This is the algorithm by GiNaC. In theory one
could extend this to add a caching mechanism such as

    complex(kind=prec) :: cache(size(x),MPLMaxQ)

    do q=1,j
      cache(:,q) = x**q/q**m
    enddo
    do q=1,MPLMaxQ
      res = t(1)

      ! Fortran uses Column-major order, hence cache(:,q) is
      ! faster than cache(q,:).
      cache(:,q+j-1) = x**(q+j-1)/(q+j-1)**m
      t(j) = t(j) + cache(j,q)
      do k=1,j-1
        t(j-k) = t(j-k) + t(j-k+1) * cache(j-k,k+q)
      enddo

      if (mod(q,2) .eq. 1) then
        if (abs(t(1)-res).lt.MPLdel) exit
      endif
    enddo

In practice this doesn't really help because any
time saved with the cache is paid back through the
allocation and clearing of cache(:,:). Both
variations work similarly well now. If at some
point we might need MPLs with many more arguments
(size(x)), this might change.