C-language real data (floating-point number)

Real data is also known as floating-point numbers or real numbers. In the C language, the real number is only used in decimal. It has two types: decimal decimal form and exponential form.

Representation of a real number

1) Decimal number form
Consists of a digital 0~ 9 and a decimal point. For example: 0.0, 25.0, 5.789, 0.13, 5.0, 300., 267.8230, etc. are all valid real numbers.

Note that there must be a decimal.

2) Exponential form
Consists of a decimal number, an additional code symbol "E" or "E", and a Step code (integer only, can be signed). The general form is:
A E N (A is a decimal number and n is a decimal integer)
Its value is a*10n. Such as:
2.1E5 (equals 2.1*105)
3.7E-2 (equals 3.7*10-2)
0.5E7 (equals 0.5*107)
-2.8E-2 (equals -2.8*10-2)

The following are not valid real numbers:
345 (no decimal point)
E7 (no digits before the order symbol E)
-5 (no order symbol)
53.-e3 (negative position is not correct)
2.7E (no order code)

"Example 3-5" outputs a real number.

2. #include <stdio.h>
4. int main(void){
6. printf("%f\ n ",356.);
8. printf("%f\ n ",356);
10. printf("%f\ n ",356.0);
12. return 0;
14. }

3) Real number in-memory storage form
Real numbers typically account for 4 bytes (32 bits) of memory space. stored as an exponential. The real number 3.14159 is stored in memory in the following form:


Description

• The greater the number of bits in the small part, the more effective the number, the higher the accuracy.
• The more digits the exponent part occupies, the greater the range of values that can be expressed.

Real variables

The real variables are divided into: single-precision (float), double-precision (dual-type) and long double-precision (long double) class three.

The single-precision type in the VC6.0 occupies 4 bytes (32-bit) of memory space, with a value range of 3.4e-38~3.4e+38 and only seven digits of valid digits. The double is a 8-byte (64-bit) memory space with a value range of 1.7e-308~1.7e+308 and a 16-bit valid number.

Type descriptor	Number of bits (bytes)	valid numbers	the range of the number
Float	32 (4)	6~7	10-37~1038
Double	64 (8)	15~16	10-307~10308
Long double	128 (16)	18~19	10-4931~104932

A real variable defines the same formatting and writing rules as an integral type. For example:

1. float x, y; //x, Y is a single-precision real amount
2. Double A, b, C; //A,b,c is a double-precision real quantity

Rounding error of real numbers

Since real numbers are made up of a finite number of storage units, the valid numbers available are always limited. The following example.

The rounding error of the "example 3-6" real number.

2. #include <stdio.h>
4. int main(void){
6. float a, b;
8. A=123456.789e5;
10. b=a+20;
12. printf("a=%f\ n", a);
14. printf("b=%f\ n", b);
16. return 0;
18. }

Note: The result of 1.0/3*3 is not equal to 1.

"Example 3-7"

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2. #include <stdio.h>
4. int main(void){
6. float a;
8. Double b;
10. A=33333.33333;
12. b=33333.33333333333333;
14. printf("a=%f\b=%f\ n", a, b);
16. return 0;
18. }

As you can see from this example:

• Because A is a single-precision floating-point type, the number of valid digits is only seven bits. And the integer is five bits, so the decimal two digits after the number is invalid.
• B is a double type with a valid bit of 16 bits. However, the VC6.0 specifies a maximum of six digits after the decimal, and the remainder is rounded.

C-language real data (floating-point number)