test_fixed_point_ln
===================

.. py:module:: test_fixed_point_ln

.. autoapi-nested-parse::

   The ln datapath's accuracy is a measured fact, like exp's.

   ln's domain is 2,147,483,647 inputs -- exhaustive in this model but not in
   simulation, so the default sweep is strided and DAU_EXHAUSTIVE=1 runs the
   whole thing. The strided sweep always includes every power-of-two boundary,
   because those are the exponent transitions where a normalizing datapath
   fails if it fails anywhere.



Attributes
----------

.. autoapisummary::

   test_fixed_point_ln._EXHAUSTIVE
   test_fixed_point_ln.LN_EXACT
   test_fixed_point_ln.LN_MEASURED_ULP


Functions
---------

.. autoapisummary::

   test_fixed_point_ln._boundary_inputs
   test_fixed_point_ln._sweep
   test_fixed_point_ln.test_the_reference_is_the_mathematics_not_an_algorithm
   test_fixed_point_ln.test_ln_of_a_non_positive_value_is_refused
   test_fixed_point_ln.test_ln_is_faithful_not_correctly_rounded
   test_fixed_point_ln.test_the_exponent_boundaries_are_exact
   test_fixed_point_ln.test_the_operating_point_meets_its_recorded_bound
   test_fixed_point_ln.test_the_two_tier_sweep_agrees_with_the_exact_reference
   test_fixed_point_ln.test_the_light_point_is_faithful_at_the_full_points_known_deviation


Module Contents
---------------

.. py:data:: _EXHAUSTIVE

.. py:data:: LN_EXACT

.. py:data:: LN_MEASURED_ULP
   :value: 1


.. py:function:: _boundary_inputs() -> list[int]

   Every 2**k and its neighbours: the exponent transitions.


.. py:function:: _sweep(point: dau_core.fixed_point.LnDatapath, values) -> tuple[int, int, int]

.. py:function:: test_the_reference_is_the_mathematics_not_an_algorithm() -> None

   Values a human can check, so the reference cannot drift into being a
   description of whatever the datapath does.


.. py:function:: test_ln_of_a_non_positive_value_is_refused() -> None

   Same position the sqrt tile takes: no value exists, and substituting
   one would be a wrong number that looks right.


.. py:function:: test_ln_is_faithful_not_correctly_rounded() -> None

   Records the class honestly. exp-light and the normal CDF reach their
   registered contracts; ln does not at this operating point, and a caller
   choosing between them should see that rather than infer it.

   Whether a correctly-rounded ln is worth having is a separate question:
   the exp arc showed the fix is either more internal precision or more
   polynomial degree, and which one binds is not predictable without
   measuring both.


.. py:function:: test_the_exponent_boundaries_are_exact() -> None

   Normalisation is the part that can be off by one power of two, and it
   shows up here or nowhere.


.. py:function:: test_the_operating_point_meets_its_recorded_bound() -> None

.. py:function:: test_the_two_tier_sweep_agrees_with_the_exact_reference() -> None

   The affordable sweep must answer what the expensive one answers.

   The harness decides in double and re-decides only near-boundary inputs
   against the 80-digit reference. That is only sound if it never differs
   from an all-exact sweep, so this checks both over a window containing a
   KNOWN deviation -- a harness that agreed everywhere except where the
   datapath is wrong would be worse than useless.


.. py:function:: test_the_light_point_is_faithful_at_the_full_points_known_deviation() -> None

   The registered light point carries the SAME 1-ULP contract, measured
   by an exhaustive sweep (3,544 of 2,147,483,647 off by one, against the
   full point's 459). Pin the shared boundary case here; the full-domain
   number lives in the registry entry and BENCHMARKS.