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Operating Systems OS X (Apple) A Fun Perfect Square Checker Using Integer Arithmetic Only... ;o) Post 302952733 by bakunin on Friday 21st of August 2015 09:29:21 AM
Old 08-21-2015
Quote:
Originally Posted by wisecracker
But I really enjoy forced restriction and non-standard solutions to a problem.

My bash version requires no knowledge of serious maths whatsoever and uses an observation that is little known to the general public...
You mean that sqares of consecutive natural numbers have the property x[i+1]**2 - x[i]**2 = 2x[i]+1 = 2x[i+1]-1?

OK, here is a short integer implementation, which comes "from top", not "from bottom" (meaning the guesses are always higher than the real value and dropping to it).

Code:
#! /bin/bash

pNextGuess ()
{
     typeset -i iLastGuess=$1
     typeset -i iSquare=$2
     typeset -i iNextGuess=$(( ( iLastGuess + iSquare / iLastGuess ) / 2 ))

     echo $iNextGuess

     return 0
}

# main ()
typeset -i iSquare=$1
typeset -i iGuess=1
typeset -i iNextGuess=0

while : ; do
     iNextGuess=$(pNextGuess $iGuess $iSquare)
     if [ $iNextGuess -eq $iGuess ] ; then
          if [ $(( iGuess * iGuess )) -eq $iSquare ] ; then
               echo "Solution is $iGuess"
          else
               echo "no perfect square, best approximation is $iGuess"
          fi
          exit 0
     fi
     iGuess=iNextGuess
done

A small problem, though: some values cause the guesses to oszillate between two values because of the integers: 960 (961 would be 31**2) is such a number, for instance, because the final guesses will be 30, 31, 30, 31, 30, ....

I (don't think this helps anyone, but) hope this increases the fun.

bakunin
 

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typeset(1)                                                         User Commands                                                        typeset(1)

NAME
typeset, whence - shell built-in functions to set/get attributes and values for shell variables and functions SYNOPSIS
typeset [ +- HLRZfilrtux [n]] [ name [ = value]]... whence [-pv] name... DESCRIPTION
typeset sets attributes and values for shell variables and functions. When typeset is invoked inside a function, a new instance of the variables name is created. The variables value and type are restored when the function completes. The following list of attributes may be specified: -H This flag provides UNIX to host-name file mapping on non-UNIX machines. -L Left justify and remove leading blanks from value. If n is non-zero it defines the width of the field; otherwise, it is determined by the width of the value of first assignment. When the variable is assigned to, it is filled on the right with blanks or trun- cated, if necessary, to fit into the field. Leading zeros are removed if the -Z flag is also set. The -R flag is turned off. -R Right justify and fill with leading blanks. If n is non-zero it defines the width of the field, otherwise it is determined by the width of the value of first assignment. The field is left filled with blanks or truncated from the end if the variable is reas- signed. The -L flag is turned off. -Z Right justify and fill with leading zeros if the first non-blank character is a digit and the -L flag has not been set. If n is non-zero it defines the width of the field; otherwise, it is determined by the width of the value of first assignment. -f The names refer to function names rather than variable names. No assignments can be made and the only other valid flags are -t, -u and -x. The flag -t turns on execution tracing for this function. The flag -u causes this function to be marked undefined. The FPATH variable will be searched to find the function definition when the function is referenced. The flag -x allows the func- tion definition to remain in effect across shell procedures invoked by name. -i Parameter is an integer. This makes arithmetic faster. If n is non-zero it defines the output arithmetic base; otherwise, the first assignment determines the output base. -l All upper-case characters are converted to lower-case. The upper-case flag, -u is turned off. -r The given names are marked readonly and these names cannot be changed by subsequent assignment. -t Tags the variables. Tags are user definable and have no special meaning to the shell. -u All lower-case characters are converted to upper-case characters. The lower-case flag, -l is turned off. -x The given names are marked for automatic export to the environment of subsequently-executed commands. The -i attribute can not be specified along with -R, -L, -Z, or -f. Using + rather than - causes these flags to be turned off. If no name arguments are given but flags are specified, a list of names (and optionally the values) of the variables which have these flags set is printed. (Using + rather than - keeps the values from being printed.) If no names and flags are given, the names and attributes of all variables are printed. For each name, whence indicates how it would be interpreted if used as a command name. The -v flag produces a more verbose report. The -p flag does a path search for name even if name is an alias, a function, or a reserved word. On this man page, ksh(1) commands that are preceded by one or two * (asterisks) are treated specially in the following ways: 1. Variable assignment lists preceding the command remain in effect when the command completes. 2. I/O redirections are processed after variable assignments. 3. Errors cause a script that contains them to abort. 4. Words, following a command preceded by ** that are in the format of a variable assignment, are expanded with the same rules as a vari- able assignment. This means that tilde substitution is performed after the = sign and word splitting and file name generation are not performed. ATTRIBUTES
See attributes(5) for descriptions of the following attributes: +-----------------------------+-----------------------------+ | ATTRIBUTE TYPE | ATTRIBUTE VALUE | +-----------------------------+-----------------------------+ |Availability |SUNWcsu | +-----------------------------+-----------------------------+ SEE ALSO
ksh(1), set(1), sh(1), attributes(5) SunOS 5.10 1 Feb 1995 typeset(1)
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