C++, operator overloading
You can only use standard c++ libraries. The key is to use fractions .
This assignment will be about numbers: your goal will be to
implement a class, number, which represents a real number with an
arbitrary number of digits (also known as an arbitrary precision
number). The class should have operators for addition, subtraction,
multiplication, division and comparisons, as well as unary minus.
Additionally, add power( int ) and sqrt( int ) as const
methods. The argument to power is the exponent. The argument of
sqrt gives the number of decimal digits that should be exact in
the result (see also below).
The constructor of number takes a single integer argument and
constructs an instance of number with the argument as its value
(this constructor should allow implicit conversions from int). A
default-constructed number should be 0.
As an example, all of the following should be valid code:
number a( 10 ), b( 25 );
number c = a + b;
number d = c / a;
number e = d * a;
assert( e == a + b );
assert( e != a );
assert( c > a );
assert( a < b );
assert( c.power( 2 ) > c );
c = number( 10 ).power( -5 );
assert( c > c.power( 2 ) );
The decimal digits supplied to sqrt should be interpreted as
follows:
number s = number( 145 ).sqrt( 3 ); /* 3 fractional digits */
/* the exact result rounded to 3 fractional places is 12.042 */
number lower = number( 120415 ) * number( 10 ).power( -4 );
number upper = number( 120425 ) * number( 10 ).power( -4 );
assert( s > lower );
assert( s < upper );
Or in other words, if your result is (single) rounded to the given
number of decimal places, it must agree in all those decimal places
with a correctly rounded exact result.
Division by zero and square roots of negative numbers are undefined.
PS: A reference solution is about 250 lines of not very dense code.
