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Date: Sat, 11 Feb 2017 23:59:46 -0500
From: James Cloos <>
Subject: catrig

There was a recent post on one of the freebsd lists about Stephen
Montgomery-Smith's catrig routines:

which is based on the paper "Implementing the complex arcsine and
arccosine functions using exception handling" by T. E. Hull, Thomas
F. Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on
Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335,

It looks to be the most accurate catrig code availalbe.  Stephen writes
that tests indicate that both the real and imaginary parts of the
results are good to within 4 ULP, that catrigl.c supports both 80 bit and
128 bit long double but that the float version is occasionally slightly
worse that 4 ULP.

I don't know how much interest the musl community has in better accuracy
for libm, but in case there is interest Stephen's code looks like a good

And I see musl already uses freebsd libm code for some of the complex trig.

James Cloos <>         OpenPGP: 0x997A9F17ED7DAEA6

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