The bit shifting operators do exactly what their name implies. They shift bits. Here's a brief (or not-so-brief) introduction to the different shift operators.
The Operators
>>
is the arithmetic (or signed) right shift operator.
>>>
is the logical (or unsigned) right shift operator.
<<
is the left shift operator, and meets the needs of both logical and arithmetic shifts.
All of these operators can be applied to integer values (int
, long
, possibly short
and byte
or char
). In some languages, applying the shift operators to any datatype smaller than int
automatically resizes the operand to be an int
.
Note that <<<
is not an operator, because it would be redundant.
Also note that C and C++ do not distinguish between the right shift operators. They provide only the >>
operator, and the right-shifting behavior is implementation defined for signed types. The rest of the answer uses the C# / Java operators.
(In all mainstream C and C++ implementations including GCC and Clang/LLVM, >>
on signed types is arithmetic. Some code assumes this, but it isn't something the standard guarantees. It's not undefined, though; the standard requires implementations to define it one way or another. However, left shifts of negative signed numbers is undefined behaviour (signed integer overflow). So unless you need arithmetic right shift, it's usually a good idea to do your bit-shifting with unsigned types.)
Left shift (<<)
Integers are stored, in memory, as a series of bits. For example, the number 6 stored as a 32-bit int
would be:
00000000 00000000 00000000 00000110
Shifting this bit pattern to the left one position (6 << 1
) would result in the number 12:
00000000 00000000 00000000 00001100
As you can see, the digits have shifted to the left by one position, and the last digit on the right is filled with a zero. You might also note that shifting left is equivalent to multiplication by powers of 2. So 6 << 1
is equivalent to 6 * 2
, and 6 << 3
is equivalent to 6 * 8
. A good optimizing compiler will replace multiplications with shifts when possible.
Non-circular shifting
Please note that these are not circular shifts. Shifting this value to the left by one position (3,758,096,384 << 1
):
11100000 00000000 00000000 00000000
results in 3,221,225,472:
11000000 00000000 00000000 00000000
The digit that gets shifted "off the end" is lost. It does not wrap around.
Logical right shift (>>>)
A logical right shift is the converse to the left shift. Rather than moving bits to the left, they simply move to the right. For example, shifting the number 12:
00000000 00000000 00000000 00001100
to the right by one position (12 >>> 1
) will get back our original 6:
00000000 00000000 00000000 00000110
So we see that shifting to the right is equivalent to division by powers of 2.
Lost bits are gone
However, a shift cannot reclaim "lost" bits. For example, if we shift this pattern:
00111000 00000000 00000000 00000110
to the left 4 positions (939,524,102 << 4
), we get 2,147,483,744:
10000000 00000000 00000000 01100000
and then shifting back ((939,524,102 << 4) >>> 4
) we get 134,217,734:
00001000 00000000 00000000 00000110
We cannot get back our original value once we have lost bits.
Arithmetic right shift (>>)
The arithmetic right shift is exactly like the logical right shift, except instead of padding with zero, it pads with the most significant bit. This is because the most significant bit is the sign bit, or the bit that distinguishes positive and negative numbers. By padding with the most significant bit, the arithmetic right shift is sign-preserving.
For example, if we interpret this bit pattern as a negative number:
10000000 00000000 00000000 01100000
we have the number -2,147,483,552. Shifting this to the right 4 positions with the arithmetic shift (-2,147,483,552 >> 4) would give us:
11111000 00000000 00000000 00000110
or the number -134,217,722.
So we see that we have preserved the sign of our negative numbers by using the arithmetic right shift, rather than the logical right shift. And once again, we see that we are performing division by powers of 2.
Best Answer
Expression: Something which evaluates to a value. Example: 1+2/x
Statement: A line of code which does something. Example: GOTO 100
In the earliest general-purpose programming languages, like FORTRAN, the distinction was crystal-clear. In FORTRAN, a statement was one unit of execution, a thing that you did. The only reason it wasn't called a "line" was because sometimes it spanned multiple lines. An expression on its own couldn't do anything... you had to assign it to a variable.
is an error in FORTRAN, because it doesn't do anything. You had to do something with that expression:
FORTRAN didn't have a grammar as we know it today—that idea was invented, along with Backus-Naur Form (BNF), as part of the definition of Algol-60. At that point the semantic distinction ("have a value" versus "do something") was enshrined in syntax: one kind of phrase was an expression, and another was a statement, and the parser could tell them apart.
Designers of later languages blurred the distinction: they allowed syntactic expressions to do things, and they allowed syntactic statements that had values. The earliest popular language example that still survives is C. The designers of C realized that no harm was done if you were allowed to evaluate an expression and throw away the result. In C, every syntactic expression can be a made into a statement just by tacking a semicolon along the end:
is a totally legit statement even though absolutely nothing will happen. Similarly, in C, an expression can have side-effects—it can change something.
because
callfunc
might just do something useful.Once you allow any expression to be a statement, you might as well allow the assignment operator (=) inside expressions. That's why C lets you do things like
This evaluates the expression x = 2 (assigning the value of 2 to x) and then passes that (the 2) to the function
callfunc
.This blurring of expressions and statements occurs in all the C-derivatives (C, C++, C#, and Java), which still have some statements (like
while
) but which allow almost any expression to be used as a statement (in C# only assignment, call, increment, and decrement expressions may be used as statements; see Scott Wisniewski's answer).Having two "syntactic categories" (which is the technical name for the sort of thing statements and expressions are) can lead to duplication of effort. For example, C has two forms of conditional, the statement form
and the expression form
And sometimes people want duplication that isn't there: in standard C, for example, only a statement can declare a new local variable—but this ability is useful enough that the GNU C compiler provides a GNU extension that enables an expression to declare a local variable as well.
Designers of other languages didn't like this kind of duplication, and they saw early on that if expressions can have side effects as well as values, then the syntactic distinction between statements and expressions is not all that useful—so they got rid of it. Haskell, Icon, Lisp, and ML are all languages that don't have syntactic statements—they only have expressions. Even the class structured looping and conditional forms are considered expressions, and they have values—but not very interesting ones.