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How to tell if a number has decimal places different than 0

 
 
Gaijinco
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      09-26-2005
Sooner or later everytime I found recreational programming challenges I
stumble with how I test if a number is has decimal places differnt than
0?

For example if I want to know if a number is a square number (i.e. a
number which square root is a positive number as 4, 9, 16 have) I do
something like:

int square = sqrt(number);

if((int)square==square)
// number is a perfect square
else
// number is not a perfect square

Is there a function or a language-specific-way to do this?

 
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Emmanuel Delahaye
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      09-26-2005
Gaijinco wrote on 26/09/05 :
> Sooner or later everytime I found recreational programming challenges I
> stumble with how I test if a number is has decimal places differnt than
> 0?
>
> For example if I want to know if a number is a square number (i.e. a
> number which square root is a positive number as 4, 9, 16 have) I do
> something like:
>
> int square = sqrt(number);
>
> if((int)square==square)
> // number is a perfect square
> else
> // number is not a perfect square
>
> Is there a function or a language-specific-way to do this?


fmod()

--
Emmanuel
The C-FAQ: http://www.eskimo.com/~scs/C-faq/faq.html
The C-library: http://www.dinkumware.com/refxc.html

"It's specified. But anyone who writes code like that should be
transmogrified into earthworms and fed to ducks." -- Chris Dollin CLC


 
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John Harrison
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      09-26-2005
Gaijinco wrote:
> Sooner or later everytime I found recreational programming challenges I
> stumble with how I test if a number is has decimal places differnt than
> 0?
>
> For example if I want to know if a number is a square number (i.e. a
> number which square root is a positive number as 4, 9, 16 have) I do
> something like:
>
> int square = sqrt(number);
>
> if((int)square==square)
> // number is a perfect square
> else
> // number is not a perfect square
>
> Is there a function or a language-specific-way to do this?
>


Language-specific? What do you mean by that?

Your test is not perfect because it will fail when square is bigger than
the biggest int. This test always works (within the limitations of
floating point accuracy).

#include <math>

double square = sqrt(number);
if (floor(square) == square)
// number is a perfect square
else
// number is not a perfect square

john
 
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Eric Sosman
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      09-26-2005


Gaijinco wrote On 09/26/05 16:07,:
> Sooner or later everytime I found recreational programming challenges I
> stumble with how I test if a number is has decimal places differnt than
> 0?
>
> For example if I want to know if a number is a square number (i.e. a
> number which square root is a positive number as 4, 9, 16 have) I do
> something like:
>
> int square = sqrt(number);
>
> if((int)square==square)
> // number is a perfect square


.... and the test is a tautology.

> else
> // number is not a perfect square
>
> Is there a function or a language-specific-way to do this?


The code you've shown will (if it doesn't invoke
undefined behavior) declare that every number is a
perfect square: 1, 2, 3.14, and even -42.

To test whether a floating-point number is an
integer with no fractional part, you could try

if ((int)fpn == fpn) ...

This runs into trouble when the magnitude of fpn
is large, so large that its value is outside the range
of numbers representable as `int'.

As an improvement you might try

if (fmod(fpn, 1.0) == 0.0) ...

This is still vulnerable to the "graininess" of
floating-point numbers, which are not mathematical real
numbers with infinite precision.

You cannot usually expect sqrt(fpn) to be the exact square
root of fpn. sqrt(fpn) will be very close to the exact root,
but will (in general) be just a little bit different from the
true value. There could be several different fpn values for
which sqrt(fpn) would deliver exactly the same slightly wrong
answer: both sqrt(4.0) and sqrt(4.0 + tiny_number) might
produce 2.0 as an answer. If you decide that a number is a
perfect square if its computed square root turns out to be an
integer, you will erroneously conclude that 4.0+tiny_number is
a perfect square.

A possibly more thorough test might compute the square
root, test whether it's an integer, and then test whether
its square equals the original number:

double root = sqrt(number);
if (fmod(root, 1.0) == 0.0 && root * root == number)

.... but even this may have some problems. I am always uneasy
when comparing floating-point quantities for exact equality,
mostly because fpn's are usually regarded as approximations
to begin with. You usually need an "approximately equal"
test of some kind, and such a test isn't well suited to the
purely yet/no nature of perfect squaredom.

For "number-theoretic" calculations you'll usually be much
better off using integers of some flavor. If the numbers grow
large you may need to resort to a "bignum" package; several
are available.

--
http://www.velocityreviews.com/forums/(E-Mail Removed)


 
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Mark McIntyre
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      09-26-2005
On Mon, 26 Sep 2005 21:05:09 GMT, in comp.lang.c , John Harrison
<(E-Mail Removed)> wrote:

(of testing to see if a float is a perfect square)

>This test always works (within the limitations of
>floating point accuracy).


I'd not be too sure of that. Remember floating point is not an exact
representation.

>double square = sqrt(number);
>if (floor(square) == square)
> // number is a perfect square
>else
> // number is not a perfect square

--
Mark McIntyre
CLC FAQ <http://www.eskimo.com/~scs/C-faq/top.html>
CLC readme: <http://www.ungerhu.com/jxh/clc.welcome.txt>

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John Harrison
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      09-26-2005
Mark McIntyre wrote:
> On Mon, 26 Sep 2005 21:05:09 GMT, in comp.lang.c , John Harrison
> <(E-Mail Removed)> wrote:
>
> (of testing to see if a float is a perfect square)
>
>
>>This test always works (within the limitations of
>>floating point accuracy).

>
>
> I'd not be too sure of that. Remember floating point is not an exact
> representation.


That's why I said 'within the limitations of floating point accuracy'.
My test always checks if a floating point number is integral. Obviously
an integral return from sqrt does not necessarily mean the sqrt
parameter was a perfect square.

john
 
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Eric Sosman
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      09-26-2005


John Harrison wrote On 09/26/05 17:20,:
> Mark McIntyre wrote:
>
>>On Mon, 26 Sep 2005 21:05:09 GMT, in comp.lang.c , John Harrison
>><(E-Mail Removed)> wrote:
>>
>>(of testing to see if a float is a perfect square)
>>
>>
>>
>>>This test always works (within the limitations of
>>>floating point accuracy).

>>
>>
>>I'd not be too sure of that. Remember floating point is not an exact
>>representation.

>
>
> That's why I said 'within the limitations of floating point accuracy'.
> My test always checks if a floating point number is integral. Obviously
> an integral return from sqrt does not necessarily mean the sqrt
> parameter was a perfect square.


On the machine in front of me right now, sqrt(1.0)
and sqrt(1.0000000000000002) both give 1.0 as the root.

--
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Martin Ambuhl
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Posts: n/a
 
      09-26-2005
Gaijinco wrote:
> Sooner or later everytime I found recreational programming challenges I
> stumble with how I test if a number is has decimal places differnt than
> 0?
>
> For example if I want to know if a number is a square number (i.e. a
> number which square root is a positive number as 4, 9, 16 have) I do
> something like:
>
> int square = sqrt(number);
>
> if((int)square==square)
> // number is a perfect square
> else
> // number is not a perfect square
>
> Is there a function or a language-specific-way to do this?
>


using modf, you can test either the integral part or the fractional
part. Look askance at any solution that involves ints.

#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <math.h>

int main(void)
{
double x, fp, ip;
int loop, cnt;
srand(time(0));
for (loop = cnt = 0; cnt < 10; loop++) {
x = (int) (100. * rand() / (1. + RAND_MAX)) / 10.;
fp = modf(x, &ip);
if (ip != x || fp)
continue;
printf("%4d: x = %g, fractional part (fp) = %g,"
"integer part (ip) = %g\n"
" (ip %s x, fp %s 0)\n", loop, x, fp, ip,
(ip == x) ? "==" : "!=", (fp == 0) ? "==" : "!=");
cnt++;
}
return 0;
}


1: x = 8, fractional part (fp) = 0,integer part (ip) = 8
(ip == x, fp == 0)
36: x = 0, fractional part (fp) = 0,integer part (ip) = 0
(ip == x, fp == 0)
63: x = 6, fractional part (fp) = 0,integer part (ip) = 6
(ip == x, fp == 0)
70: x = 1, fractional part (fp) = 0,integer part (ip) = 1
(ip == x, fp == 0)
79: x = 5, fractional part (fp) = 0,integer part (ip) = 5
(ip == x, fp == 0)
87: x = 5, fractional part (fp) = 0,integer part (ip) = 5
(ip == x, fp == 0)
128: x = 4, fractional part (fp) = 0,integer part (ip) = 4
(ip == x, fp == 0)
147: x = 1, fractional part (fp) = 0,integer part (ip) = 1
(ip == x, fp == 0)
148: x = 8, fractional part (fp) = 0,integer part (ip) = 8
(ip == x, fp == 0)
162: x = 1, fractional part (fp) = 0,integer part (ip) = 1
(ip == x, fp == 0)
 
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John Harrison
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      09-26-2005
>
> On the machine in front of me right now, sqrt(1.0)
> and sqrt(1.0000000000000002) both give 1.0 as the root.
>


Am I missing something? What point are you making?

john
 
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Keith Thompson
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      09-26-2005
John Harrison <(E-Mail Removed)> writes:
[...]
> #include <math>
>
> double square = sqrt(number);
> if (floor(square) == square)
> // number is a perfect square
> else
> // number is not a perfect square


I suggest that "square" is a really bad name for a variable that hold
the result of a call to sqrt().

--
Keith Thompson (The_Other_Keith) (E-Mail Removed) <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
 
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