References:



In [1]:

    
import sys
import math
import ctypes
import struct



In [2]:

    
sys.float_info









    Out[2]:





sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)



In [3]:

    
sys.int_info









    Out[3]:





sys.int_info(bits_per_digit=30, sizeof_digit=4)



In [4]:

    
format(0.125, '.12g')









    Out[4]:





'0.125'



In [5]:

    
format(0.101, '.12g')









    Out[5]:





'0.101'



In [6]:

    
0.3









    Out[6]:





0.3



In [7]:

    
0.1









    Out[7]:





0.1



In [8]:

    
0.1 + 0.1 + 0.1 == 0.3









    Out[8]:





False



In [9]:

    
f"{0x1234:b}"









    Out[9]:





'1001000110100'

Binary representation of an integer

With formatting



In [10]:

    
a = 1



In [11]:

    
"{0:b}".format(a)









    Out[11]:





'1'

with bin()



In [12]:

    
bin(a)









    Out[12]:





'0b1'

Binary representation of a float

radix point: the symbol used in numerical representations to separate the integer part of a number (to the left of the radix point) from its fractional part (to the right of the radix point)

Double precision:

sign (+/-): 1 bit
exponent: 11 bits
significand precision: 53 bits (52 explicitly stored)

$e$ biased exponent

$(-1)^{sign} \left( 1.b_{p-1} b_{p-2} ... b_{0} \right)_{2} \cdot 2^{e-1023}$

$(-1)^{sign} \left( 1 + \sum_{i=1}^{p} b_{52-i} 2^{-i} \right) \cdot 2^{e-1023}$



In [13]:

    
sys.float_info









    Out[13]:





sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)



In [14]:

    
a = 1.0
a









    Out[14]:





1.0



In [15]:

    
bin(ctypes.c_uint.from_buffer(ctypes.c_float(a)).value)









    Out[15]:





'0b111111100000000000000000000000'



In [16]:

    
bin(struct.unpack('!i',struct.pack('!f',a))[0])









    Out[16]:





'0b111111100000000000000000000000'



In [17]:

    
a = 2.0
a









    Out[17]:





2.0



In [18]:

    
bin(ctypes.c_uint.from_buffer(ctypes.c_float(a)).value)









    Out[18]:





'0b1000000000000000000000000000000'



In [19]:

    
bin(struct.unpack('!i',struct.pack('!f',a))[0])









    Out[19]:





'0b1000000000000000000000000000000'



In [20]:

    
a = 4.0
a









    Out[20]:





4.0



In [21]:

    
bin(ctypes.c_uint.from_buffer(ctypes.c_float(a)).value)









    Out[21]:





'0b1000000100000000000000000000000'



In [22]:

    
bin(struct.unpack('!i',struct.pack('!f',a))[0])









    Out[22]:





'0b1000000100000000000000000000000'



In [23]:

    
a = 8.0
a









    Out[23]:





8.0



In [24]:

    
bin(ctypes.c_uint.from_buffer(ctypes.c_float(a)).value)









    Out[24]:





'0b1000001000000000000000000000000'



In [25]:

    
bin(struct.unpack('!i',struct.pack('!f',a))[0])









    Out[25]:





'0b1000001000000000000000000000000'



In [26]:

    
a = 2.0**500
a









    Out[26]:





3.273390607896142e+150



In [27]:

    
bin(ctypes.c_uint.from_buffer(ctypes.c_float(a)).value)









    Out[27]:





'0b1111111100000000000000000000000'



In [28]:

    
bin(struct.unpack('!i',struct.pack('!f',a))[0])









    



---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)
<ipython-input-28-9085d3719c70> in <module>()
----> 1 bin(struct.unpack('!i',struct.pack('!f',a))[0])

OverflowError: float too large to pack with f format



In [ ]:

    
a = -2.0
a



In [ ]:

    
bin(ctypes.c_uint.from_buffer(ctypes.c_float(a)).value)



In [ ]:

    
bin(struct.unpack('!i',struct.pack('!f',a))[0])

Representation errors



In [ ]:

    
sum([0.1] * 10) == 1.0



In [ ]:

    
math.fsum([0.1] * 10) == 1.0



In [ ]: