Add libeta and libetac, the logarithms of ibeta and ibetac

[NAThompson]

Logs of the smaller of ibeta and ibetac, switching to log-space power terms over the continued fraction where it underflows. Closes #1173.

Builds on #1498 (lbeta), so its first commits are that PR's; supersedes #1359.

ulps against Arb's arb_hypgeom_beta_lower: libeta/libetac in blue, log(ibeta)/log(ibetac) in orange; crosses are clipped or -inf. The scatter near the mean is ibeta's own error, which libeta inherits there (ibeta(1000, 1000, x) is off by up to 391 eps near x = 0.5).

🤖 Generated with Claude Code

[NAThompson]

reporting/performance/libeta_performance.cpp. Ordinary arguments: a, b log-uniform in [0.5, 1000], x uniform in (0, 1). Underflow: a = b log-uniform in [1e4, 1e5], x in [0.05, 0.4], where log(ibeta) is -inf. Median of 5 repetitions, Apple M-series, Homebrew clang 23, -O3.

	float	double	long double
libeta, ordinary	129 ns	237 ns	236 ns
log(ibeta), ordinary	111 ns	222 ns	220 ns
libeta, underflow	72 ns	136 ns	137 ns

[mborland]

@NAThompson please add the CUDA tests here as well. If need be I can go back through your flurry of recent PRs and add them where need be. Need to also fix the breakage identified this morning

[dschmitz89]

Thanks @NAThompson , things are moving quite fast here lately. This will be very helpful over at SciPy!

I know that it is a big ask but would it be possible to test all the already existing ibeta cases with libeta as well (if not already done, cannot evaluate the full diff arm)? The incomplete beta has many branches and special cases that caused some pain in the past.

[NAThompson]

@dschmitz89 : Good point-I created ulps plots for tons of regimes locally but didn't post them.

I also think that the ulps plot code needs to be extended to 2D so that we can tackle more regimes in a single graphic. Lemme create an issue.

[mdhaber]

Thank you for this!