/*
 * the device calculates the function
 *
 *   f'(n) = x'
 *         + v'    *n
 *         + a'/2  *n*(n-1)
 *         + j'/6  *n*(n-1)*(n-2)
 *         + s'/24 *n*(n-1)*(n-2)*(n-3)
 *         + c'/120*n*(n-1)*(n-2)*(n-3)*(n-4)
 *
 * while we have our parameters in the form
 *
 *   f(n) = x + v*n + a/2*n^2 + j/6*n^3 + s/24*n^4 + c/120*n^5
 *
 * which is equivalent to
 *   f(n) = x
 *        + (v + a/2 + j/6 + s/24 + c/120)    * n
 *        +          (a + j + 7/12*s +c/4)/2  * n*(n-1)
 *        +            (j + 3/2*s + 5/4*c)/6  * n*(n-1)*(n-2)
 *        +                        (s+2*c)/24 * n*(n-1)*(n-2)*(n-3)
 *        +                             c /120* n*(n-1)*(n-2)*(n-3)*(n-4)
 *
 * so we have
 *   x' = x
 *   v' = v + a/2 + j/6 + s/24 + c/120
 *   a' = a + j + 7/12*s +c/4
 *   j' = j + 3/2*s + 5/4*c
 *   s' = s + 2*c
 *   c' = c
 *
 * and for the other direction
 *   x = x'
 *   v = v' - a'/2 + j'/3 + s'/4 + c'/5
 *   a = a' - j' + 11/12*s' - 5/6*c'
 *   j = j' - 3/2*s' + 7/4*c'
 *   s = s' - 2*c'
 *   c = c'
 */