stillwater-sc / universal
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feat(elreal): window euler_gamma's A-accumulation over online mul (#1061 Phase 3b) (#1078)

Last eager hot loop in Phase 3b. euler_gamma's Brent-McMillan inner loop spent
nearly all its time in fold(A, mul(w_k, H_k)) -- a full eager product per term
(~2n terms). Unlike a monotone series, w_k = (n^k/k!)^2 GROWS to a peak at k=n
then decays, so windowing against a running peak would only help the tail.

Two-pass instead: a cheap scalar pre-pass finds the GLOBAL peak exponent of w_k,
then the accumulation pulls each w_k*H_k product (now mul_online) only down to
A's significance floor (peakExp - cap*k). Products whose blocks all sit below
that floor -- the tiny early terms AND the decaying tail -- contribute nothing
and are skipped; only the ~sqrt(n) terms near the peak are multiplied in full.

Builds on #1075's take_while_above + the online mul/div. The ln(n) half of the
old cost wall (#1053: ~107s of eager ln2) already vanished when odd_power_series
went online (#1075).

Measured (double host), value-identical (matches s_euler_gamma):
  depth 12: 61s -> 6.5s   (9.4x)
  depth 20: ~300s -> 12.2s, 305 digits (>= the 300 bar)
  constants_highprecision LEVEL_4 suite: now PASSes in ~34s

PASS on gcc + clang (Release) and gcc Debug with assertions on; basic constants
and LEVEL_4 constants suites green.

With this, every elreal series/constant hot loop (odd_power_series #1075,
exp/sin/cos #1077, euler_gamma here) is online. Remaining Phase 3b polish: the
scalar w-recurrence and B-fold stay eager (cheap), and #1076 (sin/cos
multi-block-argument precision).

Relates to #1061, #1053

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

12 of 12 new or added lines in 1 file covered. (100.0%)

15 existing lines in 3 files now uncovered.

47835 of 56557 relevant lines covered (84.58%)

6763580.48 hits per line

Relevant lines Covered
56557 RELEVANT LINES 47835 COVERED LINES
6763580.48 HITS PER LINE
Source Files on Ravenwater-patch-1

Recent builds

Builds Branch Commit Type Ran Committer Via Coverage
27655383319 main feat(elreal): window euler_gamma's A-accumulation over online mul (#1061 Phase 3b) (#1078) Last eager hot loop in Phase 3b. euler_gamma's Brent-McMillan inner loop spent nearly all its time in fold(A, mul(w_k, H_k)) -- a full eager product per te... push web-flow github
84.58
27655381801 feat/issue-1061-phase3b-euler-gamma-loop Merge a33f26336 into ae39fe0ef Pull #1078 web-flow github
84.59
27632534737 main feat(elreal): online streaming exp/sin/cos Taylor series (#1061 Phase 3b) (#1077) * feat(elreal): online streaming exp/sin/cos Taylor series (#1061 Phase 3b) Second Phase 3b increment, after odd_power_series (#1075). exp, sin_series and cos_seri... push web-flow github
84.6
27630655146 feat/issue-1061-phase3b-online-transcendentals Merge eb70193f8 into c603f7444 Pull #1077 web-flow github
84.6
27621119076 main feat(elreal): online streaming odd_power_series (#1061 Phase 3b) (#1075) odd_power_series (artanh/atan: sum x^(2n+1)/(2n+1)) backs pi, ln2, ln10, log2_10, log, atan, asin, acos. It was EAGER: compute every term to the full working depth, accumula... push web-flow github
84.57
27621115655 feat/issue-1061-phase3b-online-series Merge 3e2a75d55 into 7789a39f3 Pull #1075 web-flow github
84.58
27584017360 main feat(elreal): full-precision exp/sin/cos coefficients (#1061 Phase 3a, closes #1058) (#1074) exp, sin_series and cos_series scaled each Taylor term by a HOST-DOUBLE reciprocal coefficient -- mul_scalar(1.0/n, ...) and 1.0/denom -- which capped th... push web-flow github
84.58
27584015733 feat/issue-1061-phase3a-transcendental-precision Merge e62498503 into 2273c692b Pull #1074 web-flow github
84.59
27559650955 feat/issue-1053-euler-gamma-highprecision Merge 475830375 into d67a022d3 Pull #1073 web-flow github
84.58
27559656978 main feat(elreal): high-precision euler_gamma via Brent-McMillan (#1053) (#1073) * feat(elreal): high-precision euler_gamma via Brent-McMillan (#1053) euler_gamma_zbcl was a stub returning a bare double literal (~17 digits) while every other constant... push web-flow github
84.58
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