegrators>` and is disabled when fluid forces are active
    (nonzero :ref:`density<option-density>` or :ref:`viscosity<option-viscosity>`).
    Midpoint integration treats external forces as zero-order-hold constants, which causes
@@ -335,7 +343,7 @@ General
    scalar arrays (``jnt_stiffness``, ``dof_damping``, etc.) continue to hold the linear coefficient and are unchanged.
    The polynomial order is defined by the new constant :ref:`mjNPOLY<glNumericSizes>`. A future breaking C-API change
    may unify the linear and higher-order coefficients into a single array.
-4. :commit:`0c337799` Added :ref:`midpoint integration<geMidpoint>` for standalone free bodies in ``implicit`` and
+4. :commit:`0c337799` Added midpoint integration for standalone free bodies in ``implicit`` and
    ``implicitfast`` :ref:`integrators<geIntegrators>`. This applies the implicit midpoint rule to the rotational
    dynamics of free bodies with no children, conserving kinetic energy to machine precision in the absence of external
    torques. The :ref:`invdiscrete<option-flag-invdiscrete>` flag now also disables midpoint integration, providing an