Equations of Integer Triple 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,

• Derive Equations for Triple Pointer

• Step 1 : Understand different methods to declare Triple Pointer

  • Declaration 1 : Integer x, Single Pointer p, Double Pointer q, Triple Pointer r are declared and assigned in same line

  • Declaration 2 : Integer x, Single Pointer p, Double Pointer q, Triple Pointer r are declared and assigned in separate lines

  • Declaration 3 : Integer x, Single Pointer p, Double Pointer q are declared in one line and assigned in another line

  • Table of Declarations for Triple Pointer

• Step 2 : Split pointer declarations and assignments into separate lines

• Step 3 : Derive Equations

• Step 4 : Apply above equations to analyse C statements

• Table of Equations for Single Pointer

• Table of Equations for Double Pointer

• Table of Equations for Triple Pointer

• Properties of a variable

  • Property 1 : Type

  • Property 2 : sizeof()

  • Property 3 : Scope, Lifetime and Memory of a variable

• Properties of Expressions

  • Table of Expressions

  • Table of Size (for Expressions)

  • Table of Types (for Expressions)

  • Table of Address/Value (for Expression)

  • Table of Function Prototype (for Expression)

• Summary

1. Equations of Triple Pointer

In this section, you are going to learn

• How to derive pointer equations for Triple pointer ?

• How to apply these equations to understand C statements ?

Derive Equations for Triple Pointer

You can derive equations looking at C declarations !

Step 1 : Understand different methods to declare Triple Pointer

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

Declaration 1 : Integer x, Single Pointer p, Double Pointer q, Triple Pointer r are declared and assigned in same line

#include <stdio.h>

int main(void)
{
        int x = 10, *p = &x, **q = &p, ***r = &q;

        *p = 20;

        **q = 200;

        ***r = 2000;

        printf("x = %d, *p = %d, **q = %d ***r = %d\n", x, *p, **q, ***r);

        return 0;
}

In this example,

• x is an integer

• p is an single integer pointer

• q is a double integer pointer

• r is a triple integer pointer

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

• x, p, q, r 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

• r is assigned with address of q

Declaration 2 : Integer x, Single Pointer p, Double Pointer q, Triple Pointer r are declared and assigned in separate lines

#include <stdio.h>

int main(void)
{
        int x = 10;

        int *p = &x;

        int **q = &p;

        int ***r = &q;

        *p = 20;

        **q = 200;

        ***r = 2000;

        printf("x = %d, *p = %d, **q = %d ***r = %d\n", x, *p, **q, ***r);

        return 0;
}

In this example,

• x is an integer

• p is a single integer pointer

• q is a double integer pointer

• r is a triple integer pointer

• x is declared in a separate line

• p is declared in a separate line

• q is declared in a separate line

• r 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

• r 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

• r is assigned with address of q

Declaration 3 : Integer x, Single Pointer p, Double Pointer q are declared in one line and assigned in another line

#include <stdio.h>

int main(void)
{
        int x;

        int *p;

        int **q;

        int ***r;

        x = 10;

        p = &x;

        q = &p;

        *p = 20;

        **q = 200;

        ***r = 2000;

        printf("x = %d, *p = %d, **q = %d, ***r = %d\n", x, *p, **q, ***r);

        return 0;
}

In this example,

• x is an integer

• p is a single integer pointer

• q is a double integer pointer

• r is a triple integer pointer

• x is declared in a separate line

• p is declared in a separate line

• q is declared in a separate line

• r 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

• r 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

• r is assigned with address of q

Table of Declarations for Triple Pointer

Decl #	Declaration	Description
Decl 1	int x = 10, *p = &x, **q = &p, ***r = &q;	Integer x, Single Pointer p, Double Pointer q, Triple Pointer r are declared and assigned in same line
Decl 2	int x = 10; int *p = &x; int **q = &p; int ***r = &q;	Integer x, Single Pointer p, Double Pointer q, Triple Pointer r are declared and assigned in separate lines
Decl 3	int x; int *p; int **q; int ***r; x = 10; p = &x; q = &p; r = &q;	Integer x, Single Pointer p, Double Pointer q, Triple Pointer r are declared in one line and assigned in another line

Step 2 : Split pointer declarations and assignments into separate lines

• 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

Step 3 : Derive Equations

Derive Equations of Single Pointer

• 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;

Derive Equations of Double Pointer

• 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;

Derive Equations of Triple Pointer

• Equation 12 : Obtained from Step 2

r = &q;

• Equation 13 : Move & to the left of First Equation. It turns in to *

*r = q;

• Equation 14 : * and [0] can be used interchangeably. Hence *r and r[0] are one and the same !

r[0] = q;

• Equation 15 : From Equation 13, Equation 14, we can derive that q, *r, r[0] all are same !

*r = r[0] = q;

• Equation 16 : From Equation 5, we know q = &p. Hence Replace q with &p in Equation 15

*r = r[0] = &p;

• Equation 17 : Move & to the left of Equation 16. It turns in to *

**r = *r[0] = p;

• Equation 18 : * and [0] can be used interchangeably

r[0][0] = p;

• Equation 19 : Comparing Equation 17, 18 we can conclude **r, *r[0], r[0][0] and p all are same !

**r = *r[0] = r[0][0] = p;

• Equation 20 : From Equation 1, p = &x. Hence replace p with &x in Equation 19

**r = *r[0] = r[0][0] = &x;

• Equation 21 : Move & to the left of Equation 16. It turns in to *

***r = **r[0] = *r[0][0] = x;

• Equation 22 : * and [0] can be used interchangeably

***r = **r[0] = r[0][0][0] = x;

Table of Equations for Single Pointer

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

Table of Equations for Double Pointer

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

Table of Equations for Triple Pointer

Equation #	Equation	Description
Equation 12	r = &q	Base condition
Equation 13	*r = q	From Equation 12, Move & from RHS to LHS to get * on LHS
Equation 14	r[0] = q	* and [0] can be used interchangeably. Hence *r and r[0] are synonyms
Equation 15	*r = r[0] = q	From Equation 13, Equation 14, we can derive that q, *r, r[0] all are same !
Equation 16	*r = r[0] = &p	From Equation 5, we know q = &p. Hence Replace q with &p in Equation 15
Equation 17	**r = *r[0] = p	Move & to the left of Equation 16. It turns in to *
Equation 18	q[0][0] = p	* and [0] can be used interchangeably
Equation 19	**r = *r[0] = r[0][0] = p;	Comparing Equation 17, 18 we can conclude **r, *r[0], r[0][0] and p all are same !
Equation 20	**r = *r[0] = r[0][0] = &x;	From Equation 1, p = &x. Hence replace p with &x in Equation 19
Equation 21	***r = **r[0] = *r[0][0] = x;	Move & to the left of Equation 16. It turns in to *
Equation 22	***r = **r[0] = r[0][0][0] = x;	* and [0] can be used interchangeably

Step 4 : Apply above equations to analyse C statements

Example 1 : See Equation 2 : Changing *p changes the value of x

*p = 100;

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

Output :

x = 100, *p = 100

Example 2 : See Equation 3 : Changing p[0] changes the value of x

p[0] = 100;

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

Output :

x = 100, p[0] = 100

Example 3 : See Equation 4 : Changing x changes the value of *p and p[0]

x = 100;

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

Output :

*p = 100, p[0] = 100

Example 4 : See Equation 10 : Changing **q changes the value of x

**q = 100;

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

Output :

x = 100, **q = 100

Example 5 : See Equation 10 : Changing *q[0] changes the value of x

*q[0] = 100;

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

Output :

x = 100, *q[0] = 100

Example 6 : See Equation 11 : Changing q[0][0] changes the value of x

q[0][0] = 100;

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

Output :

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

Example 7 : See Equation 6 : *q, p are synonyms. Means chaning *q also changes p

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

Example 8 : See Equation 7 : q[0], p are synonyms. Means chaning q[0] also changes p

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 = &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

Example 9 : See Equation 22 : Changing ***r changes the value of x

***r = 100;

printf("x = %d, ***r = %d\n", x, ***r);

Output :

x = 100, ***r = 100

Example 10 : See Equation 22 : Changing **r[0] changes the value of x

**r[0] = 100;

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

Output :

x = 100, **r[0] = 100

Example 11 : See Equation 22 : Changing r[0][0][0] changes the value of x

r[0][0][0] = 100;

printf("x = %d, r[0][0][0] = %d\n", x, r[0][0][0]);

Output :

x = 100, r[0][0][0] = 100

Example 12 : See Equation 19 : Changing **r changes the value of p

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

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

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

y = 200;

**r = &y;
//Step 1 : Apply Equation 19 : **r = &y also means  p = &y
//Step 2 : Now all equations having p like Equation 6, 7, 8 are affected  because *q = p
//         Now, *q = &y, q[0] = &y since p, *q, q[0] all are same
//         Now, **q = y, *q[0] = y, q[0][0] = y
//         Now, **q = 200, *q[0] = 200, q[0][0] = 200
//Step 3 : ***r, *r[0], r[0][0][0] = y also means  *p = y

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

Output :

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

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

Example 13 : See Equation 19 : Changing *r[0] changes the value of p

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

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

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

y = 200;

*r[0] = &y;
//Step 1 : Apply Equation 19 : *r[0] = &y also means  p = &y
//Step 2 : Now all equations having p like Equation 6, 7, 8 are affected  because *q = p
//         Now, *q = &y, q[0] = &y since p, *q, q[0] all are same
//         Now, **q = y, *q[0] = y, q[0][0] = y
//         Now, **q = 200, *q[0] = 200, q[0][0] = 200
//Step 3 : ***r, *r[0], r[0][0][0] = y also means  *p = y

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

Output :

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

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

Example 14 : See Equation 19 : Changing r[0][0] changes the value of p

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

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

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

y = 200;

r[0][0] = &y;
//Step 1 : Apply Equation 19 : r[0][0] = &y also means  p = &y
//Step 2 : Now all equations having p like Equation 6, 7, 8 are affected because *q = p
//         Now, *q = &y, q[0] = &y since p, *q, q[0] all are same
//         Now, **q = y, *q[0] = y, q[0][0] = y
//         Now, **q = 200, *q[0] = 200, q[0][0] = 200
//Step 3 : ***r, *r[0], r[0][0][0] = y also means  *p = y

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

Output :

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

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

Example 15 : See Equation 15 : Changing *r changes the value of q

int x, *p, **q, ***r;

int m, *p1;

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

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

m = 200;
p1 = &m;

*r = &p1;
//Step 1 : Apply Equation 15 : *r = &p1 also means q = &p1
//Step 2 : **r = p1 and *q = p1
//Step 3 : **r = &m and *q = &m
//Step 4 : ***r = m and **q = m
//Step 5 : ***r = 200 and **q = 200

//Note p is no changed so far. Hence *p, p[0] is still 100

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

Output :

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

*p = 100, p[0] = 100, **q = 200, ***r = 200

Step 5 : Complete program

#include <stdio.h>

int main(void)
{
        int x;

        int *p;

        int **q;

        int ***r;

        x = 10;

        p = &x;

        q = &p;

        r = &q;

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

        x = 20;

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

        *p = 30;

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

        p[0] = 40;

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

        **q = 50;

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

        ***r = 60;

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

        return 0;
}

Output :

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

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

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

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

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

x = 50, *p = 50, p[0] = 50 **q = 50, ***r = 60

2. Properties of a variable

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 ?

Property 1 : Type

Property 1.1 : type_of(variable)

int x;

int *p;

int **q;

int ***r;

p = &x;

q = &p;

r = &q;

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

Variable	Type	Description
type_of(x)	int	See Line 1
type_of(p)	int *	See Line 3
type_of(q)	int **	See Line 5
type_of(r)	int ***	See Line 7

Property 1.2 : type_of(&variable)

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

int x;

int *p;

int **q;

int ***r;

p = &x;

q = &p;

r = &q;

*p = 10;

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

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 ***
type_of(&r)	int ****	type_of(r) is int *** Hence, type_of(&r) is int ****

Property 2 : sizeof()

Property 2.1 : sizeof() of basic types

Sizeof(type)	Size
sizeof(char)	1 Bytes
sizeof(int)	4 Bytes
sizeof(float)	4 Bytes
sizeof(double)	8 Bytes

Property 2.2 : sizeof() of pointer types

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(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.,

Property 2.3 : sizeof(&variable) - sizeof address of variable

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)	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;

Property 2.4 : sizeof() of variable

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

int x;

int *p;

int **q;

int ***r;

p = &x;

q = &p;

*p = 10;

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

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
sizeof(r)	8 Bytes	How ? Step 1 : sizeof(r) equals sizeof(typeof(r)) Step 2 : type_of(r) is int *** Step 3 : sizeof(int ***) is 8 Bytes Hence, sizeof(r) is 8 Bytes

Property 3 : Scope, Lifetime and Memory of a variable

• 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)

Properties of Expressions

Let us write-down expression tables for below code snippet

int x;

int *p;

int **q;

p = &x;

q = &p;

*p = 10;

**q = 100;

Table of Expressions

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 is an integer, because *p = x. See Equation 2
p[0]	p[0] is an integer, because p[0] = x. See Equation 3
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 holds the address of integer x. See Equation 9 *q is a single pointer. *q = p. See Equation 8
q[0]	q[0] holds the address of integer x. See Equation 9 q[0] is a single pointer. *q = p. See Equation 8
**q	**q is an integer. See Equation 10
*q[0]	*q[0] is an integer. See Equation 10
q[0][0]	q[0][0] is an integer. See Equation 11
r	r is a triple pointer and holds the address of a double pointer
&r	&r is a fourth pointer
*r	*r is a double pointer. See Equation 15 *r holds the address of a single pointer. See Equation 16
r[0]	*r is a double pointer. See Equation 15 *r holds the address of a single pointer. See Equation 16
**r	**r is a single pointer. See Equation 17 **r holds the address of an integer. See Equation 20
*r[0]	*r[0] is a single pointer. See Equation 17 *r[0] holds the address of an integer. See Equation 20
r[0][0]	r[0][0] is a single pointer. See Equation 19 r[0][0] holds the address of an integer. See Equation 20
***r	***r is an integer. See Equation 22
**r[0]	**r[0] is an integer. See Equation 22
r[0][0][0]	r[0][0][0] is an integer. See Equation 22

Table of Size (for Expressions)

Expression	Size	Description
sizeof(x)	4 Bytes	See Property 2.4
sizeof(&x)	8 Bytes	See Property 2.3
sizeof(p)	8 Bytes	See Property 2.4
sizeof(&p)	8 Bytes	See Property 2.3
sizeof(*p)	4 Bytes	Step 1 : sizeof(*p) equals sizeof(x) See Equation 2 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes
sizeof(p[0])	4 Bytes	Step 1 : sizeof(p[0]) equals sizeof(x)``= x See Equation 3 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes
sizeof(q)	8 Bytes	See Property 2.4
sizeof(&q)	8 Bytes	See Property 2.3
sizeof(*q)	8 Bytes	Step 1 : sizeof(*q) equals sizeof(p). See Equation 8 Step 2 : sizeof(p), equals sizeof(type_of(p)) See Property 2.4 Step 3 : sizeof(type_of(p)) equals sizeof(int *) See Property 1.1 Step 4 : sizeof(int *) equals 8 Bytes
sizeof(q[0])	8 Bytes	Step 1 : sizeof(q[0]) equals sizeof(p) See Equation 8 Step 2 : sizeof(p) equals sizeof(type_of(p)) See Property 2.4 Step 3 : sizeof(type_of(p)) equals sizeof(int *) See Property 1.1 Step 4 : sizeof(int *) equals 8 Bytes
sizeof(**q)	4 Bytes	Step 1 : sizeof(**q) equals sizeof(x) See Equation 10 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes
sizeof(*q[0])	4 Bytes	Step 1 : sizeof(*q[0]) equals sizeof(x) See Equation 10 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes
sizeof(q[0][0])	4 Bytes	Step 1 : sizeof(q[0][0]) equals sizeof(x) See Equation 11 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes
sizeof(r)	8 Bytes	See Property 2.4
sizeof(&r)	8 Bytes	See Property 2.3
sizeof(*r)	8 Bytes	Step 1 : sizeof(*r) equals sizeof(q). See Equation 15 Step 2 : sizeof(q) equals sizeof(type_of(q)) Step 3 : sizeof(type_of(q)) equals sizeof(int **) Step 4 : sizeof(int **) equals 8 Bytes
sizeof(r[0])	8 Bytes	Step 1 : sizeof(r[0]) equals sizeof(q). See Equation 15 Step 2 : sizeof(q) equals sizeof(type_of(q)) Step 3 : sizeof(type_of(q)) equals sizeof(int **) Step 4 : sizeof(int **) equals 8 Bytes
sizeof(**r)	8 Bytes	Step 1 : sizeof(**r) equals sizeof(p). See Equation 19 Step 2 : sizeof(p) equals sizeof(type_of(p)) See Property 2.4 Step 3 : sizeof(type_of(p)) equals sizeof(int *) See Property 1.1 Step 4 : sizeof(int *) equals 8 Bytes
sizeof(*r[0])	8 Bytes	Step 1 : sizeof(*r[0]) equals sizeof(p). See Equation 19 Step 2 : sizeof(p) equals sizeof(type_of(p)) See Property 2.4 Step 3 : sizeof(type_of(p)) equals sizeof(int *) See Property 1.1 Step 4 : sizeof(int *) equals 8 Bytes
sizeof(r[0][0])	8 Bytes	Step 1 : sizeof(r[0][0]) equals sizeof(p). See Equation 19 Step 2 : sizeof(p) equals sizeof(type_of(p)) See Property 2.4 Step 3 : sizeof(type_of(p)) equals sizeof(int *) See Property 1.1 Step 4 : sizeof(int *) equals 8 Bytes
sizeof(***r)	4 Bytes	Step 1 : sizeof(***r) equals sizeof(x). See Equation 22 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes. See Equation 22
sizeof(**r[0])	4 Bytes	Step 1 : sizeof(**r[0]) equals sizeof(x). See Equation 22 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes. See Equation 22
sizeof(r[0][0][0])	4 Bytes	Step 1 : sizeof(r[0][0][0]) equals sizeof(x). See Equation 22 Step 2 : sizeof(x) equals sizeof(type_of(x)) See Property 2.4 Step 3 : sizeof(type_of(x)) equals sizeof(int) See Property 1.1 Step 4 : sizeof(int) equals 4 Bytes

Table of Types (for Expressions)

Expression	Type	Description
type_of(x)	int	See Property 1.1
type_of(&x)	int *	See Property 1.2
type_of(p)	int *	See Property 1.1
type_of(&p)	int **	See Property 1.2
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 **	See Property 1.1
type_of(&q)	int ***	See Property 1.2
type_of(*q)	int *	Step 1 : type_of(*q) equals type_of(p). See Equation 8 Step 2 : type_of(p), equals int * See Property 1.1
type_of(q[0])	int *	Step 1 : type_of(q[0]) equals type_of(p) See Equation 8 Step 2 : type_of(p) equals int * See Property 1.1
type_of(**q)	int	Step 1 : type_of(**q) equals type_of(x) See Equation 10 Step 2 : type_of(x) equals int See Property 1.1
type_of(*q[0])	int	Step 1 : type_of(*q[0]) equals type_of(x) See Equation 10 Step 2 : type_of(x) equals int See Property 1.1
type_of(q[0][0])	int	Step 1 : type_of(q[0][0]) equals type_of(x) See Equation 11 Step 2 : type_of(x) equals int See Property 1.1
type_of(r)	int ***	See Property 2.4
type_of(&r)	int ****	See Property 2.3
type_of(*r)	int **	Step 1 : type_of(*r) equals type_of(q). See Equation 15 Step 2 : type_of(q) equals int **
type_of(r[0])	int **	Step 1 : type_of(r[0]) equals type_of(q). See Equation 15 Step 2 : type_of(q) equals int **
type_of(**r)	int *	Step 1 : type_of(**r) equals type_of(p). See Equation 19 Step 2 : type_of(type_of(p)) equals int * See Property 1.1
type_of(*r[0])	int *	Step 1 : type_of(*r[0]) equals type_of(p). See Equation 19 Step 2 : type_of(type_of(p)) equals int * See Property 1.1
type_of(r[0][0])	int *	Step 1 : type_of(r[0][0]) equals type_of(p). See Equation 19 Step 2 : type_of(type_of(p)) equals int * See Property 1.1
type_of(***r)	int	Step 1 : type_of(***r) equals type_of(x). See Equation 22 Step 2 : type_of(x) equals int See Property 2.4
type_of(**r[0])	int	step 1 : type_of(**r[0]) equals type_of(x). see equation 22 step 2 : type_of(x) equals int see property 2.4
type_of(r[0][0][0])	int	step 1 : type_of(r[0][0][0]) equals type_of(x). see equation 22 step 2 : type_of(x) equals int see property 2.4

Table of Address/Value (for Expression)

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
r	Address	Step 1 : r = &q See Equation 12 Step 2 : & operator indicates address
&r	Address	Step 1 : & operator indicates address
*r	Address	Step 1 : *r = q See Equation 15 Step 2 : *r = &p See Equation 16 Step 3 : & operator indicates address
r[0]	Address	Step 1 : *r = q See Equation 15 Step 2 : *r = &p See Equation 16 Step 3 : & operator indicates address
**r	Address	Step 1 : **r = p See Equation 19 Step 2 : **r = &x See Equation 20 Step 3 : & operator indicates address
*r[0]	Address	Step 1 : *r[0] = p See Equation 19 Step 2 : *r[0] = &x See Equation 20 Step 3 : & operator indicates address
r[0][0]	Address	Step 1 : r[0][0] = p See Equation 19 Step 2 : r[0][0] = &x See Equation 20 Step 3 : & operator indicates address
***r	Value	Step 1 : ***r = x See Equation 22 Step 2 : x is an integer Step 3 : r[0][0][0] is a Value
**r[0]	Value	Step 1 : **r[0] = x See Equation 22 Step 2 : x is an integer Step 3 : r[0][0][0] is a Value
r[0][0][0]	Value	Step 1 : r[0][0][0] = x See Equation 22 Step 2 : x is an integer Step 3 : r[0][0][0] is a Value

Table of Function Prototype (for Expression)

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);	See Property 1.1
fun(&x)	void fun(int *p);	See Property 1.2
fun(p)	void fun(int *p);	See Property 1.1
fun(&p)	void fun(int **p);	See Property 1.2
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);	See Property 1.1
fun(&q)	void fun(int ***q);	See Property 1.2
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)
fun(r)	void fun(int ***r);	Step 1 : fun(r) equals fun(type_of(r)) Step 2 : fun(type_of(r)) equals fun(int ***)
fun(&r)	void fun(int ****s);	Step 1 : fun(&r) equals fun(type_of(&r)) Step 2 : fun(type_of(&r)) equals fun(int ****)
fun(*r)	void fun(int **q);	Step 1 : fun(*r) equals fun(q) See Equation 15 Step 2 : fun(q) equals fun(type_of(q)) Step 3 : fun(type_of(q)) equals fun(int **)
fun(r[0])	void fun(int **q);	Step 1 : fun(r[0]) equals fun(q) See Equation 15 Step 2 : fun(q) equals fun(type_of(q)) Step 3 : fun(type_of(q)) equals fun(int **)
fun(**r)	void fun(int *p);	Step 1 : fun(**r) equals fun(p) See Equation 19 Step 2 : fun(p) equals fun(type_of(p)) Step 3 : fun(type_of(p)) equals fun(int *)
fun(*r[0])	void fun(int *p);	Step 1 : fun(*r[0]) equals fun(p) See Equation 19 Step 2 : fun(p) equals fun(type_of(p)) Step 3 : fun(type_of(p)) equals fun(int *)
fun(r[0][0])	void fun(int *p);	Step 1 : fun(**r) equals fun(p) See Equation 19 Step 2 : fun(p) equals fun(type_of(p)) Step 3 : fun(type_of(p)) equals fun(int *)
fun(***r)	void fun(int x);	Step 1 : fun(***r) equals fun(x) See Equation 22 Step 2 : fun(x) equals fun(type_of(x)) Step 3 : fun(type_of(x)) equals fun(int)
fun(**r[0])	void fun(int x);	Step 1 : fun(**r[0]) equals fun(x) See Equation 22 Step 2 : fun(x) equals fun(type_of(x)) Step 3 : fun(type_of(x)) equals fun(int)
fun(r[0][0][0])	void fun(int x);	Step 1 : fun(r[0][0][0]) equals fun(x) See Equation 22 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);
r	Triple Pointer	8	int ***	Address	fun(r)	void fun(int ***r);
&r	Fourth Pointer	8	int ****	Address	fun(&r)	void fun(int ****s);
*r	Double Pointer	8	int **	Address	fun(*r)	void fun(int **q);
r[0]	Double Pointer	8	int **	Address	fun(r[0])	void fun(int **q);
**r	Single Pointer	8	int *	Address	fun(**r)	void fun(int *p);
*r[0]	Single Pointer	8	int *	Address	fun(*r[0])	void fun(int *p);
r[0][0]	Single Pointer	8	int *	Address	fun(r[0][0])	void fun(int *p);
***r	Integer	4	int	Value	fun(***r)	void fun(int x);
**r[0]	Integer	4	int	Value	fun(**r[0])	void fun(int x);
r[0][0][0]	Integer	4	int	Value	fun(r[0][0][0])	void fun(int x);

See Also

• Equations of Integer Single Pointer

• Equations of Integer Triple pointer

See Also

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  • Malloc and Pointers

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  • Pre Increment with Pointers

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