test_fixed_point_ln¶

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¶

`_EXHAUSTIVE`
`LN_EXACT`
`LN_MEASURED_ULP`

Functions¶

`_boundary_inputs`() → list[int]	Every 2**k and its neighbours: the exponent transitions.
`_sweep`(point, values) → tuple[int, int, int]
`test_the_reference_is_the_mathematics_not_an_algorithm`() → None	Values a human can check, so the reference cannot drift into being a
`test_ln_of_a_non_positive_value_is_refused`() → None	Same position the sqrt tile takes: no value exists, and substituting
`test_ln_is_faithful_not_correctly_rounded`() → None	Records the class honestly. exp-light and the normal CDF reach their
`test_the_exponent_boundaries_are_exact`() → None	Normalisation is the part that can be off by one power of two, and it
`test_the_operating_point_meets_its_recorded_bound`() → None
`test_the_two_tier_sweep_agrees_with_the_exact_reference`() → None	The affordable sweep must answer what the expensive one answers.
`test_the_light_point_is_faithful_at_the_full_points_known_deviation`() → None	The registered light point carries the SAME 1-ULP contract, measured

Module Contents¶

test_fixed_point_ln._EXHAUSTIVE¶

test_fixed_point_ln.LN_EXACT¶

test_fixed_point_ln.LN_MEASURED_ULP = 1¶

test_fixed_point_ln._boundary_inputs() → list[int]¶: Every 2**k and its neighbours: the exponent transitions.

test_fixed_point_ln._sweep(point: dau_core.fixed_point.LnDatapath, values) → tuple[int, int, int]¶

test_fixed_point_ln.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.

test_fixed_point_ln.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.

test_fixed_point_ln.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.

test_fixed_point_ln.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.

test_fixed_point_ln.test_the_operating_point_meets_its_recorded_bound() → None¶

test_fixed_point_ln.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.

test_fixed_point_ln.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.