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Add convergence-tapered direct recurrence for D2 - #9

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MatrixFreeSama merged 10 commits into
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direct-convergence-window
Aug 24, 2026
Merged

Add convergence-tapered direct recurrence for D2#9
MatrixFreeSama merged 10 commits into
mainfrom
direct-convergence-window

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@MatrixFreeSama MatrixFreeSama commented Aug 24, 2026

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Adds Convergence-Tapered Direct Recurrence (CTDR) specifically to the original scalar/direct D2 evaluator, with no binary splitting and no exact quadratic-field product tree in the series. The formula and recurrence stay unchanged; only the recurrence working precision falls as term magnitude decreases, while the F and theta-F accumulators remain at full target precision.

The same CTDR schedule is applied to D2 and to the D=163 / Chudnovsky direct recurrence for a matched comparison. At 200,000 digits with a 16-term taper block, D2 direct falls from 22.369212151 s to 9.841870785 s (~2.27x faster), while Chud direct falls from 39.258158445 s to 17.253968477 s. D2 CTDR / Chud CTDR = 0.570412x, preserving almost all of the formula-level ~0.568 term-count advantage. Every reported accelerated output is byte-identical to the Chudnovsky-BS reference.

A more aggressive local low-precision window accumulator was tested and rejected because it lost deep mantissa digits. The merged candidate keeps only the valid precision-tapering part. Results and claim boundaries are documented in validation/direct_convergence_taper_results.md; make d2directtaperbench reproduces the direct-state benchmark.

@MatrixFreeSama MatrixFreeSama changed the title Test convergence-window acceleration on direct D2 recurrence Add convergence-tapered direct recurrence for D2 Aug 24, 2026
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MatrixFreeSama merged commit d168b65 into main Aug 24, 2026
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