FLOATING POINT REPRESENTATION.

Python | Float type and its methods.

The float type in Python represents the floating-point number. Float is used to represent real numbers and is written with a decimal point dividing the integer and fractional parts. For example, 97.98, 32.3+e18, -32.54e100 all are floating-point numbers.

Python float values are represented as 64-bit double-precision values. The maximum value any floating-point number can be is approx 1.8 x 10308. Any number greater than this will be indicated by the string inf in Python.

# Python code to demonstrate float values. 

print(1.7e308) 

# greater than 1.8 * 10^308 

# will print 'inf' 

print(1.82e308) 

OUTPUT:

1.7e+308

inf

Floating-point numbers are represented in computer hardware as base 2 (binary) fractions. For example, the decimal fraction 0.125 has value 1/10 + 2/100 + 5/1000, and in the same way the binary fraction 0.001 has value 0/2 + 0/4 + 1/8. These two fractions have identical values, the only real difference being that the first is written in base 10 fractional notation, and the second in base 2.
Unfortunately, most decimal fractions cannot be represented exactly as binary fractions. A consequence is that, in general, the decimal floating-point numbers you enter are only approximated by the binary floating-point numbers actually stored in the machine.

The type implements the abstract base class. Returns an expression which is converted into floating-point number. float also has the following additional methods:

float.as_integer_ratio() : Returns a pair of integers whose ratio is exactly equal to the actual float having a positive denominator. In the case of infinite, it raises overflow error and value errors on Not a number (NaNs).

# Python3 program to illustrate 

# working of float.as_integer_ratio() 

def frac(d): 

# Using as_integer_ratio 

b = d.as_integer_ratio() 

return b 

# Driver code 

if __name__=='__main__': 

b = frac(3.5) 

print(b[0], "/", b[1]) 

OUTPUT:

7/2

float.is_integer() : Returns True in case the float instance is finite with integral value, else, False.

# Python3 program to illustrate 

# working of float.is_integer() 

def booln(): 

# using is_integer 

print((-5.0).is_integer()) 

print((4.8).is_integer()) 

print(float.is_integer(275.0)) 

# Driver code 

if __name__=='__main__': 

booln() 

OUTPUT:

True

False

True

float.hex() : Returns a representation of a floating-point number as a hexadecimal string.

# Python3 program to illustrate 

# working of float.hex() 

def frac(a): 

# using float.hex() 

a = float.hex(35.0) 

return a 

# Driver code 

if __name__=='__main__': 

b = frac(35.0) 

print(b) 

output:

0*1.180000000000p+5

float.from hex(s): Returns the float represented by a hexadecimal string s. String s may have leading and trailing whitespaces.

# Python3 program to illustrate 

# working of float.fromhex() 

def frac(a): 

# using a float.fromhex() 

a = float.fromhex('0x1.1800000000000p+5') 

return a 

# Driver code  

if __name__=='__main__': 

b = frac('0x1.1800000000000p+5') 

print(b) 

OUTPUT:

35.0

Note : float.hex() is an instance method, but float.fromhex() is a class method.