test: characterize SScalar and document what it is

[oberbichler]

Why

SScalar is 746 lines with 20 C++ test cases covering the operators and a handful of functions, and 4 Python tests. The plan is to change its storage — and without a net, a change of that size cannot be verified, only hoped for. It is the same gap that let three memory-safety bugs through on the DDScalar side earlier in this series.

This is step 1 of three: characterize, then change the storage (#next), then second order.

What

test/src/test_sscalar.cpp covers the functions the existing cases miss — reciprocal, cbrt, the inverse trigonometric and all hyperbolic functions, the exponential and logarithmic family, abs — plus the behaviour nothing pinned at all: construction and the factories, comparison by value only, eval against a displacement, what size counts, and printing. Expected values derived symbolically, so they share no formulas with the header.

Python goes from 4 tests to 12, aimed at what the bindings add rather than at the mathematics: the operator set including the reverse and in-place forms, the NumPy aliases against their primary names, __len__, __abs__, __pow__, __repr__, and that copy, deepcopy and pickle all raise.

Validated by mutation

Five deliberate faults in the header, each failing three assertions:

mutation
cbrt derivative 3 → 2	3 failed
acos loses its sign	3 failed
atanh denominator sign	3 failed
log10 on the wrong base	3 failed
sinh derivative cosh → sinh	3 failed

Two fixes, both prerequisites rather than scope

m_f was indeterminate. The defaulted constructor left it uninitialized, so a test asserting S().f() == 0 would have been testing luck rather than behaviour. Initialized now.

eval copied the name on every iteration. clang-tidy had never reported it because nothing instantiated eval — the new tests do, and the warning appeared immediately. That is the same instantiation-coverage effect as in #75 and #79, this time with a measurable defect as the payoff. With 20 names past the small-string limit:

before:  1657 ns, 20.00 allocations per call
after:    287 ns,  0.00 allocations per call

Two findings recorded rather than changed

• The order of terms in operator<< is unspecified, because the derivatives live in an unordered_map. The tests assert the value comes first and that every term appears — not the whole string.
• Names survive an operation even where the derivative cancels: s1 - s1 has size() == 3, not 0.

Documentation

The README said nothing about any of this. It now states that SScalar is first order only, that the variable set does not have to be known in advance, that an unknown name is zero rather than an error, that there is no serialization, and what eval does with names present on only one side. Every example number was checked against the module.

Verification

• C++ 112 test cases, 1425 assertions — Debug and Release with -Werror, and under clang with ASan+UBSan
• Python 248 passed
• clang-tidy back to 50 findings, clang-format --Werror and ruff format --check clean

.clang-tidy drops modernize-use-std-numbers: it cannot tell an expected test value that happens to sit near a constant from a constant written out by hand, and it flagged cbrt(3) as log2e while itself reporting that the two differ by 4.45e-04.