stillwater-sc / universal / 31918371682

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fix(takum_log): evaluate wide-configuration addition in extended precision (#1320)

The remaining half of #1300.  takum_log's multiply and divide became exact
integer work on l in #1312, but addition and subtraction have no logarithmic
shortcut and evaluated through a double.  l carries p fraction bits with p
reaching maxCharBits, so takum_log<64,3> holds 59 against a double's 53 and both
operands were quantized before the addition: 99.22% of 64-bit sums came back
incorrectly rounded.

Configurations with nbits > 54 + rbits now factor the larger operand out and
evaluate  l_result = l_big + 2 log(1 +/- e^(d/2))  in extended precision.  That
form is not merely more accurate than forming e^(la/2) and e^(lb/2) and adding
them -- it is the only one with the format's range, since the naive route
overflows a double for l beyond ~1420 and rbits = 5 reaches 2^32.

The extended precision is a LOCAL two-double type with its own exp and log rather
than dd_cascade.  dd_cascade is accurate enough -- ~103 bits for exp and ~105 for
log against an 80-digit reference -- but an addition built on it costs 27 us
against the double path's 117 ns, and the cost is in its arithmetic, not only its
transcendentals.  The local type brings that to 2.8 us: 20x rather than 229x, at
the same ~106-bit accuracy.

Verified correctly rounded on 133,878 operand pairs against an 80-digit
reference: 0 incorrect, worst case 0.499996 ulp.  The suite checks three layers
and each catches what the others miss -- reverting to the double path fails 7479
add and 7426 sub cases, while an inexact Taylor reciprocal is caught only by the
transcendental layer.

Two measured findings kept in the comments: scaling Taylor terms by 1.0/i rather
than dividing by i costs 33 bits, and std::fma compiles to a library call without
-mfma, which cost 214 ns per double-double multiply until Dekker's split replaced
it at 4.9 ns.  UBSan caught a real defect: a double-double's low limb is routinely
negative and castin... (continued)

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