Yes, everywhere I said "double precision" I meant "doubled precision."
I think the papers by Hull et al were perfectly happy with a ULP of around 4.
I have been trying to do a little better, but like you I am noticing that log1p isn't that good either.
I have tried some other things. I am attaching this example which gets a ULP a little over 2. I simulate high precision arithmetic by expanding everything out into integers. I certainly didn't aim for a speedy program.
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