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Date: Sun, 13 Feb 2005 13:08:37 -0500
From: David Schultz <das@FreeBSD.ORG>
To: Bruce Evans <bde@zeta.org.au>
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cc: FreeBSD-gnats-submit@FreeBSD.ORG
cc: freebsd-i386@FreeBSD.ORG
cc: bde@FreeBSD.ORG
Subject: Re: i386/67469: src/lib/msun/i387/s_tan.S gives incorrect results
	for large inputs
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On Mon, Feb 14, 2005, Bruce Evans wrote:
> It seems that the hardware trig functions aren't worth using.  I want
> to test them on a 486 and consider the ranges more before discarding
> them.  This may take a while.

Fair enough.  I would be happy to have a hybrid implementation
that uses the hardware only when appropriate.  However, your 486
benchmarks notwithstanding, I would just as soon rely on fdlibm
entirely for the trig functions.  It just doesn't seem worthwhile
to me, given that the only parts of the domain where the hardware
is faster *and* correct are, roughly speaking, [0,2^-28) and
[pi/4,pi/2-eps].

> I did a quick test of some other functions:
> - hardware sqrt is much faster
> - hardware exp is slightly faster on the range [1,100]
> - hardware atan is slower on the range [0,1.5]
> - hardware acos is much slower (139 nsec vs 57 nsec!) on the range [0,1.0].

sqrt isn't transcendental, so it should be faster and correctly
rounded on every hardware platform.  I found similar results to
yours for atan() and acos() when writing amd64 math routines, but
of course amd64 has the overhead of switching between the SSE and
i387 units.  Maybe they should go away, too...