  We present a numerical solution of the revised version of the small-$x$
helicity evolution equations at large $N_c$ and $N_f$. (Here $N_c$ and $N_f$
are the numbers of quark colors and flavors, respectively.) The evolution
equations are double-logarithmic in the Bjorken $x$ variable, resumming powers
of $\alpha_s \, \ln^2 (1/x)$ with $\alpha_s$ the strong coupling constant. The
large-$N_c \& N_f$ evolution we consider includes contributions of small-$x$
quark emissions and is thus more realistic than the large-$N_c$ one, which only
involves gluon emissons. The evolution equations are written for the so-called
``polarized dipole amplitudes", which are related to the helicity distribution
functions and the $g_1$ structure function. Unlike the previously reported
solution of the earlier version of helicity evolution equations at large $N_c
\& N_f$, our solution does not exhibit periodic oscillations in $\ln (1/x)$ for
$N_f < 2 N_c$, while only showing occasional sign reversals. For $N_f = 2 N_c$,
we report oscillations with $\ln (1/x)$, similar to those found earlier. We
determine the intercept of our evolution for $N_f < 2 N_c$ as well as the
parameters of the oscillatory behavior for $N_f = 2 N_c$. We compare our
results to the existing resummation and finite-order calculations for
helicity-dependent quantities in the literature.
