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Full Discussion: A Fun Perfect Square Checker Using Integer Arithmetic Only... ;o)
Operating Systems OS X (Apple) A Fun Perfect Square Checker Using Integer Arithmetic Only... ;o) Post 302952995 by bakunin on Monday 24th of August 2015 08:11:16 PM
Old 08-24-2015
OK, here is another take at finding the square root: it does not use any operation other than subtraction/addition and it is no approximation method.

The math is simple: we know that

Code:
           2    2          2
  ( a + b )  = a  + 2ab + b

or, in the special case of b = 1:

Code:
           2    2          
  ( n + 1 )  = n  + 2n + 1

which we can more conveniently write as:

Code:
           2    2
  ( n + 1 )  = n  + n + ( n + 1 ))

This means that
Code:
   n
  ---             2
  \   2i + 1   = n
  /__ 
  i=0

In less mathematical terms: we have two counters, x and y. We start with x=0, y=1 and we add them both to a sum, incrementing the counters at each pass. Here is a little table:

Code:
  Pass  x y   sum
  1     0 1     1
  2     1 2     4
  3     2 3     9
  4     3 4    16

As you can see the "y"-column always holds the root to the square in the "sum"-column.


To find the root i simply reversed that and subtracted (instead of added) from the value originally given down to 0. The code is very simple:

Code:
#! /bin/bash

typeset -i iInput=$1
typeset -i iCnt1=0
typeset -i iCnt2=1

while [ $iInput -gt 0 ] ; do
     (( iInput = iInput - iCnt1 ))
     if [ $iInput -lt $iCnt2 ] ; then
          echo "Not a perfect square."
          exit 0
     fi
     (( iInput = iInput - iCnt2 ))
     (( iCnt1++ ))
     (( iCnt2++ ))
done

echo Solution: $iCnt1

exit 0

bakunin
 

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LEARN ABOUT MOJAVE

locale::codes::langfam5.18

Locale::Codes::LangFam(3pm)				 Perl Programmers Reference Guide			       Locale::Codes::LangFam(3pm)

NAME

       Locale::Codes::LangFam - standard codes for language extension identification

SYNOPSIS

	  use Locale::Codes::LangFam;

	  $lext = code2langfam('apa');		       # $lext gets 'Apache languages'
	  $code = langfam2code('Apache languages');    # $code gets 'apa'

	  @codes   = all_langfam_codes();
	  @names   = all_langfam_names();

DESCRIPTION

       The "Locale::Codes::LangFam" module provides access to standard codes used for identifying language families, such as those as defined in
       ISO 639-5.

       Most of the routines take an optional additional argument which specifies the code set to use. If not specified, the default ISO 639-5
       language family codes will be used.

SUPPORTED CODE SETS

       There are several different code sets you can use for identifying language families. A code set may be specified using either a name, or a
       constant that is automatically exported by this module.

       For example, the two are equivalent:

	  $lext = code2langfam('apa','alpha');
	  $lext = code2langfam('apa',LOCALE_LANGFAM_ALPHA);

       The codesets currently supported are:

       alpha
	   This is the set of three-letter (lowercase) codes from ISO 639-5 such as 'apa' for Apache languages.

	   This is the default code set.

ROUTINES

       code2langfam ( CODE [,CODESET] )
       langfam2code ( NAME [,CODESET] )
       langfam_code2code ( CODE ,CODESET ,CODESET2 )
       all_langfam_codes ( [CODESET] )
       all_langfam_names ( [CODESET] )
       Locale::Codes::LangFam::rename_langfam  ( CODE ,NEW_NAME [,CODESET] )
       Locale::Codes::LangFam::add_langfam  ( CODE ,NAME [,CODESET] )
       Locale::Codes::LangFam::delete_langfam  ( CODE [,CODESET] )
       Locale::Codes::LangFam::add_langfam_alias  ( NAME ,NEW_NAME )
       Locale::Codes::LangFam::delete_langfam_alias  ( NAME )
       Locale::Codes::LangFam::rename_langfam_code  ( CODE ,NEW_CODE [,CODESET] )
       Locale::Codes::LangFam::add_langfam_code_alias  ( CODE ,NEW_CODE [,CODESET] )
       Locale::Codes::LangFam::delete_langfam_code_alias  ( CODE [,CODESET] )
	   These routines are all documented in the Locale::Codes::API man page.

SEE ALSO

       Locale::Codes
	   The Locale-Codes distribution.

       Locale::Codes::API
	   The list of functions supported by this module.

       http://www.loc.gov/standards/iso639-5/id.php
	   ISO 639-5 .

AUTHOR

       See Locale::Codes for full author history.

       Currently maintained by Sullivan Beck (sbeck@cpan.org).

COPYRIGHT

	  Copyright (c) 2011-2013 Sullivan Beck

       This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

perl v5.18.2							    2013-11-04					       Locale::Codes::LangFam(3pm)
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