Float type and its methods in python

A float (floating-point number) is a data type used to represent real numbers with a fractional component. It is commonly used to store decimal values and perform mathematical calculations that require precision.

Characteristics of Float Type

• Floats support decimal and exponential notation.
• They occupy 8 bytes (64 bits) in memory.
• Operations involving floats may lead to rounding errors due to binary representation limitations.

Example:

a = 10.5  # Float declaration
b = -3.14 # Negative float
c = 2.0   # Even if it looks like an integer, it's a float
d = 1.23e4  # Scientific notation (1.23 × 10⁴ = 12300.0)
e = 5e-3   # Scientific notation (5 × 10⁻³ = 0.005)
print(a,b,c,d,e)

Built-in Methods for float type

Python provides several built-in methods for float objects.

Built-in Methods for float Type in Python

1. float.as_integer_ratio()

The as_integer_ratio() method returns a tuple of two integers, whose ratio equals the float. This method is useful for precise representation of floating-point numbers as fractions, which can help avoid floating-point precision errors in arithmetic calculations. The returned integers represent the numerator and denominator of the fraction.

f = 2.75
ratio = f.as_integer_ratio()
print(ratio) 

(11, 4)

Here, 2.75 is exactly represented as 11/4. The method breaks down the float into an exact fraction by multiplying it by a power of 2 internally and simplifying it into two integers.

2. float.conjugate()

The conjugate() method returns the same float value. This method exists primarily for compatibility with complex numbers, where the conjugate of a complex number negates its imaginary part. Since a float has no imaginary part, calling conjugate() on a float simply returns itself.

f = 5.5
print(f.conjugate())  

5.5

This method does not modify the float; it just returns the same value. It ensures compatibility when working with complex numbers, where the conjugate of a + bi is a - bi.

3. float.fromhex(s)

The fromhex() method converts a hexadecimal string representation of a floating-point number into a float. This is useful when dealing with binary representations or low-level floating-point operations.

s = "0x1.91eb851eb851fp+1"
a = float.fromhex(s)
print(a)  

3.14

The hexadecimal string represents a floating-point number in scientific notation. The p+1 denotes a power of two exponent. Converting from hexadecimal ensures precise representation of binary floating-point numbers.

4. float.hex()

The hex() method returns the hexadecimal representation of a float. This is useful for debugging floating-point precision issues and for storing exact binary representations.

f = 3.14
print(f.hex())  

0x1.91eb851eb851fp+1

The output is a hexadecimal scientific notation representing the float. The p+1 means multiplying by 2^1. This format is useful for exact floating-point storage and computation.

5. float.is_integer()

The is_integer() method checks if a float has no decimal part and returns True if it is equivalent to an integer. This is useful when working with numerical computations where integer-like behavior is required.

print((4.0).is_integer())  
print((4.5).is_integer())  

True
False

Here, 4.0 is equivalent to the integer 4, so is_integer() returns True. However, 4.5 has a decimal part, so it returns False.

6. float.__abs__()

The __abs__() method returns the absolute value of a float, which is the non-negative version of the number. It is equivalent to the built-in abs() function.

f = -7.3
print(f.__abs__())  
print(abs(f))       

7.3
7.3

The negative value -7.3 is converted to its positive equivalent 7.3. This is useful when working with distances, magnitudes, or other computations where only the positive value is needed.

7. float.__add__

The __add__() method performs addition between two float values. This is automatically used when we use the + operator.

a = 5.5
b = 2.2
print(a.__add__(b))  
print(a + b)        

7.7
7.7

Here, 5.5 + 2.2 results in 7.7. The + operator internally calls the __add__() method.

8. float.__sub__

The __sub__() method performs subtraction between two float values. It is used when we apply the - operator.

a = 10.5
b = 3.2
print(a.__sub__(b))  
print(a - b)         

7.3
7.3

Here, 10.5 - 3.2 results in 7.3. The - operator calls __sub__() internally.

9. float.__mul__(other)

The __mul__() method performs multiplication between two float values.

a = 4.2
b = 2.0
print(a.__mul__(b))   
print(a * b)          

8.4
8.4

Multiplication of 4.2 * 2.0 results in 8.4. The * operator invokes __mul__() internally.

10. float.__truediv__(other)

The __truediv__() method performs true division (returns a float even when dividing two integers).

a = 7.5
b = 2.5
print(a.__truediv__(b))   
print(a / b)              

3.0
3.0

The division 7.5 / 2.5 results in 3.0, ensuring a floating-point output.

11. float.__floordiv__(other)

The __floordiv__() method performs floor division, which returns the largest integer less than or equal to the quotient.

a = 7.5
b = 2.5
print(a.__floordiv__(b))   
print(a // b)              

3.0
3.0

The quotient is 3.0 with no remainder, so the floor division is the same as normal division here.

12. float.__mod__(other)

The __mod__() method returns the remainder of division.

a = 10.5
b = 4.0
print(a.__mod__(b))   
print(a % b)          

2.5
2.5

Here, 10.5 / 4.0 results in 2 with a remainder of 2.5.

13. float.__pow__(other)

The __pow__() method raises the float to the power of another number.

a = 3.0
b = 2.0
print(a.__pow__(b))   
print(a ** b)        

9.0
9.0

The expression 3.0 ** 2.0 calculates 3.0 raised to the power of 2.0, which is 9.0.

14. float.__round__(n)

The __round__() method rounds the float to n decimal places.

f = 3.14159
print(f.__round__(2))  
print(round(f, 2))      

3.14
3.14

The float 3.14159 is rounded to 3.14 when specifying 2 decimal places.