* Bug Fixes								-*-org-*-


** Not working Arithmetic
***  as.bigz(1:4) + as.bigq(7) fails

***  bigz  %% und %/%  fail with "division by zero"
     whereas the numeric/integer version of these work fine, returning NA;
     see matOuter() and eqA[] in tests/arith-ex.R
***  bigq  %% and %/%  are not even defined (but are for 'numeric')!

** Miscellaneous


* Vectorization; other "desiderata"
***  fibnum(), etc are not vectorized -- learn from chooseZ() !

** allow  +/- Inf "bigq" ?? --  +Inf :=: 1/0   -Inf :=:  (-1)/0
   This would allow the bigq (and bigz) arithmetic to be closer to the
   other R arithmetic rules.
   Currently we get "division by 0" instead... not really desirably in
   quite some cases.


* Matrix things

***  3*M and M*3  are not the same: the first forgets the "nrow" ...

***  x <- as.bigz(2:5); x[1] <- -1; x # --- is a matrix !!!!

***  also want different  M[1,] and M[1] for big[zq] matrices

***  as.matrix(as.bigq(1:4)),  as.matrix(as.bigz(1:4)) both fail:
**** Now have asNumeric() ... we can *well* reconsider the following:
**** MM: I'd want   as.matrix(<big* matrix>) to convert *back* to
double/integer matrix, as we have no other convenient way for that yet.

***  abs(.) or sign(<big..matrix>) {and probably many others!}
     return vector instead of matrix, i.e.., lose the "nrow" attribute.

***  cbind(<bigz>, <bigq>)  returns raw ...

* More general, previous 'TODO':

***  The print() method is improved; but matrices are not "noted" yet.
   Still needs discussion; should be shorter for length 1 ?
   We could have an option() .. to suppress the initial line. Fine for
   bigq, but not for bigz

*** frexpZ(z) is sufficient; want faster simpler sizeinbase()
  i.e.  sizeinbase(x, base)  returning the number "digits" in base 'base'.
  Notably  sizeinbase(z, 2)  would directly give frexpZ(z)$exp  (minus 1 ?),
  and could be used in Rmpfr's getPrec() for  bigz -> mpfr conversion.

***  provide more functions for bigintegers, such as
   sort, order ...

***  Bernoulli() {-> Rmpfr / copula } should return a  "bigq"
*** more matrix and linear algebra computation functions (SVD, eigen values,
    determinant).

*** provide basic algorithms and number theoretic symbols (CRA, Jacobi symbol)

*** provide binary-to-biginteger interface with bitwise operations (i.e., bit access to big integers)

*** Create pochZ() for the Pochhammer symbol to complement  chooseZ()
    the same as pochMpfr() in "Rmpfr" complements chooseMpfr()

* Systematic Testing

*** Arithmetic, Comparison, etc: ensure pairwise compatibility <bigz>, <bigq>, <numeric>

*** tests/gmp-test.R: contains Antoine's previous test suite;
    should add more tests about *correct* result.

