Computer Science Canada

Turing "mod" fail
Author:  difi13 [ Fri May 04, 2012 3:01 pm ]
Post subject:  Turing "mod" fail
Hello Guys and Girlz.
I want to share the magic of turing with you.

ok so lets start with taking a cube root of something for example
Turing:

put 64 ** (1/3) %will output 4

Turing:

put 4 mod 1 %will output 0

and finally
Turing:

put (64 ** (1/3)) mod 1 %will output 1 !!!!!!!!!


I would love to know why this happens and possibly the solution
Please specify what version of Turing you are using
last one.
Author:  Tony [ Fri May 04, 2012 3:10 pm ]
Post subject:  RE:Turing "mod" fail
64 ** (1/3) likely results in a real (floating point) type, not int. What do you get when you run
code:

put round((64 ** (1/3))) mod 1
Author:  difi13 [ Fri May 04, 2012 3:55 pm ]
Post subject:  RE:Turing "mod" fail
its 0 , thanks.

but there is one more problem if make a for loop.

for x : 1..1000
if x ** (1/3) mod 1 = 0 then
put "Cool"
end if

it will never print cool

but if we go

for x : 1..1000
if round(x ** (1/3)) mod 1 = 0 then
put "Cool"
end if

Cool will print 1000 times.


So the question is how to make it print something if a cube root of a number is an integer(has no decimals)
Author:  Tony [ Fri May 04, 2012 4:09 pm ]
Post subject:  RE:Turing "mod" fail
what does round function do?
Author:  difi13 [ Fri May 04, 2012 4:14 pm ]
Post subject:  RE:Turing "mod" fail
It is obvious that it rounds the number so anything rounded mod 1 will equal to 0. Now the problem comes "how to make it print something if a cube root of a number is an integer(has no decimals)"
Author:  crossley7 [ Fri May 04, 2012 4:17 pm ]
Post subject:  RE:Turing "mod" fail
think about the easiest way to check if a number is an integer or not. Refer to Tony's last post for a clue.

In fact, you answered your own question in the same post. Think about it a bit and you will see your answer.

Don't use mod for this type of thing since it really works best with integers only and not with reals.
Author:  difi13 [ Fri May 04, 2012 5:05 pm ]
Post subject:  RE:Turing "mod" fail
I tried so much stuff. Even stupid check like this:

if 64 ** (1/3) = round (64 **(1/3)) then
put "Good"
end if

will never print Good. But both numbers are 4
Author:  Tony [ Fri May 04, 2012 5:21 pm ]
Post subject:  RE:Turing "mod" fail
no, they are not both 4

The first number is 4.0
The second number is 4

ProTip, don't use = comparison on float-point numbers. 4.0 = 4.0 is not necessary true (you'd need to understand float-point standard to understand why that might be the case). So hint: you'd need to compare integers; but round(x) = round(x) obviously doesn't tell you anything useful, so there's some extra work to be done.
Author:  difi13 [ Fri May 04, 2012 6:04 pm ]
Post subject:  RE:Turing "mod" fail
I give up ...
Author:  Tony [ Fri May 04, 2012 7:10 pm ]
Post subject:  RE:Turing "mod" fail
lets try with a specific example: 4.2

is it an integer? How do you know?
Author:  difi13 [ Fri May 04, 2012 8:37 pm ]
Post subject:  RE:Turing "mod" fail
it is not because there is a decimal.
Author:  Aange10 [ Sat May 05, 2012 10:13 am ]
Post subject:  RE:Turing "mod" fail
And you learned that if there is a decimal, (such as 4.2 OR the output of 64 ** (1/3)) then when you mod it by 1 it is not= 0. Likewise you know that if it is an integer (has no decimals) and is modded by 1, then it comes out to be 0.


With the above logic, you can tell if a number is an integer (not decimals) or a real number (has decimals). Unless the real number ends with .0, such as 4.0. If that matters to you, I suggest using your numbers as strings and seeing if they contain a ".".


Also I wanted to point out that the round() function turns a real number into an integer (takes away the decimals).
Author:  difi13 [ Sat May 05, 2012 11:59 am ]
Post subject:  Re: RE:Turing "mod" fail
Aange10 @ Sat May 05, 2012 10:13 am wrote:

Also I wanted to point out that the round() function turns a real number into an integer (takes away the decimals).


Heh .. It seems that turing disagrees with you on that.

round(64**(1/3)) still returns 4.0 and will never be = to 4.
Author:  Dreadnought [ Sat May 05, 2012 12:28 pm ]
Post subject:  Re: Turing "mod" fail
difi13 wrote:

Aange10 @ Sat May 05, 2012 10:13 am wrote:

Also I wanted to point out that the round() function turns a real number into an integer (takes away the decimals).


Heh .. It seems that turing disagrees with you on that.

round(64**(1/3)) still returns 4.0 and will never be = to 4.

Have you tried it?
Turing:
put round(64 ** (1/3)) = 4
>> true

put round(64 ** (1/3))
>> 4

% Using Turing 4.1.1 (last official release of Turing)


Please give suggestions a try before saying they don't work.
Author:  difi13 [ Sat May 05, 2012 12:45 pm ]
Post subject:  RE:Turing "mod" fail
Sorry I meant that this would not work in my case since I need this sort of construction.

for x : 1..1000
if round(x ** (1/3)) mod 1 = 0 then
put "Cool"
end if

I am looking to find which numbers (cubed) will not give me any decimals.

If I round it, the outcome will be that all the numbers will have no decimals.

I hope that you understand what I am saying
Author:  Dreadnought [ Sat May 05, 2012 1:15 pm ]
Post subject:  Re: Turing "mod" fail
So you want to test for perfect cubes. You can take the cube root of a number and get a real number.

You are trying to check if the real value is an integer, however, real numbers are, at times, imperfect so this only works with a few cubes (1, 27 and 216 for numbers between 1 and 1000 it seems).

The mod operator can't really do much better. You know how to round that real number to an integer. Try to think of some way to use the rounded cube root to check if the original number was indeed a perfect cube.
Author:  Aange10 [ Sat May 05, 2012 3:55 pm ]
Post subject:  RE:Turing "mod" fail
Do mods in all languages do that?
Author:  mirhagk [ Sat May 05, 2012 5:20 pm ]
Post subject:  RE:Turing "mod" fail
depends on the langauge. In some cases mod only works on integers, in other cases it just does weird things with real numbers.
Author:  Aange10 [ Sat May 05, 2012 8:48 pm ]
Post subject:  RE:Turing "mod" fail
That's actually very interesting. I wonder why that is... could you elaborate?
Author:  Dreadnought [ Sat May 05, 2012 11:27 pm ]
Post subject:  Re: Turing "mod" fail
Well, modular arithmetic is only defined for integers so how you extend the concepts into real numbers is not clear. For example, say you had a theorem in modular arithmetic that requires a number to be prime. How do you extend this to real numbers?
Author:  mirhagk [ Sun May 06, 2012 8:37 am ]
Post subject:  RE:Turing "mod" fail
the way the computer handles mod for integers is actually the exact same way they handle division (it's actually calculated at the same time). Floating point numbers are handled completely different, and are not precise.

Basically if your program relies on modular arithmetic for real numbers, change your program.
Author:  Aange10 [ Sun May 06, 2012 10:03 am ]
Post subject:  RE:Turing "mod" fail
Interesting, thank you both. What about 125 ** 1/3 not= 5?
Author:  evildaddy911 [ Sun May 06, 2012 10:17 am ]
Post subject:  RE:Turing "mod" fail
because 5 is an integer, whereas 125 ** 1/3 is a real number, 125 ** 1/3 will never equal "5"
Author:  Dreadnought [ Sun May 06, 2012 2:54 pm ]
Post subject:  Re: Turing "mod" fail
evildaddy911 wrote:

because 5 is an integer, whereas 125 ** 1/3 is a real number, 125 ** 1/3 will never equal "5"

Although that does seem to be a valid explanation, I'm afraid it is not.

Notice this
Turing:
for i: 1..10
    put i, "  ", (i ** 3) ** (1/3) = i
end for

% The result is
1  true
2  false
3  true
4  false
5  false
6  true
7  false
8  false
9  false
10  false

Notice that the cube roots of 1, 27and 216 are actually equal to 1, 3 and 6 even though the roots are real and 1, 3 and 6 are not.

The true reason is that real numbers are not perfectly accurate (they only store so many digits). The Wikipedia page has a nice example for 1/3.

Try this
Turing:
var num : real := 125 ** (1 / 3)
put frealstr(num, 16,15)

var num2 : real :=216 ** (1 / 3)
put frealstr(num2, 16,15)

% Result
5.00000000000000088817841970012523233890533447265625
6.00000000000000000000000000000000000000000000000000

Basically, 216 ** (1/3) (don't forget that 1/3 is a real too) happens to come out as 6 exactly once it is rounded (usually real numbers have 16 digits of accuracy). But this is not so for 125.

Hope this clear thing up.
Author:  Aange10 [ Sun May 06, 2012 5:00 pm ]
Post subject:  RE:Turing "mod" fail
I knew that evildaddy, i didn't mean the typespecs to be equal, i meant the value.

@Dread, so the value of 125 ** 1/3 is 5.00000000000000088817841970012523233890533447265625, not because of exponential function, but because of the inaccuracy of 1/3 (.3repeating)?
Author:  Tony [ Mon May 07, 2012 1:01 am ]
Post subject:  Re: RE:Turing "mod" fail
Aange10 @ Sun May 06, 2012 5:00 pm wrote:
@Dread, so the value of 125 ** 1/3 is 5.00000000000000088817841970012523233890533447265625, not because of exponential function, but because of the inaccuracy of 1/3 (.3repeating)?

Kind of, but probably not for the reasons that you are thinking of. See http://en.wikipedia.org/wiki/IEEE_754 for the standard in how floating-point numbers are actually represented:
Quote:

(-1)^s * c * b^q

Where the base b is typically 2 (binary representation of the number). As such, there is simply no exact mapping between some decimal fractions and binary encodings. For what integer values of c and q would
code:

0.1 = c * 2^q

be true?

So something like 1/10 is just as problematic as 1/3.

A way to deal with this is to never compare numbers directly, but only with less-than and greater-than checks, within deltas. In the quoted example, 125 ** 1/3 is less than 0.000000000000001 away from 5.0. If that is acceptable for your calculations, you can just call it 5.0. Some languages have that build in.
Author:  Amarylis [ Thu May 10, 2012 5:30 am ]
Post subject:  RE:Turing "mod" fail
So, would doing something like...

[syntax="turing]if num > 5 and num < 5.000001 then
num := 5
end if[/syntax]


Solve the problem for 125 ** (1/3)? (What would be a better solution for this though?)
Author:  Dreadnought [ Thu May 10, 2012 7:45 am ]
Post subject:  Re: Turing "mod" fail
Dreadnought wrote:
You know how to round that real number to an integer. Try to think of some way to use the rounded cube root to check if the original number was indeed a perfect cube.

Here I was hinting at a simple way of doing things. Say I give you 28, you compute 28 ** (1/3) and round it to an integer, this gives you 3. How can you easily figure out if 3 is the cube root of 28? (which will tell you if 28 is a perfect cube)
Author:  evildaddy911 [ Thu May 10, 2012 3:36 pm ]
Post subject:  RE:Turing "mod" fail
if a ** b = c then
c ** (1 / b) = a
end if
Author:  Dreadnought [ Thu May 10, 2012 4:02 pm ]
Post subject:  Re: Turing "mod" fail
evildaddy911 wrote:

if a ** b = c then
c ** (1 / b) = a
end if

Except when b = 0. Razz
But that's the idea.

This gives an easy check for a perfect cube
Turing:
if (round (a ** (1/3)) ** 3) = a then
   put "a is a perfect cube"
end if

:


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