lapackers

["Hatem Ltaief" <Hatem.Ltaief@kaust.edu.sa>]

All,
There is a bug in this auxiliary routine of LAPACK.
This routine applies a single reflector V to a general dense block.
If V is of size less than 11, the routine provides an unrolled
way of computing the operations (for eventual compiler optimizations).
The bug is in single and double complex for the case "LEFT".
The conjugate of TAU needs to be used rather than TAU itself when
[c,z]larf are called (if size of V is of size > 11) or when the unrolled
version is selected (if size of V is <= 11).

Also, as some of us pointed out, since the first element of V is unit,
some flops can be saved in the unrolled version (for all 4 precisions).

Attached are the proposed patches for the 4 precisions xLARFX.
I am attaching the four precisions as I am not sure how the precision
generation of LAPACK is done.
Note that we are using this routine as one of the main kernels for the bulge 
chasing
procedure.

Thanks,
Hatem

Attachment: dlarfx.f
Description: dlarfx.f

Attachment: clarfx.f
Description: clarfx.f

Attachment: zlarfx.f
Description: zlarfx.f

Attachment: slarfx.f
Description: slarfx.f