stillwater-sc / universal / 27655383319

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Commit Message

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>

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