see https://github.com/Reference-LAPACK/lapack/issues/333

Fix argument in SLASET call to zero S

fixes #1859 in accordance with https://github.com/LAPACK-Reference/issue/296

for #1811

The problem is that OpenBLAS sets the LAPACKE_LIB and the TMGLIB to the
same object and uses the `ar` feature to update the archive file. If the
underlying filesystem does not have sub-second timestamp resolution and
the system is fast enough (or `ccache` is used), the timestamp of the
builds which should be added to the previously generated archive is the
same as the archive file itself and therefore `make` does not update the
archive.

Since OpenBLAS takes care to not run the different targets updating the
archive in parallel, the easiest solution is to declare the respective
targets `.PHONY`, forcing `make` to always update them.

fixes #1682

Remove an unused variable from several LAPACKE 2stage_work functions

Copied from Reference-LAPACK PR283

Copied from Reference-LAPACK PR283

Copied from Reference-LAPACK PR283

This could cause spurious "parameter has an illegal value" errors in DSYEVR and related routines, see https://github.com/Reference-LAPACK/lapack/issues/262

Fixes from Lapack-Reference PR 253

When minimal workspace is given in ?hesv_aa, ?sysv_aa, ?hesv_aa_2stage, ?sysv_aa_2stage, now no error is given
Quick return for ?laqr1

LAPACKE interfaces for Aasen's functions now call ?sytrf_aa and ?hetrf_aa instead of ?sytrf and ?hetrf

should fix 1574

LAPACKE fixes from lapack PR249

Copied from Reference-LAPACK/lapack#249, this fixes out-of-bounds memory accesses
in the nancheck calls of the LAPACKE lacgv, lassq,larfg,larfb,larfx and mtr functions

To allow compiling with gcc versions older than 4.9

This was added in #1046 citing a problem with mingw, but in effect it quietly reduces thread safety on all non-Windows platforms (while -fopenmp is already disabled for Windows builds through the toplevel Makefile.system). Removing the filter fixes #1425

From Reference-LAPACK issue 228, remove spurious EXTERNAL reference to unused and nonexistent function xLACGV that could cause linking problems.

The macOS ar aborts when it gets called with no input, see #1398

Inf values in the input vector will survive rescaling, causing an infinite loop. The value of 1000 is arbitrarily chosen as a large but finite value with the intention to never interfere with regular calculations.

From netlib PR#144

From netlib PR#144

From netlib PR#144

from netlib PR #144

* Fix integer overflow in DBDSQR

As noted in lapack issue 135, an integer overflow in the calculation of the iteration limit could lead to an immediate return without any iterations having been performed if the input matrix is sufficiently big.

* Fix integer overflow in SBDSQR

As noted in lapack issue 135, an integer overflow in the calculation of the iteration limit could lead to an immediate return without any iterations having been performed if the input matrix is sufficiently big.

* Fix integer overflow in threshold calculation

Related to lapack issue 135, the threshold calculation can overflow as well as the multiplication is evaluated from left to right.
Without explicit parentheses, the calculation would overflow for N >= 18919

* Fix integer overflow in threshold calculation

Related to lapack issue 135, the threshold calculation can overflow as well as the multiplication is evaluated from left to right.
Without explicit parentheses, the calculation would overflow for N >= 18919

Remove unused (and nonexistent) functions ZHETRD_SY2SB and ZHETRD_SB2ST from comment and EXTERNAL declaration

Remove unused (and nonexistent) ZHETRD_SY2SB and ZHETRD_SB2ST

ZHBTRD_HB2ST  should be ZHETRD_HB2ST

EXTERNAL declaration of subroutines missed a comma before the continuation line,
causing a strange run-together name to appear in the object when compiled with ifort.

EXTERNAL declaration of subroutines missed a comma before the continuation line,
causing a strange run-together name to appear in the object when compiled with ifort.

EXTERNAL declaration of subroutines missed a comma before the continuation line,
causing a strange run-together name to appear in the object when compiled with ifort.

EXTERNAL declaration of subroutines missed a comma before the continuation line,
causing a strange run-together name to appear in the object when compiled with ifort.

Changes made upstream in Reference LAPACK in
https://github.com/Reference-LAPACK/lapack/pull/128

Copied from lapack https://github.com/Reference-LAPACK/lapack/pull/127  by vladimir-ch (with earlier changes from echeresh's  
PR 115 "lapacke_*ormlq_work: move declarations under if" there as they touched some of the same files)

Fixed in Reference LAPACK in commit:

07e1fbd897

Missed the splitting of the actual ar call

Split obj list to allow building with mingw (argument list too long for the msys ar)