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

DeformBend

static void simpleDeform_bend(const float factor, const float dcut[3], float *co)
{    
    float x = co[0], y = co[1], z = co[2];
    float theta, sint, cost;

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

    if(fabsf(factor) > 1e-7f)
    {
        co[0] = -(y-1.0f/factor)*sint;
        co[1] =  (y-1.0f/factor)*cost + 1.0f/factor;
        co[2] = z;
    }


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