From https://www.reddit.com/r/blender/comments/1x10ba/help_with_understanding_the_simple_deform_bend/

new_gist_file_0

static void simpleDeform_twist(const float factor, const float *dcut, float *co)
{
    float x = co[0], y = co[1], z = co[2];
    float theta, sint, cost;

    theta = z*factor;
    sint  = sin(theta);
    cost  = cos(theta);

    co[0] = x*cost - y*sint;
    co[1] = x*sint + y*cost;
    co[2] = z;

    if(dcut)
    {
        co[0] += dcut[0];
        co[1] += dcut[1];
        co[2] += dcut[2];
    }
}