Equations of Float Double Pointer
=============================================================

In this section, you are going to learn

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        What are the different ways of declarations ?

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        How to dervie equations ?

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        What are the Properties of Variable ?

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        What are the Properties of Expression ?

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        Topics in this section,

                * :ref:`Derive Equations for Double Pointer <variable_and_ptr_dp_float_ptr_ex_1>`

                * :ref:`Step 1 : Understand different methods to declare Double Pointer <variable_and_ptr_dp_float_ptr_ex_2>`

                        * :ref:`Declaration 1 : float x, Single Pointer p, Double Pointer q are declared and assigned in same line <variable_and_ptr_dp_float_ptr_ex_3>`
                        * :ref:`Declaration 2 : float x, Single Pointer p, Double Pointer q are declared and assigned in separate lines <variable_and_ptr_dp_float_ptr_ex_4>`
                        * :ref:`Declaration 3 : float x, Single Pointer p, Double Pointer q are declared in one line and assigned in another line <variable_and_ptr_dp_float_ptr_ex_5>`
                        * :ref:`Table of Declarations for Double Pointer <variable_and_ptr_dp_float_ptr_ex_6>`

                * :ref:`Step 2 : Split pointer declarations and assignments into separate lines <variable_and_ptr_dp_float_ptr_ex_7>`

                * :ref:`Step 3 : Derive Equations <variable_and_ptr_dp_float_ptr_ex_8>`

                * :ref:`Step 4 : Apply above equations to analyse C statements <variable_and_ptr_dp_float_ptr_ex_9>`

                * :ref:`Table of Equations for Single Pointer <variable_and_ptr_dp_float_ptr_ex_10>`
                * :ref:`Table of Equations for Double Pointer <variable_and_ptr_dp_float_ptr_ex_22>`

                * :ref:`Properties of a variable <variable_and_ptr_dp_float_ptr_ex_11>`

                        * :ref:`Property 1 : Type <variable_and_ptr_dp_float_ptr_ex_12>`
                        * :ref:`Property 2 : sizeof() <variable_and_ptr_dp_float_ptr_ex_13>`
                        * :ref:`Property 3 : Scope, Lifetime and Memory of a variable <variable_and_ptr_dp_float_ptr_ex_14>`

                * :ref:`Properties of Expressions <variable_and_ptr_dp_float_ptr_ex_15>`

                        * :ref:`Table of Expressions <variable_and_ptr_dp_float_ptr_ex_16>`
                        * :ref:`Table of Size (for Expressions) <variable_and_ptr_dp_float_ptr_ex_17>`
                        * :ref:`Table of Types (for Expressions) <variable_and_ptr_dp_float_ptr_ex_18>`
                        * :ref:`Table of Address/Value (for Expression) <variable_and_ptr_dp_float_ptr_ex_19>`
                        * :ref:`Table of Function Prototype (for Expression) <variable_and_ptr_dp_float_ptr_ex_20>`

                * :ref:`Summary <variable_and_ptr_dp_float_ptr_ex_21>`


1. Equations of Double Pointer
***********************************************************************

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	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 ?

.. _variable_and_ptr_dp_float_ptr_ex_1:

.. tab-set::

    .. tab-item:: Derive Equations for Double Pointer

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		You can derive equations looking at C declarations !

.. _variable_and_ptr_dp_float_ptr_ex_2:

        .. tab-set::

            .. tab-item:: Step 1 : Understand different methods to declare Double Pointer

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

.. _variable_and_ptr_dp_float_ptr_ex_3:

                .. tab-set::

                    .. tab-item:: Declaration 1 : Float ``x``, Single Pointer ``p``, Double Pointer ``q`` are declared and assigned in same line

                        .. code-block:: c
                                :linenos:
				:emphasize-lines: 5

				#include <stdio.h>

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

					*p = 20;

					**q = 200;

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

					return 0;
				}

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                            In this example,
                                * ``x`` is a float
                                * ``p`` is an single float pointer
                                * ``q`` is an double float 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``

.. _variable_and_ptr_dp_float_ptr_ex_4:

                .. tab-set::

                    .. tab-item:: Declaration 2 : Float ``x``, Single Pointer ``p``, Double Pointer ``q`` are declared and assigned in separate lines

                        .. code-block:: c
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				#include <stdio.h>

				int main(void)
				{
					float x = 10;

					float *p = &x;

					float **q = &p;

					*p = 20;

					**q = 200;

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

					return 0;
				}

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                            In this example,
                                * ``x`` is a float
                                * ``p`` is a single float pointer
                                * ``q`` is a double float 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``

		.. _variable_and_ptr_dp_float_ptr_declaration_3:

.. _variable_and_ptr_dp_float_ptr_ex_5:

                .. tab-set::

                    .. tab-item:: Declaration 3 : Float ``x``, Single Pointer ``p``, Double Pointer ``q`` are declared in one line and assigned in another line

                        .. code-block:: c
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				#include <stdio.h>

				int main(void)
				{
					float x;

					float *p;

					float **q;

					x = 10;

					p = &x;

					q = &p;

					*p = 20;

					**q = 200;

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

					return 0;
				}

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                            In this example,
                                * ``x`` is a float
                                * ``p`` is a single float pointer
                                * ``q`` is a double float 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``

.. _variable_and_ptr_dp_float_ptr_ex_6:

	.. tab-set::

	    .. tab-item:: Table of Declarations for Double Pointer

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

.. _variable_and_ptr_dp_float_ptr_ex_7:

        .. tab-set::

            .. tab-item:: 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 :ref:`Declaration 3 <variable_and_ptr_dp_float_ptr_declaration_3>`
        
.. _variable_and_ptr_dp_float_ptr_ex_8:

        .. tab-set::

            .. tab-item:: Step 3 : Derive Equations

        	.. tab-set::

	            .. tab-item:: Derive Equations of Single Pointer

			.. _variable_and_ptr_dp_float_ptr_eq_1:
        
	                * Equation 1 : Obtained from ``Step 2``

        	        .. code-block:: c

                	        p = &x;

			.. _variable_and_ptr_dp_float_ptr_eq_2:

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

                	.. code-block:: c
	
        	                *p = x;
                
			.. _variable_and_ptr_dp_float_ptr_eq_3:

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

                	.. code-block:: c

	                        p[0] = x;


			.. _variable_and_ptr_dp_float_ptr_eq_4:

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

                	.. code-block:: c

                        	*p = p[0] = x;

        	.. tab-set::

	            .. tab-item:: Derive Equations of Double Pointer

			.. _variable_and_ptr_dp_float_ptr_eq_5:

	                * Equation 5 : Obtained from ``Step 2``

        	        .. code-block:: c

                	        q = &p;

			.. _variable_and_ptr_dp_float_ptr_eq_6:

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

        	        .. code-block:: c

                	        *q = p;

			.. _variable_and_ptr_dp_float_ptr_eq_7:

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

        	        .. code-block:: c

                	        q[0] = p;

			.. _variable_and_ptr_dp_float_ptr_eq_8:

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

        	        .. code-block:: c

                	        *q = q[0] = p;

			.. _variable_and_ptr_dp_float_ptr_eq_9:

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

        	        .. code-block:: c

                	        *q = q[0] = &x;

			.. _variable_and_ptr_dp_float_ptr_eq_10:

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

        	        .. code-block:: c

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

			.. _variable_and_ptr_dp_float_ptr_eq_11:

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

        	        .. code-block:: c

                	        q[0][0] = x;

.. _variable_and_ptr_dp_float_ptr_ex_10:

		.. tab-set::

		    .. tab-item:: 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
			===========  ==================  ===========================================================================

.. _variable_and_ptr_dp_float_ptr_ex_22:

		.. tab-set::

		    .. tab-item:: 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
			===========  ==================  ===========================================================================

.. _variable_and_ptr_dp_float_ptr_ex_9:

        .. tab-set::

            .. tab-item:: Step 4 : Apply above equations to analyse C statements

	        .. tab-set::

	            .. tab-item:: Example 1 : :ref:`See Equation 2 <variable_and_ptr_dp_float_ptr_eq_2>` : Changing ``*p`` changes the value of ``x``

	                .. code-block:: c

        	                *p = 100;

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

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	                        Output :
					``x`` = 100, ``*p`` = 100

	        .. tab-set::

	            .. tab-item:: Example 2 : :ref:`See Equation 3 <variable_and_ptr_dp_float_ptr_eq_3>` : Changing ``p[0]`` changes the value of ``x``

	                .. code-block:: c

        	                p[0] = 100;

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

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	                        Output :
					``x`` = 100, ``p[0]`` = 100

	        .. tab-set::

	            .. tab-item:: Example 3 : :ref:`See Equation 4 <variable_and_ptr_dp_float_ptr_eq_4>` : Changing ``x`` changes the value of ``*p`` and ``p[0]``

	                .. code-block:: c

        	                x = 100;

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

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	                        Output :
					``*p`` = 100, ``p[0]`` = 100

	        .. tab-set::

	            .. tab-item:: Example 4 : :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>` : Changing ``**q`` changes the value of ``x``

	                .. code-block:: c

        	                **q = 100;

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

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	                        Output :
					``x`` = 100, ``**q`` = 100

	        .. tab-set::

	            .. tab-item:: Example 5 : :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>` : Changing ``*q[0]`` changes the value of ``x``

	                .. code-block:: c

        	                *q[0] = 100;

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

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	                        Output :
					``x`` = 100, ``*q[0]`` = 100

	        .. tab-set::

	            .. tab-item:: Example 6 : :ref:`See Equation 11 <variable_and_ptr_dp_float_ptr_eq_11>` : Changing ``q[0][0]`` changes the value of ``x``

	                .. code-block:: c

        	                q[0][0] = 100;

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

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	                        Output :
					``x`` = 100, ``q[0][0]`` = 100

	        .. tab-set::

	            .. tab-item:: Example 7 : :ref:`See Equation 6 <variable_and_ptr_dp_float_ptr_eq_6>` : ``*q``, ``p`` are synonyms. Means chaning ``*q`` also changes ``p``

	                .. code-block:: c

				float 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);

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	                        Output :
					``*p`` = 100, ``p[0]`` = 100, ``**q`` = 100

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

	        .. tab-set::

	            .. tab-item:: Example 8 : :ref:`See Equation 7 <variable_and_ptr_dp_float_ptr_eq_7>` : ``q[0]``, ``p`` are synonyms. Means chaning ``q[0]`` also changes ``p``

	                .. code-block:: c

				float 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);

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	                        Output :
					``*p`` = 100, ``p[0]`` = 100, ``**q`` = 100

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

        .. tab-set::

            .. tab-item:: Step 5 : Complete program

                	.. code-block:: c
                                :linenos:

				#include <stdio.h>

				int main(void)
				{
					float x;

					float *p;

					float **q;

					x = 10;

					p = &x;

					q = &p;

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

					x = 20;

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

					*p = 30;

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

					p[0] = 40;

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

					**q = 50;

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

					return 0;
				}

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                        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
***********************************************************************

.. _variable_and_ptr_dp_float_ptr_ex_11:

.. tab-set::

    .. tab-item:: Properties of a variable
        	                
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		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 ?

.. _variable_and_ptr_dp_float_ptr_ex_12:

	.. tab-set::

	    .. tab-item:: Property 1 : Type

		.. _variable_and_ptr_dp_float_ptr_property_1_1:

		.. tab-set::

		    .. tab-item:: Property 1.1 : type_of(variable)

        	        .. code-block:: c
				:linenos:
				:emphasize-lines: 1, 3, 5

	                        float x;

				float *p;

				float **q;

				p = &x;

				q = &p;


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

			===========  =========== ==============================================================================
			Variable     Type        Description
			===========  =========== ==============================================================================
			type_of(x)   float       See Line 1
			type_of(p)   float \*    See Line 3
			type_of(q)   float \*\*  See Line 5
			===========  =========== ==============================================================================

		.. _variable_and_ptr_dp_float_ptr_property_1_2:

		.. tab-set::

		    .. tab-item:: Property 1.2 : type_of(&variable)

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

        	        .. code-block:: c
				:linenos:
				:emphasize-lines: 1, 3, 5

	                        float x;

				float *p;

				float **q;

				p = &x;

				q = &p;

				*p = 10;

			* In above code snippet, there are two variables ``x``, ``p``

			===========  ============ ==============================================================================
			Variable     Type         Description
			===========  ============ ==============================================================================
			type_of(&x)  float \*     * ``type_of(x)`` is ``float``
					          * Hence, ``type_of(&x)`` is ``float *``
			type_of(&p)  float \*\*   * ``type_of(p)`` is ``float *``
					          * Hence, ``type_of(&p)`` is ``float **``
			type_of(&q)  float \*\*\* * ``type_of(q)`` is ``float **``
					          * Hence, ``type_of(&q)`` is ``float ***``
			===========  ============ ==============================================================================

.. _variable_and_ptr_dp_float_ptr_ex_13:

	.. tab-set::

	    .. tab-item:: Property 2 : sizeof()

		.. tab-set::

		    .. tab-item:: 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
			======================= =======

		.. tab-set::

		    .. tab-item:: Property 2.2 : sizeof() of pointer types

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				``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., 
			======================= =======

		.. _variable_and_ptr_dp_float_ptr_property_2_3:

		.. tab-set::

		    .. tab-item:: Property 2.3 : sizeof(&variable) - sizeof address of variable

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	                        :column: col-lg-12 p-2
        	                :card: shadow
			
				``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 ``float 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;``
			======================= ======= ========================

		.. _variable_and_ptr_dp_float_ptr_property_2_4:

		.. tab-set::

		    .. tab-item:: Property 2.4 : sizeof() of variable
		
                	.. panels::
                        	:container: container pb-4
	                        :column: col-lg-12 p-2
        	                :card: shadow

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

	                .. code-block:: c
				:linenos:
				:emphasize-lines: 1, 3, 5

	                        float x;

				float *p;

				float **q;

				p = &x;

				q = &p;

				*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 ``float``
                               	                            * Step 3 : ``sizeof(float)`` 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 ``float *``
                       	                                    * Step 3 : ``sizeof(float *)`` 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 ``float **``
                       	                                    * Step 3 : ``sizeof(float **)`` is ``8 Bytes``
                               	                            * Hence, ``sizeof(q)`` is ``8 Bytes``
			======================= ======= ================================================================================

.. _variable_and_ptr_dp_float_ptr_ex_14:

	.. tab-set::

	    .. tab-item:: Property 3 : Scope, Lifetime and Memory of a variable

		* Global Scope and Lifetime.

		* Local Scope and Lifetime

3. Properties of Expressions
***********************************************************************

.. panels::
	:container: container pb-4
	:column: col-lg-12 p-2
	:card: shadow

	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)

.. _variable_and_ptr_dp_float_ptr_ex_15:

.. tab-set::

    .. tab-item:: Properties of Expressions

		.. tab-set::

		    .. tab-item:: Let us write-down expression tables for below code snippet

			.. code-block:: c
				:linenos:
				:emphasize-lines: 1, 3, 5

				float x;

				float *p;

				float **q;

				p = &x;

				q = &p;

				*p = 10;

				**q = 100;

.. _variable_and_ptr_dp_float_ptr_ex_16:

		.. tab-set::

		    .. tab-item:: Table of Expressions


			==========  ==================================================================================================
			Expression  Description
			==========  ==================================================================================================
			x           * ``x`` is a float
			&x          * ``&x`` is address of a float
				    * ``&x`` is a single pointer
			p           * ``p`` is a pointer to a float
				    * ``p`` is a single pointer
			&p          * ``&p`` is address of a pointer
				    * ``&p`` is a double pointer
			\*p         * ``*p`` is a float, because ``*p = x``. :ref:`See Equation 2 <variable_and_ptr_dp_float_ptr_eq_2>`
			p[0]        * ``p[0]`` is a float, because ``p[0] = x``. :ref:`See Equation 3 <variable_and_ptr_dp_float_ptr_eq_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 float x. :ref:`See Equation 9 <variable_and_ptr_dp_float_ptr_eq_9>`
				    * ``*q`` is a single pointer. ``*q = p``. :ref:`See Equation 8 <variable_and_ptr_dp_float_ptr_eq_8>`
			q[0]        * ``q[0]`` holds the address of float x. :ref:`See Equation 9 <variable_and_ptr_dp_float_ptr_eq_9>`
				    * ``q[0]`` is a single pointer. ``*q = p``. :ref:`See Equation 8 <variable_and_ptr_dp_float_ptr_eq_8>`
			\*\*q	    * ``**q`` is a float. :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
			\*q[0]	    * ``*q[0]`` is a float. :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
			q[0][0]	    * ``q[0][0]`` is a float. :ref:`See Equation 11 <variable_and_ptr_dp_float_ptr_eq_11>`
			==========  ==================================================================================================

.. _variable_and_ptr_dp_float_ptr_ex_17:

		.. tab-set::

		    .. tab-item:: Table of Size (for Expressions)

			===============  ======= =================================================================
			Expression       Size    Description
			===============  ======= =================================================================
			sizeof(x)        4 Bytes * :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
			sizeof(&x)       8 Bytes * :ref:`See Property 2.3 <variable_and_ptr_dp_float_ptr_property_2_3>`
			sizeof(p)        8 Bytes * :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
			sizeof(&p)       8 Bytes * :ref:`See Property 2.3 <variable_and_ptr_dp_float_ptr_property_2_3>`
			sizeof(\*p)      4 Bytes * Step 1 : ``sizeof(*p)`` equals ``sizeof(x)`` :ref:`See Equation 2 <variable_and_ptr_dp_float_ptr_eq_2>`
						 * Step 2 : ``sizeof(x)`` equals ``sizeof(type_of(x))`` :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
						 * Step 3 : ``sizeof(type_of(x))`` equals ``sizeof(float)`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
						 * Step 4 : ``sizeof(float)`` equals 4 Bytes
			sizeof(p[0])     4 Bytes * Step 1 : ``sizeof(p[0])`` equals ``sizeof(x)``= x`` :ref:`See Equation 3 <variable_and_ptr_dp_float_ptr_eq_3>`
						 * Step 2 : ``sizeof(x)`` equals ``sizeof(type_of(x))`` :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
						 * Step 3 : ``sizeof(type_of(x))`` equals ``sizeof(float)`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
						 * Step 4 : ``sizeof(float)`` equals 4 Bytes
			sizeof(q)	 8 Bytes * :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
			sizeof(&q)	 8 Bytes * :ref:`See Property 2.3 <variable_and_ptr_dp_float_ptr_property_2_3>` 
			sizeof(\*q)	 8 Bytes * Step 1 : ``sizeof(*q)`` equals ``sizeof(p)``. :ref:`See Equation 8 <variable_and_ptr_dp_float_ptr_eq_8>`
						 * Step 2 : ``sizeof(p)``, equals ``sizeof(type_of(p))`` :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
                                                 * Step 3 : ``sizeof(type_of(p))`` equals ``sizeof(float *)`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
						 * Step 4 : ``sizeof(float *)`` equals 8 Bytes
			sizeof(q[0])	 8 Bytes * Step 1 : ``sizeof(q[0])`` equals ``sizeof(p)`` :ref:`See Equation 8 <variable_and_ptr_dp_float_ptr_eq_8>`
						 * Step 2 : ``sizeof(p)`` equals ``sizeof(type_of(p))`` :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
                                                 * Step 3 : ``sizeof(type_of(p))`` equals ``sizeof(float *)`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
                                                 * Step 4 : ``sizeof(float *)`` * equals 8 Bytes
			sizeof(\*\*q)	 4 Bytes * Step 1 : ``sizeof(**q)`` equals ``sizeof(x)`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
						 * Step 2 : ``sizeof(x)`` equals ``sizeof(type_of(x))`` :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
						 * Step 3 : ``sizeof(type_of(x))`` equals ``sizeof(float)`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
						 * Step 4 : ``sizeof(float)`` equals 4 Bytes
			sizeof(\*q[0])	 4 Bytes * Step 1 : ``sizeof(*q[0])`` equals ``sizeof(x)`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
						 * Step 2 : ``sizeof(x)`` equals ``sizeof(type_of(x))`` :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
						 * Step 3 : ``sizeof(type_of(x))`` equals ``sizeof(float)`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
						 * Step 4 : ``sizeof(float)`` equals 4 Bytes
			sizeof(q[0][0])	 4 Bytes * Step 1 : ``sizeof(q[0][0])`` equals ``sizeof(x)`` :ref:`See Equation 11 <variable_and_ptr_dp_float_ptr_eq_11>`
						 * Step 2 : ``sizeof(x)`` equals ``sizeof(type_of(x))`` :ref:`See Property 2.4 <variable_and_ptr_dp_float_ptr_property_2_4>`
						 * Step 3 : ``sizeof(type_of(x))`` equals ``sizeof(float)`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
						 * Step 4 : ``sizeof(float)`` equals 4 Bytes
			===============  ======= =================================================================

.. _variable_and_ptr_dp_float_ptr_ex_18:

		.. tab-set::

		    .. tab-item:: Table of Types (for Expressions)

			================  ============ =================================================================================================================
			Expression        Type         Description
			================  ============ =================================================================================================================
			type_of(x)        float        * :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			type_of(&x)       float \*     * :ref:`See Property 1.2 <variable_and_ptr_dp_float_ptr_property_1_2>`
			type_of(p)        float \*     * :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			type_of(&p)       float \*\*   * :ref:`See Property 1.2 <variable_and_ptr_dp_float_ptr_property_1_2>`
			type_of(\*p)      float        * Step 1 : ``type_of(*p)`` equals ``type_of(x)``, because ``*p = x``. :ref:`See Equation 2 <variable_and_ptr_dp_float_ptr_eq_2>`
						       * Step 2 : ``type_of(x)`` equals ``float``
			type_of(p[0])     float        * Step 1 : ``type_of(p[0])`` equals ``type_of(x)``, because ``p[0] = x``. :ref:`See Equation 3 <variable_and_ptr_dp_float_ptr_eq_3>`
						       * Step 2 : ``type_of(x)`` equals ``float``
			type_of(q)	  float \*\*   * :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			type_of(&q)	  float \*\*\* * :ref:`See Property 1.2 <variable_and_ptr_dp_float_ptr_property_1_2>`
			type_of(\*q)	  float \*     * Step 1 : ``type_of(*q)`` equals ``type_of(p)``. :ref:`See Equation 8 <variable_and_ptr_dp_float_ptr_eq_8>`
						       * Step 2 : ``type_of(p)``, equals ``float *`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			type_of(q[0])	  float \*     * Step 1 : ``type_of(q[0])`` equals ``type_of(p)`` :ref:`See Equation 8 <variable_and_ptr_dp_float_ptr_eq_8>`
						       * Step 2 : ``type_of(p)`` equals ``float *`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			type_of(\*\*q)	  float        * Step 1 : ``type_of(**q)`` equals ``type_of(x)`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
						       * Step 2 : ``type_of(x)`` equals ``float`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			type_of(\*q[0])	  float        * Step 1 : ``type_of(*q[0])`` equals ``type_of(x)`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
						       * Step 2 : ``type_of(x)`` equals ``float`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			type_of(q[0][0])  float        * Step 1 : ``type_of(q[0][0])`` equals ``type_of(x)`` :ref:`See Equation 11 <variable_and_ptr_dp_float_ptr_eq_11>`
						       * Step 2 : ``type_of(x)`` equals ``float`` :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			================  ============ =================================================================================================================

.. _variable_and_ptr_dp_float_ptr_ex_19:

		.. tab-set::

		    .. tab-item:: Table of Address/Value (for Expression)

			==========  ============== ====================================================
			Expression  Address/Value  Description
			==========  ============== ====================================================
			x           Value          * Step 1 : ``x`` is a float
						   * Step 2 : Hence ``x`` is a value
			&x          Address        * & operator indicates address
			p           Address        * Step 1 : ``p = &x`` :ref:`See Equation 1 <variable_and_ptr_dp_float_ptr_eq_1>`
						   * Step 2 : & operator indicates address
			&p          Address        * & operator indicates address
			\*p         Value          * Step 1 : ``*p`` is a float. ``*p = x`` :ref:`See Equation 2 <variable_and_ptr_dp_float_ptr_eq_2>`
						   * Step 2 : Hence ``*p`` is a value
			p[0]        Value          * Step 1 : ``p[0]`` is a float. ``p[0] = x`` :ref:`See Equation 3 <variable_and_ptr_dp_float_ptr_eq_3>`
						   * Step 2 : Hence ``p[0]`` is a value
			q	    Address        * Step 1 : ``q = &p`` :ref:`See Equation 5 <variable_and_ptr_dp_float_ptr_eq_5>`
						   * Step 2 : & operator indicates address
			&q	    Address        * & operator indicates address
			\*q	    Address	   * Step 1 : ``*q = p`` :ref:`See Equation 6 <variable_and_ptr_dp_float_ptr_eq_6>`
				    		   * Step 2 : ``p = &x`` 
						   * Step 3 : & operator indicates address
			q[0]	    Address	   * Step 1 : ``q[0] = p`` :ref:`See Equation 7 <variable_and_ptr_dp_float_ptr_eq_7>`
				    		   * Step 2 : ``p = &x`` 
						   * Step 3 : & operator indicates address
			\*\*q	    Value	   * Step 1 : ``**q = x`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
						   * Step 2 : ``x`` is a float
						   * Step 3 : ``**q`` is a Value
			\*q[0]	    Value	   * Step 1 : ``*q[0] = x`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
						   * Step 2 : ``x`` is a float
						   * Step 3 : ``*q[0]`` is a Value
			q[0][0]	    Value	   * Step 1 : ``q[0][0] = x`` :ref:`See Equation 11 <variable_and_ptr_dp_float_ptr_eq_11>`
						   * Step 2 : ``x`` is a float
						   * Step 3 : ``q[0][0]`` is a Value
			==========  ============== ====================================================

.. _variable_and_ptr_dp_float_ptr_ex_20:

		.. tab-set::

		    .. tab-item:: Table of Function Prototype (for Expression)
                        
			.. panels::
                            :container: container pb-4
                            :column: col-lg-12 p-2
                            :card: shadow

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

			=============  ======================== ====================================================================
			Function call  Function Prototype       Description
			=============  ======================== ====================================================================
			fun(x)         void fun(float x);       * :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			fun(&x)        void fun(float \*p);     * :ref:`See Property 1.2 <variable_and_ptr_dp_float_ptr_property_1_2>`
			fun(p)         void fun(float \*p);     * :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			fun(&p)        void fun(float \*\*p);   * :ref:`See Property 1.2 <variable_and_ptr_dp_float_ptr_property_1_2>`
			fun(\*p)       void fun(float x);       * Step 1 : ``fun(*p)`` equals ``fun(x)``:ref:`See Equation 2 <variable_and_ptr_dp_float_ptr_eq_2>`
							        * Step 2 : ``fun(x)`` equals ``fun(type_of(x))``
			                                        * Step 3 : ``fun(type_of(x))`` equals ``fun(float)``
			fun(p[0])       void fun(float x);      * Step 1 : ``fun(p[0])`` equals ``fun(x)``:ref:`See Equation 2 <variable_and_ptr_dp_float_ptr_eq_2>`
							        * Step 2 : ``fun(x)`` equals ``fun(type_of(x))``
			                                        * Step 3 : ``fun(type_of(x))`` equals ``fun(float)``
			fun(q)         void fun(float \*\*q);   * :ref:`See Property 1.1 <variable_and_ptr_dp_float_ptr_property_1_1>`
			fun(&q)        void fun(float \*\*\*q); * :ref:`See Property 1.2 <variable_and_ptr_dp_float_ptr_property_1_2>`
			fun(\*q)       void fun(float \*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(float *)``
			fun(q[0])      void fun(float \*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(float *)``
			fun(\*\*q)     void fun(float x);       * Step 1 : ``fun(**q)`` equals ``fun(x)`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
			                                        * Step 2 : ``fun(x)`` equals ``fun(type_of(x))``
			                                        * Step 3 : ``fun(type_of(x))`` equals ``fun(float)``
			fun(\*q[0])    void fun(float x);       * Step 1 : ``fun(*q[0])`` equals ``fun(x)`` :ref:`See Equation 10 <variable_and_ptr_dp_float_ptr_eq_10>`
			                                        * Step 2 : ``fun(x)`` equals ``fun(type_of(x))``
			                                        * Step 3 : ``fun(type_of(x))`` equals ``fun(float)``
			fun(q[0][0])   void fun(float x);       * Step 1 : ``fun(q[0][0])`` equals ``fun(x)`` :ref:`See Equation 11 <variable_and_ptr_dp_float_ptr_eq_11>`
			                                        * Step 2 : ``fun(x)`` equals ``fun(type_of(x))``
			                                        * Step 3 : ``fun(type_of(x))`` equals ``fun(float)``
			=============  ======================== ====================================================================

.. _variable_and_ptr_dp_float_ptr_ex_21:

4. Summary
***********************************************************************


======= ============== ============= ============  ================ ============= ======================= 
#       ?              Size in Bytes Type          Address or Value Function call Function Prototype
======= ============== ============= ============  ================ ============= =======================
x       Float          4             float         Value            fun(x)        void fun(float x);               
&x      Single Pointer 8             float \*      Address          fun(&x)       void fun(float \*p);
p       Single Pointer 8             float \*      Address          fun(p)        void fun(float \*p);
&p      Double Pointer 8             float \*\*    Address          fun(&p)       void fun(float \*\*q);
\*p     Float          4             float         Value            fun(\*p)      void fun(float x); 
p[0]    Float          4             float         Value            fun(p[0])     void fun(float x); 
q       Double Pointer 8             float \*\*    Address          fun(q)        void fun(float \*\*q);
&q      Triple Pointer 8             float \*\*\*  Address          fun(&q)       void fun(float \*\*\*r);
\*q     Single Pointer 8             float \*      Address          fun(\*q)      void fun(float \*p);
q[0]    Single Pointer 8             float \*      Address          fun(q[0])     void fun(float \*p);
\*\*q   Float          4             float         Value            fun(\*\*q)    void fun(float x);
\*q[0]  Float          4             float         Value            fun(\*q[0])   void fun(float x);
q[0][0] Float          4             float         Value            fun(q[0][0])  void fun(float x);
======= ============== ============= ============  ================ ============= =======================

.. card:: See Also

        * :doc:`sp_float_ptr`
        * :doc:`tp_float_ptr`

.. card:: See Also

        * Current Module

                * :doc:`variable_and_ptr`

        * Next Module

                * :doc:`../array_n_ptrs/array_n_ptrs`


        * Other Modules

                * :doc:`../malloc_ptr/malloc_ptr`
                * :doc:`../typecasting_n_ptr/typecasting_n_ptr`
                * :doc:`../funcs_n_ptrs/funcs_n_ptrs`
                * :doc:`../memcpy_ptr/memcpy_ptr`
                * :doc:`../const_ptr/const_ptr`
                * :doc:`../void_ptr/void_ptr`
                * :doc:`../array_of_ptr/array_of_ptr`
                * :doc:`../ptr_to_array/ptr_to_array`
                * :doc:`../function_ptr/function_ptr`
                * :doc:`../pre_incr_ptr/pre_incr_ptr`
                * :doc:`../post_incr_ptr/post_incr_ptr`
                * :doc:`../pre_decr_ptr/pre_decr_ptr`
                * :doc:`../post_decr_ptr/post_decr_ptr`