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<?php |
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if (!$STDNWPSTYLE_INCLUDED) |
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{ |
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include("stdnwpstyle.inc"); |
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$STDNWPSTYLE_INCLUDED=1; |
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} |
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?> |
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<?php |
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// |
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//******************************************************************************** |
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//Copyright (C) 2003 David T. Ashley |
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//******************************************************************************** |
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//This program or source file is free software; you can redistribute it and/or |
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//modify it under the terms of the GNU General Public License as published by |
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//the Free Software Foundation; either version 2 of the License, or (at your |
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//option) any later version. |
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// |
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//This program or source file is distributed in the hope that it will |
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//be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of |
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//MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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//GNU General Public License for more details. |
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// |
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//You may have received a copy of the GNU General Public License |
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//along with this program; if not, write to the Free Software |
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//Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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//******************************************************************************** |
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// |
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//Returns TRUE if the passed argument is a digit, or FALSE otherwise. If the |
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//passed string has length > 1, only the least significant digit is |
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//considered. |
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function euclid_gcd_isdigit($Digit) |
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{ |
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$Digit = (string)$Digit; |
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|
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//If the string has zero length, this is an error condition and return 0. |
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$Length = strlen($Digit); |
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|
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if ($Length==0) |
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{ |
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return(0); |
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} |
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|
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//Obtain the trailing character of the string. |
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$Trailing_char = Substr($Digit, $Length-1, 1); |
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|
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//Do a switch and return an integer based on the character. |
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switch($Trailing_char) |
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{ |
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case "9": |
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return 1; |
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break; |
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case "8": |
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return 1; |
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break; |
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case "7": |
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return 1; |
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break; |
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case "6": |
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return 1; |
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break; |
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case "5": |
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return 1; |
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break; |
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case "4": |
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return 1; |
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break; |
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case "3": |
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return 1; |
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break; |
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case "2": |
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return 1; |
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break; |
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case "1": |
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return 1; |
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break; |
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case "0": |
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return 1; |
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break; |
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default: |
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return 0; |
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break; |
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} |
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} |
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// |
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// |
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//Returns TRUE if the passed argument is a simple integer (no error |
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//codes, no commas), or FALSE otherwise. |
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function euclid_gcd_issimpleint($Intnum) |
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{ |
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$Intnum = (string)$Intnum; |
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|
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//If the string has zero length, this is an error condition and return 0. |
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$Length = strlen($Intnum); |
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|
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if ($Length==0) |
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{ |
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return(0); |
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} |
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|
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//If the first digit is "0", this must be the only character in the string, |
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//otherwise there is a leading-zero violation. |
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if (Substr($Intnum, 0, 1)=="0") |
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{ |
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if ($Length==1) |
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{ |
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return 1; |
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} |
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else |
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{ |
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return 0; |
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} |
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} |
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|
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//If the first character is a "-" sign, it may not be the only character, |
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//and it may not precede a "0" (which would again be a leading 0 violation). |
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//If it is a "-", we can exclude "0" and parse as a positive. |
| 117 |
if (Substr($Intnum, 0, 1)=="-") |
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{ |
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if ($Length==1) |
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{ |
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return 0; |
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} |
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else |
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{ |
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if (Substr($Intnum, 1, 1) == "0") |
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{ |
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//This is illegal (a "-" followed by a "0"). |
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return 0; |
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} |
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else |
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{ |
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//We can just remove the "-" and parse as a positive. |
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$Intnum = Substr($Intnum, 1, $Length - 1); |
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$Length--; |
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} |
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} |
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} |
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|
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//It is known at this point that the length is at least 1 and the leading |
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//character is not zero. All we need to do at this point is check that each |
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//and every character is a digit. |
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for ($index=0; $index < $Length; $index++) |
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{ |
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if (!euclid_gcd_isdigit(Substr($Intnum, $index, 1))) |
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return 0; |
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} |
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|
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return 1; |
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} |
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// |
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// |
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//Returns the number of digits in the argument, which must be a valid simple |
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//integer. |
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function euclid_gcd_ndigits($Intnum) |
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{ |
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$Intnum = (string)$Intnum; |
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|
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if (Substr($Intnum, 0, 1) == "-") |
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{ |
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$rv = strlen($Intnum) - 1; |
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} |
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else |
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{ |
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$rv = strlen($Intnum); |
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} |
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|
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return($rv); |
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} |
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// |
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// |
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//Given a string, converts the final character to an integer. If the character |
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//is not a digit, returns 0. |
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function euclid_gcd_digittoint($Digit) |
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{ |
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//echo "Digit is: "; |
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//echo $Digit; |
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//echo "<br>"; |
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|
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$Digit = (string)$Digit; |
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|
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//echo "Digit is: "; |
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//echo $Digit; |
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//echo "<br>"; |
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|
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//If the string has zero length, this is an error condition and return 0. |
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$Length = strlen($Digit); |
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|
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//echo "Length is: "; |
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//echo $Length; |
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//echo "<br>"; |
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|
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if ($Length==0) |
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{ |
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return(0); |
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} |
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|
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//Obtain the trailing character of the string. |
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$Trailing_char = Substr($Digit, $Length-1, 1); |
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|
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//echo "Trailing char is: "; |
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//echo $Trailing_char; |
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//echo "<br>"; |
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|
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//Do a switch and return an integer based on the character. |
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//The default case gives 0. |
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|
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switch($Trailing_char) |
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{ |
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case "9": |
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return 9; |
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break; |
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case "8": |
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return 8; |
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break; |
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case "7": |
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return 7; |
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break; |
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case "6": |
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return 6; |
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break; |
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case "5": |
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return 5; |
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break; |
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case "4": |
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return 4; |
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break; |
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case "3": |
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return 3; |
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break; |
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case "2": |
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return 2; |
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break; |
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case "1": |
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return 1; |
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break; |
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default: |
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return 0; |
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break; |
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} |
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} |
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|
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//Decommanates an integer and removes all other crap without respect for |
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//whether the commas are in the right place or the integer is syntactically valid. |
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function euclid_gcd_decommanate(&$arg) |
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{ |
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$temp = ""; |
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|
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$len = strlen($arg); |
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|
| 250 |
for ($i=0; $i<$len; $i++) |
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{ |
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$c = (string)Substr($arg, $i, 1); |
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|
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if (euclid_gcd_isdigit($c) || ($c == "-")) |
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$temp = $temp . $c; |
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} |
| 257 |
|
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$arg = (string)$temp; |
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} |
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|
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//Commanates an integer which is assumed to by syntactically correct. |
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function euclid_gcd_commanate(&$arg) |
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{ |
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euclid_gcd_decommanate($arg); |
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|
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$temp = ""; |
| 267 |
|
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$len = strlen($arg); |
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|
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for ($i=0; $i<$len; $i++) |
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{ |
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$c = (string)Substr($arg, $len - $i - 1, 1); |
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|
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$temp = $c . $temp; |
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|
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if ($i != ($len-1)) |
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{ |
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if (Substr($arg, $len-$i-2, 1) != "-") |
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{ |
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if (($i % 3) == 2) |
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$temp = "," . $temp; |
| 282 |
} |
| 283 |
} |
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} |
| 285 |
|
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$arg = (string)$temp; |
| 287 |
} |
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|
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function do_header(&$style) |
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{ |
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$style->header_title("GCD Calculator (Euclid's Algorithm)", |
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"GCD Calculator", |
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"This cgi-bin form calculates the greatest common divisor of two positive " . |
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"integers using " . |
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"<a href=\"http://mathworld.wolfram.com/EuclideanAlgorithm.html\">Euclid's classic algorithm</a>."); |
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} |
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|
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function do_footer(&$style) |
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{ |
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$style->hrule_std(); |
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echo "<p align=\"center\">This utility is powered by the "; |
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echo "<a href=\"http://www.swox.com/gmp\"><img hspace=\"5\" vspace=\"5\" src=\"../genimages/gmplogo1.png\" width=\"232\" height=\"104\" align=\"absmiddle\"></a>. All source code is available "; |
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echo "<a href=\"../howtos/nth_web_gmp_src_code_dist/obtain_all_source.htm\">here</a>.</p>\n"; |
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$style->footer_std(); |
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} |
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|
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function do_form($N1_refresh, $N2_refresh, $Buttontext, $max_gcd_digits) |
| 308 |
{ |
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echo "<form method=get action=\"euclid_gcd.php\" width=\"100%\">\n"; |
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echo "<table align=\"center\">\n"; |
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echo "<tr>\n"; |
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echo " <td width=\"10%\">\n"; |
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echo " <p align=\"right\"><b>N1</b> (" . number_format($max_gcd_digits) . "-digit maximum):</td>\n"; |
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echo " <td width=\"18%\"><p align=\"left\"><input type=\"text\" "; |
| 315 |
if (strlen($N1_refresh)) |
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{ |
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echo "value=\"" . $N1_refresh . "\" "; |
| 318 |
} |
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echo "name=\"N1\" size=\"50\"></p></td>\n"; |
| 320 |
echo " </tr>\n"; |
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echo " <tr>\n"; |
| 322 |
echo " <td width=\"10%\">\n"; |
| 323 |
echo " <p align=\"right\"><b>N2</b> (" . number_format($max_gcd_digits) . "-digit maximum):</td>\n"; |
| 324 |
echo " <td width=\"18%\"><p align=\"left\"><input type=\"text\" "; |
| 325 |
if (strlen($N2_refresh)) |
| 326 |
{ |
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echo "value=\"" . $N2_refresh . "\" "; |
| 328 |
} |
| 329 |
echo "name=\"N2\" size=\"50\"></p></td>\n"; |
| 330 |
echo " </tr>\n"; |
| 331 |
echo " <tr>\n"; |
| 332 |
echo " <td width=\"20%\" colspan=\"2\">\n"; |
| 333 |
echo " <p align=\"center\"><input type=\"submit\" value=\""; |
| 334 |
echo $Buttontext; |
| 335 |
echo "\" name=\"B1\" style=\"margin-top: 12\"></td>\n"; |
| 336 |
echo " </tr>\n"; |
| 337 |
echo "</table>\n"; |
| 338 |
echo "</form>\n"; |
| 339 |
} |
| 340 |
|
| 341 |
function do_err_msg($Err_msg) |
| 342 |
{ |
| 343 |
echo "<p align=\"center\"><b><font color=\"#FF0000\">"; |
| 344 |
echo $Err_msg; |
| 345 |
echo "</font></b></p>\n"; |
| 346 |
} |
| 347 |
|
| 348 |
|
| 349 |
//Main script begins here. |
| 350 |
// |
| 351 |
// |
| 352 |
//Let's agree on a maximum for number of digits in either |
| 353 |
//of the two arguments. This has been checked out and seems |
| 354 |
//to be within operational parameters (script won't time out). |
| 355 |
$max_gcd_digits = 200; |
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// |
| 357 |
$style = new Stdnwpstyle; |
| 358 |
//Assign the current style in force. Also, starts the CPU |
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//usage clock. |
| 360 |
|
| 361 |
//Do the header unconditionally. The header is always used on this page. |
| 362 |
do_header($style); |
| 363 |
// |
| 364 |
// |
| 365 |
//If N1 was supplied, decommanate it and be sure it is a string. |
| 366 |
if (isset($N1)) |
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euclid_gcd_decommanate($N1); |
| 368 |
|
| 369 |
//Same for N2. |
| 370 |
if (isset($N2)) |
| 371 |
euclid_gcd_decommanate($N2); |
| 372 |
// |
| 373 |
//There are a few cases to break into here, and this affects the overall layout of the page. |
| 374 |
//The header and footer are fixed, but the "guts" will change. |
| 375 |
if (!isset($N1) && !isset($N2)) |
| 376 |
{ |
| 377 |
//In this case, we are probably visiting the form for the first time, and have not done a submit. |
| 378 |
//Just display the form itself. |
| 379 |
do_form("", "", "Calculate GCD", $max_gcd_digits); |
| 380 |
} |
| 381 |
elseif (!isset($N1) && isset($N2)) |
| 382 |
{ |
| 383 |
//Only $N2 is supplied. |
| 384 |
do_err_msg("You must supply both N1 and N2 to calculate a GCD. Only N2 was supplied. Please try again."); |
| 385 |
$style->hrule_std(); |
| 386 |
euclid_gcd_commanate($N2); |
| 387 |
do_form("", $N2, "Calculate GCD", $max_gcd_digits); |
| 388 |
} |
| 389 |
elseif (isset($N1) && !isset($N2)) |
| 390 |
{ |
| 391 |
//Only $N1 is supplied. |
| 392 |
do_err_msg("You must supply both N1 and N2 to calculate a GCD. Only N1 was supplied. Please try again."); |
| 393 |
$style->hrule_std(); |
| 394 |
euclid_gcd_commanate($N1); |
| 395 |
do_form($N1, "", "Calculate GCD", $max_gcd_digits); |
| 396 |
} |
| 397 |
elseif (!euclid_gcd_issimpleint($N1) || !euclid_gcd_issimpleint($N2)) |
| 398 |
{ |
| 399 |
//$N1 and $N2 are both supplied, but one or both is malformed. Need to advise. |
| 400 |
if (!euclid_gcd_issimpleint($N1) && !euclid_gcd_issimpleint($N2)) |
| 401 |
{ |
| 402 |
do_err_msg("N1 and N2 are both malformed integers. Choose new values and try again."); |
| 403 |
$style->hrule_std(); |
| 404 |
do_form($N1, $N2, "Calculate GCD", $max_gcd_digits); |
| 405 |
} |
| 406 |
elseif (!euclid_gcd_issimpleint($N1)) |
| 407 |
{ |
| 408 |
do_err_msg("N1 is a malformed integer. Choose a new value for N1 and try again."); |
| 409 |
$style->hrule_std(); |
| 410 |
euclid_gcd_commanate($N2); |
| 411 |
do_form($N1, $N2, "Calculate GCD", $max_gcd_digits); |
| 412 |
} |
| 413 |
else |
| 414 |
{ |
| 415 |
do_err_msg("N2 is a malformed integer. Choose a new value for N2 and try again."); |
| 416 |
$style->hrule_std(); |
| 417 |
euclid_gcd_commanate($N1); |
| 418 |
do_form($N1, $N2, "Calculate GCD", $max_gcd_digits); |
| 419 |
} |
| 420 |
} |
| 421 |
elseif ((strlen($N1) > $max_gcd_digits) || (strlen($N2) > $max_gcd_digits)) |
| 422 |
{ |
| 423 |
if ((strlen($N1) > $max_gcd_digits) && (strlen($N2) > $max_gcd_digits)) |
| 424 |
{ |
| 425 |
do_err_msg("N1 and N2 are both too long (a " . number_format($max_gcd_digits) . "-digit maximum is " . |
| 426 |
"in effect). Choose shorter values and try again."); |
| 427 |
$style->hrule_std(); |
| 428 |
euclid_gcd_commanate($N1); |
| 429 |
euclid_gcd_commanate($N2); |
| 430 |
do_form($N1, $N2, "Calculate GCD", $max_gcd_digits); |
| 431 |
} |
| 432 |
elseif (strlen($N1) > $max_gcd_digits) |
| 433 |
{ |
| 434 |
do_err_msg("N1 is too long (a " . number_format($max_gcd_digits) . "-digit maximum is " . |
| 435 |
"in effect). Choose a shorter value and try again."); |
| 436 |
$style->hrule_std(); |
| 437 |
euclid_gcd_commanate($N1); |
| 438 |
euclid_gcd_commanate($N2); |
| 439 |
do_form($N1, $N2, "Calculate GCD", $max_gcd_digits); |
| 440 |
} |
| 441 |
else |
| 442 |
{ |
| 443 |
do_err_msg("N2 is too long (a " . number_format($max_gcd_digits) . "-digit maximum is " . |
| 444 |
"in effect). Choose a shorter value and try again."); |
| 445 |
$style->hrule_std(); |
| 446 |
euclid_gcd_commanate($N1); |
| 447 |
euclid_gcd_commanate($N2); |
| 448 |
do_form($N1, $N2, "Calculate GCD", $max_gcd_digits); |
| 449 |
} |
| 450 |
} |
| 451 |
else |
| 452 |
{ |
| 453 |
//N1 and N2 were both supplied and seem to be valid integers. |
| 454 |
// |
| 455 |
//If either integer is negative, make it positive. |
| 456 |
if (Substr($N1, 0, 1)=="-") |
| 457 |
$N1 = Substr($N1, 1, strlen($N1)-1); |
| 458 |
if (Substr($N2, 0, 1)=="-") |
| 459 |
$N2 = Substr($N2, 1, strlen($N2)-1); |
| 460 |
|
| 461 |
//If either is "0", make it "1". |
| 462 |
if ($N1=="0") |
| 463 |
$N1 = (string)"1"; |
| 464 |
if ($N2=="0") |
| 465 |
$N2 = (string)"1"; |
| 466 |
|
| 467 |
//We can now run the external program to do the calculation. |
| 468 |
$cgi_command_string = "./arith_large_cgi gcd " . $N1 . " " . $N2; |
| 469 |
//echo "CGI command string is : " . $cgi_command_string . "<br>\n"; |
| 470 |
|
| 471 |
exec($cgi_command_string, $cgi_result); |
| 472 |
$cgi_result_nelem = count($cgi_result); |
| 473 |
|
| 474 |
//echo "Result is : " . $cgi_result_nelem . "<br>\n"; |
| 475 |
|
| 476 |
//for ($i=0; $i<$cgi_result_nelem; $i++) |
| 477 |
//{ |
| 478 |
// echo $cgi_result[$i] . "<br>\n"; |
| 479 |
//} |
| 480 |
|
| 481 |
//We need to perform some sanity checks on the CGI output to be sure it |
| 482 |
//is what we want. If it seems wrong, we need to generate an error message |
| 483 |
//and not try to display the output. |
| 484 |
$cgi_output_is_sane = 1; |
| 485 |
if ($cgi_result_nelem == 0) |
| 486 |
$cgi_output_is_sane = 0; |
| 487 |
if ($cgi_result_nelem > 0) |
| 488 |
{ |
| 489 |
if (($cgi_result_nelem % 5) != 0) |
| 490 |
$cgi_output_is_sane = 0; |
| 491 |
if ($cgi_result[0] != "S") |
| 492 |
$cgi_output_is_sane = 0; |
| 493 |
if ($cgi_result[$cgi_result_nelem - 1] != "S") |
| 494 |
$cgi_output_is_sane = 0; |
| 495 |
} |
| 496 |
|
| 497 |
if (!$cgi_output_is_sane) |
| 498 |
{ |
| 499 |
do_err_msg("An unspecified error occurred when interacting with the CGI-BIN program. Please advise the webmaster."); |
| 500 |
$style->hrule_std(); |
| 501 |
euclid_gcd_commanate($N1); |
| 502 |
euclid_gcd_commanate($N2); |
| 503 |
do_form($N1, $N2, "Calculate GCD", $max_gcd_digits); |
| 504 |
} |
| 505 |
else |
| 506 |
{ |
| 507 |
euclid_gcd_commanate($cgi_result[1]); |
| 508 |
euclid_gcd_commanate($cgi_result[2]); |
| 509 |
euclid_gcd_commanate($cgi_result[$cgi_result_nelem - 2]); |
| 510 |
|
| 511 |
echo "<p align=\"center\"><font size=\"4\">The greatest common divisor of "; |
| 512 |
echo $cgi_result[1]; |
| 513 |
echo " and "; |
| 514 |
echo $cgi_result[2]; |
| 515 |
echo " is "; |
| 516 |
echo $cgi_result[$cgi_result_nelem - 2]; |
| 517 |
echo ".</font></p>\n"; |
| 518 |
|
| 519 |
$style->hrule_std(); |
| 520 |
|
| 521 |
echo "<p align=\"left\"><b>Notes on the algorithm: </b>\n"; |
| 522 |
echo "Euclid's classic GCD algorithm was known no later than about 200 B.C. and is documented \n"; |
| 523 |
echo "at the \n"; |
| 524 |
echo "<a href=\"http://mathworld.wolfram.com/EuclideanAlgorithm.html\">Wolfram Research site</a> \n"; |
| 525 |
echo "and also in Knuth's classic reference work, "; |
| 526 |
echo "<a href=\"http://www.amazon.com/exec/obidos/tg/detail/-/0201896842/qid=1041826693/sr=8-2/ref=sr_8_2/102-1371170-8580943?v=glance&s=books&n=507846\"><i>The \n"; |
| 527 |
echo "Art Of Computer Programming</i></a>. Euclid's GCD algorithm ends with the GCD being the \n"; |
| 528 |
echo "last non-zero remainder (in yellow below unless <i>a</i> is a multiple of <i>b</i>).\n"; |
| 529 |
echo "</p>\n"; |
| 530 |
|
| 531 |
//Assign the table column widths. They are centralized here for easy change. |
| 532 |
$width[0] = 5; |
| 533 |
$width[1] = 10; |
| 534 |
$width[2] = 10; |
| 535 |
$width[3] = 10; |
| 536 |
$width[4] = 10; |
| 537 |
|
| 538 |
echo "<table align=\"center\" border=\"1\" width=\"90%\">\n"; |
| 539 |
|
| 540 |
for ($i=0; $i <= ($cgi_result_nelem/5 - 1); $i++) |
| 541 |
{ |
| 542 |
echo "<tr>\n"; |
| 543 |
|
| 544 |
echo " <td width=\"" . $width[0] . "%\">\n"; |
| 545 |
if ($i==0) |
| 546 |
{ |
| 547 |
echo " <p align=\"center\"><b>Round</b></p>\n"; |
| 548 |
} |
| 549 |
else |
| 550 |
{ |
| 551 |
euclid_gcd_commanate($cgi_result[$i*5-2]); |
| 552 |
echo " <p align=\"center\">" . $cgi_result[$i*5-2] . "</p>\n"; |
| 553 |
} |
| 554 |
echo " </td>\n"; |
| 555 |
|
| 556 |
echo " <td width=\"" . $width[1] . "%\">\n"; |
| 557 |
if ($i==0) |
| 558 |
{ |
| 559 |
echo " <p align=\"center\"><b>a</b></p>\n"; |
| 560 |
} |
| 561 |
else |
| 562 |
{ |
| 563 |
euclid_gcd_commanate($cgi_result[$i*5-1]); |
| 564 |
echo " <p align=\"right\">" . $cgi_result[$i*5-1] . "</p>\n"; |
| 565 |
} |
| 566 |
echo " </td>\n"; |
| 567 |
|
| 568 |
echo " <td width=\"" . $width[2] . "%\">\n"; |
| 569 |
if ($i==0) |
| 570 |
{ |
| 571 |
echo " <p align=\"center\"><b>b</b></p>\n"; |
| 572 |
} |
| 573 |
else |
| 574 |
{ |
| 575 |
euclid_gcd_commanate($cgi_result[$i*5]); |
| 576 |
echo " <p align=\"right\">" . $cgi_result[$i*5] . "</p>\n"; |
| 577 |
} |
| 578 |
echo " </td>\n"; |
| 579 |
|
| 580 |
echo " <td width=\"" . $width[3] . "%\">\n"; |
| 581 |
if ($i==0) |
| 582 |
{ |
| 583 |
echo " <p align=\"center\"><b>a <i>div</i> b</b></p>\n"; |
| 584 |
} |
| 585 |
else |
| 586 |
{ |
| 587 |
euclid_gcd_commanate($cgi_result[$i*5+1]); |
| 588 |
echo " <p align=\"right\">" . $cgi_result[$i*5+1] . "</p>\n"; |
| 589 |
} |
| 590 |
echo " </td>\n"; |
| 591 |
|
| 592 |
if ($i > 0) |
| 593 |
euclid_gcd_commanate($cgi_result[$i*5+2]); |
| 594 |
echo " <td width=\"" . $width[4] . "%\""; |
| 595 |
if (($i > 0) && ($cgi_result[$i*5+2] == $cgi_result[$cgi_result_nelem - 2])) |
| 596 |
echo " bgcolor=\"#FFFF00\""; |
| 597 |
echo ">\n"; |
| 598 |
if ($i==0) |
| 599 |
{ |
| 600 |
echo " <p align=\"center\"><b>a <i>mod</i> b</b></p>\n"; |
| 601 |
} |
| 602 |
else |
| 603 |
{ |
| 604 |
//euclid_gcd_commanate($cgi_result[$i*5+2]); |
| 605 |
echo " <p align=\"right\">" . $cgi_result[$i*5+2] . "</p>\n"; |
| 606 |
} |
| 607 |
echo " </td>\n"; |
| 608 |
|
| 609 |
echo "</tr>\n"; |
| 610 |
} |
| 611 |
|
| 612 |
echo "</table><br>\n"; |
| 613 |
$style->hrule_std(); |
| 614 |
|
| 615 |
euclid_gcd_commanate($N1); |
| 616 |
euclid_gcd_commanate($N2); |
| 617 |
do_form($N1, $N2, "Calculate Another GCD", $max_gcd_digits); |
| 618 |
} |
| 619 |
} |
| 620 |
|
| 621 |
//Now do the footer unconditionally. The footer is always used on this web page. |
| 622 |
do_footer($style); |
| 623 |
?> |
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