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.

 

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