stillwater-sc / universal / 27913967582

85%

master: 84%

push

github

perf(elreal): Abel-summed euler_gamma A-accumulation (~2.3-3.1x) (#1061 Phase 3b) (#1088)

The Brent-McMillan B1 A(n) = sum_k w_k H_k accumulation (a full per-term ZBCL x ZBCL
multiply + per-term harmonic maintenance) is replaced by Abel summation:

  sum_k w_k H_k  ==  sum_{k>=0} tail_k/(k+1),  tail_k = sum_{j>k} w_j = B - B_k

All-positive accumulation, no harmonic numbers, no full multiply: pass A sums
B = sum w_k; pass B walks the same recurrence keeping tail = B - B_k and folds the
single-block scalar division tail_k/(k+1) into A. The tail-subtraction's cancellation
right of the w-peak stays inside the cap-block guard.

depth 8: 4408 -> 1890 ms (~2.3x); depth 16: 10986 -> 3578 ms (~3.1x). Validated to
305 digits vs the 320-digit reference (REGRESSION_LEVEL_4) on gcc + clang; full
elreal ctest 42/42 both compilers.

Adds docs/design/elreal-euler-gamma.md (algorithm, derivation, cancellation analysis,
deferred binary-splitting alternative). Brent-McMillan is still O(n) products; the
asymptotic win (binary-splitting einteger P/Q/B/T) is a separate effort.

Relates to #1061

17 of 17 new or added lines in 1 file covered. (100.0%)

48083 of 56796 relevant lines covered (84.66%)

6840019.72 hits per line