ANCOPT optimizer not consistent for `gcc @ macOS-14.6.1`

Describe the bug Geometry optimizer leads to different results for ifort @ ubuntu-20.04 and gcc @ macOS-14.6.1.

To Reproduce Steps to reproduce the behaviour:

xtb_dev C13H14.xyz --opt --gfn 2 --cycles 1

Relevant lines of code

      write(*,*) "Uaug before davidson"
      do i = 1, nvar1
         write(*,*) Uaug(i,1)
      end do
      call solver_sdavidson(nvar1,r4dum,Aaug,Uaug,eaug,fail,.false.)
      write(*,*) "Uaug after davidson"
      do i = 1, nvar1
         write(*,*) Uaug(i,1)
      end do

solver_sdavidson leads to different results for both architectures for Uaug, even though all input variables are equal for both architectures. Possible reasons might be blas_dot or sdot functions that lead to different results for different architectures and compilers. (In some examples, norm2 and sqrt(sdot(x, var1, 1, var1, 1)) led to different results.

Output showing the error

Please provide all input and output file such that we confirm your report.

........................................................................
.............................. CYCLE    1 ..............................
........................................................................

 iter      E             dE          RMSdq      gap      omega  full diag
   1    -35.5785110 -0.355785E+02  0.129E-04    4.46       0.0  T
   2    -35.5785110 -0.205844E-10  0.784E-05    4.46     245.5  T
   3    -35.5785110  0.249401E-10  0.458E-05    4.46     419.8  T
     SCC iter.                  ...        0 min,  0.003 sec
     gradient                   ...        0 min,  0.002 sec
 * total energy  :   -34.9341040 Eh     change       -0.7595276E-09 Eh
   gradient norm :     0.0325983 Eh/α   predicted     0.0000000E+00 (-100.00%)
 Uaug before davidson
  -6.26123365E-05
  -9.22085601E-05
  -6.20031715E-05
  -4.61859192E-04
....
  0.999469101    
 Uaug after davidson
  -6.26123365E-05
  -9.22085601E-05
  -6.20031715E-05
  -4.61859192E-04
  ...
  0.999469101    
   displ. norm   :     0.0325983 α      lambda        0.0000000E+00
   maximum displ.:     0.0170929 α      in ANC's #43, #45, #63, ...

   *** FAILED TO CONVERGE GEOMETRY OPTIMIZATION IN 1 ITERATIONS ***

Expected behaviour Numerically equal results for all systems, on which xtb is compilable.

........................................................................
.............................. CYCLE    1 ..............................
........................................................................

 iter      E             dE          RMSdq      gap      omega  full diag
   1    -35.5785110 -0.355785E+02  0.271E-05    4.46       0.0  T
   2    -35.5785110 -0.175504E-11  0.151E-05    4.46    1277.3  T
   3    -35.5785110 -0.177636E-12  0.996E-06    4.46    1931.4  T
     SCC iter.                  ...        0 min,  0.004 sec
     gradient                   ...        0 min,  0.003 sec
 * total energy  :   -34.9341040 Eh     change       -0.3772840E-09 Eh
   gradient norm :     0.0325980 Eh/α   predicted     0.0000000E+00 (-100.00%)

 Uaug before davidson
 -6.2612402E-05
 -9.2208698E-05
 -6.2002968E-05
 -4.6185814E-04
 ...
  0.9994691    
 Uaug after davidson
 -4.5103282E-03
 -6.6389972E-03
 -4.4081416E-03
 -3.2373566E-02
...
  0.9863185    
   displ. norm   :     0.1671367 α      lambda       -0.3699289E-02
   maximum displ.:     0.0759934 α      in ANC's #43, #15, #45, ...

   *** FAILED TO CONVERGE GEOMETRY OPTIMIZATION IN 1 ITERATIONS ***

Additional context C13H14.xyz.txt xtb.log

grimme-lab / xtb

ANCOPT optimizer not consistent for `gcc @ macOS-14.6.1` #1099