  SIGMA     = [0, 1, 4, 5, 8, 9, 12, 13, 2, 3, 6, 7, 10, 11, 14, 15]
  SIGMA_INV = [0, 1, 8, 9, 2, 3, 10, 11, 4, 5, 12, 13, 6, 7, 14, 15]
  kernel rho= [0, 1, 8, 9, 2, 3, 10, 11, 4, 5, 12, 13, 6, 7, 14, 15]
  [1] sigma and sigma_inv are inverses: True
  [1] kernel rho == SIGMA_INV (the GATHER form): True
  [2] rho is an involution: False  (must be False -- rho[rho[2]]=4)
  [3] gather form rel=1.354e-02   scatter form substituted rel=1.224e+00   (must be O(1))
PERM DIRECTION: PASS
