Revision as of 13:42, 7 June 2014

Data Types and Operators in $C$

$C$ is a just a language specification and C compilers (which translates C code to machine code) are made by different organizations/individuals. So, in order to make a C program work across multiple compilers, C standard is important.

A little about C standard

<timelinetable title="Evolution of C" footer="C Standards" headers=Y> 1969|1973| $$C$$ language developed by Dennis Ritchie 1978|1978| <math>K\&R</math> book released, which was used as a reference for $C$ 1989|1989| $ANSI$ standard for $C$ ($C89$) released 1990|1990|$ISO$ released $C90$ %ANSI standard got approved by International Standards Organization (ISO) and got named as C90} 1999|1999| $C99$ released by $ISO$ %A new standard for C was released by ISO which made programming in C little more easier } 2011|2011| $ISO$ released $C11$ standard %which supports new features which are being given by latest hardware like multi threading, transactional memory etc.

</timelinetable> \begin{chronology}[5]{1969}{2011}{80ex}{500px} \event[1969]{1973} {$C$ language developed by Dennis Ritchie} \event{1978} {$K\&R$ book released, which was used as a reference for $C$ } \event{1989}{$ANSI$ standard for $C$ ($C89$) released} \event[1990]{1990}{$ISO$ released $C90$} %ANSI standard got approved by International Standards Organization (ISO) and got named as C90} \event[1999]{1999}{$C99$ released by $ISO$} %A new standard for C was released by ISO which made programming in C little more easier } \event[2011]{2011}{$ISO$ released $C11$ standard } %which supports new features which are being given by latest hardware like multi threading, transactional memory etc.} %\event{\decimaldate{25}{12}{2001}}{three} \end{chronology}

Till $ANSI$ standard which is almost the same as $C90$ (also called $C89/C90$) was published, the standard specified in $K\&R$ book was used as a reference for C standard. Each new standard aimed at easing the programming difficulty as well as making use of the new hardware features. We'll be following as much of $C11$ standard as possible as it adds some significant changes to C language.

Data types

Data types are used to represent data and data comes from real world. In real world we have the following data types

1. Integer
2. Character
3. Real Numbers

All other data types can be formed from these basic types (for example, a string is just a sequence of characters). So, in $C$ language we have only these basic types but they are supported in various data sizes as follows

1. short int
2. int
3. long int
4. long long int
5. char
6. float
7. double
8. long double

Now, each of these type is supported in unsigned version also. In signed version, one bit is used to identify if the number is positive or negative. So, for a $32$ bit signed integer, it can represent only up to $2^{31} - 1$, while a $32$ bit unsigned integer can represent up to $2^{32} - 1$. A boolean data type is also present in C standard which can be used to hold a bit. This data type can be used using the keyword $\_Bool$. If we use an $int$ (or $char$), to get a boolean value, we need to logical $AND$ (\&) it with $1$. With $\_Bool$, this conversion is not necessary as the byte representing the boolean will always have the most significant $7$ bits as $0$.

So, let's see what these data types mean to computer. As we have seen in the previous chapter, all data must be converted into a bit stream before being given to the processor. So, even though we use alphabets and digits while writing programs, they are converted to bits while stored in memory and then given to processor. How many bits a data type takes is defined by the $sizeof$ the data type. In $C$ language, the operator $sizeof$ gives the no. of bytes (i.e., $8$ * no. of bits) a data type takes. Since, memory accesses are restricted to multiple of bytes ($RAM$ doesn't allow to access data at a granularity lower than 8 bits at a time due to practical reasons) $sizeof$ always return at least $1$ for any data type. (A $\_Bool$ also take a byte of storage as that's the smallest accessible unit in a memory, though it actually requires just a bit of storage)

Now, lets see the $sizeof$ the various data types in $C$. Since, the data types are directly given to the processor, the $sizeof$ data types depend on the processor architecture. So, $C$ standard just tells the minimum required size specification and have let the compiler designers choose their size as per the processor architecture- $C$ compilers are used for $8$ bit embedded processors to $64$ bit desktop processors. So, this size variation does make sense.

$sizeof$ $char$ is $1$ byte as it was sufficient for $ASCII$ encoding. But for extended $ASCII$ character support, $wchar\_t$ which supports up to $16$ bits is defined in $<stddef.h>$. $C11$ standard also defines $char16\_t$ or $char32\_t$ in $<uchar.h>$ header file thus supporting Unicode characters which requires up to $21$ bits. So, in today's world, a $char$ and an $int$ take the same size and integer variable ($char32\_t$ of $4$ bytes) is used to store Unicode characters and the data type $char$ is used mainly to refer to a $byte$ of data than an actual character.

Constants and variables

We have seen the data types, but to use them in a program we need to have a variable. A $variable$ is a named entity to represent a specific data type. The type of a variable is fixed during the program run, but its value can be changed, and hence the name variable. (In an object oriented language like $CPP$, a class can be taken as a data type and its instance become a variable). To assign a value to a variable we use $constants$. The following are the example usage of variables and constants.

int a; // 'a' is an int variable
a = 5; // 5 is an int constant

Constant Types

In $C$ language we have the following constants

1. Integer constant
   1. Decimal constant
   2. Octal constant
   3. Hexadecimal constant
2. Floating constant
3. Character constant
4. Enumeration constant

Integer Constant

C standard supports decimal, octal and hexa-decimal constants being used to assign integer values. Their example usage is as shown below.

#include <stdio.h>
int main()
{
   enum month{jan = 1, feb, mar, apr, may, jun, july, aug, sep, oct, nov, dec};//jan is having int value 1, feb value 2 and so on 
   int a,b,c; 
   a = 10; //10 is a decimal constant
   b = 0xa; // a is a hexadecimal constant
   c = 012; //12 is an octal constant
   enum month d = oct; //oct is an enumeration constant

   printf("a = %d, b = %d, c = %d, d = %d ",a,b,c,d);
   return 0;
}

We can use an $int$ instead of $enum$ as both takes same amount of memory. But the use of $enum$ ensures that a variable can hold only a particular set of integer values rather than the whole range of integers. Thus it leads to less program errors and makes the code more readable by providing a set of defined constants

Here, $a$ is having the decimal value of $10$. So, in memory $a$ will be like

000...1010

Similarly, $b$ will be in memory like

000...1010

and $c$ and $d$ will also be like

000...1010

i.e.; all $a$, $b$, $c$ and $d$ are having same integer values given using different constants. The memory to be allotted to an integer constant is determined by its value, minimum being the $sizeof(int)$. For example, $40$ is allotted the $sizeof(int)$ while 0xfffffffff is allotted $sizeof(long)$ as it won't fit the $sizeof(int)$ (assuming $sizeof(int)$ is $4$ and $sizeof(long)$ is $8$).

Floating Constant

The representation of a floating point number is implementation specific. $C11$ do specifies $IEC$ $60559$ format for floating point representation but its not mandatory that all implementations must support them. But most current implementations do support them and hence it's good to have a look at them. This link [ http://steve.hollasch.net/cgindex/coding/ieeefloat.html%7C IEEE format] is a good look as $IEEE$ $754$ is identical to $IEC$ $60559$.

Constant values can be assigned to float or double variables in various ways as shown below. If a constant cannot be exactly representable in the float or double variable the implementation is recommended to show a warning as per C standard. But this is just a recommendation and not a strict requirement.

#include <stdio.h>
int main()
{
   float a = 10.2;
   float b = 2.3f;
   double c = 3.4l;
   double d = 1.2e-3;
   printf("a = %.2f, b = %5.2f, c = %05.2lf, d = %le\n",a,b,c,d); //Just diff format specifiers
   //%.2f means 2 digits after decimal point will be printed 
   //%5.2f means the output will have a total of minimum 5 places including 2 decimal digits and a point. If lesser digits are there, then the remaining space is filled with white space.
   //%05.2f is same as %5.2f except that the remaining space, if any, are filled with 0s than white space
       
   return 0;
}

Character Constant

Characters can be assigned value either by using a character in single quotes or by giving the integer value from the character code. And this int value can be given using hex or octal representation as well, as shown below. Escape sequences are applicable to character constants like $'\backslash n'$, $'\backslash t'$ etc.

#include <stdio.h>
int main()
{
   char a, b, c, d, e;
   a = 'a';
   b = '\0';
   c = 0;
   d = '\x41'; //41 is a hexa decimal value whose corresponding ANSII char is assigned to d
   
   e = '\101'; //101 is an octal constant whose corresponding ASCII char is assigned to e 

   printf("a = %d, b = %d, c = %d, d = %c e = %c",a,b,c,d,e);
   
   return 0;
}

Here, $a$ is having the $ASCII$ value of $'a'$ which is $97$. So, in memory $a$ will be like

01100001

Similarly, $b$ and $c$ will be in memory like

00000000 //ASCII value of \0 is 0

and $d$ and $e$ will be like

01000001

Enumeration Constant

Enumeration constants are assigned integer values starting from a given initial value which by default is $0$. An example is shown below:

enum player{ Dhoni = 1, Kohli, Yuvraj, Aswin = 5, Jadeja, Mishra = 10};

Here, Dhoni is having an integer value 1, Kohli 2, Yuvraj 3, Aswin 5, Jadeja 6 and Mishra 10. That is, these names can be used wherever these values are needed.

String Literal

A character string literal is a sequence of zero or more characters enclosed in double-quotes, as in $``xyz"$. A $UTF−8$ string literal is the same, except prefixed by $u8$. A wide string literal is the same, except prefixed by the letter $L$, $u$, or $U$. All escape sequences applicable to a character constant is applicable for a string literal except that for $'$ an escape sequence is not mandatory. Any sequence of string literals will be combined into a single string literal during the translation phase of the compiler. Thus, $``abc"$ $``de"$ is equivalent to $``abcde"$. Another important property of string literal is that it cannot be modified and is usually stored in the $RO$ Data segment.

char p[] = "hello world";
char *q = "hello world";

Here, individual characters of p can be modified as the characters of the string literal ``hello world" are copied to the memory allocated to $p$ which is $12$ bytes. But, individual characters of the content of $q$ can only be read and not modifiable as $p$ is pointing to a string literal, which is stored in the $RO$ data segment of the program. i.e.

p[2] = 'p'; //valid
char c = q[2]; //valid
q[3] = 'q'; //Invalid 

The last statement causes segmentation fault as explained in Fault

Implicit Type Conversion

We can round off this chapter with an important point about implicit type conversion. Whenever we do an operation with different data types, the lower ranked data type is promoted to the higher ranked one, as, operations are meant to be performed on same types of data. For example when we add an $int$ and a $float$, the $int$ is promoted to $float$ and addition of two $floats$ takes place using two floating point registers. Similarly, when we add a $char$ and an $int$, the $8$ bits of char is made into $32$ bits (assuming $4$ byte size for $int$), by padding it with $0's$.

One important point about implicit type conversion is that, it depends only on the source operands and is independent of the resultant data type. So, if we multiple two $integers$ and store in a $long$, the result will be calculated as $int$ (usually 4 bytes) and then stored in $long$ (usually 8 bytes). Another common example of this behavior is for division operation. When we divide two $integers$, the result will be $int$ only, even if we assign it to a $float$. So, in these cases the programmer has to explicitly cast one operand to the desired output type.

What exactly happens during type conversion

Before reading the description below, think how it can happen- you won't think wrong.

1. $unsigned$ to $signed$ or vice verse: There is no change in the representation in memory. When casting to signed, the most significant bit is taken as a sign bit which would otherwise be used for representing the number. So, this type casting is necessary during conditional checks as a negative number when type casted to unsigned will give a huge $int$ value.
2. $char$ to $int$: If $int$ is $4$ bytes- the top $3$ bytes are filled with 0's and bottom most byte is the same byte used to represent the $char$.
3. $int$ to $char$: Only the lowermost byte of the $int$ is taken and made to a $char$. So, if $int$ value is $511$, its char value will be $255$.

00000000 00000000 01111111 11111111 //511
//11111111 is 255

1. $int$ to $float$ or $double$: The fixed integer is converted to a representable floating point value. So, this might cause a change to entire bits used to represent the integer.
2. $float$ or $double$ to $int$: The integral part of the floating point value is saved as integer. The decimal part is ignored. For example, $5.9$ will be changed to $5$.
3. $float$ to $double$: The extra mantissa bits supported in $double$ are filled with $0$'s so are the extra exponent bits. The bits of float ($32$ of them) are used without modification.
4. $double$ to $float$: The extra mantissa bits supported in $double$ are truncated in floating representation so do the extra exponent fields. If the truncated exponent field were non zeroes, it might cause a change to other mantissa bits as well as the number would then need an approximation to fit in a float size.

<quiz display="simple"> {Consider an implementation where int is 4 bytes and long int is 8 bytes. Which of the following initializations are correct? <syntaxhighlight lang="c">

1. include <stdio.h>

int main() {

  long int a = 0x7fffffff * 0x7ffffff;
  long int b = 0x7ffffffff * 0x7ffffff;
  long int c = 0x7fffffff * 0x7fffffff;
  long int d = 0x7fffffff * 0x7fffffffl;
  printf("a = %ld, b = %ld, c = %ld, d = %ld\n", a, b, c, d);
  return 0;

} </syntaxhighlight> |type="()" /} -All are correct -a, c, d +b, d -a, d ||a and c choices cause integer overflow. Even though long int can hold 8 bytes as given in the question, the operands are of 4 bytes only and hence the result is also 4 bytes.
In b choice, 0x7ffffffff is taking more than 4 bytes and hence is considered a long int. So, the next operand is implicitly typecasted to long int and the result is also calculated as long int. Hence there'll be no overflow.
In d choice, by adding l at the end, we force the compiler to use long int operand and hence the operations will be done using 8 byte operands and there will be no overflow.

{Consider an implementation where int is 4 bytes and long int is 8 bytes. What will be the output of the following code? <syntaxhighlight lang="c">

1. include <stdio.h>

int main() {

  int i = 0;
  size_t a = sizeof i, b = sizeof (long);
  printf("a = %zd, b = %zd\n", a, b); //If %zd is given the compiler will automatically give it the correct type whether short, long or normal. This is useful for special data types like size_t whose size is implementation specific
  return 0;

} </syntaxhighlight> |type="()" /} -Compile error -Runtime error -a = 4, b = 4 +a = 4, b = 8 ||sizeof is an operator and hence we don't need a parentheses for giving variables to sizeof. So, sizeof i will return 4 which is the size of int and sizeof(long) will return 8

{What will be the output of the following code? <syntaxhighlight lang="c">

1. include <stdio.h>

int main() {

  unsigned int a = 5;
  if(a > -1)
     printf("5 is > -1\n");
  return 0;

} </syntaxhighlight> |type="()" /}

-5 is > -1 +No output -Compile Error -Runtime Error ||When an operation involves different data types the lower ranked one is promoted to higher ranked one. So, when we compare a signed int with an unsigned int, the signed int will be promoted to unsigned (unsigned has higher rank than signed).
a > -1
will turn to
00...101 > 11...111
and will evaluate to false

If a was declared as signed, then the if condition would have behaved as expected.
(Ideally an unsigned integer would never be compared with a negative number in real world and so do in programs)

{What will be printed by the following code? <syntaxhighlight lang="c">

1. include <stdio.h>
2. include <string.h>

int main() {

  char buff[255] = "abc\

pee";

  printf("%s", buff);
  return 0;

} </syntaxhighlight> |type="()" /}

+
abcpee -
abc
pee -
Compile error -
abc
ee

||\ followed by a newline will make the compiler escape both the characters. So, this is used to write long lines of code across multiple lines for enhancing readability. So,
"abc\
pee";
is equivalent to
"abcpee";

{What will be printed by the following code? <syntaxhighlight lang="c">

1. include <stdio.h>
2. include<string.h>

int main() {

   char buff[] = "abc" "hello";
   printf("%zd\n", strlen(buff));
   return 0;

} </syntaxhighlight> |type="()" /}

+8 -9 -10 -Compile Error ||Compiler will append any continuous string literals given inside "" and make a single string literal ignoring the space(s) between them. So, "abc" "hello" will become "abchello" and its length is 8

{How can you print the following sentence exactly as it is by changing the assignment to buff? "Hello\\" "World\\" <syntaxhighlight lang="c">

1. include <stdio.h>
2. include <string.h>

int main() {

   char buff[255] = "\0";
   printf("%s", buff);
   return 0;

} </syntaxhighlight> |type="()" /}

-char buff[255] = "\"Hello/\/\\" \"World/\/\\""; +char buff[255] = "\"Hello\\\\\" \"World\\\\\""; -char buff[255] = ""Hello\\" "World\\""; -char buff[255] = ""Hello\\\\\" "World\\\\""; ||To put " in a string we have to escape it with \. i.e., use \" instead of ". For '\' also we do the same \\ instead of \

{What will be the output of the following code? (Assume a 64 bit machine/compiler) <syntaxhighlight lang="c">

1. include <stdio.h>

int main() {

   char *p = "Hello World";
   char q[] = "Hello World";
   printf("%zd %zd", sizeof p, sizeof *p);
   printf("\n");
   printf("%zd %zd", sizeof q, sizeof *q);
   return 0;

} </syntaxhighlight> |type="()" /}

+
8 1
12 1 -
12 1
12 1 -
Compile error -
11 1
12 1 ||p is a char pointer and all pointers on 64 bit platform takes 64bits -> 8 bytes
*p is a char and size of char is 1 byte
q is an array and sizeof array is the no. of elements in the array X sizeof an element
= 12 (including \0 which is added by compiler at the end of all string literals) * 1   = 12 bytes ||*q is a char and sizeof char is 1 byte

{What will be the output of the following code? <syntaxhighlight lang="c">

1. include <stdio.h>

int main() {

  {
     char a = 5;
     int b = 5;
     if(a == b)          
        printf("char and int compared equal\n");    }
  {
     int a = 5;
     long int b = 5;

if(a == b)

        printf("int and long compared equal\n");
  }
  {
     float a = 5.0;
     double b = 5.0;
     if(a == b)
        printf("float and double compared equal\n");
  }
  {
     float a = 5.2;
     double b = 5.2;
     if(a == b)
        printf("float and double again compared equal\n");
  }
  {
     float a = 5.2;
     if(a == 5.2)
        printf("float compared equal with constant\n");
  }
  {
     double a = 5.2;
     if(a == 5.2)
        printf("double compared equal with constant\n");
  }
  return 0;

} </syntaxhighlight> |type="()" /} +
char and int compared equal
int and long compare equal
float and double compared equal
double compared equal with constant

-
char and int compared equal
int and long compare equal
double compared equal with constant

-
char and int compared equal
int and long compare equal
float and double again compared equal
double compared equal with constant

-
char and int compared equal
int and long compare equal
float and double compared equal

||
When we compare an int and a char, the char will be promoted to int by adding 0s to the left. So, signed integers less than 128 (the maximum value representable by a signed char is 127) will compare equal with char.

||When we compare a long and an int, int is promoted to long by adding 0s to the left. So, any long number than can be represented by an int will compare equal with int.

||Like above , float will be promoted to double. If the float number is exactly representable (without any approximation) within a float, then it'll compare equal with its double counterpart.

||Here, 5.2 cannot be exactly representable using a float. Hence, its double version will have more accuracy and won't compare equal with float.

||By default all real values are taken as double. If we want to take as float we have to use

if(a == 5.2f)
instead of

if(a == 5.2)

</quiz>