#Jonathan Hudson
#Student Number 12347890
#Date: 2020-08-26
#Lecture Practice

# Topic 4: Information and Data

## Base 2 decimals

#A decimal number is a sum of values in 10s, 100s, 1000s and 1/10s, 1/100s, 1/1000s, etc

#Ex.

#1/8 in base 10

#0.125 base 10 = 1/10 + 2/100 + 5/1000 in base 10

#We can represent a binary decimal the same way
#2s, 4s, 8s, and 1/2s, 1/4s, 1/8s

#Ex.

#1/8 in base 2

#0.001 base 2 = 0/2 + 0/8 + 1/8

#Some numbers are not repeating in either base like 1/8

#However some are

#0.1 = 1/10 is non-repeating in base 10

#but is repeating in base 2

#You've done decimal approximation in the past. Often when you need to approximate a base 10 number you do

#1/3 = 0.33333..... repeating

#or use 

#3/10 or 33/100 or 333/1000 for a level of accuracy

#However what is repeating in base 10 is not repeating in base 2

#1/10 which is not repeating in base 10 is repeating in base 2

#1/8 is not repeating in base 2 or base 10

#Converting 0.1 base 10 to base 2

#0.1 * 2 = 0.2   -> 0

#0.2 * 2 = 0.4   -> 0

#0.4 * 2 = 0.8   -> 0

#0.8 * 2 = 1.6   -> 1

#0.6 * 2 = 1.2   -> 1

#0.2 * 2 = 0.4   -> 0

# ... forever

#0.0001100110011001100... base 2

## Danger of repeating base 2 decimals

#Let's look at what is stored for some base 10 decimals in python

#print(1/10)
#print(1/8)

#"""Seems fine?"""

#print("%.50f" % (1/10))
#print("%.50f" % (1/8))

#Wait that's a lot of junk in the 1/10?

## Storing base 2 fractions (storing floating point numbers in python)

#We use binary fractions to represent floats


#var = 1/10
#Before garbage is seen
#print("%.16f" % var)
#Bit of garbage
#print("%.17f" % var)
#All the garbage
#print("%.55f" % var)

#"""I'm going to recreate that garbage filled float"""

#print("%.55f" % (3602879701896397 / 2 ** 55))

#"""How did I know that"""

#print(var.as_integer_ratio())

#Store a numerator (integer) using first 53 bits (1 is sign bit) 

#Store a exponent (integer) using 11 bits

## What are the issues?

#Floating point error. This can really screw up your math program. Doing 'math class' is not doing the same as 'computing' math


#print(0.1+0.1+0.1)
#print(0.3)

#print("%.55f" % (0.1+0.1+0.1))
#print("%.55f" % (0.3))

#print(0.1+0.1+0.1 == 0.3)

#var1 = 0.1+0.1+0.1
#var2 = 0.3
#print(var1.as_integer_ratio())
#print(var2.as_integer_ratio())

#print(0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1)
#print("%.55f" % (0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1))

## Max representation sizes

#Integers


#import sys
#print(sys.maxsize)
##32 bit computer
#print(2**31-1)
##64 bit computer
#print(2**63-1)

#However if we overflow our int (integer) type then python uses a different storage structure to get a bigger size"""

#print(sys.maxsize+1)

#"""Floating points"""

#print("%.100f" % sys.float_info.max)
#print(sys.float_info.max.as_integer_ratio())

#"""Note if we get bigger from our max floating point that info just disappears"""

#print("%.100f" % (sys.float_info.max+1))
#print((sys.float_info.max== (sys.float_info.max+1)))
#print((sys.float_info.max== (sys.float_info.max+0.1)))


#print(sys.float_info.max.as_integer_ratio())

#print((sys.float_info.max+1).as_integer_ratio())