Wrong logarithmic grid in the grid mode

I looked to recent code to understand, how it's supposed to look.

            gint x1 = x;

            if (base->non_linear)
            {
                x1 *= pow (1.02, x1);
                if (x1 >= w)
                    break;
            }

            /* draw vertical line */
            cairo_move_to (cr, w - 1 - x1 + 0.5, 0.5);
            cairo_line_to (cr, w - 1 - x1 + 0.5, h - 1 + 0.5);

This makes it to expand towards past rather than shrink. It even uses different log base than for data map (1.04). Even assuming there's some sort of decade - I couldn't deduce resonable value. Ideally - in order to map values from linear to visible space - equation has to be solved: x*x^2 = x1 for x. I utterly failed to do so.

Last I tried is to use divide and conquer, there's awk example to play with:

echo 6 | awk '{ x1=$0; d=1; while(1){ d2 = log(x1/d) / log(1.04); print d2" "d" "(d+d2)/2; if (d2 > x1*2) d = (x1+d)/2; else if (d2-d>0.2 || d-d2>0.2) d = (d2+d)/2; else break } }'

Unfortunally, I can't get stability.

I could only get working this crude approximation:

-                x1 *= pow (1.02, x1);
+                x1 = log (x1) / log (NONLINEAR_MODE_BASE);

Which made first tick 45px wide. Of course, there must be some decades with different tick detail level (it takes ~17px for 2x factor change).