C++ for Scientists - Technische Universität Dresden

28 CHAPTER 2. C++ BASICS
The bitwise operations can be used to characterize properties in a very compact form as in the
following example:
#include
int main ()
{
int concave = 1, monotone = 2, continuous = 4;
int f is = concave | continuous;
std::cout ≪ ”f is ” ≪ f is ≪ std::endl;
std::cout ≪ ”Is f concave? (0 means no, 1 means yes) ”
≪ (f is & concave) ≪ std::endl;
f is = f is | monotone;
f is = f is ˆ concave;
std::cout ≪ ”f is now ” ≪ f is ≪ std::endl;
return 0 ;
}
Line 5 introduces three properties that can be combined arbitrarily. The numbers are powers
of two so that their binary representations contain a single 1-bit respectively. In line 7 we used
bitwise OR to combine two properties. Bitwise AND allows for masking single or multiple bits
as shown in line 11. In line 13 an additional property is set with bitwise OR. Bitwise exclusive
OR (XOR) like in line 14 allows for toggling a property. Operating systems and hardware driver
use this style of operations exhaustively. But it needs some practice to get used to it.
Shift operations provide an efficient way to multiply with or divide by powers of 2 as shown in
the following code:
int i = 78;
std::cout ≪ ”i ∗ 8 is ” ≪ (i ≪ 3)
≪ ”, i / 4 is ” ≪ (i ≫2) ≪ std::endl;
Obviously, that needs some familiarization as well.
On the performance side, processors are today quite fast in multiplying integers so that you
will not see a big performance boost when replacing your products by left shifts. Division is
still a bit slow and a right shift can make a difference. Even then the price of this source code
obfuscation is only justified if the operation is critical for the overall performance of your entire
application.
2.3.4 Compound assignment
The compound assignment operators apply an arithmetic operation to the left and right-hand
side and store the result in the left hand side.
There operators are +=, −=, ∗=, /=, %=, ≫=, ≪=, &=, ˆ=, and |=.
The statement a+=b is equal to the statement a=a+b.