stillwater-sc / universal / 23762858847
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feat(ucalc): dd/qd error-free transformation steps (#680)

* feat(ucalc): dd/qd error-free transformation steps (#657)

Add double-double/quad-double step-by-step decomposition showing:

Addition:
  1. Decompose: (hi, lo) limb pairs
  2. two_sum(a.hi, b.hi): sum + error = a.hi + b.hi EXACTLY
  3. Accumulate error terms: two_sum_error + a.lo + b.lo
  4. Renormalize with fast_two_sum
  5. Result: (hi, lo) pair

Multiplication:
  1. Decompose limb pairs
  2. two_prod(a.hi, b.hi): product + error via FMA (EXACT)
  3. Cross terms: a.hi*b.lo + a.lo*b.hi
  4. Accumulate errors
  5. Renormalize
  6. Result

Students see how error-free transformations capture rounding errors
in lower limbs, giving ~32 digits from double-precision hardware.

Detects dd/qd/cascade types by type_tag.

Resolves #657

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* fix(ucalc): resolve CodeRabbit review items for dd steps

Three fixes:

1. Labels corrected: "Renormalize with two_sum" (was "fast_two_sum"
   but code calls two_sum_eft). Detail strings also updated.

2. Added "triple-double" to type detection so td_cascade routes to
   explain_dd instead of falling through to IEEE decomposition.

3. The lo=0 limitation is already documented in the existing comment
   at line 42-44: "Since we only have the double approximation,
   a_hi = a_val, a_lo = 0."

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

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