[CppAD] Use of global var for tape

[Iakov Nakhimovski]

Dear Brad,

I've just started to use CppAD and so the answer to my question might
be obvious.
It seems that use of global variable for storing tape is giving a lot
of troubles in multithreading case. Have you considered other options?
For instance:
1) Use ref counting, e.g., boost::shared_ptr
- tape_this pointer in the AD<Base> is a boost::shared_ptr<ADTape<Base> >
- Independent(X) constructs a new ADTape and then sets the tape
pointers in the X
- All the assignment operators transfer the tape_ptr from arguments to
the left hand side.
- Dependent() transfers the tape to ADFunc and then cleans the tape
pointers in the AD<Base> objects. It should check that the tape is the
same as in X or NULL in all the Y.

2) Make the tape creation explicit to the user
- tape_this pointer in the AD<Base> is a normal pointer to ADTape<Base>
- Independent(X) either returns a tape pointer or the user is expected
to construct ADTape and then call Independent on it
- All the assignment operators transfer the tape_ptr from arguments to
the left hand side
- Dependent() might clone the tape object or just store a pointer to
it in ADFunc

I can think of some more options that are variations of the above.

When it comes to OpenMP and CppAD I can think of two use cases that
might be of general interest:
1. Automatically use threads to speed up Jacobian/Hessian calculation.
2. When modeling coupled subsystems parts of calculation may be done
in parallel:
- Independent(X1,X2)
- In paralllel (might use some omp private AD<Base> variables):
thread1: tmp1(X1), thread2: tmp2(X2).
- In serial: Y1(tmp1, tmp2), Y2(tmp1, tmp2)
- Dependent(Y, X)

Thanks is advance!

/Iakov