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**NOTE:** for operations on values of type `BigInt`

see `IntOperations`

and `NumTheory`

The class `BigInt`

is intended to represent integers of practically
unlimited range. CoCoALib relies on an external library for handling big
integers: currently it is based on the the GMP *multiple precision*
library. This CoCoALib code simply forms the interface to the underlying
big integer library.

Computations with `BigInt`

values do not suffer from overflow, but
they are significantly slower than with machine integers. All
`BigInt`

values are stored on the heap.

It is important not to confuse values of type `BigInt`

with values of type
`RingElem`

which happen to belong to the ring `RingZZ`

. In summary, the
operations available for `RingElem`

are those applicable to elements of
any ordered commutative ring, whereas the range of operations on `BigInt`

values is wider (since we have explicit knowledge of the type).

See `BigRat`

for representing and handling rational numbers.

A value of type `BigInt`

may be created from:

- nothing, in which case the value is zero
- another value of type
`BigInt`

(its value is copied) - a machine integer
- a string containing the decimal digits (optionally preceded by a minus sign)
- a GMP
`mpz_t`

value

Note: No direct constructor for creating a `BigInt`

from a `char*`

is
provided because it introduces an ambiguity in `BigInt(0)`

-- since
`0`

is valid as a `char*`

. However C++ will automatically convert
a `char*`

into a `std::string`

, so you can still use a C-string if
you want.

**NOTE:** for operations on values of type `BigInt`

see `IntOperations`

- Functions violating encapsulation
`mpzref(n)`

-- this gives a (const) reference to the`mpz_t`

value inside a`BigInt`

object. You should use this accessor very sparingly (but it is handy for calling GMP functions directly).

The implementation is structurally very simple, just rather long and
tedious. The value of a `BigInt`

object is represented as an `mpz_t`

;
this is a private data member, but to facilitate interfacing with code
which uses `mpz_t`

values directly I have supplied the two functions
called `mpzref`

which allow access to this data member.

The output function turned out to be trickier than one might guess.
Part of the problem was wanting to respect the `ostream`

settings.

Of course, input is a mess. Nothing clever here.

Check also the documentation for `MachineInt`

to understand how
that class is used.

Currently functions which return `BigInt`

values will copy the result (upon
each return) -- an attempt to avoid the waste with proxy classes caused a
problem see test-bug4.C Move semantics in C++11 should solve this.

The official GMP interface (`mpz_class`

) is certainly more efficient;
should CoCoALib eventually switch to using `mpz_class`

?
It seems most unlikely that GMP will be displaced from its
position as the foremost library for big integer arithmetic, so
such explicit dependence on it should not matter.

No bit operations: bit setting and checking, and/or/xor/not.

The code is long, tedious and unilluminating. Are there any volunteers to improve it?

**2012**

- May (v0.9951):
- moved common operations on
`BigInt`

and`MachineInt`

together into`IntOperations`

-**2011**

- moved common operations on
- August (v0.9950):
- class
`ZZ`

renamed into`BigInt`

: avoid confusion with`RingZZ`

and its name in CoCoA system `random`

has changed (was`random(lo,hi)`

): see`RandomZZStream`

,`RandomLongStream`

- class