A Fun Perfect Square Checker Using Integer Arithmetic Only... ;o) Post: 302952733

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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

08-21-2015

Registered User

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

bakunin

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LEARN ABOUT DEBIAN

funcolumnlookup

funcolumnlookup(3)						SAORD Documentation						funcolumnlookup(3)

NAME

       FunColumnLookup - lookup a Funtools column

SYNOPSIS

	 #include <funtools.h>

	 int FunColumnLookup(Fun fun, char *s, int which,
			     char **name, int *type, int *mode,
			     int *offset, int *n, int *width)

DESCRIPTION

       The FunColumnLookup() routine returns information about a named (or indexed) column.  The first argument is the Fun handle associated with
       this set of columns. The second argument is the name of the column to look up.  If the name argument is NULL, the argument that follows is
       the zero-based index into the column array of the column for which information should be returned.  The next argument is a pointer to a
       char *, which will contain the name of the column. The arguments that follow are the addresses of int values into which the following
       information will be returned:

       o   type: data type of column:

	   o   A: ASCII characters

	   o   B: unsigned 8-bit char

	   o   I: signed 16-bit int

	   o   U: unsigned 16-bit int (not standard FITS)

	   o   J: signed 32-bit int

	   o   V: unsigned 32-bit int (not standard FITS)

	   o   E: 32-bit float

	   o   D: 64-bit float

       o   mode: bit flag status of column, including:

	   o   COL_ACTIVE      1 is column activated?

	   o   COL_IBUF        2 is column in the raw input data?

	   o   COL_PTR	       4 is column a pointer to an array?

	   o   COL_READ      010 is read mode selected?

	   o   COL_WRITE     020 is write mode selected?

	   o   COL_REPLACEME 040 is this column being replaced by user data?

       o   offset: byte offset in struct

       o   n: number of elements (i.e. size of vector) in this column

       o   width: size in bytes of this column

       If the named column exists, the routine returns a positive integer, otherwise zero is returned. (The positive integer is the index+1 into
       the column array where this column was located.)

       If NULL is passed as the return address of one (or more) of these values, no data is passed back for that information.  For example:

	 if( !FunColumnLookup(fun, "phas", 0, NULL NULL, NULL, NULL, &npha, NULL) )
	   gerror(stderr, "can't find phas column
");

       only returns information about the size of the phas vector.

SEE ALSO

       See funtools(7) for a list of Funtools help pages

version 1.4.2							  January 2, 2008						funcolumnlookup(3)