Python while loop inconstancy

Question

Never seen anything like this. Simple while loop:

t_end = 100.0
t_step= 0.1
time = 0
while time<=t_end:
 time+=t_step
 print time

Last 3 printed values:

...
99.9
100.0
100.1

Looks right to me.

Now, I change t_step to 0.01:

t_end = 100.0
t_step= 0.01
time = 0
while time<=t_end:
 time+=t_step
 print time

Last 3 printed values:

...
99.98
99.99
100.0

Question: Why it doesn't go for the final loop when time = t_end =100.0 ?

What is the alternative solution?

• DSM: Related: strange python while loop behavior with comparison.
• chucksmash: Many (most, actually?) base 10 numbers with a decimal component cannot be stored exactly in base 2. You are not actually dealing with the numbers .1base10 and .01base10> and thus when you are doing arithmetic with them you can't count on them being entirely accurate.

Answer 1

Because this 100.0 (result of a sum) can be bigger than 100.0 you write by hand. You should not compare float numbers for equality...

You should read this:

What Every Computer Scientist Should Know About Floating-Point Arithmetic

Possible solution:

>>> t_end = 100.0
>>> t_step = 0.01
>>> total = int(t_end/t_step)
>>> for x in itertools.accumulate((t_step for i in range(total + 1))):
 print(x)

So the last element will be: 100.01000000001426

• user1513100: How would you do the same task ?
• JBernardo: @user1513100 You can use a for loop and define the number of steps you want.
• JBernardo: @user1513100 I added a solution for your problem

Answer 2

Floating point round-off error. This is what I got for my last three values:

99.98000000001424
99.99000000001425
100.00000000001425

Answer 3

This is stemming from the inaccuracy of floating point calculations. You are relying on the == operator to compare two floating point values, which is a no-go. What you see as '100.0' might actually be something like '100.000000000314'