C++ for Scientists - Technische Universität Dresden

2.4. EXPRESSIONS AND STATEMENTS 31
A= Bˆ2;
A is B squared. So far so good. That the original meaning of ˆ is a bitwise XOR does not
worry us because we do not plan implementing bitwise operations on matrices.
Now we add C:
A= Bˆ2 + C;
Looks nice. But does not work (or does something weird). — Why?
Because + has a higher priority than ˆ. Thus, the compiler understands our expression as:
A= B ˆ (2 + C);
Oops. That looks wrong. 9 The operator gives a concise and intuitive interface but its priority
would cause a lot of confusion. Thus, it is advisable to refrain from this overloading.
2.4 Expressions and Statements
C and C ++ distinguish between expressions and statements. Very casually spoken, one could
just say that every expression becomes a statement if an semicolon is appended. However, we
would like to discuss this topic a bit more.
Let us build this recursively from bottom up. Any variable name (x, y, z, . . . ), constant or
literal is an expression. One or more expressions with an operator is an expression, e.g. x + y or
x ∗ y + z. In several languages, e.g. Pascal, the assignment is a statement. In C and C ++ it is an
expression, e.g. x= y + z. As a consequence it can be used in another assignment: x2= x= y + z.
Assignments are evaluated from right to left. Input and output operations as
std::cout ≪ ”x is ” ≪ x ≪ ”\n”;
are also expressions.
A function call with expressions as arguments is an expression, e.g. abs(x), abs(x ∗ y + z). Therefor,
function calls can be nested: pow(abs(x), y). In languages where a function call is a statement
this would not be possible. As the assignment is an expression, it can be used as argument of a
function: abs(x= y). Or I/O operations as those above. Needless to say that this is quite bad programming
style. An expression surrounded by parenthesis is an expression as well, e.g. x + y.
This allows us to change the order of evaluation, e.g. x ∗ (y + z) computes the addition first
although the multiplication has the higher priority.
A very special operator in C ++ is the ‘comma operator’ that provides a sequential evaluation.
The meaning is simply evaluating first the sub-expression left of the comma and then that right
of it. The value of the whole expression is that of the right sub-expression. The sub-expressions
can contain the comma operator as well so that arbitrarily long sequences can be defined. With
the help of the comma operator, one can evaluate multiple expressions in program locations
where only one expression is allowed. If used as function argument it the comma expression
needs surrounding parentheses; otherwise the comma is interpreted as separation of function
arguments. The comma operator can be overloaded with a user-defined semantics. This can
9 The precise interpretation is A.operator=(operatorˆ(B, operator+(2, C)));