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Variables and constants are the basic data objects manipulated in a program. Declarations list the variables to be used, and state what type they have and perhaps what their initial values are. Operators specify what is to be done to them. Expressions combine variables and constants to produce new values. The type of an object determines the set of values it can have and what operations can be performed on it. These building blocks are the topics of this chapter.
The ANSI standard has made many small changes and additions to basic types and expressions. There are now signed and unsigned forms of all integer types, and notations for unsigned constants and hexadecimal character constants. Floatingpoint operations may be done in single precision; there is also a long double type for extended precision. String constants may be concatenated at compile time. Enumerations have become part of the language, formalizing a feature of long standing. Objects may be declared const, which prevents them from being changed. The rules for automatic coercions among arithmetic types have been augmented to handle the richer set of types.
Although we didn't say so in Chapter 1, there are some restrictions on the names of variables and symbolic constants. Names are made up of letters and digits; the first character must be a letter. The underscore `` '' counts as a letter; it is sometimes useful for improving the readability of long variable names. Don't begin variable names with underscore, however, since library routines often use such names. Upper and lower case letters are distinct, so x and X are two different names. Traditional C practice is to use lower case for variable names, and all upper case for symbolic constants.
At least the first 31 characters of an internal name are significant. For function names and external variables, the number may be less than 31, because external names may be used by assemblers and loaders over which the language has no control. For external names, the standard guarantees uniqueness only for 6 characters and a single case. Keywords like if else int float, etc., are reserved: you can't use them as variable names. They must be in lower case.
It's wise to choose variable names that are related to the purpose of the variable, and that are unlikely to get mixed up typographically. We tend to use short names for local variables, especially loop indices, and longer names for external variables.
There are only a few basic data types in C:
char 
a single byte, capable of holding one character in the local character set 
int 
an integer, typically reflecting the natural size of integers on the host machine 
float 
singleprecision floating point 
double 
doubleprecision floating point 
In addition, there are a number of qualifiers that can be applied to these basic types. short and long apply to integers:
The word int can be omitted in such declarations, and typically it is.
The intent is that short and long should provide different lengths of integers where practical; int will normally be the natural size for a particular machine. short is often 16 bits long, and int either 16 or 32 bits. Each compiler is free to choose appropriate sizes for its own hardware, subject only to the the restriction that shorts and ints are at least 16 bits, longs are at least 32 bits, and short is no longer than int, which is no longer than long
The qualifier signed or unsigned may be applied to char or any integer. unsigned numbers are always positive or zero, and obey the laws of arithmetic modulo 2^{n}, where n is the number of bits in the type. So, for instance, if chars are 8 bits, unsigned char variables have values between 0 and 255, while signed chars have values between 128 and 127 (in a two's complement machine.) Whether plain chars are signed or unsigned is machinedependent, but printable characters are always positive.
The type long double specifies extendedprecision floating point. As with integers, the sizes of floatingpoint objects are implementationdefined; float double and long double could represent one, two or three distinct sizes.
The standard headers <limits.h> and <float.h> contain symbolic constants for all of these sizes, along with other properties of the machine and compiler. These are discussed in Appendix B.
Exercise 21. Write a program to determine the ranges of char short int, and long variables, both signed and unsigned, by printing appropriate values from standard headers and by direct computation. Harder if you compute them: determine the ranges of the various floatingpoint types.
An integer constant like is an int. A long constant is written with a terminal l (ell) or L, as in 123456789L; an integer constant too big to fit into an int will also be taken as a long. Unsigned constants are written with a terminal u or U, and the suffix ul or UL indicates unsigned long
Floatingpoint constants contain a decimal point ( ) or an exponent (1e2) or both; their type is double, unless suffixed. The suffixes f or F indicate a float constant; l or L indicate a long double
The value of an integer can be specified in octal or hexadecimal instead of decimal. A leading (zero) on an integer constant means octal; a leading 0x or 0X means hexadecimal. For example, decimal 31 can be written as in octal and 0x1f or 0x1F in hex. Octal and hexadecimal constants may also be followed by L to make them long and U to make them unsigned 0XFUL is an unsigned long constant with value 15 decimal.
A character constant is an integer, written as one character within single quotes, such as 'x'. The value of a character constant is the numeric value of the character in the machine's character set. For example, in the ASCII character set the character constant has the value 48, which is unrelated to the numeric value 0. If we write instead of a numeric value like 48 that depends on the character set, the program is independent of the particular value and easier to read. Character constants participate in numeric operations just as any other integers, although they are most often used in comparisons with other characters.
Certain characters can be represented in character and string constants by escape sequences like n (newline); these sequences look like two characters, but represent only one. In addition, an arbitrary bytesized bit pattern can be specified by
where ooo is one to three octal digits (07) or by
where hh is one or more hexadecimal digits (09, af, AF). So we might write
or, in hexadecimal,
The complete set of escape sequences is
a 
alert (bell) character 
backslash 

b 
backspace 
question mark 

f 
formfeed 
single quote 

n 
newline 
double quote 

r 
carriage return 
ooo 
octal number 
t 
horizontal tab 
xhh 
hexadecimal number 
v 
vertical tab 
The character constant represents the character with value zero, the null character. is often written instead of to emphasize the character nature of some expression, but the numeric value is just 0.
A constant expression is an expression that involves only constants. Such expressions may be evaluated at during compilation rather than runtime, and accordingly may be used in any place that a constant can occur, as in
or
A string constant, or string literal, is a sequence of zero or more characters surrounded by double quotes, as in
or
The quotes are not part of the string, but serve only to delimit it. The same escape sequences used in character constants apply in strings; represents the doublequote character. String constants can be concatenated at compile time:
is equivalent to
This is useful for splitting up long strings across several source lines.
Technically, a string constant is an array of characters. The internal representation of a string has a null character at the end, so the physical storage required is one more than the number of characters written between the quotes. This representation means that there is no limit to how long a string can be, but programs must scan a string completely to determine its length. The standard library function strlen(s) returns the length of its character string argument s, excluding the terminal . Here is our version:
strlen and other string functions are declared in the standard header <string.h>
Be careful to distinguish between a character constant and a string that contains a single character: 'x' is not the same as 'x'. The former is an integer, used to produce the numeric value of the letter x in the machine's character set. The latter is an array of characters that contains one character (the letter x) and a
There is one other kind of constant, the enumeration constant. An enumeration is a list of constant integer values, as in
The first name in an enum has value 0, the next 1, and so on, unless explicit values are specified. If not all values are specified, unspecified values continue the progression from the last specified value, as the second of these examples:
Names in different enumerations must be distinct. Values need not be distinct in the same enumeration.
Enumerations provide a convenient way to associate constant values with names, an alternative to #define with the advantage that the values can be generated for you. Although variables of enum types may be declared, compilers need not check that what you store in such a variable is a valid value for the enumeration. Nevertheless, enumeration variables offer the chance of checking and so are often better than #defines. In addition, a debugger may be able to print values of enumeration variables in their symbolic form.
All variables must be declared before use, although certain declarations can be made implicitly by content. A declaration specifies a type, and contains a list of one or more variables of that type, as in
Variables can be distributed among declarations in any fashion; the lists above could well be written as
The latter form takes more space, but is convenient for adding a comment to each declaration for subsequent modifications.
A variable may also be initialized in its declaration. If the name is followed by an equals sign and an expression, the expression serves as an initializer, as in
If the variable in question is not automatic, the initialization is done once only, conceptionally before the program starts executing, and the initializer must be a constant expression. An explicitly initialized automatic variable is initialized each time the function or block it is in is entered; the initializer may be any expression. External and static variables are initialized to zero by default. Automatic variables for which is no explicit initializer have undefined (i.e., garbage) values.
The qualifier const can be applied to the declaration of any variable to specify that its value will not be changed. For an array, the const qualifier says that the elements will not be altered.
The const declaration can also be used with array arguments, to indicate that the function does not change that array:
The result is implementationdefined if an attempt is made to change a const
The binary arithmetic operators are , and the modulus operator . Integer division truncates any fractional part. The expression
produces the remainder when x is divided by y, and thus is zero when y divides x exactly. For example, a year is a leap year if it is divisible by 4 but not by 100, except that years divisible by 400 are leap years. Therefore
The operator cannot be applied to a float or double. The direction of truncation for and the sign of the result for are machinedependent for negative operands, as is the action taken on overflow or underflow.
The binary and operators have the same precedence, which is lower than the precedence of and , which is in turn lower than unary and . Arithmetic operators associate left to right.
Table 1 at the end of this chapter summarizes precedence and associativity for all operators.
The relational operators are
They all have the same precedence. Just below them in precedence are the equality operators:
Relational operators have lower precedence than arithmetic operators, so an expression like i < lim1 is taken as i < (lim1), as would be expected.
More interesting are the logical operators && and . Expressions connected by && or are evaluated left to right, and evaluation stops as soon as the truth or falsehood of the result is known. Most C programs rely on these properties. For example, here is a loop from the input function getline that we wrote in Chapter 1:
Before reading a new character it is necessary to check that there is room to store it in the array s, so the test i < lim1 must be made first. Moreover, if this test fails, we must not go on and read another character.
Similarly, it would be unfortunate if c were tested against EOF before getchar is called; therefore the call and assignment must occur before the character in c is tested.
The precedence of && is higher than that of , and both are lower than relational and equality operators, so expressions like
need no extra parentheses. But since the precedence of is higher than assignment, parentheses are needed in
to achieve the desired result of assignment to c and then comparison with 'n'
By definition, the numeric value of a relational or logical expression is 1 if the relation is true, and 0 if the relation is false.
The unary negation operator converts a nonzero operand into 0, and a zero operand in 1. A common use of is in constructions like
rather than
It's hard to generalize about which form is better. Constructions like !valid read nicely (``if not valid''), but more complicated ones can be hard to understand.
Exercise 2 Write a loop equivalent to the for loop above without using && or
When an operator has operands of different types, they are converted to a common type according to a small number of rules. In general, the only automatic conversions are those that convert a ``narrower'' operand into a ``wider'' one without losing information, such as converting an integer into floating point in an expression like f + i. Expressions that don't make sense, like using a float as a subscript, are disallowed. Expressions that might lose information, like assigning a longer integer type to a shorter, or a floatingpoint type to an integer, may draw a warning, but they are not illegal.
A char is just a small integer, so chars may be freely used in arithmetic expressions. This permits considerable flexibility in certain kinds of character transformations. One is exemplified by this naive implementation of the function atoi, which converts a string of digits into its numeric equivalent.
As we discussed in Chapter 1, the expression
gives the numeric value of the character stored in s[i], because the values of , etc., form a contiguous increasing sequence.
Another example of char to int conversion is the function lower, which maps a single character to lower case for the ASCII character set. If the character is not an upper case letter, lower returns it unchanged.
This works for ASCII because corresponding upper case and lower case letters are a fixed distance apart as numeric values and each alphabet is contiguous  there is nothing but letters between A and Z. This latter observation is not true of the EBCDIC character set, however, so this code would convert more than just letters in EBCDIC.
The standard header <ctype.h>, described in Appendix B, defines a family of functions that provide tests and conversions that are independent of character set. For example, the function tolower is a portable replacement for the function lower shown above. Similarly, the test
can be replaced by
We will use the <ctype.h> functions from now on.
There is one subtle point about the conversion of characters to integers. The language does not specify whether variables of type char are signed or unsigned quantities. When a char is converted to an int, can it ever produce a negative integer? The answer varies from machine to machine, reflecting differences in architecture. On some machines a char whose leftmost bit is 1 will be converted to a negative integer (``sign extension''). On others, a char is promoted to an int by adding zeros at the left end, and thus is always positive.
The definition of C guarantees that any character in the machine's standard printing character set will never be negative, so these characters will always be positive quantities in expressions. But arbitrary bit patterns stored in character variables may appear to be negative on some machines, yet positive on others. For portability, specify signed or unsigned if noncharacter data is to be stored in char variables.
Relational expressions like i > j and logical expressions connected by && and are defined to have value 1 if true, and 0 if false. Thus the assignment
sets d to 1 if c is a digit, and 0 if not. However, functions like isdigit may return any nonzero value for true. In the test part of if while for, etc., ``true'' just means ``nonzero'', so this makes no difference.
Implicit arithmetic conversions work much as expected. In general, if an operator like or that takes two operands (a binary operator) has operands of different types, the ``lower'' type is promoted to the ``higher'' type before the operation proceeds. The result is of the integer type. Section 6 of Appendix A states the conversion rules precisely. If there are no unsigned operands, however, the following informal set of rules will suffice:
Notice that floats in an expression are not automatically converted to double; this is a change from the original definition. In general, mathematical functions like those in <math.h> will use double precision. The main reason for using float is to save storage in large arrays, or, less often, to save time on machines where doubleprecision arithmetic is particularly expensive.
Conversion rules are more complicated when unsigned operands are involved. The problem is that comparisons between signed and unsigned values are machinedependent, because they depend on the sizes of the various integer types. For example, suppose that int is 16 bits and long is 32 bits. Then 1L < 1U, because 1U, which is an unsigned int, is promoted to a signed long. But 1L > 1UL because 1L is promoted to unsigned long and thus appears to be a large positive number.
Conversions take place across assignments; the value of the right side is converted to the type of the left, which is the type of the result.
A character is converted to an integer, either by sign extension or not, as described above.
Longer integers are converted to shorter ones or to chars by dropping the excess highorder bits. Thus in
the value of c is unchanged. This is true whether or not sign extension is involved. Reversing the order of assignments might lose information, however.
If x is float and i is int, then x = i and i = x both cause conversions; float to int causes truncation of any fractional part. When a double is converted to float, whether the value is rounded or truncated is implementation dependent.
Since an argument of a function call is an expression, type conversion also takes place when arguments are passed to functions. In the absence of a function prototype, char and short become int, and float becomes double. This is why we have declared function arguments to be int and double even when the function is called with char and float
Finally, explicit type conversions can be forced (``coerced'') in any expression, with a unary operator called a cast. In the construction
(type name) expression
the expression is converted to the named type by the conversion rules above. The precise meaning of a cast is as if the expression were assigned to a variable of the specified type, which is then used in place of the whole construction. For example, the library routine sqrt expects a double argument, and will produce nonsense if inadvertently handled something else. (sqrt is declared in <math.h>.) So if n is an integer, we can use
to convert the value of n to double before passing it to sqrt. Note that the cast produces the value of n in the proper type; n itself is not altered. The cast operator has the same high precedence as other unary operators, as summarized in the table at the end of this chapter.
If arguments are declared by a function prototype, as the normally should be, the declaration causes automatic coercion of any arguments when the function is called. Thus, given a function prototype for sqrt
the call
coerces the integer into the double value without any need for a cast.
The standard library includes a portable implementation of a pseudorandom number generator and a function for initializing the seed; the former illustrates a cast:
Exercise 23. Write a function htoi(s), which converts a string of hexadecimal digits (including an optional 0x or 0X) into its equivalent integer value. The allowable digits are through a through f, and A through F
C provides two unusual operators for incrementing and decrementing variables. The increment operator adds 1 to its operand, while the decrement operator subtracts 1. We have frequently used to increment variables, as in
The unusual aspect is that and may be used either as prefix operators (before the variable, as in ++n), or postfix operators (after the variable: n++). In both cases, the effect is to increment n. But the expression ++n increments n before its value is used, while n++ increments n after its value has been used. This means that in a context where the value is being used, not just the effect, ++n and n++ are different. If n is 5, then
sets x to 5, but
sets x to 6. In both cases, n becomes 6. The increment and decrement operators can only be applied to variables; an expression like (i+j)++ is illegal.
In a context where no value is wanted, just the incrementing effect, as in
prefix and postfix are the same. But there are situations where one or the other is specifically called for. For instance, consider the function squeeze(s,c), which removes all occurrences of the character c from the string s
Each time a nonc occurs, it is copied into the current j position, and only then is j incremented to be ready for the next character. This is exactly equivalent to
Another example of a similar construction comes from the getline function that we wrote in Chapter 1, where we can replace
by the more compact
As a third example, consider the standard function strcat(s,t), which concatenates the string t to the end of string s strcat assumes that there is enough space in s to hold the combination. As we have written it, strcat returns no value; the standard library version returns a pointer to the resulting string.
As each member is copied from t to s, the postfix is applied to both i and j to make sure that they are in position for the next pass through the loop.
Exercise 24. Write an alternative version of squeeze(s1,s2) that deletes each character in s1 that matches any character in the string s
Exercise 25. Write the function any(s1,s2), which returns the first location in a string s1 where any character from the string s2 occurs, or if s1 contains no characters from s (The standard library function strpbrk does the same job but returns a pointer to the location.)
C provides six operators for bit manipulation; these may only be applied to integral operands, that is, char short int, and long, whether signed or unsigned.
& 
bitwise AND 
bitwise inclusive OR 

bitwise exclusive OR 

<< 
left shift 
>> 
right shift 
one's complement (unary) 
The bitwise AND operator & is often used to mask off some set of bits, for example
sets to zero all but the loworder 7 bits of n
The bitwise OR operator is used to turn bits on:
sets to one in x the bits that are set to one in SET_ON
The bitwise exclusive OR operator sets a one in each bit position where its operands have different bits, and zero where they are the same.
One must distinguish the bitwise operators & and from the logical operators && and , which imply lefttoright evaluation of a truth value. For example, if x is 1 and y is 2, then x & y is zero while x && y is one.
The shift operators << and >> perform left and right shifts of their left operand by the number of bit positions given by the right operand, which must be nonnegative. Thus x << 2 shifts the value of x by two positions, filling vacated bits with zero; this is equivalent to multiplication by 4. Right shifting an unsigned quantity always fits the vacated bits with zero. Right shifting a signed quantity will fill with bit signs (``arithmetic shift'') on some machines and with 0bits (``logical shift'') on others.
The unary operator yields the one's complement of an integer; that is, it converts each 1bit into a 0bit and vice versa. For example
sets the last six bits of x to zero. Note that x & ~077 is independent of word length, and is thus preferable to, for example, x & 0177700, which assumes that x is a 16bit quantity. The portable form involves no extra cost, since is a constant expression that can be evaluated at compile time.
As an illustration of some of the bit operators, consider the function getbits(x,p,n) that returns the (right adjusted) nbit field of x that begins at position p. We assume that bit position 0 is at the right end and that n and p are sensible positive values. For example, getbits(x,4,3) returns the three bits in positions 4, 3 and 2, rightadjusted.
The expression x >> (p+1n) moves the desired field to the right end of the word. is all 1bits; shifting it left n positions with ~0<<n places zeros in the rightmost n bits; complementing that with makes a mask with ones in the rightmost n bits.
Exercise 26. Write a function setbits(x,p,n,y) that returns x with the n bits that begin at position p set to the rightmost n bits of y, leaving the other bits unchanged.
Exercise 27. Write a function invert(x,p,n) that returns x with the n bits that begin at position p inverted (i.e., 1 changed into 0 and vice versa), leaving the others unchanged.
Exercise 28. Write a function rightrot(x,n) that returns the value of the integer x rotated to the right by n positions.
An expression such as
in which the variable on the left side is repeated immediately on the right, can be written in the compressed form
The operator is called an assignment operator.
Most binary operators (operators like that have a left and right operand) have a corresponding assignment operator op , where op is one of
If expr_{1} and expr_{2} are expressions, then
is equivalent to
except that expr_{1} is computed only once. Notice the parentheses around expr_{2}:
means
rather than
As an example, the function bitcount counts the number of 1bits in its integer argument.
Declaring the argument x to be an unsigned ensures that when it is rightshifted, vacated bits will be filled with zeros, not sign bits, regardless of the machine the program is run on.
Quite apart from conciseness, assignment operators have the advantage that they correspond better to the way people think. We say ``add 2 to i'' or ``increment i by 2'', not ``take i, add 2, then put the result back in i''. Thus the expression i += 2 is preferable to i = i+ In addition, for a complicated expression like
the assignment operator makes the code easier to understand, since the reader doesn't have to check painstakingly that two long expressions are indeed the same, or to wonder why they're not. And an assignment operator may even help a compiler to produce efficient code.
We have already seen that the assignment statement has a value and can occur in expressions; the most common example is
The other assignment operators ( , etc.) can also occur in expressions, although this is less frequent.
In all such expressions, the type of an assignment expression is the type of its left operand, and the value is the value after the assignment.
Exercise 29. In a two's complement number system, x &= (x1) deletes the rightmost 1bit in x. Explain why. Use this observation to write a faster version of bitcount
The statements
compute in z the maximum of a and b. The conditional expression, written with the ternary operator `` '', provides an alternate way to write this and similar constructions. In the expression
the expression expr_{1} is evaluated first. If it is nonzero (true), then the expression expr_{2} is evaluated, and that is the value of the conditional expression. Otherwise expr_{3} is evaluated, and that is the value. Only one of expr_{2} and expr_{3} is evaluated. Thus to set z to the maximum of a and b
It should be noted that the conditional expression is indeed an expression, and it can be used wherever any other expression can be. If expr_{2} and expr_{3} are of different types, the type of the result is determined by the conversion rules discussed earlier in this chapter. For example, if f is a float and n an int, then the expression
is of type float regardless of whether n is positive.
Parentheses are not necessary around the first expression of a conditional expression, since the precedence of is very low, just above assignment. They are advisable anyway, however, since they make the condition part of the expression easier to see.
The conditional expression often leads to succinct code. For example, this loop prints n elements of an array, 10 per line, with each column separated by one blank, and with each line (including the last) terminated by a newline.
A newline is printed after every tenth element, and after the nth. All other elements are followed by one blank. This might look tricky, but it's more compact than the equivalent ifelse. Another good example is
Exercise 210. Rewrite the function lower, which converts upper case letters to lower case, with a conditional expression instead of ifelse
Table 1 summarizes the rules for precedence and associativity of all operators, including those that we have not yet discussed. Operators on the same line have the same precedence; rows are in order of decreasing precedence, so, for example, , and all have the same precedence, which is higher than that of binary and . The ``operator'' refers to function call. The operators > and . are used to access members of structures; they will be covered in Chapter 6, along with sizeof (size of an object). Chapter 5 discusses (indirection through a pointer) and & (address of an object), and Chapter 3 discusses the comma operator.
Operators 
Associativity 
() [] > . 
left to right 
(type) sizeof 
right to left 
left to right 

left to right 

<< >> 
left to right 
< <= > >= 
left to right 
left to right 

& 
left to right 
left to right 

left to right 

&& 
left to right 
left to right 

right to left 

= += = *= /= %= &= ^= = <<= >>= 
right to left 
left to right 
Unary & +, , and * have higher precedence than the binary forms.
Table 1: Precedence and Associativity of Operators
Note that the precedence of the bitwise operators & , and falls below and . This implies that bittesting expressions like
must be fully parenthesized to give proper results.
C, like most languages, does not specify the order in which the operands of an operator are evaluated. (The exceptions are && and ` '.) For example, in a statement like
f may be evaluated before g or vice versa; thus if either f or g alters a variable on which the other depends, x can depend on the order of evaluation. Intermediate results can be stored in temporary variables to ensure a particular sequence.
Similarly, the order in which function arguments are evaluated is not specified, so the statement
can produce different results with different compilers, depending on whether n is incremented before power is called. The solution, of course, is to write
Function calls, nested assignment statements, and increment and decrement operators cause ``side effects''  some variable is changed as a byproduct of the evaluation of an expression. In any expression involving side effects, there can be subtle dependencies on the order in which variables taking part in the expression are updated. One unhappy situation is typified by the statement
The question is whether the subscript is the old value of i or the new. Compilers can interpret this in different ways, and generate different answers depending on their interpretation. The standard intentionally leaves most such matters unspecified. When side effects (assignment to variables) take place within an expression is left to the discretion of the compiler, since the best order depends strongly on machine architecture. (The standard does specify that all side effects on arguments take effect before a function is called, but that would not help in the call to printf above.)
The moral is that writing code that depends on order of evaluation is a bad programming practice in any language. Naturally, it is necessary to know what things to avoid, but if you don't know how they are done on various machines, you won't be tempted to take advantage of a particular implementation.
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