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feat(efloat): BBP pi identity-verification demonstration (#1099) (#1148)

* feat(efloat): BBP pi identity-verification demonstration (#1099)

Adds applications/precision/adaptive/mathematical_identities.cpp: evaluates the
Bailey-Borwein-Plouffe series pi = sum 1/16^n (4/(8n+1) - 2/(8n+4) - 1/(8n+5)
- 1/(8n+6)) with the SAME templated summation on double and efloat<16> (512-bit),
checking each against an independent oracle -- efloat_pi(), the stored ~1000-digit
constant (#1142).

double bottoms out at ~15 digits (its ceiling) no matter how many terms are
summed, while efloat gains ~1.2 digits/term: 27 -> 52 -> ... -> 152 digits across
20..150 terms, so it numerically verifies the identity to well over 100 digits
and doubles as an oracle for checking algorithms.

No CMake change: the adaptive glob (#1096) builds it as
adaptive_mathematical_identities. README updated with the new demo row. Builds
and runs on gcc 13.3.0 and clang 18.1.3.

Resolves #1099

* style(efloat): clang-format the BBP demo per project config (CodeRabbit #1148)

Ran the project's clang-format (.clang-format, LLVM-based) on
mathematical_identities.cpp. Note AlignConsecutiveAssignments is enabled, so the
sum/inv16 assignment alignment is kept; the changes are comment spacing, anon-
namespace indentation, joined int main()/catch, and operand line breaks. No
behavior change (double ~15 digits, efloat ~152); builds on gcc and clang.

49479 of 58413 relevant lines covered (84.71%)

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Coverage Regressions

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