Bo2SS

Course Content#

Mathematical Operations in C Language#

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• = Assignment

  • Can be combined with other operators: +=, <<=, ...

• / Division

  1. Both sides are integers: integer division, rounding down
  2. At least one side is a floating-point number: the result is a floating-point number

• () Increase operation precedence

• ⭐Bitwise Operations, high efficiency

  • Computers store different data types uniformly as binary data, i.e., stored by bits
  • 8 bits → 1 byte
  • The int type is 32 bits, and for signed integers, the maximum representable value is 2^31-1
  • In bitwise operations, ① first expand to binary representation, ② only the corresponding bits have relationships
  • Bitwise operations do not support floating-point numbers?
    • It is meaningless. For a 64-bit floating-point number, the highest bit is the sign bit S, the next 11 bits are the exponent E, and the remaining 52 bits are the significant digits M.
    • If bitwise AND is applied, what are the rules for the first 12 bits? What is the significance of the result of the exponent bits being ANDed? This is the essence; there is no mathematical meaning in ANDing two floating-point numbers.
  • ^ XOR
    • Characteristics: it is the inverse operation of itself; supports commutative and associative laws
    • Inverse operation
      • Premise: conforms to the commutative law
        • Subtraction and division do not conform
        • Subtraction is the inverse operation of addition, but not vice versa
        • Division is the inverse operation of multiplication, but not vice versa [not strictly, does not consider the multiplier being 0]

• << Left Shift >> Right Shift

  • Left shift by one bit, multiply by 2
  • Right shift by one bit, divide by 2, rounding down, sign unchanged
    • The left side continuously fills the sign bit (the highest bit is the sign bit for signed numbers)
    • The left side forcibly fills with 0 (for unsigned numbers)

Mathematical Functions in C Language#

Header file: math.h

Note: The abs() function is in stdlib.h

In-Class Exercises#

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• The control character for double type is “%lf”
• The control character for scanf must correspond to the type of the parameter, otherwise it will not read in

  • double x;

  • When using scanf, be sure to use “%lf” for correspondence, not “%f”, otherwise:

    • 
    • printf is not as strict; the control character does not have to match the type exactly, there should be type conversion
    • Code
      • 
      • Cleverly using pow, the one-third power represents the cube root
        • ⭐1/ 3**.0** instead of 1 / 3
      • When compiling with gcc, add the math library, -lm
• 
• Note that π can be obtained more accurately using acos(-1)
• Code
  • 
  • Dividing first and then multiplying is safer and less likely to overflow

Highlight Notes#

• The control character for double type is “%lf”
• π can be obtained more accurately using acos(-1)

Code Demonstration#

Exercises#

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• Using XOR for swapping is an interesting idea, but it is not actually recommended

  • It can only be used for integers to perform XOR
  • The speed is not faster than using temp
  • Swapping the same variable will result in 0: swap(a, a)

Additional Knowledge Points#

• Operator Precedence and Associativity Table-Baidu
  • The operation order of *p-- is ① p's address - 1, ② then use * to get the value at that address
    • (*p)-- is ① first get the variable value at p's address, then subtract 1 from the variable's value
• XOR Properties
  • a ^ a = 0;
  • 0 ^ a = a;
  • Can find a number that appears only once in an array where all other numbers appear twice
• Xshell runs C language without warnings
  • g++ *.cpp -Wall
    • Using this option allows all useful warnings that GCC can provide
    • You can also use -W{warning} to specify certain warnings.
    • 

Points for Consideration#

• What are the benefits of using XOR operations for variable swapping?
  • Saves memory for a third-party variable
  • Principle consideration
    • Just perform the inverse operation
  • Or
  • XORing itself results in 0
    * Any variable XORed with 0 remains unchanged
  • Considering the above principle, can it also be done using +- operations?
    • a' = a + b
    • b = a' - b = a
    • a = a' - b = a' - a = b
    • However, this approach does not utilize the efficiency of bitwise operations, and it must ensure that the sum of the two numbers does not overflow~

Tips#

• C Language Documentation in Chinese-Geek Academy Translation

  • The C language has about 29 function libraries

• Reference textbook chapters

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