Re: [eigen] Re: 4x4 matrix inverse

[Hauke Heibel <hauke.heibel@xxxxxxxxxxxxxx>]

On Tue, Dec 15, 2009 at 5:25 AM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:

There is one thing where I didn't follow Intel's code: they use a
RCPSS instruction to compute 1/det approximately, then followed by a
Newton-Raphson iteration. This sacrifices up to 2 bits of precision in
the mantissa, which already is a bit nontrivial for us (4x4 matrix
inversion is a basic operation on which people will rely very
heavily).

Hi Benoit, I recognized that you wrote in your commit log "that elsewhere in Eigen we dont allow ourselves this approximation" (Newton-Raphson). I just recalled stumbling once over such an approximation hidden in Eigen. It is for the SSE computation of the inverse square root.

The approximation takes place overe here in Packet4f ei_psqrt(Packet4f _x) at the very bottom.

- Hauke