anchor.diff:      ! compute value and derivative of log p(a | x)
       use constants
       use gamma_funcs, only: digamma, trigamma, quadgamma
  -    use dirichlet_mod, only: alphabet_size, n_empty_bins, n_data, multi,&
  +    use dirichlet_mod, only: alphabet_size, n_data, multi,&
            multi_z
       use dirichlet_mod, only: log_pna, alpha_prior
   
  
positive.code:   implicit none
  
    integer(int32)              :: n_data
    real(real64)                :: n_empty_bins
    real(real64)                :: alphabet_size
    integer(int32), allocatable :: multi_z(:)
    integer(int32), allocatable :: multi(:)
  
negative.code:     integer(int32)              :: err
      integer(int32)              :: nmax
      integer(int32), allocatable :: multi0(:)
      real(real64)                :: n_empty_bins
      integer(int32)              :: n_multi
  
      ! compute multiplicities
  