IMPORTANT NOTE:
BigRatOps for basic operations on values of type BigRat
NumTheory for more advanced operations
The class BigRat is intended to represent (exact) rational numbers
of practically unlimited range; it is currently based on the
implementation in the GMP multiple precision library. This code forms
the interface between CoCoALib and the big integer/rational library
upon which it relies. It seems most unlikely that GMP will be
displaced from its position as the foremost library of this type; as a
consequence the class BigRat may eventually be replaced by GMP's
own C++ interface.
It is important not to confuse values of type BigRat with values of type
RingElem which happen to belong to the ring RingQQ. The distinction
is analogous to that between values of type BigInt and value 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 BigRat
values is wider (since we have explicit knowledge of the type).
A value of type BigRat may be created from:
BigRat() default ctor, the value is zero
BigRat(n) where n is an integer: warning: do not write BigRat(2/3), it compiles but works unexpectedly!
BigRat(q) where q is another value of type BigRat (its value is copied)
BigRat(n,d) where n and d are both integers (machine integers or
BigInts) specifying numerator and denominator in that order
BigRat(BigRat::OneOverZero) create the "infinity" rational 1/0 (will trigger
an error if you try to perform arithmetic with it, but you can access num and den)
BigRatFromString(str) where str is a string of the form N or N/D
where N is the decimal representation of the numerator and
D that of the denominator (leading and trailing whitespace is permitted)
BigRatFromMPQ(mpq_value) copy a GMP rational (of type mpq_t) into
a BigRat; helps interfacing between CoCoALib and code using GMP directly.
The ctors BigRat(n,d) and BigRatFromString(str) accept an optional final
arg BigRat::AlreadyReduced which asserts that the value is already reduced
(i.e. positive denominator, and numerator and denominator are coprime).
Use this feature only if you are absolutely certain that there is no
common factor between the given numerator and denominator.
See Bugs section for why there is no ctor from a single integer.
mpqref(n)-- this gives a (const) reference to the mpq_t value inside
a BigRat object. You should use this accessor very sparingly!
Nothing very clever. Conversion from a string was a bit tedious.
I have replaced the bodies of the BigRat ctors which take two integers
as arguments by a call to the common body BigRat::myAssign. This does
mean that some wasteful temporaries are created when either of the
arguments is a machine integer. Time will tell whether this waste is
intolerable.
The reason for having "strange" ctors fromstd::string and mpq_t
was to avoid problems with BigRat(0). Note that expressions such
as BigInt(2/3) are equivalent to BigInt(0) but should be forbidden
at compile time; however, at the moment mpq_t is a pointer type, so
BigRat(2/3) is seen as BigRat(0), and 0 can be interpreted as
a null-pointer... so BigRat(mpq_t) would be an almost perfect match!
This code is probably not exception safe; I do not know what the mpq_*
functions do when there is insufficient memory to proceed. Making the
code exception safe could well be non-trivial: I suspect a sort of
auto_ptr to an mpq_t value might be needed.
Removed BigRat ctors from a single (machine) integer because too often
I made the mistake of writing something like BigRat(1/2) instead of
BigRat(1,2).
Should the BigRatFromString pseudo-ctor also accept numbers with decimal points?
e.g. BigRat("3.14159")? We'll wait and see whether there is demand for this
before implementing; note that GMP does not offer this capability.
2018
BigRatOps
string and mpq_t; replaced them by pseudo-ctors.
This means that BigRat(0) and BigRat(1/2) etc. now give compile-time errors.
2011
QQ renamed into BigRat:
to avoid confusion with RingQQ and its name in CoCoA system