[data storage] storage of floating point data in memory

Catalog

1-0 Common floating point numbers

1-1 Floating point numbers are stored in memory

1-2 Rules for storing floating point numbers

1-3 Rules for fetching floating point numbers  

1-4 Revisit the question introduced ：（ Combined storage and retrieval ）

1-6 About this floating-point and integer output conversion ：

1-7 The end , And the flower , wait , Let's have a little test :

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1-0 Common floating point numbers

Two representations ：

To express directly ：3.14

It's like scientific counting ：1E10

Common types of floating point numbers ：float ,double（ More details in float.h In the definition of , Available software everything Search inside ）

1-1 Floating point numbers are stored in memory

Let's first look at the introduction of a problem

#include<stdio.h>
// The storage of floating-point data in memory 
int main()
{
	
	int a = 9;
	printf("%d\n", a);
	float* pa = (float*)&a;
	printf("%f\n", *pa);

	
	*pa = 9.0;
	printf("%d\n", a);
	printf("%f\n", *pa);

	return 0;
}

 

Come to the conclusion that ：

1. By integer （ Floating point numbers ） The way to save , At the same time, according to the integer （ Floating point numbers ） It's normal to take out the angle of view

2. But in whole numbers （ Floating point numbers ） The way to save , At the same time, according to the floating point number （ Integers ） It's not normal to take out the angle of view （ It's different from what we started to think ） Of

summary ：

From here, we can see that there are differences between integer and floating-point numbers in memory

1-2 Rules for storing floating point numbers

Any binary floating point number V It can be expressed in the following form ：（ Can be associated with the decimal system of scientific counting ）

• (-1)^S*M*2^E
• (-1)^S The sign bit , When S=0,V Is a positive number , When S by 1,V It's a negative number
• M Represents a significant number ,1<=M<2
• 2^E Indicates the index bit ：

Bit weight of each bit when floating-point data is written in binary ：

For example ： 

 

about float:

S The data represented accounts for 1bite

E The data represented accounts for 8bite

M The data represented accounts for 23bite 

 

  about double:

S The data represented accounts for 1bite 

E The data represented accounts for 11 individual bite

M The data represented accounts for 52 individual bite

about M and E There are special rules ：

M（ Significant figures ）：（ Omit the value ）1<=E<2, Due to the particularity of the scope , This E The number represented must be 1.XXX, therefore It is stipulated that there is no such thing 1, Only exist XXX, When you take it out, just add 1. That's it

E（ Index ）：（ Correction value ） As for the index E,E For an unsigned integer （unsigned int）--- The specified calculation value can only be a positive integer .
It means , If E by 8 position , Its value range is 0-255： If E by 11 position , Its value range is 0-2047, however , We know , In scientific counting E Yes, there can be negative Of , So the rules are , In memory E The true value of must be added with an intermediate number , about 8 Bit E, The middle number is 127： about 11 Bit E, The middle number is 1023. such as , Example index E yes 10 When , Save as 32 When floating-point numbers are in place , Must be saved as 10+127=137, namely 10001001.

  Let's look at two examples of decimal conversion to binary storage format in memory ：

Example 1：float a=5.5

Example 2：float b=0.5;

1-3 Floating point number takes The rules of  

situation 1. When E Incomplete 0 Or all 1 when

In this case, the floating-point number is ： Index E The calculated value of minus 127（ or 1023）, Get the real value , Put significant numbers in M Add the first 1

situation 2. When E For all 0 when

At this time , The exponent of a floating point number E be equal to 1-127（ perhaps 1-1023） That's the true value （ Regulations ）

Significant figures M No more first 1, It's reduced to 0.XXX Decimals of , This is to show that +0 and -0, And close to 0 A very small number .

situation 3. When E For all 1 When

At this time , Floating point exponents E be equal to 255-127=128, That is, the index part is 2^128, This is a very large number , It means positive infinity or negative infinity .（ Here we leave the reader with an example ）

1-4 Revisit the question introduced ：（ Combined storage and retrieval ）

1. Save as an integer , At the same time, from the perspective of floating point numbers

 1-5. Save it as a floating-point number , At the same time, from the perspective of integer numbers

 

 

1-6 About this floating-point and integer output conversion ：

1. When converting long data to short data output , Its value cannot exceed the allowable value range of short data , otherwise An error will occur during conversion .

2. Data type of output f(d) And output format %d(%f) Errors often occur when there is a discrepancy

1-7 The end , And the flower , wait , Let's have a little test :

If you define :float a=1.0f;

problem : Through the debug memory window, you can see &a What is it ?

answer :  0000803f