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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::langext5.18

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

NAME

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

SYNOPSIS

	  use Locale::Codes::LangExt;

	  $lext = code2langext('acm');		       # $lext gets 'Mesopotamian Arabic'
	  $code = langext2code('Mesopotamian Arabic'); # $code gets 'acm'

	  @codes   = all_langext_codes();
	  @names   = all_langext_names();

DESCRIPTION

       The "Locale::Codes::LangExt" module provides access to standard codes used for identifying language extensions, such as those as defined in
       the IANA language registry.

       Most of the routines take an optional additional argument which specifies the code set to use. If not specified, the default IANA language
       registry codes will be used.

SUPPORTED CODE SETS

       There are several different code sets you can use for identifying language extensions. 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 = code2langext('acm','alpha');
	  $lext = code2langext('acm',LOCALE_LANGEXT_ALPHA);

       The codesets currently supported are:

       alpha
	   This is the set of three-letter (lowercase) codes from the IANA language registry, such as 'acm' for Mesopotamian Arabic.

	   This is the default code set.

ROUTINES

       code2langext ( CODE [,CODESET] )
       langext2code ( NAME [,CODESET] )
       langext_code2code ( CODE ,CODESET ,CODESET2 )
       all_langext_codes ( [CODESET] )
       all_langext_names ( [CODESET] )
       Locale::Codes::LangExt::rename_langext  ( CODE ,NEW_NAME [,CODESET] )
       Locale::Codes::LangExt::add_langext  ( CODE ,NAME [,CODESET] )
       Locale::Codes::LangExt::delete_langext  ( CODE [,CODESET] )
       Locale::Codes::LangExt::add_langext_alias  ( NAME ,NEW_NAME )
       Locale::Codes::LangExt::delete_langext_alias  ( NAME )
       Locale::Codes::LangExt::rename_langext_code  ( CODE ,NEW_CODE [,CODESET] )
       Locale::Codes::LangExt::add_langext_code_alias  ( CODE ,NEW_CODE [,CODESET] )
       Locale::Codes::LangExt::delete_langext_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.iana.org/assignments/language-subtag-registry
	   The IANA language subtag registry.

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::LangExt(3pm)
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