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Message-ID: <565eeea-4c28-8b71-aab1-201782a6ef86@esi.com.au>
Date: Wed, 5 Aug 2026 09:59:21 +1000 (AEST)
From: Damian McGuckin <damianm@....com.au>
To: MUSL <musl@...ts.openwall.com>
Subject: Re: fix acosh for x<0
Currently acosh(x) and acoshf(x) are not wildly accurate. But they have a
very small footprint.
If there is any interest in a more accurate acosh(x) with a larger
footprint, I might publish a paper on the work
In single precision, the worst ULP error drops under 0.8 ULP (and goes
even better if you have the ability to use hard or soft FMA). Still not
correctly rounded. It uses a Remez polynomial in the subdomain [1..2],
acosh(x) = sqrt(2z) * (1 + R(z))
where z = 1 and R(z) is the Ramez polynomial and the rounding error in
sqrt(2z) is recovered.
It also changes the subdomains where the log() approximations are used.
Later - Damian
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