long integers and float numbers in python

lecture 5 of MIT open course on python http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-00-introduction-to-computer-science-and-programming-fall-2008/video-lectures/lecture-5/

in python shell, type:

>>> 2**999

5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688L

notice that at the end, there is a mysterious L, it just means that it is a long integer( python's internal long format)

>>>2**1000

5357543035931336604742125245300009052807024058527668037218751941851755255624680612465991894078479290637973364587765734125935726428461570217992288787349287401967283887412115492710537302531185570938977091076523237491790970633699383779582771973038531457285598238843271083830214915826312193418602834034688L

what happens if 2**1000 is divided by 2**999?

>>> a= 2**999

>>> b= 2**1000

>>> b/a

2L

L stays with 2.

float number

>>> s=0

>>> for i in range(10):

            s+=0.1

>>> s

0.9999999999999999

it is not 1! 

it has to do with the ieee 754 standard to store numbers in computer

http://en.wikipedia.org/wiki/IEEE_floating_point

>>> print s

1.0 

print statement round it to 1.

another example:

>>> import math

>>> a=math.sqrt(2)

>>>a

1.4142135623730951

>>> a*a==2

False

in fact

>>> a*a

2.0000000000000004

so, never test  a float number == some other number

usually test :

abs(a*a-2.0) < epsilon

where epsilon is a given small number