RE: [PING] libm functions for x86-64

["Menezes, Evandro" <evandro dot menezes at amd dot com>]

(Attachments sent on request.)

Please, see the files in attach with the accuracy and performance information on both an Opteron (table7o.html) and on a P4 (table7p.html).  Those suffixed routines with "_amd64" are the proposed ones and those suffixed with "_nat64" are the current ones in GLIBC.

As you can see, the proposed routines are generally faster and as or more accurate.  The exceptions being:

- acos, asin, atan2, cos, exp, exp2, hypot, log, pow, sin, tan: slightly less accurate, but better performance over its domain.

- asinh, asinhf, atanf, atan2f, cosf, hypotf, log1p, log1pf, sinf, tanf, tanh: more accurate, but lower performance.

- atan: less accurate and slower; withdrawn.

- fdim, fdimf: as accurate and as fast; withdrawn.

- finite, finitef, modf, modff: as accurate, but slower; withdrawn.

A word on the proposed sin: although the maximum error is much higher than the current one, it is so only at +/- 90Â offset by 1ulp.  This error also shows at the sine as returned by sincos.  You can verify this in the other files in attach (*.summary).  We are working on fixing it.

I'd really appreciate your feedback on this data.  I'll be glad to answer any question you may have.

Thank you,

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Evandro Menezes               AMD            Austin, TX