test_fixed_point_normal_cdf
===========================

.. py:module:: test_fixed_point_normal_cdf

.. autoapi-nested-parse::

   The normal CDF datapath, swept over EVERY representable input.

   This is the one transcendental whose useful domain is small enough that the
   correctness claim is a proof rather than a sample: 573,441 inputs, all of
   them checked here by default. exp is 1.45M (feasible but slower, so strided
   by default) and ln is 2.1 billion (never exhaustive in the suite).



Attributes
----------

.. autoapisummary::

   test_fixed_point_normal_cdf.CDF_EXACT
   test_fixed_point_normal_cdf.CDF_MEASURED_ULP


Functions
---------

.. autoapisummary::

   test_fixed_point_normal_cdf._sweep
   test_fixed_point_normal_cdf.test_the_registered_point_is_correctly_rounded_over_every_input
   test_fixed_point_normal_cdf.test_the_tile_is_total_and_saturates_exactly
   test_fixed_point_normal_cdf.test_symmetry_holds_exactly
   test_fixed_point_normal_cdf.test_a_cheaper_point_is_not_correctly_rounded


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

.. py:data:: CDF_EXACT

.. py:data:: CDF_MEASURED_ULP
   :value: 0


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

   (worst ULP, wrong, checked) over the whole domain. Double decides the
   ordinary inputs; anything too close to a rounding boundary for it is
   re-decided against the 80-digit reference.


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

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

   No error path: every int32 input has an answer, and the saturation IS
   the correctly rounded value rather than a clamp.


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

   The datapath folds on it, so a break here is a wrong answer for every
   negative input at once.


.. py:function:: test_a_cheaper_point_is_not_correctly_rounded(table_bits: int, degree: int) -> None

   Pins WHY the registered point costs what it does: the obvious cheaper
   configuration misses, so the extra segments are load-bearing rather than
   conservative.