stillwater-sc / universal / 32575727434
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feat(elreal): a thousand-digit demonstration on both float and double hosts (#1376)

* feat(elreal): a thousand-digit demonstration on both float and double hosts

Adds applications/precision/elreal/thousand_digit_sqrt.cpp: one Newton iteration
for sqrt(2), instantiated on native double, elreal<float> and elreal<double>.

The kernel is ordinary templated numeric code with no elreal in it:

    template <typename Real>
    Real newton_sqrt(const Real& a, int iterations) {
        Real x = a / Real(2.0);
        for (int i = 0; i < iterations; ++i) x = (x + a / x) / Real(2.0);
        return x;
    }

On a native double it stalls at 16 digits however many iterations it is given. On
elreal it converges past 1150 digits on BOTH hosts -- 1178 on float, 1159 on double
-- verified against a 1200-digit sqrt(2) computed in exact integer arithmetic
outside this library. Float needs ~2.2x the blocks for the same digits, its limb
carrying 24 bits to double's 53; that is the only difference the host type makes to
the answer, which is the point of the demonstration.

Part 3 uses the one elreal-specific API the demo needs. Newton doubles the correct
BITS per step, so ramping precision() alongside the iterate rather than paying the
final precision from the first step costs 4s and 25s instead of 25s and 206s, and
prints the convergence as it goes:

    elreal<double>: 32 64 130 261 521 1041 1159 digits
    elreal<float >: 17 32 62 124 248 493 988 1178 digits

Includes a small ZBCL-to-decimal renderer (via the exact dyadic conversion), since
elreal's operator<< prints only a host-double approximation -- so the demo can show
the digits rather than just count them.

Registered with compile_all("false"): a demonstration, not a regression test. It is
built so it cannot silently rot, but not run by ctest, since the float host takes
~25s to converge. CI_LITE does not build applications at all.

This was not possible before now. Division by a multi-block value capped at ~271
... (continued)

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