Test integerness

Test integerness is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given a real numeric value, test whether or not it is an integer.

To be clear, we're not talking about whether the number is stored with the specific data type for integers, but instead we want to test whether there exists an integer with the exact same value. In other words, we want to test for integerness in the mathematical sense, not as a data type.

Extra credit

Extend the test for complex number. Remember that $\mathbf {Z} \subset \mathbf {C}$.

J

<lang J>(= <.) 3.14 7</lang>

Output:

0 1

Perl 6

<lang perl6>say pi.narrow ~~ Int; say 1e5.narrow ~~ Int;</lang>

Output:

False
True

Python

<lang python>>>> def isint(f):

   return int(f) == f

>>> isint(3.14) False >>> isint(3.0) True >>> </lang>

REXX

This example is incorrect. Please fix the code and remove this message. Details: Can be zero and negative

<lang rexx>/* REXX ---------------------------------------------------------------

• 20.06.2014 Walter Pachl
• zero and negative whole numbers are integers, right?
• --------------------------------------------------------------------*/

Call test_integer 3.14 Call test_integer 1.00000 Call test_integer 33 Call test_integer 999999999 Call test_integer 99999999999 Call test_integer 1e272 Call test_integer 'AA' Call test_integer '0' Call test_integer '-3' Exit test_integer: Parse Arg x Numeric Digits 1000 Select

 When datatype(x)<>'NUM' Then
   Say x 'is not an integer (not even a number)'
 /***********************************************
 When x=0 Then
   Say x 'is zero and thus not an integer'
 When x<0 Then
   Say x 'is negative and thus not an integer'
 ***********************************************/
 Otherwise Do
   If datatype(x,'W') Then
     Say x 'is an integer'
   Else
     Say x 'isnt an integer'
   End
 End

Return </lang> output

3.14 isn't an integer
33 is an integer
1.00000 is an integer
999999999 is an integer
99999999999 is an integer
1E272 is an integer
AA is not an integer (not even a number)
0 is an integer
-3 is an integer

Tcl

The simplest method of doing this is testing whether the value is equal to the value after casting it to a integral value. <lang tcl>proc isNumberIntegral {x} {

   expr {$x == entier($x)}

} foreach x {3.14 7 1000000000000000000000} {

   puts [format "%s: %s" $x [expr {[isNumberIntegral $x] ? "yes" : "no"}]]

}</lang>

Output:

3.14: no
7: yes
1000000000000000000000: yes