  We perform a detailed study of the black hole spin of Cyg X-1, using accurate
broad-band X-ray data obtained in the soft spectral state by simultaneous NICER
and NuSTAR observations, supplemented at high energies by INTEGRAL data. We use
the relativistic disk model kerrbb together with different models of the
Comptonization high energy tail and the relativistically-broadened reflection
features. Unlike most previous studies, we tie the spin parameters of the disk
and relativistic broadening models, thus combining the continuum and reflection
methods of spin determination. We also consider a likely increase of the disk
color correction due to a partial support of the disk by large scale magnetic
fields. We find that such models yield the spin parameter of $a_*=
0.87^{+0.04}_{-0.03}$ if the disk inclination is allowed to be free, with $i=
39^{+1}_{-1}$ degree. Assuming $i=27.5$ degree, as determined by optical
studies of the binary, worsens the fit, but leads to similar values of the
spin, $a_*= 0.90^{+0.01}_{-0.01}$. In addition, we consider the presence of a
warm Comptonization layer on top of the disk, motivated by successful modeling
of soft X-ray excesses in other sources with such a model. This dramatically
lowers the spin, to $a_*\lesssim 0.1$, consistent with the spin measurements
from black-hole mergers. On the other hand, if the natal spin of Cyg X-1 was
low but now $a_*\approx 0.9$, a period of effective super-critical accretion
had to take place in the past. Such accretion could be facilitated by photon
advection, as proposed for ultraluminous X-ray sources.
