Floating point calculations and control flow

Question

Here is part of my code:

students = 0
weight = 0
height = 0

while students < 5:
    name = input("Please enter the name. ")
    students = students + 1

while weight == 0:
    try:
        weight = float(input("Please enter the weight in kgs "))

        if weight <= 0:
            print ("Please enter a number greater than zero ")
            weight = 0
            continue

    except ValueError:
        print ("No number found, please enter a number greater than zero ")
        weight = 0
        continue

while height == 0:
    try:
        height = float(input("Please enter the height in metres "))


        if height <= 0:
            print ("Please enter a number greater than zero ")
            height = 0
            continue

    except ValueError:
        print ("No number found, please enter a number greater than zero ")
        height = 0
        continue

BMI = (weight/(height*height))
print (name, "has the BMI of", "%.2f" %BMI)
if BMI < 18.5:
    print ("The student is underweight.")
elif 18.5 <= BMI <= 27:
    print ("The student is a healthy weight.")
elif BMI > 27:
    print ("The student is overweight.")

weight = 0
height = 0

However, when the BMI is 18.5 it says that the student is underweight and when the BMI is 27 it says the student is overweight, when both should actually be a healthy weight? e.g. 53.456 for weight and 1.7m for height shows up as underweight

Post ALL the relevant parts of your code (where are the values for `weight` and `height`? — inspectorG4dget, Aug 28 '14 at 02:45
possible duplicate of [Python rounding error with float numbers](http://stackoverflow.com/questions/5997027/python-rounding-error-with-float-numbers) — timrau, Aug 28 '14 at 02:47
...and you're certain that `BMI` is *exactly* 18.5? Not the rounded-up value that you might see by truncating its presentation to two decimal places? — Makoto, Aug 28 '14 at 02:49
updated, I just want to know whether there is a simple solution for this? The link you posted looks...not simple ._. — Valkyrie Yan, Aug 28 '14 at 02:50
Makoto, I tried it by 1.7*1.7*18.5 on a calculator to check my code, so it should be right. — Valkyrie Yan, Aug 28 '14 at 02:51
You sure that's the calculation you used? That's a *much* higher number than one would expect. — Makoto, Aug 28 '14 at 02:53

score 2 · Answer 1 · answered Aug 28 '14 at 02:52

2

>>> 53.456/(1.7*1.7)
18.496885813148793
>>> 53.456/(1.7*1.7) <= 18
False

Seems to me like its just floating point errors, try

>>> round(53.456/(1.7*1.7), 2)
18.5
>>> round(53.456/(1.7*1.7), 2) <= 18.5
True

Problem solving strategy for the future: whenever something doesn't quite seem right, crack open the python shell and mess around a bit, you might find the solution yourself.

answered Aug 28 '14 at 02:52

user2085282

1,077
1
8
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[Rounding](https://docs.python.org/3.5/library/functions.html#round) is not guaranteed to allow equality testing of floating point numbers. – Andrew Johnson Aug 28 '14 at 03:18
Which might be a problem if equality was the only condition being tested for, in which case a tolerance would be in order. But its not, and in this case, the number would have been rounded anyways by whatever human doing this paperwork. – user2085282 Aug 28 '14 at 03:22
The op is testing boundary cases and is asking why `BMI = 18.5` matches the condition `BMI < 18.5`. So yes, this is a question of exact equality. – Andrew Johnson Aug 28 '14 at 03:27
@AndrewJohnson: It would be very surprising indeed (and worthy of a bug report) if `BMI = 18.5; BMI < 18.5` gave a result of `True` in Python. It seems much more likely that the OP is testing a value that *isn't* exactly equal to `18.5`. – Mark Dickinson Aug 28 '14 at 10:52

score 0 · Answer 2 · answered Aug 28 '14 at 02:55

Generally speaking, floating-point numbers are not exact due to the nature of how they are represented in the computer. They are just really close approximations. Therefore, testing for exact equality with a floating point number is bound to lead to frustration. You should probably either round your numbers off or not test for equality.

The link posted by timrau is actually a pretty good introduction to the topic if you're interested in exploring it further.

score 0 · Answer 3 · answered Aug 28 '14 at 02:59

0

Floating point numbers only approximate decimal numbers. Your comparison could go over/under depending on what order you multiply or divide or the time of day... not quite. If you want meaningful equality comparisons then take a look at the decimal library in python. You can set the precision to two decimal places and suddenly your comparisons and calculator math should work.

answered Aug 28 '14 at 02:59

Andrew Johnson

3,078
1
18
24

"If you want meaningful equality comparisons..." Not really: both `decimal.Decimal` and `float` are floating-point types, and equality comparisons are exactly as meaningful in one type as in the other. – Mark Dickinson Aug 28 '14 at 13:44
From the [decimal](https://docs.python.org/2/library/decimal.html#module-decimal) docs "Decimal numbers can be represented exactly. In contrast, numbers like 1.1 and 2.2 do not have exact representations in binary floating point." – Andrew Johnson Aug 28 '14 at 14:24
Well yes, of course: numbers that can be exactly expressed in decimal can be exactly represented by `Decimal`. Similarly, numbers that can be exactly expressed in binary (and don't have more than 53 bits of precision, etc.) can be exactly represented by `float`. This has nothing to do with 'meaningful equality'. – Mark Dickinson Aug 28 '14 at 15:21

Floating point calculations and control flow

3 Answers3