This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 4 years ago.
What is the explanation for this unexpected results in Python??!;
from math import *
>>>log(1000,10) ## expecting 3.0
2.9999999999999996
>>>1000**(1/3) ## expecting 10.0
9.999999999999998
Basically value of these functions are calculated using some series. As python by default uses floating values, so it calculates values very precisely.
You can see this...
Efficient implementation of natural logarithm (ln) and exponentiation
That`s why it gives these types of result.
You can use Fraction class from fractions to convert these values to integer.
https://docs.python.org/3.1/library/fractions.html
Related
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 1 year ago.
I use math.pi with python:
import Decimal as dc
dc.getcontext().prec=100
pi = dc.Decimal(math.pi)
and I get:
3.141592653589793115997963468544185161590576171875
and on Internet, I get:
3,141592653589793238462643383279502884197169399375
Why doesn't python give a good value? How to improve the situation?
I tried with and without Decimal.
As indicated in the comments and in the documentation of Python math module, math.pi holds a floating-point value. Floating-point is inaccurate by design, because there is a finite number of bits dedicated to keeping the precision. You can read https://docs.python.org/3/tutorial/floatingpoint.html to understand how float is represented, and how this will impact you during programming (in all languages, not only Python).
How to get your accurate value of pi? As mentioned by Tom Karzes, you can use Decimal module and feed it with as many digits as you want. Let's take the first 30 digits of pi from https://www.angio.net/pi/digits/pi1000000.txt, and your code would look like this:
pi_30_decimal_places = Decimal("3.141592653589793238462643383279")
This question already has answers here:
Is floating point math broken?
(31 answers)
Floating Point Numbers [duplicate]
(7 answers)
Closed 4 years ago.
I am trying to understand the decimal rounding behavior in python. What I find strange is the following:
1) Multiplying 70 by 11.46950 gives me 802.865
2) Multiplying 70 by 11.46750 gives me 802.7249999999999
Why is there extra precision in the second case and not the first case? I understand that internally, the decimal cannot be represented exactly. But that reason should also apply to the first case as well?
I am using python3.6.
Thanks
This question already has answers here:
Is floating point math broken?
(31 answers)
Why does Python return 0 for simple division calculation?
(6 answers)
Closed 5 years ago.
This is driving me mad... Of all the years I've been using python, this is just now starting to present itself. How I managed to dodge it up until now is beyond me.
If you open a python idle and try this equation...
4/32*100
You'll get '0' as an answer. Now try the same equation using floats....
4.0/32.0*100.0 (or just the first number 4.0/32*100)
You now get an actual percentage.
WTF!?
Is this some kind of python error!? Even a calculation can do the equation and spit out a percentage.
So why can't python see a 4 as 4.0. Better question... What is the interpreter actually seeing if it's not seeing a 4(4.0)?
Someone please clear this up so I can feel professional with python again (lol).
In Python 2, int type division ignores the decimal values of the division.
For example, 1/2 = 0.5, but in int type division, 1/2 will evaluate to 0 because it ignores the decimal values.
Thus, in your case with 4/32*100, 4/32will first evaluate to 0 and then 0*100 will finally equal 0.
On the other hand, in float type division, it will evaluate answers as we would expect (not in a strictly precise definition though, look here for further information).
For Python 2.x, dividing two integers or longs uses integer division, also known as "floor division"(applying the floor function after division)
For Python 3.x, "/" does "true division" for all types.
To make python perform true division, cast any of the denominator for numerator to become float.
float(4)/32*100
or
4/float(32)*100
or doing below to make python 2 division behave like python 3 division
from __future__ import division
4/32*100
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 5 years ago.
Can someone explain this?
Input:
58/100*100
Result:
57.99999999999999
Yet...
Input:
26/100*100
Result:
26.0
Also, how can I consistently get results like in the second case?
This is all due to floating point arithmetic
and a subtle change in the way python evaluates expressions containing numeric literals.
Since python 3, your expressions above will be calculated in floating point; before then integer arithmetic would have be used.
In IEEE754 floating point, 0.58 is further away from the true value than 0.26. That's enough to throw off the heuristics that your output formatter is using.
Performing the multiplication before the division can help in some circumstances, and will do here as the product can be represented exactly.
This question already has answers here:
How can I force division to be floating point? Division keeps rounding down to 0?
(11 answers)
Closed 8 years ago.
I'm trying to have this function work, but i'm not getting the results expected. I fully believe it because I'm new to Python.... Here is my code:
waterLevel = (-(25/144) * sensorValue) + (14725/72) ;
And here is the equation:
y=-25x/144 + 14725/72
So when x=1178 then y=0 (y=waterLevel) and when x=602 then y=100.
I am getting this, when x=1178 then y=204.
What am I doing wrong here?
Update This is a different question because I didn't know it was floating point python nonsense .... just that my math wasn't working. Just because the answer is the same doesn't mean it is a duplicate. ;)
You are falling foul of integer division as opposed to float division.
In Python 2.x 25/144 will produce integer division which means it will result in 0.
If you're going to be dealing with floating point numbers then you should use floating point numbers, i.e. 25.0/144.0.
In Python 3.x the division of integers will default to returning the floating point value and instead you must explicitly choose integer division using //. If you would like this behaviour in Python 2 then use from __future__ import division at the top of your script (thanks to jwodder for the comment).
Use floats instead of ints
waterLevel = (-(25.0/144.0) * sensorValue) + (14725.0/72.0)
By the way, there is an adicional parethesis in the beginning of the equation, is it a typo?