Equations of Integer Double Pointer

In this section, you are going to learn

What are the different ways of declarations ?

How to dervie equations ?

What are the Properties of Variable ?

What are the Properties of Expression ?

Topics in this section,

1. Equations of Double Pointer

In this section, you are going to learn

  • How to derive pointer equations for Double pointer ?

  • How to apply these equations to understand C statements ?

You can derive equations looking at C declarations !

There are many methods in C, using which a Double pointer can be declared. See below

 1#include <stdio.h>
 2
 3int main(void)
 4{
 5        int x = 10, *p = &x, **q = &p;
 6
 7        *p = 20;
 8
 9        **q = 200;
10
11        printf("x = %d, *p = %d, **q = %d\n", x, *p, **q);
12
13        return 0;
14}
In this example,

  • x is an integer

  • p is an single integer pointer

  • q is an double integer pointer

  • x, p, q are declared in one Single Line

  • x, p, q are assigned in one Single Line

  • x is assigned with value 10

  • p is assigned with address of x

  • q is assigned with address of p

 1#include <stdio.h>
 2
 3int main(void)
 4{
 5        int x = 10;
 6
 7        int *p = &x;
 8
 9        int **q = &p;
10
11        *p = 20;
12
13        **q = 200;
14
15        printf("x = %d, *p = %d, **q = %d\n", x, *p, **q);
16
17        return 0;
18}
In this example,

  • x is an integer

  • p is a single integer pointer

  • q is a double integer pointer

  • x is declared in a separate line

  • p is declared in a separate line

  • q is declared in a separate line

  • x is assigned in the same line of declaration

  • p is assigned in the same line of declaration

  • q is assigned in the same line of declaration

  • x is assigned with value 10

  • p is assigned with address of x

  • q is assigned with address of p

 1#include <stdio.h>
 2
 3int main(void)
 4{
 5        int x;
 6
 7        int *p;
 8
 9        int **q;
10
11        x = 10;
12
13        p = &x;
14
15        q = &p;
16
17        *p = 20;
18
19        **q = 200;
20
21        printf("x = %d, *p = %d, **q = %d\n", x, *p, **q);
22
23        return 0;
24}
In this example,

  • x is an integer

  • p is a single integer pointer

  • q is a double integer pointer

  • x is declared in a separate line

  • p is declared in a separate line

  • q is declared in a separate line

  • x is assigned and is not part of declaration

  • p is assigned and is not part of declaration

  • q is assigned and is not part of declaration

  • x is assigned with value 10

  • p is assigned with address of x

  • q is assigned with address of p

Decl #

Declaration

Description

Decl 1

  • int x = 10, *p = &x, **q = &p;

Integer x, Single Pointer p, Double Pointer q are declared and assigned in same line

Decl 2

  • int x = 10;

  • int *p = &x;

  • int **q = &p;

Integer x, Single Pointer p, Double Pointer q are declared and assigned in separate lines

Decl 3

  • int x;

  • int *p;

  • int **q;

  • x = 10;

  • p = &x;

  • q = &p;

Integer x, Single Pointer p, Double Pointer q are declared in one line and assigned in another line

  • Whenever we see any of the above methods of declarations, we need to rewrite them such that, declarations and assignments are not in same line. Similar to Declaration 3

  • Equation 1 : Obtained from Step 2

p = &x;

  • Equation 2 : Move & to the left of First Equation. It turns in to *

*p = x;

  • Equation 3 : * and [0] can be used interchangeably. Hence *p and p[0] are one and the same !

p[0] = x;

  • Equation 4 : From Equation 2, Equation 3, we can derive that x, *p, p[0] all are same !

*p = p[0] = x;

  • Equation 5 : Obtained from Step 2

q = &p;

  • Equation 6 : Move & to the left of First Equation. It turns in to *

*q = p;

  • Equation 7 : * and [0] can be used interchangeably. Hence *q and q[0] are one and the same !

q[0] = p;

  • Equation 8 : From Equation 6, Equation 7, we can derive that p, *q, q[0] all are same !

*q = q[0] = p;

  • Equation 9 : From Equation 1, we know p = &x. Hence Replace p with &x in Equation 8

*q = q[0] = &x;

  • Equation 10 : Move & to the left of Equation 9. It turns in to *

**q = *q[0] = x;

  • Equation 11 : * and [0] can be used interchangeably

q[0][0] = x;

Equation #

Equation

Description

Equation 1

p = &x

Base condition

Equation 2

*p = x

From Equation 1, Move & from RHS to LHS to get * on LHS

Equation 3

p[0] = x

* and [0] can be used interchangeably. Hence *p and p[0] are synonyms

Equation 4

*p = p[0] = x

From Equation 2, 3 we can conclude *p, p[0], x are synonyms

Equation #

Equation

Description

Equation 5

q = &p

Base condition

Equation 6

*q = p

From Equation 5, Move & from RHS to LHS to get * on LHS

Equation 7

q[0] = p

* and [0] can be used interchangeably. Hence *q and q[0] are synonyms

Equation 8

*q = q[0] = p

From Equation 6, Equation 7, we can derive that p, *q, q[0] all are same !

Equation 9

*q = q[0] = &x

From Equation 1, we know p = &x. Hence Replace p with &x in Equation 8

Equation 10

**q = *q[0] = x

From Equation 9, Move & from RHS to LHS to get * on LHS

Equation 11

q[0][0] = x

* and [0] can be used interchangeably

 
*p = 100;

printf("x = %d, *p = %d\n", x, *p);
Output :

x = 100, *p = 100

p[0] = 100;

printf("x = %d, p[0] = %d\n", x, p[0]);
Output :

x = 100, p[0] = 100

x = 100;

printf("*p = %d, p[0] = %d\n", *p, p[0]);
Output :

*p = 100, p[0] = 100

**q = 100;

printf("x = %d, **q = %d\n", x, **q);
Output :

x = 100, **q = 100

*q[0] = 100;

printf("x = %d, *q[0] = %d\n", x, *q[0]);
Output :

x = 100, *q[0] = 100

q[0][0] = 100;

printf("x = %d, q[0][0] = %d\n", x, q[0][0]);
Output :

x = 100, q[0][0] = 100

int x, y, *p, **q;

x = 100;
p = &x;
q = &p;

printf("*p = %d, p[0] = %d, **q = %d\n", *p, p[0], **q);

y = 200;

// *q, p are synonyms.
// Means *q = &y also means p = &y
*q = &y;

printf("*p = %d, p[0] = %d, **q = %d\n", *p, p[0], **q);
Output :

*p = 100, p[0] = 100, **q = 100

*p = 200,``p[0]`` = 200, **q = 200

int x, y, *p, **q;

x = 100;
p = &x;
q = &p;

printf("*p = %d, p[0] = %d, **q = %d\n", *p, p[0], **q);

y = 200;

// q[0], p are synonyms.
// Means q[0] = &y also means p = &y
q[0] = &y;

printf("*p = %d, p[0] = %d, **q = %d\n", *p, p[0], **q);
Output :

*p = 100, p[0] = 100, **q = 100

*p = 200,``p[0]`` = 200, **q = 200

 1#include <stdio.h>
 2
 3int main(void)
 4{
 5        int x;
 6
 7        int *p;
 8
 9        int **q;
10
11        x = 10;
12
13        p = &x;
14
15        q = &p;
16
17        printf("x = %d, *p = %d, p[0] = %d, **q = %d\n", x, *p, p[0], **q);
18
19        x = 20;
20
21        printf("x = %d, *p = %d, p[0] = %d, **q = %d\n", x, *p, p[0], **q);
22
23        *p = 30;
24
25        printf("x = %d, *p = %d, p[0] = %d, **q = %d\n", x, *p, p[0], **q);
26
27        p[0] = 40;
28
29        printf("x = %d, *p = %d, p[0] = %d, **q = %d\n", x, *p, p[0], **q);
30
31        **q = 50;
32
33        printf("x = %d, *p = %d, p[0] = %d, **q = %d\n", x, *p, p[0], **q);
34
35        return 0;
36}
Output :

x = 10, *p = 10, p[0] = 10 **q = 10

x = 20, *p = 20, p[0] = 20 **q = 20

x = 30, *p = 30, p[0] = 30 **q = 30

x = 40, *p = 40, p[0] = 40 **q = 40

x = 50, *p = 50, p[0] = 50 **q = 50

2. Properties of a variable

In this section, you are going to learn

  • Properties of a variable

    • Type of a variable ?

    • Size of a variable ?

    • Scope, Lifetime and Memory of a variable ?

1int x;
2
3int *p;
4
5int **q;
6
7p = &x;
8
9q = &p;

  • In above code snippet, there are three variables x, p, q

Variable

Type

Description

type_of(x)

int

See Line 1

type_of(p)

int *

See Line 3

type_of(q)

int **

See Line 5

Adress of variable must be stored in next level pointer type always

 1int x;
 2
 3int *p;
 4
 5int **q;
 6
 7p = &x;
 8
 9q = &p;
10
11*p = 10;

  • In above code snippet, there are two variables x, p

Variable

Type

Description

type_of(&x)

int *

  • type_of(x) is int

  • Hence, type_of(&x) is int *

type_of(&p)

int **

  • type_of(p) is int *

  • Hence, type_of(&p) is int **

type_of(&q)

int ***

  • type_of(q) is int **

  • Hence, type_of(&q) is int ***

Sizeof(type)

Size

sizeof(char)

1 Bytes

sizeof(int)

4 Bytes

sizeof(float)

4 Bytes

sizeof(double)

8 Bytes

sizeof(pointer types) is always 8 Bytes, where pointer is single, double, triple etc.,:

Sizeof(type *)

Size

sizeof(char *)

8 Bytes

sizeof(int *)

8 Bytes

sizeof(float *)

8 Bytes

sizeof(double *)

8 Bytes

sizeof(struct xyz *)

8 Bytes

sizeof(union xyz *)

8 Bytes

Sizeof(type **)

Size

sizeof(char **)

8 Bytes

sizeof(int **)

8 Bytes

sizeof(float **)

8 Bytes

sizeof(double **)

8 Bytes

sizeof(struct xyz **)

8 Bytes

sizeof(union xyz **)

8 Bytes

etc.,

sizeof(&variable) is always 8 Bytes, where type_of(variable) can be anything

Sizeof(&variable)

Size

Declaration

sizeof(&x)

8 Bytes

char x;

sizeof(&x)

8 Bytes

int x;

sizeof(&x)

8 Bytes

float x;

sizeof(&x)

8 Bytes

double x;

sizeof(&x)

8 Bytes

struct xyz x;

sizeof(&x)

8 Bytes

union xyz x;

Sizeof(&variable)

Size

Declaration

sizeof(&x)

8 Bytes

char *x;

sizeof(&x)

8 Bytes

int *x;

sizeof(&x)

8 Bytes

float *x;

sizeof(&x)

8 Bytes

double *x;

sizeof(&x)

8 Bytes

struct xyz *x;

sizeof(&x)

8 Bytes

union xyz *x;

Sizeof(&variable)

Size

Declaration

sizeof(&x)

8 Bytes

char **x;

sizeof(&x)

8 Bytes

int **x;

sizeof(&x)

8 Bytes

float **x;

sizeof(&x)

8 Bytes

double **x;

sizeof(&x)

8 Bytes

struct xyz **x;

sizeof(&x)

8 Bytes

union xyz **x;

sizeof(variable) equals sizeof(typeof(variable))

 1int x;
 2
 3int *p;
 4
 5int **q;
 6
 7p = &x;
 8
 9q = &p;
10
11*p = 10;

  • In above code snippet, there are three variables x, p, q

Sizeof(Variable)

Size

Description

sizeof(x)

4 Bytes
  • How ?

    • Step 1 : sizeof(x) equals sizeof(typeof(x))

    • Step 2 : type_of(x) is int

    • Step 3 : sizeof(int) is 4 Bytes

    • Hence, sizeof(x) is 4 Bytes

sizeof(p)

8 Bytes
  • How ?

    • Step 1 : sizeof(p) equals sizeof(typeof(p))

    • Step 2 : type_of(p) is int *

    • Step 3 : sizeof(int *) is 8 Bytes

    • Hence, sizeof(p) is 8 Bytes

sizeof(q)

8 Bytes
  • How ?

    • Step 1 : sizeof(q) equals sizeof(typeof(q))

    • Step 2 : type_of(q) is int **

    • Step 3 : sizeof(int **) is 8 Bytes

    • Hence, sizeof(q) is 8 Bytes

  • Global Scope and Lifetime.

  • Local Scope and Lifetime

3. Properties of Expressions

In this section, you are going to learn

  • Properties of Expressions

    • What is an Expression ?

    • Table of Expressions

    • Table of Size (for Expressions)

    • Table of Type (for Expressions)

    • Table of Address/Value (for Expression)

    • Table of Function Prototype (for Expression)

 1int x;
 2
 3int *p;
 4
 5int **q;
 6
 7p = &x;
 8
 9q = &p;
10
11*p = 10;
12
13**q = 100;

Expression

Description

x

  • x is an integer

&x

  • &x is address of an integer

  • &x is a single pointer

p

  • p is a pointer to an integer

  • p is a single pointer

&p

  • &p is address of a pointer

  • &p is a double pointer

*p

p[0]

q

  • q is a double pointer and holds the address of a single pointer

&q

  • &q is address of a double pointer

  • &q is a triple pointer

*q

q[0]

**q

*q[0]

q[0][0]

Expression

Size

Description

sizeof(x)

4 Bytes

sizeof(&x)

8 Bytes

sizeof(p)

8 Bytes

sizeof(&p)

8 Bytes

sizeof(*p)

4 Bytes

sizeof(p[0])

4 Bytes

sizeof(q)

8 Bytes

sizeof(&q)

8 Bytes

sizeof(*q)

8 Bytes

sizeof(q[0])

8 Bytes

sizeof(**q)

4 Bytes

sizeof(*q[0])

4 Bytes

sizeof(q[0][0])

4 Bytes

Expression

Type

Description

type_of(x)

int

type_of(&x)

int *

type_of(p)

int *

type_of(&p)

int **

type_of(*p)

int

  • Step 1 : type_of(*p) equals type_of(x), because *p = x. See Equation 2

  • Step 2 : type_of(x) equals int

type_of(p[0])

int

  • Step 1 : type_of(p[0]) equals type_of(x), because p[0] = x. See Equation 3

  • Step 2 : type_of(x) equals int

type_of(q)

int **

type_of(&q)

int ***

type_of(*q)

int *

type_of(q[0])

int *

type_of(**q)

int

type_of(*q[0])

int

type_of(q[0][0])

int

Expression

Address/Value

Description

x

Value

  • Step 1 : x is an integer

  • Step 2 : Hence x is a value

&x

Address

  • & operator indicates address

p

Address

  • Step 1 : p = &x See Equation 1

  • Step 2 : & operator indicates address

&p

Address

  • & operator indicates address

*p

Value

  • Step 1 : *p is an integer. *p = x See Equation 2

  • Step 2 : Hence *p is a value

p[0]

Value

  • Step 1 : p[0] is an integer. p[0] = x See Equation 3

  • Step 2 : Hence p[0] is a value

q

Address

  • Step 1 : q = &p See Equation 5

  • Step 2 : & operator indicates address

&q

Address

  • & operator indicates address

*q

Address

  • Step 1 : *q = p See Equation 6

  • Step 2 : p = &x

  • Step 3 : & operator indicates address

q[0]

Address

  • Step 1 : q[0] = p See Equation 7

  • Step 2 : p = &x

  • Step 3 : & operator indicates address

**q

Value

  • Step 1 : **q = x See Equation 10

  • Step 2 : x is an integer

  • Step 3 : **q is a Value

*q[0]

Value

  • Step 1 : *q[0] = x See Equation 10

  • Step 2 : x is an integer

  • Step 3 : *q[0] is a Value

q[0][0]

Value

  • Step 1 : q[0][0] = x See Equation 11

  • Step 2 : x is an integer

  • Step 3 : q[0][0] is a Value

If fun(v) is function call then, fun(type_of(v)) is the prototype

Function call

Function Prototype

Description

fun(x)

void fun(int x);

fun(&x)

void fun(int *p);

fun(p)

void fun(int *p);

fun(&p)

void fun(int **p);

fun(*p)

void fun(int x);

  • Step 1 : fun(*p) equals fun(x)See Equation 2

  • Step 2 : fun(x) equals fun(type_of(x))

  • Step 3 : fun(type_of(x)) equals fun(int)

fun(p[0])

void fun(int x);

  • Step 1 : fun(p[0]) equals fun(x)See Equation 2

  • Step 2 : fun(x) equals fun(type_of(x))

  • Step 3 : fun(type_of(x)) equals fun(int)

fun(q)

void fun(int **q);

fun(&q)

void fun(int ***q);

fun(*q)

void fun(int *q);

  • Step 1 : fun(*q) equals fun(p)

  • Step 2 : fun(p) equals fun(type_of(p))

  • Step 3 : fun(type_of(p)) equals fun(int *)

fun(q[0])

void fun(int *q);

  • Step 1 : fun(q[0]) equals fun(p)

  • Step 2 : fun(p) equals fun(type_of(p))

  • Step 3 : fun(type_of(p)) equals fun(int *)

fun(**q)

void fun(int x);

  • Step 1 : fun(**q) equals fun(x) See Equation 10

  • Step 2 : fun(x) equals fun(type_of(x))

  • Step 3 : fun(type_of(x)) equals fun(int)

fun(*q[0])

void fun(int x);

  • Step 1 : fun(*q[0]) equals fun(x) See Equation 10

  • Step 2 : fun(x) equals fun(type_of(x))

  • Step 3 : fun(type_of(x)) equals fun(int)

fun(q[0][0])

void fun(int x);

  • Step 1 : fun(q[0][0]) equals fun(x) See Equation 11

  • Step 2 : fun(x) equals fun(type_of(x))

  • Step 3 : fun(type_of(x)) equals fun(int)

4. Summary

#

?

Size in Bytes

Type

Address or Value

Function call

Function Prototype

x

Integer

4

int

Value

fun(x)

void fun(int x);

&x

Single Pointer

8

int *

Address

fun(&x)

void fun(int *p);

p

Single Pointer

8

int *

Address

fun(p)

void fun(int *p);

&p

Double Pointer

8

int **

Address

fun(&p)

void fun(int **q);

*p

Integer

4

int

Value

fun(*p)

void fun(int x);

p[0]

Integer

4

int

Value

fun(p[0])

void fun(int x);

q

Double Pointer

8

int **

Address

fun(q)

void fun(int **q);

&q

Triple Pointer

8

int ***

Address

fun(&q)

void fun(int ***r);

*q

Single Pointer

8

int *

Address

fun(*q)

void fun(int *p);

q[0]

Single Pointer

8

int *

Address

fun(q[0])

void fun(int *p);

**q

Integer

4

int

Value

fun(**q)

void fun(int x);

*q[0]

Integer

4

int

Value

fun(*q[0])

void fun(int x);

q[0][0]

Integer

4

int

Value

fun(q[0][0])

void fun(int x);
See Also
See Also